High-Temperature Superconducting Bolometers for

High-Temperature Superconducting Bolometers for Space Applications

Shahid Aslam St. Cross College, Oxford

Hilary Term 2006

A thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy

High-Temperature Superconducting Bolometers for Space Applications Shahid Aslam St. Cross College, Oxford

A thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy at the University of Oxford

Hilary Term 2006

Abstract A HTS YBCO bolometer based on a Si:B membrane has been fabricated with an output noise level that is dominated by the fundamental phonon noise. Based on spectral noise voltage density measurements, the electrical Noise Electrical Power, NEPe , is 3.2 " 10#12 W/ Hz at a measurement frequency of 10Hz. This value corresponds to a specific detectivity of D* = 3.2 " 1010 cm Hz / W . Preliminary optical response measurements

! ! indicate a time constant for this device of 14ms. By micromachining the membrane to reduce the thermal ! adding an optimized absorption layer it is expected that the same NEP value for conductance even further and by detection of FIR with a wavelength of 84.4µm will be achieved. Additionally, high quality MgB2 thin film was successfully grown on a SiN-Si substrate. This structure was not constructed into a bolometer, However, the film was characterized for temperature coefficient of resistance and noise performance. The film showed a zero resistance at 38.16K and a sharp superconducting transition width of 0.23K. The mid-point of superconducting transition is at 38.24K and the film showed a high temperature coefficient of resistance of 12.4Ω/K. From spectral noise voltage density measurements the Noise Equivalent Temperature Difference, NETD, was evaluated to be 6.8 nV/√Hz, this shows that MgB2 films grown on SiN can provide better signal-to-noise ratio than current cuprate-based HTS bolometers. The substrate material, SiN-Si, is ideally suited for micromachining low thermal capacity membranes with optimal thermal conductance. This is very encouraging news for the development of a highly sensitive MgB2 based bolometer for integration into space instrumentation that can meet the cooling requirements of 30K. ii

Acknowledgements It is my pleasure to thank my supervisor Simon Calcutt for the guidance and freedom he gave me to develop my abilities as an independent researcher. I admire his uncanny ability to reduce complex problems to their essence and I am especially grateful for his optimism and his confidence in the eventual success even at times when progress on this thesis was stagnating. I thank the head of the Planetary Physics Group, Fred Taylor, for giving me the opportunity to do this research. I thank the other senior members of the Group, Guy Peskett and the late Steve Werrett for their astute observations and countless discussions that kept the work on track. I must thank all the staff in the Group who assisted in my research work, especially Chris Hepplewhite, Neil Bowles, Bob Watkins, Nick O’Donnell, Andy Clack, and Jonathen Temple. I also thank Francis Pratt for his contagious enthusiasm, interest in science, passion for music and for serving as the outside reader. Special thanks goes to Sarah Harrington who ensured that my thesis submission went smoothly. Some of the work presented in this thesis was accomplished at the Goddard Space Flight Centre, USA while working with Brook Lakew and John Brasunas. I thank them both for their expert insights into the subtleties of bolometer characterization and for their continual support. I thank Steven Graham for his friendship and assistance when I first arrived to work at Goddard. I am indebted to Fred Herrero who inspired and pushed me to complete my thesis when the situation was looking desperate. I am grateful to Hollis Jones and Conor Nixon for the many enlightening discussions, ranging from excitons to the meaning of life, and for providing me with my daily dosage of wit and irony that maintained some order of sanity in the laboratory. My time at Oxford would have been much less educational without my friends so I am especially grateful to Rosie White, Graeme Mason, Julian Nicholas, Mariano Deporto, Ewald Schroeder, Jim Williamson and Rafael Lloyd for everything they taught me and for the shared experiences and escapades we had together. Most importantly, I would like to thank my mum and dad who installed the love of learning in me and laid the foundation that allowed me to pursue this degree. This thesis is dedicated to them.

iii

Contents Abstract

(ii)

Acknowledgements

(iii)

Table of Contents

(iv)

Chapter 1: Introduction

1-1

1.1

Basic concepts

1-2

1.1.1

Infrared radiation

1-2

1.1.2

Infrared detectors

1-5

1.1.3

Bolometer operation

1-7

1.1.4

HTS application to bolometer design

1-8

1.2

Noise in an ideal thermal detector

1-10

1.3

Ideal photon detectors

1-13

1.4

Comparison of thermal and photon detector D" fundamental limits

1-15

1.5

The case for moderately cooled HTS bolometers

1-17

1.6

Previous work on membrane HTS bolometers ! Thesis overview

1-19

1.7

References

1-23 1-26

Chapter 2: Bolometer Theory

2-1

2.1

Introduction

2-2

2.2

Bolometer model

2-2

2.3

Bolometer responsivity with constant current bias

2-3

2.4

Bolometer responsivity with constant voltage bias

2-5

2.5

Optimization of bolometer responsivity

2-6

2.6

Noise Equivalent Power (NEP) of the bolometer

2-11

2.6.1

Photon noise

2-11

2.6.2

Phonon noise

2-12

2.6.3

Johnson noise

2-13

2.6.4

1/ f or current noise

2-14

2.6.5

Front-end amplifier noise

2-15

2.7 2.8

2.6.6 Total Noise Equivalent Power (NEP) ! ETF effect on noise contributions Optimization of bolometer NEP

2-15 2-16 2-20

iv

2.9

Effective radiance

2-23

2.10

Radiation on bolometer

2-25

References

2-29

Chapter 3: Bolometer materials selection

3-1

3.1

Introduction

3-2

3.2

HTS materials

3-2

3.2.1

Cuprate compounds

3-2

3.2.2

Magnesium diboride (MgB2)

3-3

3.2.3

HTS thin film deposition techniques

3-4

3.2.4

Electrical and magnetic properties

3-4

3.2.5

Thermal Capacity

3-6

3.2.6

Thermal conductivity

3-8

3.2.7

Thermal expansion

3-9

3.2.8

Electrical contact to HTS thin films

3.3

3.4

3.5

3.6

3-10

Substrate materials

3-12

3.3.1

Silicon substrates

3-14

3.3.2

Sapphire substrates

3-14

3.3.3

Monolithic substrates

3-14

Spaceflight considerations

3-15

3.4.1

Stress induced degradation

3-15

3.4.2

Irradiation effects

3-16

3.4.3

Chemical stability

3-17

Spaceborne HTS bolometers

3-18

3.5.1

Requirements on HTS thin films set by bolometer design

3-18

3.5.2

Requirements on HTS thin film set by fabrication techniques

3-19

Proposed HTS-substrate systems

3-20

References

3-21

Chapter 4: Bolometer Design

4-1

4.1

Introduction

4-2

4.2

Design concept – assumptions and parameters

4-2

4.2.1

HTS thin film

4-2

4.2.2

Substrate dimensions and thermal capacity

4-4

4.2.3

Radiation absorber

4-4

Mechanical properties of membrane

4-6

4.3.1

Thermal stress

4-7

4.3.2

Membrane fracture stress

4.3

4-8 v

4.3.3

Membrane deflection

4-8

4.4

Lumped thermal model

4-15

4.5

Nodal thermal model

4-18

4.5.1

Basic heat transfer equations

4-18

4.5.2

Thermal model

4-19

4.6

Polysilicon heater

4-27

4.7

Final design concept

4-27

References

4-31

Chapter 5: Bolometer Device Fabrication 5.1

5.2

5-1

Substrate fabrication

5-2 ++

5.1.1

Fabrication of Si membranes using p - boron etch stop

5-2

5.1.2

Fabrication of Si membranes using SOI process

5-7

5.1.3

Fabrication of SiN membranes

5-7

5.1.4

Fabrication of sapphire membranes

5-9

HTS deposition

5-11

5.2.1

YBCO on Si membranes

5-11

5.2.2

YBCO on monolithic sapphire membranes

5-12

5.2.3

MgB2 deposition on silicon nitride

5-13

References

5-15

Chapter 6: Instrumentation

6-1

6.1

Introduction

6-2

6.2

Cryogen dewar

6-2

6.2.1

Thermal mount

6-3

6.2.2

Heater supply

6-5

6.3

R "T measurements

6-6

6.4

Voltage noise spectral density measurements

6-7

6.4.1

Transfer function for low-noise transformer

6-9

6.4.2

DC-blocking capacitor and its effect on noise measurement

6-10

6.4.3

Low-noise amplifier

6-15

6.4.4

Spectrum analyzer

6-17

!

6.5

Noise power density measurement system calibration

6-18

6.5.1

Noise voltage gain

6-18

6.5.2

Noise spectra roll-off frequency

6-20

References

6-23

vi

Chapter 7: Excess noise measurements

7-1

7.1

Introduction

7-2

7.2

Temperature coefficient of resistance for YBCO thin film bolometer

7-2

7.3

System noise for YBCO thin film measurements

7-5

7.4

Temperature dependence of YBCO film noise voltage

7-6

7.5

YBCO noise voltage correlation with dR / dT

7-7

7.6

Noise voltage correlation with phonon noise

7-7

7.7

7-20

7.8

Temperature coefficient of resistance for MgB2 thin film thermistor ! Temperature dependence of MgB2 thin film noise voltage

7.9

MgB2 noise voltage correlation with dR / dT

7-28

7.10

MgB2 thin film temperature noise

7-29

References

7-21

7-31

!

Chapter 8: Conclusions

8-1

8.1

Introduction

8-2

8.2

Summary of results

8-2

8.2.1

YBCO bolometer

8-2

8.2.2

MgB2 thin film on SiN

8-3

8.3

8.4

Improvements

8-3

8.3.1

Choice of supporting membrane

8-3

8.3.2

Reduction of the thermal capacity

8-3

8.3.3

Reduction of the thermal conductance

8-4

8.3.4

Application of an absorber

8-4

Prospects for HTS bolometers

8-4

Appendix A: Detector figures of merit

A-1

A.1

Introduction

A-1

A.2

Responsivity

A-2

A.3

Responsive time constant

A-2

A.4

Blackbody Noise Equivalent Power, NEPBB

A-3

A.5

Blackbody detectivity, DBB

A-3

A.6

Blackbody D-star, D"

A-3

!

!

!

vii

Appendix B: Square-wave chopped incident radiation

B-1

Appendix C: Normalized responsivity

C-1

Appendix D: Photolithographic masks

D-1

D.1

Chip alignment patterns

D-1

D.2

Double-side aligning specification

D-1

D.3

Mask levels

D-2

Appendix E: Deposition of YSZ barrier layer and HTS

E-1

E.1

YSZ and YBCO deposition on oxidized Si wafers

E-1

E.2

YSZ and YBCO deposition on SiO2-SiN-SiO2 membranes

E-2

Appendix F: Low noise transformer measurements

F-1

F.1

Introduction

F-1

F.2

Transform network analysis

F-1

F.2.1

F-3

Voltage gain

F.3

Transformer noise

F-6

F.4

Effect of Load resistance on internal noise

F-16

F.5

Effect of source resistance on input noise

F-18

F.6

Noise matching

F-19

F.7

Noise Figure

F-20

F.8

Transformer output resistance

F-26

References

F-27

Appendix G: Preliminary results on YBCO bolometer

G-1

G.1

Optical response

G-1

G.2

Frequency response measurement

G-2

viii

Chapter 1

Introduction

1-1

Chapter 1. Introduction

1.

1-2

Introduction

This thesis describes the development of a High Temperature Superconducting (HTS) transition edge bolometer [bolometer is a composite word of Greek origin, bole (beam, ray) and metron (meter, measure)]. The work was primarily motivated by the need for improved sensitivity in studies of the atmospheres of the Earth and planets using spectroscopic remote sensing techniques from spacecraft in the thermal infrared. These studies are based upon the measurement of radiation emitted or absorbed by the molecules in the atmosphere that undergo vibrational and/or rotational transitions. The measurements give rise to an atmospheric spectrum from the nearinfra-red through to the sub-millimetre region (i.e. 0.75µm-1000µm). Satellite-borne experiments in the far-IR through to the sub-millimetre spectral region (15µm-1000µm) use grating, Fabry-Perot or Fourier transform spectrometers. These instruments use either cooled detectors (e.g. doped Ge or Si bolometers) operating at below 10K or room temperature detectors (e.g. thermopiles, pyroelectrics). Cooled detectors have excellent performance but require the use of stored cryogen, leading to high payload and costs, thus limiting their use to relatively short periods in Earth orbiting spacecraft. Uncooled detectors, although easy to use, seriously limit the performance of instruments currently being designed since they give signal-to-noise performance orders of magnitude worse than cryogenic detectors. The advantage of a HTS bolometer, operating in the range 30-120K, will be its improved signal-tonoise performance. These temperatures can be achieved in space for long periods, without the use of stored cryogen, by using radiative coolers for the 60-120K temperature range or adiabatic demagnetization refrigerators for the 30-60K temperature range.

1.1

Basic concepts

1.1.1 Infrared radiation Infra-Red (IR) radiation forms part of the spectral distribution of blackbody radiation [1] and can be considered as photons of energy E = h" = hc # , where h (Js) is Planck’s constant, " (Hz) and " (m) are the frequency and wavelength respectively and c (ms-1) is the speed of light. The frequency, " , corresponding to 1µm

! ! ! ! wavelength radiation is 2.998 " 1014 Hz. In spectroscopy, reciprocal of wavelength is known as the wave !

!

!


1-3

number, " , and is expressed as reciprocal centimetres (cm-1). The wave number corresponding to 1µm wavelength radiation is 10, 000 cm-1. The IR region (0.7-1000µm) can be subdivided into the following spectral

! regions: Near Infra-Red (NIR, 0.7–1.4 µm), Short Wavelength IR (SWIR, 1.4–3 µm), Mid Wavelength IR (MWIR, 3–8 µm), Long Wavelength IR (LWIR, 8–15 µm) and Far IR (FIR, 15–1000 µm). The blackbody radiation laws, described by the Planck radiation equations, deal with two distinctly different physical systems at temperature T (K), namely the radiation from the surface of a blackbody and photon gas (electromagnetic radiation) contained in an evacuated cavity with perfectly reflecting walls. In both cases the laws can be expressed ! in terms of frequency, " , or in wavelength, " . In terms of wavelength the Planck radiation equations can be written as,

!

dE" =

!

8#hc 1 d" "5 exp( hc "k BT ) $ 1

(a) (1.1)

2

dL " =

2#hc 1 d" 5 exp( hc "k BT ) $ 1 "

(b)

k B is Boltzmann’s constant. In equations (1.1), dE " d" (Jm-4) gives the spectral energy density per unit ! wavelength at wavelength " for a blackbody contained in an evacuated cavity at temperature T and dL" / d"

!

! (Wm-3) gives the intensity (power per unit of surface area) per unit wavelength at wavelength " from a

! ! ! total intensity of blackbody at temperature T . From equation (1.1), it can be seen that dL" d" = cdE" 4d" . The ! blackbody radiation is obtained by integrating the Planck radiation equations over the entire range of wavelength ! ! of blackbody radiation in an evacuated cavity at (or frequency). Integrating dE" gives the total energy density temperature T , whereas integrating dL" gives the total power emitted per unit area of a blackbody at

! temperature T . The spectral energy density relationship in equations (1.1) can be used to derive the Stefan-

! Boltzmann law, i.e.,

!

! ET =

!

!

LT =

$ $

# 0

dE" =

# 0

dL" =

8 %k B4T 4 c 3h 3

2 %k B4T 4 c 2h 3

$ $

# 0

# 0

x3 8% 5 k B4T 4 dx = = ' (T 4 15c 3 h 3 ( exp(x) & 1)

(1.2a)

x3 2% 5 k B4T 4 dx = = 'T 4 15c 2 h 3 ( exp(x) & 1)

(1.2b)


(

1-4

)

(

)

where, " # = 8$ 5 k B4 15c 3 h 3 = 7.561 % 10&16 Jm-3K-4 and " = 2# 5 k B4 15c 2 h 3 = 5.67 " 10 8 Wm-2K4. Note that the proportionality constants are different and it is " that is the standard Stefan-Boltzmann constant and also ! ! ! note that " = (c / 4)" # . The position of the maximum in the blackbody spectrum depends on the temperature of

! the blackbody and is given by Wien displacement law. Equating the first derivative of equation (1.1) to zero

! gives,

d d"

# & 1 xe x % ( = 5 ) =0 % "5 [ exp( hc / "k T )] ( ex ) 1 B $ '"= "m

(1.3)

where, x = hc " m k BT = 4.965 and " m = hc 4.965k BT leading to " mT = 2896.8 µmK. As an example solar ! radiation has a wavelength of 0.5µm near the middle of the visible spectrum. Therefore the approximate surface

! temperature of the sun is 5800K. ! ! (black or gray bodies) on Earth terra firma are Because most viewed images near 300K, the corresponding wavelength distribution is centred around 10µm. The contribution from the IR, visible and UV ranges ( LIR , LVIS , LUV ) of radiation at any particular temperature are obtained by integrating (1.2b) over the corresponding range of the electromagnetic spectrum in

!

terms of wavelength, i.e.,

15"T 4 #4

%

LVIS =

15"T 4 #4

%

LUV =

15"T 4 #4

LIR =

X2 0

%

X1 X2

& X1

x3 15"T 4 dx = I IR exp(x) $ 1 #4 x3 15"T 4 dx = I VIS exp(x) $ 1 #4

(1.4)

x3 15"T 4 dx = IUV exp(x) $ 1 #4

where, x = hc "k B T , X 2 = hc " 2 k B T , X1 = hc "1k B T and "1 = 380nm , " 2 = 780nm define the visible ! range. This gives X 2 = 18932 /T and X1 = 37864 /T . The integral expressions above can be solved numerically.

!

! ! ! ! Table 1.1 shows the integral values for temperatures between 300K and 6000K and highlights that the IR ! to the total background ! contribution radiation is virtually 100% for temperatures below 500K.


1-5

Temperature (K) 300 400 500 ! 1000 2000 3000 4000 5000 6000

I IR 6.494 6.494 6.494 ! 6.494 6.403 5.740 4.661 3.615 2.771

I VIS

IUV -22

1.033 x 10 3.148 x 10-16 2.115 x 10-12 ! 4.786 x 10-5 9.132 x 10-2 7.454 x 10-1 1.741 2.541 2.970

%IR -49

3.151 x 10 6.776 x 10-36 5.834!x 10-28 2.113 x 10-12 4.784 x 10-5 8.481 x 10-3 9.135 x 10-2 3.383 x 10-1 7.538 x 10-1

100 100 100 99.99 98.59 88.39 71.78 55.66 42.67

Table 1.1: Numerical values of the integrals in equation (1.4) and percentage contribution of IR to the total blackbody radiation.

1.1.2 Infrared detectors In general, there are three categories of IR detectors: photon detectors, thermal detectors and coherent detectors. Excellent reviews of these types of detectors are provided by the classic texts of Willardson and Beer [2], Keyes [3], Kingston [4], Wolfe and Zissis [5], Blaney [6] and the more recent texts of Richards [7], Dereniak and Boreman [8] and Rieke [9]. In the following only the first two categories are considered. In photon detectors (mainly developed from semiconductors) the radiation is absorbed within the material by interaction with electrons, either bound to lattice atoms or to impurity atoms or with free electrons. The observed electrical output signal results from the changed electronic energy distribution. This class of detector shows a selective wavelength dependence of response per unit incident radiation power. They exhibit both high quantum efficiency and a very fast response. Photon detectors with wavelength cut-offs above 3µm require cryogenic cooling to reduce the thermal generation of carriers. Presently, the most important photon detectors include intrinsic detectors, extrinsic detectors, Schottky barrier (e.g. PtSi) detectors and quantum well detectors. In thermal detectors the incident radiation is absorbed to change the temperature of the material and the resultant change in some physical property is used to generate an output signal. The detector element is thermally isolated from the heat sink. The output signal does not depend on the photon nature of the incident radiation making thermal effects wavelength independent, i.e. the output signal depends upon the radiant power (or its rate of change) but not on its spectral content. Examples of room temperature (RT) thermal detectors include the thermocouple or thermopile [10], the Golay cell [11], the pyroelectric detector [12,13] and the thermistor bolometer [14]. Some sensitivity improvement can be obtained by cooling RT detectors however for


1-6

low light levels specifically cooled thermal detectors such as the semiconductor bolometer [15] or the superconducting bolometer [16, 17] are detectors of choice.

Type

thermopile

THERMAL

pyroelectric

Principle of operation induced thermoelectric voltage change of polarization or charge

Detectivity, D * (cm√Hz/W)

BiTe-TiSbTe poly-Si !

1.5 " 9 # 10 8 4 " 10 9 (170K)

TGS, (Ba,Sr)TiO 3 Pb(Sc0.5Ta0.5)TiO!3 LiTaO3 !

9

1" 10 (300K)

VOx α-Si, SiGe ! magnetite oxide

300K bolometer

1" 6 # 10 8 (300K)

Advantages

Disdvantages

- Low cost - RT operation - robust - wide f range - ease of use

- slow response - low D * at high f

! !

! HTS bolometer

YBCO, GdBaCuO,! MgB2

change of resistance

semiconductor bolometer

!

Si, Ge

4.2- 6 " 10 9 (80-95K)

- cryocooler operation - MEMS compatibility

- fragile - controlled environment

9 " 1011 (2-4K)

- high D " - fast response

- He cooling

- high D " ! - fast response - SQUID electronics !

- He cooling - fragile - short lifetime

low- Tc bolometer

! Al, Ta, Sn, Nb, NbN

BLIP

intrinsic

IV - VI " PbS, PbSe II - VI " HgCdTe III - V " InGaAs

2 " 1010 (77K)

- stable material

- high TCE - large permittivity

Si:Ga Si:As Ge:Cu

2 " 1010 - 1" 1011 (3-4K)

- detect long wavelengths - simple technique

- high thermal generation - N2 cooling

- low cost - high yield

- low efficiency - low temperature operation

1" 3 # 1010 (20-77K)

-mature material - low thermal generation - wavelength tunability

- complicated design - fabrication difficult

not enough good data

- low-thermal generation

- complicated design -fabrication difficult

extrinsic

PHOTON

Materials

free carrier

quantum wells

quantum dots

! ! !

optical excitation of free carriers (electrons or holes) to work in either PV or PC mode

PtSi Pt2Si IrSi

!

! ! !

III - V InAs/InGaSb InAs/InAs/Sb III-V (GaAs/AlGaAs/ InGaAs/InAsSb) ! InAs/GaAs InGaAs/InGaP Ge/Si

Table 1.2: Summary of the most important thermal and photon IR detectors [18].


1-7

Detector PbS (PC) InSb(PV) HgCdTe(PC) GeHg(PC) HgCdTe(PV) GeCu(PC) SiAs(PC) SiGa(PC) SiSb(PC)

Operational temperature 77K 77K 77K 28K 77K 4.2K 4.2K 4.2K 4.2K

Figure 1.1: Comparison of D" for commercially available IR detectors, reproduced from Hanel et al. [19].

! A summary of the most important thermal and photon IR detector technologies existing to date are given in Table 1.2 and the spectral detectivity (see Appendix A) curves for a number of commercially available IR detectors operating at the indicated temperature, with a hemispherical field-of-view and 295K background, are shown in Figure 1.1.

1.1.3 Bolometer operation A bolometer consists of a thermometer (temperature transducer) with heat capacity C mounted on an absorbing substrate, weakly coupled to a sink temperature T 0 via a thermal conductance G ; see Figure 2.1 in Chapter 2.

! Infrared radiation incident on the absorber heats the thermometer, whose resistance R(T ) is a strong function of ! ! thermometer creates a voltage temperature. A bias current through the drop across the device, which is then amplified for detection. Equating the input radiation power to the output ! conducted through the thermal link to the sink results in a temperature rise given by,

"T =

!

P+# G

(1.1)


1-8

where, P and " represent the electrical power and optical infrared power, respectively. Larger temperature excursions (a larger signal) can be achieved by reducing the structurally coupled thermal conductance G of the

! thermometer ! to the sink. To reduce low–frequency noise (1/ f ) noise, the infrared signal must be modulated at ! some frequency " = (2#f ) higher than the onset frequency for dominance of 1/ f noise. Therefore, to develop a ! highly sensitive thermal detector, the corresponding (synchronous) temperature change due to the absorbed ! optical infrared power must be as large as possible given ! modulated by (see §2.3),

"T =

"# G 1+ $ 2% 2

(1.2)

where, " = C /G is the time constant of the device. To maximize the temperature sensitivity in equation (1.2), ! the thermal capacity of the detecting area, C , and the structurally coupled thermal conductance, G , should be

! minimized. However, the conductance G cannot be lowered arbitrarily to increase the dc response without ! ! high sensitivity of forcing the time constant " to unacceptably large values (see §2.3). Due to this trade-off ! in the low frequency range. It is interesting to note that equation (1.2) is thermal detectors can be obtained ! equivalent to the dc response convolved with a low-pass filter.

1.1.4 HTS material application to bolometer design An important area of work, since the discovery in 1986 by Bednorz and Muller [20] of the new metal-oxide based HTS materials, has been in the application of these materials in bolometer design. HTS materials include YBCO, GdBaCuO, Bi(Pb)SSCO. Cooling these detectors is less complicated than for metallic superconductors requiring temperatures < 4K, since the transition temperatures for these materials typically lie in the range 80120K, above the boiling point of liquid nitrogen. Also, temperature control is less stringent than for metallic superconductors where temperature stabilities of mK precision are required to hold the device at mid-point of transition. HTSs have transition widths typically in the range 1-3K making them better suited to bolometer construction. A new addition to the HTS family, discovered by Nagamatsu et al. [21] in 2001, is MgB2 that shows a transition at 39K. High quality thin films of the cuprate HTS materials have been grown on substrates such as SrTiO3, MgO and LaAlO3 [22].

However, these substrates are not ideally suited for bolometer


1-9

development because reduction of thermal capacity through micromachining is difficult. Silicon as a substrate material is more desirable since it is compatible with MEMS processing technology and on-chip electronics implementation. Sapphire also shows promise since it can be chemically thinned. In this work, two HTS materials, YBCO and MgB2 grown on the substrate materials, silicon and sapphire are investigated for bolometer design and construction. These material systems are discussed more fully in Chapter 3. Kruse [23] discusses three possible modes of HTS bolometer operation (i) bolometric or equilibrium mode, which relies on the sharp resistance change as a function of temperature in the superconducting transition region, (ii) non-bolometric or non-equilibrium mode that involves the breaking up of Cooper electron pairs by the incident photons, thus destroying superconductivity and (iii) photon assisted tunnelling that is associated with a tunnel junction (e.g. Josephson junction) where the incident photons breaks Cooper pairs which result in a change of the I " V characteristics of the junction. Much debate and confusion exists about the second and third modes since not enough experimental work has been done in this area to develop a conclusive theory. In the

! following and throughout this work only the first, i.e. bolometric mode of operation is addressed. As mentioned earlier, a HTS bolometer uses the relative rapid change in the resistance of a HTS film as it goes through the normal to superconducting state transition. For example, Figure 1.2 shows a normalized

R(T ) curve for a typical HTS film, the curve shows a sharp transition that is dependent on the electrical transport property of the film. A commonly used figure of merit to quantify the curve is the semi-relative

!

sensitivity function or the Temperature Coefficient of Resistance (TCR), " = ( d (ln R) dT ) = (1/ R)(dR / dT ) [K1

]. A typical value of " for a HTS is on the order of 0.2/K (compared with 0.002/K for a metallic

! superconductor and 0.01/K for a semiconductor). Thus, a sharp ! superconducting transition leads to a high value ! of TCR, a pre-requisite for a highly sensitive thermometer (see §2.3). A HTS bolometer biased using a constant current is operated by stabilizing its temperature at the midpoint of transition. As the HTS film heats in response to an increase in incident power, "# , the resistance, R , increases and the dissipated electrical power P = V / R decreases, minimizing the temperature excursion about

! in Chapter 2), the!signal at the the operating point. Including this electro-thermal feedback (discussed more fully thermometer becomes,

!

"T =

!

"# G e 1 + $ 2% e2

(1.3)


1-10

where G e = G " #P is the effective thermal conductance to the bath, " e = C /G e is the effective time constant. The effective time constant " e is shorter than the physical time constant " = C /G by a factor " , typically

!

several hundred.

!

!

!

8 YBCO/CeO2 on R-plane sapphire

7 6

Resistance (A.U)

!

5 4 !R 3 !T

2 1 88

89

90 Temperature (K)

91

92

Figure 1.2: Resistance as a function of temperature for a typical laser pulse deposited YBCO film on R-plane sapphire. The sharp transition gives rise to a high positive value of " = (1/ R)(dR / dT ) .

!

1.2

Noise in an ideal thermal detector

The optimal detector performance occurs when the incoming background radiation determines the noise of the detector. Lewis [1] showed that the mean square fluctuation in the background radiation power absorbed by a sensitive detector area A and subtending a solid angle " at the detector in a direction making an angle " with the normal to the detector is,

!

! 4(k BT ) 5 "W = A# cos $"f c 2h 3 2

!

! &

4 x

' (ex %e1) x

0

2

f (x)dx

(1.4)


1-11

where, x = h" / k BT , "f is the bandwidth of the front-end amplifier and f (x) is a function that accounts for any blackbody radiation deviation or departure from perfect blackness of the detector surface. For blackbody

! radiation and ! a black detector f (x) =1. If f (x) = " , where !" is the emissivity, a constant independent of wavelength then gives for a 2π sr field of view,

!

!

!

"W 2 = 8#$kBT 5 A"f

(1.5)

where " is Stefan-Boltzmann’s radiation constant and k B is Boltzmann’s constant. Equation (1.5) gives the ! mean square fluctuation in the power absorbed by a sensitive detector area A at temperature T in thermal

!

! equilibrium with the background temperature. Then the noise equivalent power (NEP), see Appendix A, i.e. the

! power that produces a signal equivalent to the noise level, for a black detector where " = 1! is given by,

NEP = 2"W 2 = 16#kBT 5 A"f

!

(1.6)

The NEP in equation (1.6) gives the performance of an ideal thermal detector with no noise ! mechanisms other than the independent statistical noise of absorbed and emitted radiation. The specific (or spectral) detectivity, D" or D" (# , f ) , is given by D" = NEP -1 A#f i.e. D" = 2.8 # 1016 T $5 cm√Hz/W and is the same quantity as the background limited infrared photodetector (BLIP) D" (referred to as BLIP D" and is ! ! ! ! more appropriately used for photon detectors). This is a useful figure-of-merit for comparing the performance of

! ! detectors since it is independent of detector area and measurement bandwidth. Care must be taken when using this figure-of-merit since not all detectors depend on area in this manner. Table 1.3 gives NEP and D" values, calculated using equation (1.6), for an ideal thermal detector in thermal equilibrium with blackbody radiation

!

temperatures of 3.9, 39, 95, 77 and 300K.

The HTS transition temperatures 39K and 95K are typical for MgB2 and YBCO respectively. For blackbody radiation at 300K (and " = 1) D" = 1.8 # 1010 cm√Hz/W, this value serves as a good benchmark for comparing existing detectors. This is a blackbody D" but the peak spectral D" is the same since the responsivity

! ! for thermal detectors is flat, see §2.3. !

!


1-12

Typical material Sn MgB2 YBCO Pyroelectric

Detector #13 D " # 1010 temperature NEP "10 cm√Hz/W (W/√Hz) (K) 3.9 0.0106 94065.6 39 ! 3.4 297.4 ! 77 18.4 54.3 95 31.1 32.1 300 551.7 1.8

Table 1.3: Theoretical NEP and D" values for a perfect thermal detector operating at 3.9, 39, 77, 95 and 300K for the case A =1cm2, " = 1 and "f = 1Hz .

!

!

!

!

In the above analysis it was assumed that the detector temperature is in equilibrium with the ambient background temperature, in real situations this is not true since invariably the detector temperature, T d , is different from the background temperature, T b . In this case the NEP is the sum of the variances of the detector temperature and the background temperature, i.e.,

!

!

NEP = 8"kB (T d5 + T b5 ) A#f

[

(

(1.7)

)]

This translates to a D" = 1 8#k!B T d5 + T b5 , this function is plotted in Figure 1.3 and shows that for a 300K detector, in a 300K ambient temperature, yields once again D" = 1.8 # 1010 cm√Hz/W. The curves shown in

! Figure 1.3 are for the ideal case in that the exchange of power between the thermal detector and its environment ! is through radiative coupling only. In the real situation thermal conduction of power through electrical leads and support structures also plays a role and will shift the D" curves downward. Figure 1.3 highlights the fact that an ideal detector operating at the boiling point of liquid nitrogen

! (77K) in a background environment of 300K only performs better by about √2, this is why thermal detectors operating at room temperature, in the Earth environment, are generally not cooled. However, for the space environment where the background temperature can be substantially lower than 300K a case can be made for cooled thermal detectors, see §1.7. From Figure 1.3 a background radiation environment of 123K (e.g. temperature of the Jupiter sphere), a thermal detector operating at 77K will outperform a 300K detector by about a factor of 9. Similarly, a thermal detector at 77K in a radiation environment of 44K (Pluto sphere) will theoretically outperform a 300K detector by about a factor of 29.


1-13

Figure 1.3: D" as a function of background temperature for an ideal thermal detector at temperatures 4K, 39K, 77K. 95K and 300K (assumes a background radiation field-of-view of 2π sr and " = 1).

!

!

1.3

Ideal photon detectors It is instructive to work out the BLIP D" of an ideal photon detector to compare its fundamental limit

with that of a thermal detector. Detectors of this type respond only to photons of energy greater than the energy

! band-gap, Eg , of the semiconductor, i.e. for all photons of energy h" # Eg , " =1 and for h" < Eg , " = 0 . This means that narrow band-gap semiconductors are required for FIR detectors. The problem with this is that at

! ! temperature the thermal energy of the charge carriers, ! k T is ! room comparable to!the energy band-gap enabling B direct band-to-band transitions to occur and hence making the thermal generation rate ( " to the dark current)

! need to be cooled so that the thermal generation rate is far very high. For practical applications photon detectors less than the optical background radiation generation rate. In this case the ! performance is determined by the background radiation (BLIP condition, see §1.2). The mean square fluctuation of the background radiation power can be evaluated by using equation (1.4) over the integration limits x c = E k BT = h" c k BT =

hc / " c k BT and # . The mean square fluctuation in the rate of arrival of photons at the detector is then given by, ! !

"n 2 =

!

4(k BT ) 3 A# cos $"f c 2h 3

&

2 x

' (ex %e1) x

xc

2

dx

(1.8)


1-14

where the integral limits are determined by the spectral response of the detector. Equation (1.8) must be solved numerically for x < 1 and can be evaluated with valid approximations for x > 1 . The NEP for a quantum detector is wavelength dependent. From the definition of NEP, the number of photons arriving at the detector

! from a !source of wavelength " will be equal to the root mean square fluctuation in the number from the background. Then D" BLIP is given by,

! !

D" =

# A$f

(1.9)

hc $n 2 D" BLIP shows a maximum for the longest wavelength at which the detector responds. Substituting equation ! (1.8) into (1.9) and using a standard series expansion for the integral [24] gives,

!

'% +$1/ 2 ) ) " c h1/ 2 x 2e x D = dx , ( 1/ 2 3/2 x 2 2# (k BT ) )* x c (e $ 1) )-

&

*

"2c . 2 #hk BT c 2

$1/ 2 ') n / $mhc 2/ 2k T" / k BT" c 22 2+) B c + 21 ( exp1 4 4, 411 + 0 mhc 3 43)mhc )* m=1 0 k BT" c 310

5

n 61 .

exp( hc k BT" c ) "2c 7 1/ 2 2 2 #hk BT c [1 + (2kBT" c hc) + 2( kBT" c hc)]

(1.10)

! Equation (1.10) shows D" (T , # c ) and assumes unit area, unit quantum efficiency and unit bandwidth. This dependence is shown in Figure 1.4 for background temperatures of 77, 150 and 300K for a 2π field-of-view. The

! series expansion was evaluated with n = 30 , however for h" >> k BT n = 1 is sufficient. The specific D" ’s for ideal thermal detectors at various operating temperatures are also shown for comparison.

!

!

!

!


1-15

Figure 1.4: D" as a function of wavelength for ideal background limited photoconductors (PC) at temperatures 77, 150 and 300K (assumes a "f = 1 , 2π field-of-view and " = 1). The detectivity of thermal detectors at 4, 39, 95 and 300K are also shown for comparison.

! !

!

1.4

Comparison of thermal and photon detector D* fundamental limits

The sensitivity of a thermal detector is fundamentally limited by the temperature fluctuation noise arising from power exchange with the background radiation (see §1.2), whereas a photon detector is limited by the

!

generation-recombination noise arising from the photon exchange with the background radiation [25]. They have different D* dependencies on the detector temperature and the background radiation. For BLIP operation, the background radiation incident on the detector, see equation (1.8), should just equal the radiation from self-

! emission of the detector itself (assumed to follow Planck’s law). If the incoming photons incident on the detector produces the same amount of noise as the detector self-emission then the equivalent photon irradiance of the detector can be calculated by converting the spectral radiant exitance described in equation (1.1a) into spectral

[

]

photon flux exitance, dLq," = 2#c "4 ( exp( hc "k BT ) $ 1) d" and integrating over the range 0 " # c [26]. Figure 1.5 shows a plot of the background photon irradiance as a function of detector temperature for

! ! with varying cut-off wavelengths. The curves highlight the minimum photon detectors operating temperature for


1-16

Figure 1.5: Photon irradiance as a function of detector temperature for BLIP operation for photon detectors with " c = 12.5 # 100µm .

!

Figure 1.6: Fundamental D" limits of a FIR photon and thermal detector as a function of detector temperature for zero and 1017 photons/cm2s background radiation.

!


1-17

BLIP operation for a given background irradiance and cut-off wavelength. If the detector is operated higher than this temperature it will not be operating in a BLIP environment. The D" BLIP for an ideal PV detector can now be plotted using the irradiance values, determined from Figure 1.5, on the detector at a particular detector temperature. Figure 1.6 shows the fundamental limit of D* for

! a HgCdTe PV photodiode at a background radiation level of " B = 1.3# 1017 ph/cm2s (130K) represented by the ! blue line and " B = 0 represented by the black line for a cut-off wavelength " c = 20µm. For a totally noise-less

! photon detector with zero background D" increases unbounded, however real photon detectors exhibit a ! ! resistance that gives rise to Johnson noise. If Johnson noise dominates the photon noise then the detector has a

! Johnson noise limited D* (i.e., D* JOLI), this is the ultimate limit attainable and is shown on Figure 1.6. Plotted on the same figure is the ideal thermal detector D" determined from equation (1.7). The theoretical D* value of

! ! thermal detectors is much less temperature dependent than for a photon detector. For the example given in ! ! Figure 1.4, at temperatures below 30K and zero background FIR thermal detectors are characterized by D" values lower than those of a 20µm cut-off photon detector. At temperatures above 45K, the limits favour thermal

! detectors. The influence of a background radiation level of " B = 1017 ph/cm2s on D* is clearly seen for both the ideal PV diode and thermal detector. Comparison of both types of detector shows that the temperature

! ! region favours thermal requirement to attain BLIP performance in the FIR detectors operating at moderately cooled temperatures (around 77K).

1.5

The case for moderately cooled HTS bolometers

In the preceding sections it was shown that there is a large difference between the fundamental D" limit of a room temperature and a moderately cooled thermal detector. Table 1.1 highlighted the theoretically obtainable

! D" i.e., 1.8 " 1010 cm√Hz/W at 300K and 5.4 " 1011 cm√Hz/W at 77K. It was established, see equation (1.6), that cooling a thermal detector reduces the thermal fluctuation (phonon) noise and as a result D" #T $5 / 2 .

!

! ! However, these limits are never reached when looking at a source much hotter than the detector or for ! frequencies much higher than "# = 1 , since the Johnson noise or electronics noise will dominate the thermal fluctuation noise, see §2.6.

!


1-18

H2 S(0)

H2 S(1)

NH3, PH 3

Figure 1.7: Jupiter thermal emission spectrum from CIRS FP1 channel, reproduced from Nixon et al. [27].

Presently available COTS pyroelectric detectors operating at 300K have D" ’s around 10 8 to 2 " 10 9 cm√Hz/W. The Cassini CIRS Fourier transform spectrometer (FTS) [28] presently orbiting Saturn has a FIR

! ! ! channel, focal plane 1 (FP1), that uses a BiTe thermoelectric detector operating at 170K, its D" # 4 $ 10 9 cm√Hz/W near the low frequency end of a 0.4 to 30Hz band pass. On CIRS journey to Saturn, data was

! collected from Jupiter flyby (January 2001). An example of a typical FP1 spectrum composed of 100 co-added spectra (each scan is 50s), of Jupiter at 0.5 cm-1 resolution is shown in Figure 1.7. The very broad absorption feature from 250-500 cm-1 is the S(0) collisionally-induced continuum of H2 and part of the S(1) absorption is seen from 500-600 cm-1. The middle spectra shows molecular absorption features more clearly when the data is smoothed out and for comparison the 100-spectrum smoothed baseline noise of the instrument is also shown (dotted line). Figure 1.7 demonstrates that even with marginally increased D" over a 300K pyroelectric a fairly high-resolution spectrum can be recorded of a cold target. Also improving the time response (i.e. making a faster

! device), " , will reduce the long integration times that are presently necessary in order to resolve the weak spectral features in the 10-600 cm-1 spectral region. Smaller averages will also enable spatial mapping of D/H

! and gaseous abundances in the same time as present global abundances. Therefore, future planetary missions, to the gas giants, Jupiter and beyond, utilizing remote sensing CIRS like instrumentation will greatly benefit from moderately cooled FIR detectors with improved D" and faster " . It is envisaged that by using a HTS bolometer

!

!


1-19

like the one described in this thesis, an overall performance increase, by a factor of 5-8, over CIRS FP1-type detectors can be realized (see §1.6).

Planet

T surface (K)

T sphere (K)

Mercury Venus Earth ! Mars Jupiter Saturn Uranus Neptune Pluto

100-700 740 288-293 ! 140-300 165 134 76 72 40

445 325 277 225 123 90 63 50 44

Table 1.4: Temperature of the planets in the solar system [29].

Until the day that nuclear reactors in space become a reality (e.g. the contemplated NASA Prometheus program), long duration mission spacecraft instrumentation will always have tight mass and power budget requirements. From the viewpoint of power constraint, the technology (passive coolers or single-stage mechanical coolers) to achieve moderate cooling of detectors at the outer planets may not be as bad as first envisaged. Practically, the radiation load on cold shields and the first cold baffle in the instrument housing sets the cooling power required to maintain the detector at the operational temperature. In a cold space environment this cooling power requirement will be reduced. So the increased D" performance of FIR thermal detectors through moderate cooling together with the ease of reaching temperatures of 77K in the outer solar system makes an attractive case

! for the development of moderately cooled FIR detectors for outer planet missions.

1.6

Previous work on membrane HTS bolometers

In this section an attempt is made to summarize some of the more notable work in the area of micromachined thinned substrate or membrane HTS bolometers. Since, Kreisler et al. [30] have already given an excellent review of previous work on thick substrate (e.g. SrTiO3, zirconia and MgO) bolometers, this category of bolometer will be excluded from further discussion. Much of the impetus to manufacture thinned membrane HTS bolometers came out of a key theoretical paper written by Richards et al. [31]. They showed that a bolometer, using the resistive transition of a HTS film


1-20

deposited on a thinned substrate, operating at liquid nitrogen temperatures potentially has better sensitivity than COTS detectors for wavelengths > 20µm. They theoretically showed that D" for a bolometer designed for

" c # 350 cm-1 is only 30% from the ideal limit. ! Verghese et al. [32], from Richard’s group, used a 20µm thick sapphire substrate to deposit 500Å

!

SrTiO3 thick buffer layer, followed by 3000Å of YBCO by pulsed laser deposition (PLD). The structure was suspended by 25µm diameter copper wire to provide thermal isolation and had an absorbing layer deposited on the back of the substrate. Using a He-Ne laser monochromatic radiation source, they reported a D" = 4.2 " 10 9 cm√Hz/W at 10Hz and " = 55ms.

! ! Brasunas et al. [33] repeated this experiment by depositing PLD 1500Å YBCO onto a 25µm thick

! with a 300Å CeO buffer layer and a carbon black absorbing layer on the back, they reported sapphire substrate 2 similar results: D* = 6 " 10 9 cm√Hz/W at 4Hz and " = 65ms. Lakew et al. [34] improved on the device performance by chemically thinning R " plane sapphire to 7µm in thickness. They deposited 2000Å of YBCO

! ! resulting structure was suspended on four gold wires (17.5µm and 200Å of CeO2 buffer layer by PLD. The

! gold black was deposited on the backside. Using a 500°C blackbody, KRS-5 diameter) and a 30µm thick window and a bias current of 6.34mA, they report a peak D" = 1.2 # 1010 cm√Hz/W at 3.8Hz and a " = 100 ms. In a follow up paper, Lakew et al. [35] report on a PLD YBCO:CeO2 film (2000Å:200Å) on a micromachined

! monolithic R " plane sapphire substrate with membrane thickness of 12µm, although !no gold black was deposited on this device, they infer from spectral noise density measurements a D* " 2 # 1010 cm√Hz/W at 4Hz.

!

The concept of using a micromachined silicon structures for bolometer construction was proposed early

! on by Aslam [36] at Oxford and early efforts to micro-machine silicon for the purposes of fabricating suspended bolometers was pursued by Kruse’s group [37]. The micromachined silicon approach has three major advantages; (i) it permits the fabrication of sub-micron thick membranes for reduction of thermal capacity, (ii) it permits the fabrication of pixel arrays and (iii) it allows for superconductor/semiconductor hybrid devices. Stratton et al. [38] at Honeywell were the first to report on a device using a low thermal mass micromachined silicon structure, it comprised of a 1800Å thick DyBaCuO film deposited on a YSZ (2000Å/SiN(4000Å) bilayer. Unlike Aslam’s design, Stratton's microbolometer does not incorporate a radiation absorber, i.e. the HTS film is irradiated directly. No noise measurements or spectral detectivity measurements were reported. Using a lamp radiation source the authors report a responsivity of 800V/W at 89K with " = 1ms.

!


1-21

Neff et al. [39] and Steinbeiß et al. [40] both report on a YSZ buffered GdBaCuO film on a 1µm thick silicon membrane. They report a D" = 4 # 10 9 cm√Hz/W and a fast time constant of 0.4ms. De Nivelle et al. [41] at SRON (Space Research Organization Netherlands) have reported on a HTS

! bolometer suspended on a SiN membrane, this device showed a slow response of " = 550ms and a record D" = 5.4 # 1010 cm√Hz/W at 0.3Hz. ! Table 1.5 summarizes the detectivity and time constant data from the key papers discussed above and

!

that provided by other workers for state-of-the-art thinned substrate/membrane and micromachined monolithic silicon based HTS bolometers.

No.

Responsivity, " (V/W)

a

17

!

b c

80 80

Measurement frequency, f (Hz) 10

!

4 3.8

NEP (W/√Hz)

Detectivity, D " (cm√Hz/W)

2.4 x 10-11

4.2 x 109 ! 6.0 x 109

1.6 x 10

-11

8.0 x 10

-12 -10

1.2 x 10

Time constant, " (ms) 55

Verghese et al. [32]

!

Reference

65

Brasunas et al [33]

10

100

Lakew et al. [34]

9

200

Khrebtov et al. [42]

d

1.4

10

2.0 x 10

e

0.3

10

3.0 x 10-9

4.2 x 107

1

Kreisler et al. [43]

f

3100

32

6.3 x 10-13

8.3 x 109

5

Berkowitz et al. [44]

g

3300

10

3.8 x 10-12

1.7 x 1010

1-5

Li H et al. [45]

h

1750

10

7.0 x 10-10

3.8 x 107

16

Li Q et al. [46]

i

not given

estimate

5.0 x 10-12

1.4 x 1010

3

Verghese et al. [47]

j

580

200

3.0 x 10-12

4.0 x 109

0.4

Neff et al. [48]

2Hz

5.5 x 10

-12

1.8 x 10

10

115

de Nivelle et al. [49]

6.9 x 10

-12

1.4 x 10

10

26


1.8 x 10

-12

5.4 x 10

10

550


1.1 x 10

-12

1.1 x 10

9

24

Johnson et al. [51]

1.1 x 10

-12

4.5 x 10

9

7

Foote et al. [52]

1.1 x 10

-11

2.3 x 10

8

0.081

Barth et al. [53]

2.5 x 10

9

0.564

Méchin et al. [54]

8

0.006

Méchin et al. [54]

9

6

k l m n o p q r s

6900 2000 20,000 60,000 8000 1290 12000 288 1730

5Hz 0.3Hz 5Hz 5Hz 100Hz -

4 x 10

-12

6.1x 10 -

-12

1.2 x 10

5.2x 10

5.6 x 10

Khrebtov et al. [55]

Table 1.5: State-of-the-art thinned substrate and micromachined monolithic silicon HTS bolometers.


1-22

Figure 1.7 shows a plot of D" as a function of " for these bolometers to illustrate the sensitivity versus time constant compromise. The performance of a typical HgCdTe MIR detector (typically, D" # 2 $ 1010

! ! cm√Hz/W and " # 0.5µs) is also shown for comparison, it is seen that the best HTS bolometers show similar

! sensitivities but the time constant needs to improve by orders of magnitude. Using the best D* value reported in

! Table 1.5, the invariant detectivity (frequency independent parameter), D" / # = 2 $ 1011 cm/J is also plotted, ! this value represents the state-of the art. It can be seen that for most HTS bolometers, the invariant detectivity ! falls between 5 " 1010 # 2 " 1011 cm/J. In order to see what level of sensitivity improvement can be realistically expected, D" / # = 5 $ 1011 cm/J, the theoretical upper bound of a bolometer operating at 90K with a 300K

! background (see §2.7), is also plotted and shows that there is still room for marked improvement. !

The results reported by other workers are extremely encouraging for the development of a more

sensitive, faster HTS bolometer, operating at cut-off wavelengths " c > 20µm, based on either micromachined monolithic silicon structures or thinned membrane substrates.

!

Figure 1.7: Detectivity, D" , as a function of time constant, " , for state-of-the-art thinned substrate (a to f) and monolithic silicon HTS bolometers (g to s).

!

!


1.7

1-23

Thesis overview

Chapter 2 will investigate in more detail the underlying theory that predicts the performance of a HTS bolometer. A simple model is used to establish the thermal equilibrium equation after which the bolometer responsivity under a constant current bias is derived. It is highlighted that operating a bolometer in this mode gives rise to a positive electro-thermal feedback that causes thermal runaway. To mitigate this effect it is shown that a HTS bolometer can be operated in a constant voltage mode. This not only gives rise to a strong negative electro-thermal feedback but also gives a reduction of the bolometer time constant; the responsivity equation under a constant voltage bias mode is derived. In order to see what parameters influence the responsivity the voltage biased bolometer responsivity is expressed in a dimensionless form as a function of normalized operating temperature. From this analysis it is shown that for any given sink temperature, the responsivity has a maximum value that is governed by the temperature coefficient of resistance, the dependence of the thermal conductance (linear or higher order) from the HTS thermistor to the sink and the background power loading. Next the NEP is considered and expressions are given for photon noise, phonon noise, Johnson noise, 1/ f noise and front-end amplifier noise that add in quadrature to give the total incoherent noise of the bolometer. From this

! analysis, theoretical values for the NEP and D" are given for technically feasible bolometer structures. More importantly, the electro-thermal feedback effect on the overall noise is taken into account, since there is an

! increase in 1/ f noise due to self-heating, from this the lower bound of NEP is calculated for some practical design parameter scenarios. The NEP is also expressed in a dimensionless form so that the optimum thermal

! conductance of the HTS bolometer as a function of power loading can be deduced. Chapter 2 concludes by calculating the effective radiance emitted from a source (at a given temperature) for some scientifically interesting FIR wavelength bands and the amount of radiation that is incident on the bolometer for a particular field-of-view. Chapter 3 addresses in detail the material selection criteria for a bolometer design that will have a low thermal mass, a fairly high thermal conductance link to the sink and is also compatible for space use. Physical properties such as thermal capacity, thermal conductance and thermal expansion for HTS films and substrate materials are discussed and tabulated. Spaceflight considerations such as stress induced degradation, irradiation effects and chemical stability are addressed. The requirements on the HTS thin film set by the bolometer design


1-24

and the fabrication process are given. From these considerations three HTS-substrate systems for inclusion into a bolometer design are proposed. In Chapter 4 a bolometer design is given. First the assumptions and parameters that go into the design concept are elucidated including the effect of HTS film thickness (hence resistance) on responsivity and the constraints on substrate dimensions due to thermal capacity. Two schemes for the radiation absorber are described, namely, a gold black coating or a space matched impedance coating; the pros and cons are given. Next, mechanical properties such as thermal stress and fracture strength of the membrane that supports the HTS film are calculated. An analytical technique is used to derive the stress and strain components in the membrane structure as a function of applied pressure. This analysis gives a high level of confidence that membranes will survive HTS deposition and photolithographic processes in the fabrication stage and will remain intact under spacecraft purging in pre-launch, launch and during deployment. A simple lumped thermal model is then given to give a rough estimate of the bolometer time constant, this is then followed by a more elaborate numerical nodal thermal analysis to establish how much heat is required to maintain the HTS at mid-point of the transition, the maximum incident radiation that would cause over heating of the device and to establish a better device time constant. Chapter 4 concludes with a pictorial representation of the bolometer design including substrate and thin film dimensions. The experimental work presented in Chapter 5 concentrates on the fabrication of a bolometer device. Several approaches were taken in the fabrication of a thinned membrane structure using standard semiconductor photolithographic processing techniques, namely, silicon membranes using a heavily doped boron layer as an etch stop, silicon membranes using a silicon-on-insulator structure, low stress silicon nitride membranes and thinned sapphire. At the start of this work only the cuprate HTS materials were considered as candidate materials for the thermistor, however it became clear that a number of research groups were making rapid progress in depositing high quality MgB2. Because its superconducting transition temperature is achievable with state-ofthe-art cooling technology it does not preclude its use in space instrumentation. Since no work (to the authors knowledge) has been reported in the literature on the potential application of this material to bolometer construction, it inspired us to pursue this material as a candidate thermistor material. The lower temperature operation of the MgB2 thermistor material promises a higher sensitivity. This being said one of the hardest tasks in this work was to acquire good quality HTS thin films on the prepared substrates. Very few academic institutes were willing to deposit HTS material on non-matched crystalline substrates (e.g. silicon) and there were next to


1-25

no commercial organizations selling such a service (especially in the UK) so this task was painfully arduous and time consuming. However, collaborative pathfinder work with GEC Hirst Research Centre did produce some encouraging results. These results are summarized in Appendix E. Fortunately, the advancement of pulsed laser deposition techniques opened up the possibility of depositing HTS materials onto lattice matched buffer layers (deposited on non lattice matched substrates) and eventually through support of colleagues at Goddard Space Flight Centre, HTS material was acquired. Two types of devices were fabricated for testing i.e. YBCO on silicon membranes and MgB2 on silicon nitride. Chapter 6 deals exclusively with the experimental set-up used to cool down and measure excess noise in the bolometer devices. Accurate measurements of the excess noise will show whether or not the HTS thermistor material will provide good signal-to-noise performance of the bolometer. The pit falls in carrying out low-noise measurements especially when the input source resistance is small (as was the case) is elucidated and a thorough analysis of low-noise transformer measurements is given in Appendix F so that errors are avoided. Although, Chapter 2 elucidates the fact that there are some advantages in operating the bolometer in voltage bias mode the measurement system described here uses current bias, primarily because of the ease of voltage signal measurement. Chapter 6 concludes with a frequency response and calibration against known resistors of the noise measurement system. Chapter 7 focuses on noise voltage measurements to establish the temperature dependence of noise voltage spectral density through the superconducting transition region for both YBCO and MgB2 thin films. The results of these measurements are then related to the Noise Equivalent Power (NEP) for the YBCO device and temperature noise for the MgB2 device, which gives a measure of the sensitivity that can be expected from such thermistor materials, since the lower the NEP or temperature noise value the better the signal-to-noise ratio. Finally in Chapter 8, a summary is given of the results obtained and a discussion is given on some sundry topics. Possible future avenues of exploration are indicated.


1-26

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R. J. Keyes, eds., "Optical and Infrared detectors", Springer-Verlag, Berlin and New York, 1977.

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1-27

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1-28

Chapter 2

Bolometer Theory

2.1

Chapter 2. Bolometer Theory

2.1

2-2

Introduction

Several authors have presented the theory of bolometer operation [1][2][3][4][5][6][7]. However, most of this analysis is for bolometers that use a semiconductor (e.g. Ge) as the thermistor material where the electrical resistance can be expressed exponentially as R = R0T 3 / 2e B /T ( R0 and B are constants), giving rise to a negative TCR, ( " = 1/ R(dR / dT ) < 1). In a HTS bolometer, because of the nature of the superconducting transition, the

! ! TCR at the mid-point of transition!is positive. The following analysis takes account of this and expressions for ! the voltage responsivity, current responsivity and NEP for an ideal HTS bolometer subject to Johnson, phonon and 1/ f noise are derived.

!

2.2

Bolometer model

Consider a bolometer element, see Figure 2.1, of heat capacity C [J/K] . Assume that this temperature sensitive element is fixed at an operating temperature T [K] and is coupled to a heat sink at temperature T 0 by a thermal

! conductance G [W/K] . The resulting time constant is " [s] equal to C /G . Assume radiation coupling with the ! ! background is negligible compared with conduction coupling to the sink and that a constant bias current I flows ! the bolometer element, generating the ! bias voltage!V . A change in absorbed radiant power, "# , gives through

! "V = I"R . rise to a change in the HTS resistance "R , consequently giving rise to a change in the output voltage ! the total power The electrical power dissipated in the bolometer ! due to the bias current is P = IV . Therefore ! ! is then, dissipated in the bolometer element is W = P + " . The dynamic thermal equilibrium equation ! !

# d (T " T 0 ) & C% ( + G (T " T 0 ) = W $ ' dt

(2.1)

where C[d (T " T 0 ) / dt] = C #T dt is the rate of heat flow into the bolometer element caused by incident ! radiation and G (T " T 0 ) = G#T is the power conducted into the heat sink. In the following discussion, it is

!

assumed that the electrical resistance change due to heating of the bolometer element is a function of

! temperature only (i.e. assume the HTS element is magnetically shielded).

2-3

!

C

HTS


V +

I

G

R

T0

Figure 2.1: HTS bolometer operated in constant current mode.

2.3

Bolometer responsivity with constant current bias

If the following assumptions are made (i) " is the fraction of incident power absorbed, (ii) the source radiation is square or sinusoidal chopped (see Appendix B) so as to produce a power signal with a time dependent

! a constant current bias is used for voltage readout, then the amplitude of the component " = " 0 e j#t and (iii) temperature variation "T of the bolometer element is found from equation (2.1),

! # d"T & d (I 2 R) C% "T + )* 0 e j+t ( + G"T = $ dt ' dT

!

(2.2)

If an effective thermal conductance G e is defined such that, !

!

Ge = G " I 2

dR = G " I 2 R# dT

(2.3)

Equation (2.2) can be written as, !

# d"T & j+t C% ( + G e "T = )* 0 e $ dt '

This first order differential equation has a solution, !

(2.4)


2-4

"T = Ke

$ Ge ' t) &# % C (

+

*+ 0

(2.5)

(,C) 2 + G e2

where K is a constant whose value at t = 0 is "T . If G e is positive then the transient term decays to zero with ! an effective thermal time constant,

!

!

!

!

"e =

C Ge

(2.6)

The peak amplitude of the temperature oscillation is given by, !

"T

p

=

#$ 0

(2.7)

(%C) 2 + G e2

From the exponential term in equation (2.5) it can be seen that if G e is zero or negative then e"t / # e grows ! increasingly larger driving the HTS resistive element into the normal state, where dR / dT is low enough to

! ! make G e positive again. From equation (2.3), the critical current I c for thermal runaway is,

! G 2 I! c = "R

!

If a parameter L0 = I / I c is defined, then,

!

(2.8)

!

L0 =

I 2 R" P" = G G

(2.9)

From equation (2.3), the effective thermal conductance can be written as, !

G e = G (1 " L0 )

Ideally the bolometer will oscillate with a peak amplitude "T ! corresponding voltage fluctuations of peak amplitude,

!

p

(2.10)

as given by equation (2.7) and will exhibit


2-5

V = I"R #T

p

=

I"R$% 0 (&C) 2 + G e2

(2.11)

Therefore the responsivity using equation (2.3), is given by, !

"V =

( +1 2 V %RGL0 = $* 2 2 2#0 ) (&C) + G (1' L0 ) ,

(2.12)

This implies that for a positive temperature coefficient, " , there is a maximum to the bias current (i.e. !

I 2 < G "R ). The optimum value of G , at a given modulating frequency, for a maximum response is when ! d" / dG = 0 i.e. when "C = G[1 # L0 ] . Equation (2.12) can be simplified further,

!

! !

!

"v =

#L 0 I (1 $ L0 ) (1 + % 2& e2 )

[V/W]

(2.13)

L0 = ("I 2 R) /G is simply the electro-thermal feedback (ETF) factor. Note that " e = " /(1 # L0 ) . Equation (2.13) ! shows that for stable operation L0 < 1 . Richards et al. [6] cite a value of L0 = 0.3 so as to eliminate thermal

!

! instability and hence optimize the voltage response. For a HTS bolometer working in constant current mode the ! to give "C # 0.7G . device should be designed

!

!

2.4

Bolometer responsivity with constant voltage bias

HTS bolometers are not usually operated with a constant voltage bias, because of the experimental difficulty of measuring very small currents. The rapid progress in cryogenic transimpedance operational amplifiers [8] and high T c superconducting quantum interference devices, have made the possibility of very low current measurements more realizable. As long as the lead resistance is lower than the bolometer resistance, so as to

! maintain constant voltage bias, the HTS bolometer current can be read out. In §2.3 it was highlighted that operating a HTS bolometer in constant current bias mode gives rise to a positive ETF that causes thermal runaway. Operating in constant voltage bias mode has significant advantages. Irwin et al. [9] showed that operating with a constant voltage bias mode with a strong negative ETF avoids this problem and also gives rise to a large reduction of the bolometer time constant [10].


2-6

Using the same method that was used to derive equation (2.13) and using a negative ETF factor gives the current responsivity,

"I =

#$Lv0 V (1+ Lv0 ) (1+ % 2& e2 )

[A/W]

(2.14)

where " e = " /(1+ Lv0 ) and Lv0 = "V 2 /(RG) . Since " is positive for HTS films there is no limitation on the bias ! voltage, hence Lv0 can be >1 and the HTS bolometer can be operated with a strong ETF. The effective time ! ! ! constant, " e , can be reduced by a factor of (1+ Lv0 ) by increasing the electrical power, P = V 2 / R . Practically,

! the increase in the ETF factor, Lv0 , is limited by the temperature difference of the operating point in the ! ! ! superconducting transition (usually mid-point) and the sink temperature. Typically this would be 10-15K if

! using liquid nitrogen cooling.

2.5

Optimization of bolometer responsivity

In the following analysis an expression for the responsivity is derived as a function of normalized operating temperature for a voltage biased bolometer, to see what effect power loading has on the current responsivity. It is assumed that the thermal conductance G is temperature dependent, see Volklein [11], and approximately has the form,

! "T % G = G0 $ ' #T0 &

(

(2.15)

The resistance of the HTS film varies with temperature broadly as, !

" T %n R(T ) = Ri + Rm $ ' #Tm &

where Ri is the residual resistance in the superconducting state and Rm is the resistance of the film at ! temperature T m . If Ri is very small, then the resistance of the film near the midpoint of transition can be

!

expressed as,

!

!

!


2-7

" T %n R(T ) = Rm $ ' #Tm &

(2.16)

this gives a positive TCR,

!

"=

1 dR n = R dT T

(2.17)

From equation (2.1) the static thermal equilibrium equation is, ! (2.18)

W = P + " = G (T # T 0 ) Using the dimensionless parameters as defined by, !

"=

T ; T # "= m; "= T0 T0 (G 0T 0 )

(2.19)

substituting (2.15) into (2.18) and using the definitions in equations (2.19 ) gives, ! ! !

P = G 0T 0[" # (" $ 1) $ % ]

(2.20)

Now the dc current output is given by I = P / R therefore using equation (2.20), and (2.16) gives the ! expression,

!

$ " 'n * / I = Rm G 0T 0 & ) # (# + 1) + , /. %# (

[

01/ 2 2 21

]

(2.21)

The effective thermal conductance G e is related to the dynamic thermal conductance G when RL " # , by the ! expression,

G e = G " #P

(see equation 2.3). Then substituting equation (2.20) into (2.18) gives,

!

! W = G 0T 0[" # (" $ 1) , differentiating with respect to T gives,

!

!

!dW d" G= = G 0 ( # + 1)" # $ #" # $1 d" dT

!

[

!

]

(2.22)


2-8

Now the dc (zero frequency) current responsivity is then,

/ 21/ 2 & $ )n , #1 Rm G 0T 0 ( + % (% - 1) - . 4 10 43 '% *

[

]

#I "I = = G e G 0 ( , + 1)% , - ,% , -1 - #G 0T 0 % , (% - 1) - .

[

]

[

]

after some manipulation and simplification, !

# R &1/ 2 "I = % m ( $ G 0T 0 '

#+ .n &1/ 2 ) 1 n%- 0 (* (* 2 1) 2 3 )( %$, * / (' 1 1 (* (1 (* 2 1) + * ) + n(* (* 2 1) 2 3 )

Let SI = " I / (Rm /G 0T 0 ) , then the dimensionless current responsivity is given by the following expression, !

-$ 'n 01/ 2 " * n/& ) (# (# + 1) + , )2 /.% # ( 21 SI = * (# (* (# + 1) + # ) + n(# * (# + 1) + , )

!

(2.23)

From equation (2.23) it can be seen that for any given sink temperature, the responsivity has a maximum value, ! which depends on the constants n, " , # and $ . Figure 2.2 show plots of the dimensionless current responsivity,

SI , as a function of the reduced temperature, " , for the cases " = 1/ 2, 1, 2 and 3 with zero background power

! loading, " = 0 , and for values of n between 50 and 125. The plots show that the maximum responsivity is not !

! sensitive to the constant " , which governs the thermal!conductance mechanism. !

! This equation is also plotted in Figure 2.3 for n = 125 , " = 1 and # = 1.1 but this time for varying

! power loading conditions varying from 0 to 0.04. Power loading the bolometer has the expected degradation in

! responsivity, it is seen that with increasing power loading!the temperature difference between the HTS element temperature and the heat sink temperature has to increase in order to maintain a maximum response. The maximum responsivity of the bolometer can now be evaluated for a particular condition, for example with a zero power loading condition and a linear thermal conductance dependence on heat sink temperature i.e. " = 1 , and

n = 125 the maximum responsivity is given by " max = 1584(Rm /G 0T 0 )1/ 2 , at the normalized temperature !

!

!


2-9

" = 1.003 , then from equation (2.20) the optimum value of power dissipated is 0.003 G 0T 0 . As shown from the above example it is now possible to tabulate the optimum power dissipation for valid values of " ,n and # . Table

!

!

2.1 lists maximum response and optimum power dissipation values for a bolometer with n = 50 , 100, 150, 200

!

and 250, zero background loading and " = 1 .

! !

Figure 2.2: Responsivity as a function of normalized temperature for n = 50 to 125 for " = 0.5, 1, 2 and 3 and zero power loading.

!

!

The responsivity variation with background loading power can be understood by calculating the normalized responsivity, Sn = S# " / S0 , where, S0 is the responsivity with zero power loading and S# " is the responsivity with loading " = " # . By considering the effect of radiant power loading on the dissipated power in

! ! the HTS thin film (see Appendix C) gives an expression for the normalized responsivity,

!

! 1/ 2

"$n# ("$%# ("$ # & 1) + " 0% &n"$n# (" 0 & 1) & "$%# ("$ # & 1))] [ (% + 1)" 0% +1 & %" 0% & n(" 0% (" 0 & 1))] [ Sn = 1/ 2 [" 0n (" 0% (" 0 & 1))] [(% + 1)"$%# +1 & %"$%# & n("$%# ("$ # & 1) + " 0% &n"$n# (" 0 & 1) & "$%# ("$ # & 1))]

!

(2.24)


!

2-10

!

n

" max /(R m /G 0T 0 )1/ 2

Popt /(G 0T 0 )

50

28

0.007

100

437 ! 5.9. 103

150 200 250

0.004 0.003

7.3.10

4

0.002

8.8.10

5

0.0015

Table 2.1: Optimum power dissipation values for a bolometer with " = 1.1, # = 1 and " = 0 .

!

!

Illustrations of equation (2.24) are given in Figure 2.4 for the values " 0 = 1.01 # 1.1, $ = 1 and n = 125 . It is clear from these plots that the responsivity becomes less sensitive to changes in the background loading power as

!

# " increases.

!

Figure 2.3: Responsivity ( SI ) as a function of normalized temperature ( " ) for various background power loading conditions with n = 125, " = 1 and # = 1.1.

!

! !


2-11

1.0

"=1 n = 125 0.8

0.6

Sn

#o =1.1 0.4

0.2

#o=1.01

0.0 0.00

0.05

0.10

0.15

0.20

!' Figure 2.4: Normalized responsivity versus loading power for different values of normalized temperature at zero loading and for the case " = 1 and n = 125 .

!

2.6

Noise Equivalent Power (NEP) of the bolometer

There are several components that contribute to the total incoherent noise in the bolometer system these are:

2.6.1 Photon noise Photon noise arises from the mean square fluctuations in the rate of arrival of photons and hence the radiation power absorbed (see §1.2) at the detector is,

2

"W =

4 ( k BT ) c 2h 3

5

&

A# cos $"f

' 0

x 4ex

(e % 1) x

2

f (x)dx

(2.25)

From equation (1.6), the !

NEP 2 = "W 2

The noise equivalent power is then ! given by,

(2.26)


2-12

2 NEPphoton

4 A"(k BT ) 5 = c 2h 3

$

% 0

x 4ex

(e # 1) x

2

f (x)dx

(

(2.27)

)

If h" " opt , where " opt is the optimum value of normalized temperature at minimum NEP, since any fluctuations in the sink temperature will give a smaller degradation in the NEP.

!

!

Figure 2.7 shows plots of the minimum values of N 2min as a function of power loading conditions

varying from 0 to 0.06 for n = 50, 100 and 125 . The optimum value of G 0 can now be deduced by fitting

! second order polynomials to the data points in Figure 2.7 and differentiating with respect to G 0 . The quadratic ! equation that defines the relationship between N 2min and " is,

! !

!

! NEP 2 min = a + b" + c" 2 4k BT 02G 0

(2.44)

!

Figure 2.6: N 2 as a function of normalized temperature for different background loadings in the range 0 to 0.05 for the case " = 1, # = 1.01 and n = 50 .

!

! substituting " = # /(G 0T 0 ) into equation (2.44) gives,

!

# ck " 2 & 2 NEPmin = 4% ak B G 0T 02 + bk BT 0" + B ( G0 ' $

!

(2.45)


2-22

The first term in this expression can be considered to be the intrinsic NEP of the bolometer that increases as G 0 increases. The second and third terms are the components that give rise to the deterioration of the NEP due to the

! smaller. heating effect of the power loading on the bolometer, the sum of these terms increases as G 0 is made Differentiating equation (2.45) with respect to G 0 gives,

! !

2 $ d (NEPmin ) #2 ' = 4& ak BT 02 " ck B 2 ) dG 0 G0 ( %

(2.46)

! gives the optimum value of G , Equating equation (2.46) to zero 0

!

" c %1/ 2 ( G0 = $ ' # a & T0

(2.47)

! comparing equations (2.19) and (2.47) gives " = (a /c)1/ 2 . The inset of Figure 2.7 gives the quadratic coefficient constants and the resultant c / a values for the curves in Figure 2.7. Figure 2.8 gives the optimum G 0 as a

! function of power loadings between 0.01-100pW as calculated from equation (2.47) for n = 50, 100 and 125 .

!

!

!

1.20 quadratic equation coefficients n = 50! n = 100! n = 125!

a = 1.0674; b = 1.9055; c = 5.4438;! a = 1.0400; b = 1.6879; c = 13.374;! a = 1.0347; b = 1.6188; c = 16.395;!

c/a = 5.10 c/a = 12.86 c/a = 15.85

1.15 n = 50 2

N min 1.10

n = 100

1.05 n = 125

1.00

0

0.01

0.02

0.03

0.04

0.05

0.06

! Figure 2.7: N 2min as a function of background power loading " = 1 and # = 1.01

! !

!

!

"

for n = 50, 100 and 125 for the case


2-23

Figure 2.8: Optimum thermal conductance of the bolometer as a function of power loading for the case " = 1 and T 0 = 80K .

!

2.9

Effective radiance

Any body at a finite temperature T emits radiation. The intensity of radiation per unit wavelength emitted by the unit area of the radiating body at a temperature T per unit solid angle can be determined from Planck’s radiation law, see §1.1.1,

! ! dL" (T ) =

2 #hc 2 $% 1 1 c $% 1 1 d" = 1 d" # # "5 [ exp(c 2 / "T ) & 1] "5 [ exp(hc / "k BT ) & 1]

(2.48)

where c1 = 2"hc 2 is the first radiation constant, c 2 = hc / k B is the second radiation constant, " is the emissivity ! of the body and " is the transmission of the optical system and atmosphere. The radiance in the "1 , " 2

! ! ! wavelength band is obtained by integrating equation (2.48) over the wavelength band,

!

! "2

L"1" 2 (T ) =

# dL

" (T )

(2.49)

"1

When the amount of radiation detected by the bolometer is evaluated, the bolometer contribution to the signal! to-noise ratio also needs to be accounted for, i.e.,


2-24

S = N

(2

) (1

"S% $ ' d( = #N& (

(2

"

*

%

) $$# DA+fP ''& d( (

(1

(2.50)

(

where "1 , " 2 is the wavelength band, (S/N) " is the monochromatic signal-to-noise ratio, D" is the specific ! detectivity of the bolometer, P" is the power of wavelength " incident on the bolometer, A is the bolometer ! ! ! receiving area and "f is the temporal bandwidth of the bolometer. The amount of power of wavelength "

! ! ! incident on the bolometer depends on the geometry of the optical set-up and the radiance of wavelength, " , !

! P" =

AAr L" d2

!

(2.51)

where Ar is the area emitting the radiation, d is the distance between the emitting and receiving areas and L" is ! the radiance at wavelength " as given in equation (2.48). If it is assumed that the emissivity and the

! ! transmission are independent of wavelength then the signal-to-noise becomes,

!

! * S Dmax Ar = N " max d 2

/ Ad 1 $%c1 0 #f 1 & 2

"2

. "1

+31 1 ( 1 d " * -4 "4 ) exp(c 2 / "T ) ' 1 ,1 5

(2.52)

Equation (2.52) shows that the signal-to-noise ratio depends on the geometry of the measuring system, the ! bolometer and its properties and on the photon flux incident in the wavelength interval ("1, " 2 ) . The effective radiance is defined as,

!

Leff "1"2

#$c1 = %

"2

(

& "1 *) exp(c 4

"1

+ 1 d" , 2 / "T ) ' 1

(2.53)

and is independent of the properties of the detector and the geometric factors. The integral in equation (2.53) can ! be evaluated using the series integration,

Leff "1 , " 2 =

!

3 #$c1 & T ) . ( + 0/ % ' c2 *

,

a

(x 2 ) -

,

a

1 (x1 )3 2

(2.53)


2-25

$

where,

!

" (x) =" m a

#3

[

]

exp(#mx) (mx) 2 + 2(mx) + 2 and x = c 2 /("T ) .

m=1

Figure 2.9 shows the effective radiance as a !function of temperature for the scientifically interesting FIR wavelength bands (a) 8-11.5µm (the window in the Earth’s atmospheric transmission); (b) 17-20µm (H2 S(0) collisionally induced continuum); (c) 20-40µm (H2 S(1) absorption) and (d) 83-143µm (pure rotational lines of CH4). In the effective radiance calculations the transmittance is assumed to be 1.

2.10 Radiation incident on bolometer The total radiation power emitted in a solid angle " by a blackbody source (Lambertian and " = 1) at temperature T s incident on an area A up to a cut-off wavelength defined by a filter " c is given by,

! "c

!

!

!

Pr =

!

# dL dAd$d cos %

(2.54)

"

0

where " represents the inclination angle of the plane of the receiving area A with respect to the surface of the ! blackbody and L" is the Planck function defined in equation (2.48). Assuming " = 1 and hc /("k BT s ) 77K . Several 2 3-y 3+y x with T c as high as 126K and more recently the discovery in 2001 of superconductivity at 39K in intermetallic

! MgB 2 . ! !

Based on material properties and the technical difficulties of HTS thin-film deposition and postdeposition processing several HTS-substrate systems are recommended for use in a bolometer construction.

3.2

HTS material

3.2.1 Cuprate compounds In 1987 Bednorz and Muller [1] observed superconductivity in perovskite copper oxides, La 2"x Ba x CuO 4 , showing a critical superconductive temperature T c between 30 and 40K. This not only demonstrated the high T c

! compared to all previously known superconductors, but also that this T c was beyond the value many theorists ! ! believed as the limit to the previously applied Bardeen-Cooper-Schrieffer (BCS) theory [2] explaining ! superconductivity. A rapid succession of discoveries followed, La 2"x Srx CuO 4 [3], YBa2 Cu3O7-x (YBCO), GdBa2Cu3O7-x (GBCO) both with T c " 90K [4] then those of similar Bi, Tl and Pb oxides with T c up to 125K

! [5][6][7][8]. There are a number of excellent review articles on cuprate HTSs [9]. The basic properties, of these ! ceramic compounds are given by Friedel et al., [10].

!

The ceramic HTS materials all have a perovskite type structure (e.g. BaTiO3 CaTiO3). The chemical and structural properties of these materials, have been given by Goodenough [11], and the development of the theory of superconductivity, based upon this structure, has been given by Phillips [12].

Chapter 3. Bolometer material selection

3-3

YBa2Cu3O 7-x

Structure

Tc

0 < x < 0.2

orthorhombic

90K

0.2 < x < 0.5 orthorhombic steady decrease to 60K ! x = 0.5 tetragonal 60K 0.5 > x >1

tetragonal

paramagnetic insulator

Table 3.1: Stochiometric forms of YBa 2Cu 3O 7"x [13].

The structure of the 123 compounds is complicated because of the possibility of having different ! oxygen contents depending on the synthesis conditions. The different stoichiometric forms for example of YBCO are shown in Table 3.1. Knowledge of the unit cell lengths for these compounds is important, since this helps in determining the correct choice of substrate material for the growth of good epitaxial films. The unit cell lengths together with the transition temperatures of several candidate HTS compounds for incorporation into a bolometer design are given in Table 3.2.

Compound

a (Å)

b (Å)

c (Å)

T c (K)

Bi2Sr2O7Ca2Cu 3O10

5.4

5.39

38.2

110

! YBa2Cu3O 7

! ! ! 3.8231 3.8864 11.6807

92

Y2Ba4Cu8O8

3.871

3.840

27.25

81

GdBa2Cu3O 7-x

3.82

3.89

11.67

89.6-92.2

MgB2

3.1432

a= b

3.5193

39

Table 3.2: Unit cell lengths and transitions of some candidate HTS compounds [14]. !

3.2.2 Magnesium diboride (MgB2) An extensive review of the superconducting properties of MgB2 has been given by Buzea et al. [15]. Akimitsu et al. [16] showed superconductivity at 39K in the binary intermetallic MgB2. The reported value of T c is above or at the limit suggested theoretically by the BCS, phonon mediated superconductivity [17]. MgB2 crystallizes in the hexagonal A1B2-type structure, which consists of alternating hexagonal layers of Mg!atoms and graphite like honeycomb layers of B atoms. The unit cell parameters for MgB2 are

!

a = 3.1432 ± 0.0315 and


3-4

c = 3.5193± 0.0223 Å∗. X-ray diffraction studies (Paranthaman et al. [18]) on MgB2 thin films, grown by electron beam evaporation, on sapphire single crystal reveal strong MgB2 (001) and (002) peaks indicating a c-

!

axis aligned film. However, the MgB2 (101) pole figure indicated the film has random in-plane texture, this could be due to the initial reaction of Mg vapours with B films at the free surface of the film. This causes bulk crystallization rather than epitaxial nucleation at the HTS film /substrate interface. The significance of this result means that MgB2 thin film can be grown on a variety of substrates without the need to worry about epitaxial growth and the consequent deterioration of superconducting properties, allowing for optimal bolometer design.

3.2.3 HTS thin film deposition techniques Fabrication of HTS thin films, for bolometer applications, must take into consideration compositional homogeneity, surface quality, large area deposition, substrate compatibility and the required electrical and magnetic properties of the deposited film. These requirements have resulted in the application of nearly every deposition technique available for HTS thin film production. The most important methods are:

Physical vapour techniques (PVD)     

Magnetron sputtering Co-evaporation Flash evaporation Molecular beam epitaxy (MBE) Pulsed Laser ablation Deposition (PLD)

Chemical vapour deposition (CVD)  

Metallo-organic CVD (MOCVD) Plasma assisted CVD (PCVD)

A discussion of all of these techniques is beyond the scope of this thesis, there are numerous articles in the literature and for a comprehensive review the reader is referred to Stoessel et al. [19].

3.2.4 Electrical and magnetic properties Epitaxial grown HTS on single crystal substrates with c-axis orientation show high critical current densities, Jc, and high critical magnetic fields. Figure 3.1 shows the real part of the magnetic susceptibility ( # " ) data as a function of temperature for a typical YBCO thin film grown epitaxially on R-plane sapphire using PLD.

! ∗ Alfa Aesar, A. Johnson Matthey Company, stock no. 88149 (98% purity)


3-5

The imaginary part of the susceptibility ( # " ) is a measure of the magnetic losses in the superconductor [20] and it shows a maximum halfway through the superconducting transition. Table 3.3 gives critical current density, Jc, values for some important HTS!thin film compositions.

YBCO #3

Suscepitibility (!' )

!'

!"

Figure 3.1: Magnetic susceptibility as a function of temperature for YBCO on sapphire [courtesy of B. Lakew, GSFC, NASA].

T c (K)

HTS thin film YBa2Cu3O 7

93

J c (A.cm "2 ) B = 0T B = 5T 2. 106 (77K) 105 (77K) 6

Reference Roas et al. [21]

5

Bi2Sr2Ca2Cu3O x ! GdBa2Cu3O 7-x

97

3.8. 10 (77K) 8. 10 (77K) Endo et al. [22] !

90

106 (4K)

Tl2Ba2Ca2Cu3O 10

120

106 (7K)

MgB2

39

4.107 (5K)

1. 104 (77K)

Pradhan et al. [23] Lee et al. [24]

1. 105 (15K) Kim et al. [28]

Table 3.3: HTS thin film critical currents.

The Jc for YBCO film at 77K decreases exponentially as a function of the applied field as it approaches 0T. The reason for the rapid fall off in Jc at low fields may be due to induced current (Lorentz force) moving off the flux filaments, this is known as flux flow, which is known to be dissipative due to eddy current losses. Defects in the crystal structure may prevent flux filament motion due to pinning. Such defects could be twin


3-6

boundaries in the 123 compounds. The flux cores will move when the Lorentz force from the current exceeds the pinning force. At very low fields, there is high critical current density because the field is below the critical magnetic field giving rise to no flux cores. Mogro-Campero et al. [25] have studied the dependence of YBCO film thickness on critical current density. Film thicknesses of 0.2 to 2.4µm were produced on SrTiO3 single crystal substrates by co-evaporation and post-deposition annealing. The results clearly showed a peak in Jc at 0.4µm (> 105 Acm-2) with a steady decrease of Jc for increasing film thickness. To maintain Jc greater than 105 Acm-2 the film thickness should be greater than 0.4µm and less than 1µm. Thin films of BiSCCO material have been made by nearly all of the techniques described in §3.3. Palastra et al. [26] and Gammel et al. [27] have shown that the Bi system has no flux lattice at high temperatures (i.e. > 40K) preventing efficient pinning. The formation of a flux lattice is crucial for the ability to carry high currents in magnetic fields because the finite shear module of the lattice allows a relatively small number of pinning centres to pin all the flux lines. Epitaxial TBCCO thin films with T c > 120K have also been made using dc sputtering. Since TBCCO has the same structure as BiSCCO without twin boundaries it is believed that this compound has no pinning at high temperatures [26].

!

Kim et al. [28] have studied the critical current density as a function of applied magnetic field for PLD MgB2 on sapphire substrates. They showed a Jc of 4 " 10 7 A/cm2 at 0T, 5K and 10 5 A/cm2 at 5T, 15K. Paranthaman et al. [29] found Jc of 2 " 10 6 A/cm2 at 0T and 2.5" 10 5 A/cm2 at 1T, measured at 20K on

! ! These high Jc demonstrate the quality of both PLD and electron beam

electron beam evaporated films.

! evaporated films for device application.

!

3.2.5 Thermal Capacity In a HTS bolometer the total heat capacity is determined from the sum of the heat capacity contributions from three distinct types of materials namely, semiconductor (and insulator) layers, metal layers and superconductor layers that make up the construction. For semiconductor or insulator materials an approximation for the specific heat i.e. the heat capacity per unit volume is given by the Debye theory [30] for heat capacity of a crystal lattice,

c vlat = (12 / 5) " 4 Nk(T /# D ) 3 [31], where

N = NA" /Z

and

NA

is Avogadro’s number (6.022x1023

molecules/mole), " is the density (g/cm3), Z is the atomic weight (g/mole) and " D is the Debye temperature

!

!

!

!

! !


3-7

(K). As an example, silicon has " D = 700K [31] which gives c vlat(Si) " 6x10#7T 3 JK -4 cm-3 while for sapphire ( " -Al2O3), " D = 890-995K [32] and c vlat(Al2O3 ) is a factor of 1.3x less when compared with silicon while for

! ! diamond, " D = 2000K [31] and c vlat(diamond ) is about 3x less than silicon. This indicates that diamond would be !

! ! an ideal choice in bolometer construction, but due to the very high costs and difficulty of producing good quality ! ! is presently not a practical choice. CVD diamond films this In metals the free electrons contribute to the specific heat and is given by, c ve = " eT where

" e depends

on the metal and is of the order of 0.6 mJ/mole K2 for common metals like copper, silver and gold and can reach as high as 10 mJ/mole K2 for some transition metals.

!

!

The heat capacity, c v , of a high temperature superconductor can then be defined as, c v = " eT + DT 3 , where D = 12" 4 Nk / 5# 3 is the material constant. By extrapolating c v /T as a function of T 2 curve down to

! ! T = 0 , c ve is found to be near zero for YBCO. This extrapolation is not possible for GBCO because of an ! ! ! antiferromagnetic transition at 2.24K. Thus, the lattice part dominates except at very low temperatures, typically

!

! below a few Kelvin. Heat capacity measurements of high temperature superconductors have been largely done on bulk ceramic and single crystal materials. Reeves et al. [33] have measured the heat capacity of YBCO (7 J/K g-atom at 90K) and GBCO (10 J/K g-atom at 90K) with an adiabatic calorimeter for bulk samples. Braun et al., [34] have presented the specific heat of the most prominent phases of the Bi and Tl complexes (Bi-2212, Bi-2223, Tl2212, Tl-2223), fabricated from hot sintered pressed powders, in the region of the transition temperatures. Agrawal et al. [35] have presented a simple Born model, which gives a good fit to the experimental data available for the TBCCO system HTS materials. Although the design of the bolometer membrane uses materials that follow the Debye relationship, contributions from any buffer layers, insulating layers, superconducting leads, metals contacts, absorber and the thermistor material must be accounted for. Therefore the total thermal capacity is given by

C = c vlat Vlat + c ve Ve + c vsVs for T > 1K , Vlat is the volume of the membrane structure, Ve is the effective volume of the buffer layers, leads, contacts and absorber and Vs is the volume of the HTS thermistor. The effect of the

!

! ! ! heat capacity of the contact leads can be minimized, by using a superconductor across the thermal isolation to provide electrical conduction.

!


3-8

3.2.6 Thermal Conductivity The majority of work presented in the literature gives thermal conductivity measurements on bulk ceramic samples, a good review is given by Uher [36]. The polycrystalline structure of the bulk materials precludes investigations of anisotropy of the thermal transport, a parameter of great importance for a thorough understanding of these materials. HTS single crystal materials in this respect would be the obvious choice but limited availability of these types of material has seriously impeded thermal conductivity studies. In particular caxis thermal conductivity data is still vary scarce. The difficulty with thin films is that established steady-state heating techniques cannot be used since the supporting substrate provides a very efficient thermal short. Volklein et al. [37] and Fanton et al. [38] have independently developed techniques for measurements of thermal conductivity and diffusivity of thin films and it is a matter of time before reliable data on the thermal properties of HTS films becomes more plentiful. This data will greatly aid the development of future HTS bolometer design. Where thin film data could not be found bulk or single crystal material thermal conductivity data has been used in the bolometer design described in this thesis, see Table 3.4. The thermal conductivity, k , of HTS materials have some common features, (i) an almost temperature independent k above T c , (ii) an increase of k at T c and (iii) T 2 dependence at low temperatures. Both free

! carriers and phonons contribute to the thermal conductivity. While phonon contribution to the thermal ! ! ! ! conductivity !k p is always present, the magnitude of the carrier contribution k e depends on the type of solid since it is directly proportional to the free carrier density. It is zero in insulators, small in semiconductors and

! dominates heat transport in metals.

!

Classical superconductors have a high free carrier density therefore the carrier thermal conductivity is the dominant contribution. In HTS materials, the Hall effect suggests a significant reduction in the carrier density. Assuming that the transport processes in perovskite superconductors are not so exotic that they totally invalidate the Wiedemann-Franz law [39], i.e. the relation between the electrical conductivity and the electronic part of the thermal conductivity, l = "k e /T , then a good estimate of the maximum possible value of k e can be made from the measured electrical resistivity, " , and the Sommerfield value of the Lorenz number

! ! l 0 = 2.45" 10#8 V2 K -2 . For YBCO it is found that k e < 4 " 10#4 Wcm-1K -1 . For sintered samples of MgB2, the

! reduced Lorentz number l / l 0 is 1.45 and 1.15 for T = 40 and 100K , respectively [40]. The estimated !

! electronic thermal conductivity amounts to no more than 10-15% of the total thermal conductivity. Similar

! estimates apply to!ceramic samples of BiSCCO and TBCCO.


3-9

A distinguishing feature of HTS materials is the strong dominance of phonons over charge carriers in the normal-state heat transport processes of these structures. This explains the increase in the heat conductivity near the transition temperature, since the electrons, which form Cooper pairs, no longer scatter the phonons. Other scattering mechanisms [36] e.g., interaction at point defects and grain boundaries, come into operation to bring about a reduction of the total thermal conductivity at lower temperatures.

Material Si

!

c specific heat capacity (J/KgK) 185.22

!

" thermal conductivity (W/Km) 750 !

" density (Kg/m3) 2330 !

" = # / c$ thermal diffusivity (m2/s) 2.6. 10-3

SiO2

231

54*, 1MeV ) on bulk YBCO. It was found that the onset temperature of the superconducting transition decreases linearly (slope: -4.3K/1018 cm-2)

! with the neutron fluence (" # t ) up to 2x1019 cm-2 where superconductivity is completely destroyed. This is comparable to the effect observed in conventional superconducting compounds, e.g. V3Si and PbMo6S8.

! However the temperature transition width and the current transport properties are more severely affected. The results are interpreted as the destruction of the weak link network connecting the superconducting grains. It is noted that if epitaxial films are used in the bolometer construction this effect will be reduced. The effect of

60

Co ionizing irradiation on the voltage noise in MgB2 thin film, maintained at 77K, has

been studied by this author and Lakew et al. [73]. The results showed that there was no degradation of the T c

! when irradiated with 100Krad (Si) " # radiation (this dose is equivalent to the energy deposited by !

3 " 1012 e/cm2 at 3MeV).

! !

3.4.3 Chemical stability Humidity/moisture induced degradation of HTS films is the cause of severe stability problems. It is well established that this is due to hydroxyl groups (OH-). Extensive work has been reported on the interaction of water and YBCO [74][75][76]. Harris et al. [77] has shown that water diffuses into the HTS through the same channels that oxygen diffuses through. Here it reacts with the barium atoms forming Ba(OH)2 which again reacts with CO2 from the atmosphere to produce BaCO3. Initially this process only affects the superconducting properties such as the critical current density relatively slowly. However, at a later stage in the process the critical current density degrades much faster and the formation of microcracks are observed. This effect is due to a volume expansion caused by the presence of BaCO3 that has a lower density ( 4.45gcm-3 ) than the original material ( 6.38gcm-3 ). The lack of barium in the Bi system results in slower degradation rates but no study of this has been found in the literature to date.

!

!

The rate at which degradation occurs depends on several factors. First, the morphology of the sample

i.e. porosity and grain sizes play important roles for diffusion of H2O and CO2 into the HTS film. It has been reported, Horowitz et al. [78], that below 30% relative humidity at 25°C no degradation is observed after 672 hrs. The temperature of the sample is an important factor in the diffusion process and it has been shown that elevated temperatures (70-90°C) enhance degradation, this is difficult to quantify since there seems to be a strong sample dependency. At 85°C and 85% relative humidity a typical bulk sample of YBCO will be


3-18

destroyed in less than 1 hour. Garland et al. [76] have reported an exponential decay of the HTS volume measured by ac susceptibility at room temperature and 98% relative humidity. They give for the exponential decay of the HTS volume, V HTS = V0 exp("t / t 0 ) with t 0 = 21.6 days. Several attempts have been made to produce protective coatings. Chang et al. [79] have used protective layers of

! silver at the substrate/film interface and at !the film surface and have shown that the deterioration times are reduced by a factor of 60 compared to films without silver when soaked in water. A protective layer between the substrate and the film also reduces substrate-film interdiffusion under annealing but has the negative effect of not promoting epitaxial growth of the HTS films.

3.5

Spaceborne HTS bolometers

From the preceding discussion it has been highlighted that the bolometer performance will depend, in a crucial way, on the material properties, the processing techniques and the requirements imposed from the bolometer system design. In this section this interdependence is described and discussed.

3.5.1 Requirements on HTS thin films set by bolometer design The ideal properties of the temperature sensitive element of the bolometer are given in Table 3.9. Three cuprate groups are listed in Table 3.10, together with MgB2, which meet these requirements. The measurements of the critical temperature at low current densities and low fields suggest that the Tl-based compounds are better than the Bi- and Y- compounds although the long-term stability of the material is a key issue and has to be taken into account. For a bolometer application the transition width, "T c , should ideally be kept below 1K. This is easily achieved (on lattice matched substrates) for YBCO and MgB2 thin films at low current densities where "T c of

! 0.6K and 0.2K respectively are observed. Table 3.10 lists the critical transition temperatures of these HTS thin film systems together with the operating temperatures. For high critical current densities in !the order of 105 A/cm2 good epitaxial films are required for YBCO. It is difficult to assess the choice of material due to limitations in J c , but some measurements suggest only weak pinning in the Bi- and Tl- compounds. As regards the critical magnetic field this does not set any serious constraints on the material choice.

!


3-19

Property Transition temperature ( T c ) Operating temperature ( T op )

Requirement 30-125K 0.5 T c < T op < 0.75 T c

Transition width ( "T c ) Critical current ! ( Jc)

105 A/cm2 > 90ms). Figure 4.20(a) shows a cross-sectional view from the back of the device with an absorber deposited in the middle of the membrane with the dimensions of the etched cavity, absorber area and the overall size of the die. The front side of the membrane will accommodate the buffer layer and HTS material. Figure 4.20(b) shows the cross section through the die. Figure 4.20(c) and (d) show enlarged views of this cross-section at the edge and at the centre of the membrane to show the thickness of films deposited. The second design shows how through geometrical architecture better thermal isolation can be attained. Figure 4.201(a) shows a cross-sectional pictorial view of the back of a die that has a SiN membrane with thermal isolation legs at each corner. Figure 4.21(b) shows the cross-section F-F of this die. Figure 4.21(c) shows an exploded view at the centre of the membrane and Figure 4.21(d) shows the thermal isolation leg geometry.

Figure 4.19: Bolometer die constructed out of SiO2-Si membrane with no thermal isolation legs.

Chapter 4. Bolometer Design

4-29

(a)

(b)

(c)

(d)

Figure 4.20: Suspended SiO2-Si membrane with no thermal isolation legs: (a) cross-sectional view of backside of die with dimensions; (b) cross-section F-F; (c) enlarged cross-sectional view at edge of membrane; (d) enlarged cross-sectional view at centre of membrane.


4-30

(a)

(b)

(c)

(d)

Figure 4.21: Suspended SiN membrane with thermal isolation legs: (a) cross-sectional view of backside of die with dimensions; (b) cross-section F-F; (c) enlarged cross-sectional view at centre of membrane; (d) dimensions of thermal isolation leg.


4-31

References [1]

N. Y. Chen et al., Appl. Phys. Lett., 67(1), 1995.

[2]

K. L. Chopra, Thin Film Phenomena, McGraw-Hill, New York, 1979.

[3]

W. Becker, R. Fettig, W. Ruppel, Infrared Phys. and Tech., 40, 431, 1999.

[4]

J. A. Schweitz and F. Ericson, Sensors and Actuators 74, p. 126, 1999.

[5]

A. C. Ugural, Stresses in Plates and Shells

[6]

W. Weibull, J. Appl. Mech., 18, p. 293, 1951.

[7]

C. J. Kircher, M. Murakami, Science, 208, 944, 1980.

[8]

M. Ohring, “The Material Science of Thin Films” Academic Press, London, 1992.

[9]

C. Wilson, A. Ormeggi and M. Narbutovskih, J. Appl. Phys., 79, p. 2386, 1996.

[10]

Sapphire data sheet, www.mkt-intl.com.

[11]

Bromley et al., J. Vac. Sci. and Tech. B, vol. 1, p.1364, 1983.

[12]

W. D. Pilkey, Formulas for stress and strain, McGraw-Hill, Inc., New York, 1989.

[13]

Suzuki et al., Technical Digest, IEEE International Electron Devices Meeting, Washington DC, p. 137, 1985.

[14]

S. Timoshenko, S. Woinowski-Kriger, Theory of Plates and Shells, New York: McGraw-Hill, 1981.

[15]

C. Cagle et al., Document JPL IM-3546-TSE-85-091.

[16]

J. A. Hultberg, F. P. O’Brien, “Thermal Analysis System I Users Manual” Jet Propulsion Laboratory Technical report 32-1416, March 1st, 1971.

Chapter 5

Bolometer Device Fabrication

5-1

Chapter 5. Bolometer Device Fabrication

5.1

5-2

Substrate fabrication

In the following sections, three different methods are reported for silicon membrane fabrication using a (i) boron etch stop, (ii) buried SiO2 layer and (iii) silicon nitride etch stop. Additionally, we report on a novel technique for the fabrication of monolithic sapphire membranes that will be useful in the construction of future bolometer designs.

5.1.1 Fabrication of Si membranes using p++- boron etch stop Silicon membrane structures, based on a

p ++ - boron etch stop, were fabricated using the PPARC

Microelectronics Fabrication Facility at Southampton University, Department of Electronics and Computer

! The mask set was designed using the mask design software package Science (pump priming grant no: PB87). Princess at Rutherford Appleton Laboratory (RAL) Electronics CAD Group. The design data was converted into GDSII files and sent to the RAL Electron Beam Lithography Facility for the 5” mask plate set (chrome on sodaglass) manufacture. The plate set comprised seven masks. These are shown with relevant dimensions, in Appendix D. Figure 5.1 shows the top-level mask (i.e. all masks superimposed) mask geometry together with a cross-section of the device. The mask set was subsequently sent to Southampton for wafer processing using standard photolithography steps. The fabrication process for crystalline silicon membranes requires four inch diameter Si (100) wafers of ≥ 5Ωcm resistivity with a top epitaxial diffused layer with a heavy concentration of boron (≈ 1020 B cm-3), this layer acts as an etch stop. The etch stop relies on the fact that silicon etch rates of all aqueous alkaline solutions (KOH, NaOH etc.) are reduced significantly if silicon is doped with boron with acceptor concentrations exceeding 2 " 1019 cm-3. At these boron concentration levels, silicon becomes degenerated. The four electrons generated by the oxidation reaction ( Si + 4OH - " Si(OH) 4 + 4e - ) have a high chance to recombine with holes

! that are available in large quantities. As a result, the four electrons are no longer available for the reduction

! reaction ( 4HOH + 4e" # 4OH " + H 2 ). An etch selectivity of about 100 can be attained of lightly doped Si (100) to the heavily B-doped Si in 10% KOH solutions. Membranes are obtained by local anisotropic etching [1] from

! the backside of the wafer until the KOH solution becomes ineffective at the degenerately doped surface layer. In the final design concept, see §4.7, a membrane thickness of 1µm was recommended, however since there were a number of processing concerns it was decided as a first attempt, until the fabrication process was


5-3

well understood, to increase the membrane thickness to ≈10µm. Boron was thermally diffused from a solid source to grow in-situ B-doped epitaxial silicon film to a thickness of ≈10µm. Wet thermal oxide (2.2µm) was then grown to consume 1µm of the Si:B surface. The silicon thickness consumed, d Si , is 0.56 " d ox where d ox is the thickness of the grown oxide layer, this is calculated from the ratio d Si / d ox = N ox / N Si , where N ox is the density of SiO 2 (= 2.8 " 10 22 cm-3 ) and N Si is

! ! ! the density of Si (= 5 " 10 22 cm-3 ) . When the thermal oxide is etched away using buffered hydrofluoric acid ! ! ! ! (BHF) a 9µm thick Si:B layer is left on the top surface. This constitutes the “start” wafer. Six wafers were ! as a batch lot using the fabrication process flow shown schematically in Figure 5.2. processed

gold contacts for wire bonding

YBCO meander and contacts

polysilicon heater

Figure 5.1: Superimposed masks for YBCO on silicon bolometer design.

In the process flow shown in Figure 5.2 the contact window step (using mask CW) is omitted for clarity; this is the process for opening up contact windows to the polysilicon heater for deposition of gold contacts. The fabrication process steps are shown in Table 1. The process was stopped at step 30 in order to optically inspect the membrane surfaces so that an assessment could be made for subsequent deposition of the growth buffer layer YSZ and the HTS YBCO. Figure 5.3(a) shows the front side and Figure 5.3(b) shows the backside of the processed wafer.


5-4

boron diffusion implant 1. Start Wafer: 10µm Si:B epitaxy on 500µm Si handle wafer

(100) 2. Grow 22,000Å wet thermal oxide, this will leave 9µm Si:B layer

3. Buffered HF etch thick oxide

MASK AL 4. Double sided alignments in chips and first level single sided alignment marks

MASK P1 5. Deposit 4000Å of polysilicon and etch

MASK BE 6. Back-etch using 20% KOH at 70 deg. C

MASK HS 7. Deposit YSZ/CeO2 and HTS and ion beam mill

MASK M1 8. Deposit Au-contact metal

Figure 5.2: Schematic of fabrication process for silicon membrane bolometer.


5-5

Oxford University HTS silicon substrates: PB87 6 Wafers processed in batch MASK 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

Inspect start wafers: SiB layer thickness= 10!m Pirana clean wafers Photolithography Mask Al (Alignment) Hardbake resist at 120°C for 90 mins Dry etch 1!m deep alignment marks using fluorine chemistry Strip resist in acetone RCA clean Oxidise 300nm SiO2 wet O2/dryO2: INCLUDE DUMMY Deposit 400nm polysilicon at 625°C Phosphorous dope polysilicon to get sheet resistivity to 10mF), yet are known for their low accuracy and temperature stability [2], they contribute noise from their leakage current and hence have been avoided in the experimental set-up [3]. For the measurements reported here a double layer capacitor is chosen, although this also shows relatively poor accuracy and stability, its high series resistance ensures that the leakage is considerably less than an electrolytic [3]. In the initial measurement system set-up a blocking capacitor, value of C g = 15mF was used and it was observed that there was added noise in the measured voltage spectral density curve between 3Hz and 4Hz. By

! of this capacitor value on the transfer using equation (F.9), see Appendix F, with Z g (s) = Rg + 1 / sC g , the effect function can be determined and its effect is shown in Figure 6.9(a). For simplicity, only frequencies below 1kHz are shown, for higher frequencies!refer to Figure 6.6. Each plot reflects a decade-value of Rg and reveals a

(

)

noticeable peaking, i.e., an increase in Q centred on f pk " 1 / 2# L p C g " 3.15 Hz for Rg < 10" . When

! compared to the curves of Figure 6.6, the cut-off frequencies are about the same. When Rg " 1# , the cut-off

! ! ! frequencies are insensitive to the input source resistance e.g. f L " 2 Hz. Also, note that the ENB for Rg " 1# of ! Figure 6.9 gives more noise content than that of Figure 6.6 for frequencies less than 1kHz. ! Z (s) is placed in The relationship in equation (F.5) is used!to derive the output impedance Ro , i.e. g parallel with the load resistance, RL . The output impedance is substituted into equation (F.29) to give the output

! ! spectral density, see Figure 6.9(b). Dividing this by the amplitude function derived above results in the input ! spectral density, see Figure 6.9(c). Compared to Figure F.6(b) the converging noise values are larger at frequencies tending to zero for all values of Rg . This is due to noise voltage generated by X g and can be compensated by applying equation (F.30) to the Rg " 0 plots of Figure 6.10(b) to get results similar to Figure

! ! F.5. Figure 6.10(a), (b) and (c) shows the amplitude density, the output noise spectral density and the input noise !

Chapter 6. Instrumentation

6-12

spectral density for a 2.35F dc blocking capacitor. Comparison of Figure 6.9(b) with Figure 6.10(b) shows that the larger dc blocking capacitor shifts the noise peak from 3.15Hz to 0.25Hz. Applying the same technique that gave rise to equation (F.42), i.e. short the capacitor to ground so as derive the equivalent voltage noise source, Vn . Then insert a large value resistor to determine the equivalent current noise source, I n . Applying equation (F.43) leads to similar results found in Figure F.9 for the source

! resistance noise. Now using the obtained Vn and I n with equation (6.1) and modifying equation (F.57) to ! account for the reactance term leads to the an expression for the noise factor as, !

!

) , # & 1 F(" ,R g ) = 1 + +SV2 (" ) + S I2 (" )%R g2 + 2 2 ( S n2 (R g ). % n + n . " C g (' $ * -

(6.2)

Figure 6.11(a) and ! (b) shows the noise figures for the PAR transformer in series with a 15mF and 2.35F dc blocking capacitor to highlight why it is advisable to use a larger capacitor. Comparison to Figure (F.14) reveals that the contours on the left-hand of the map shifts right in response to the reactance added to the input circuit. This is expected since the bandwidth is narrower and there is extra power due to the reactance X g . Despite this, the optimum noise resistance and frequency undergo very little change. In fact compared to Figure F.16, Rn in

! Figure 6.11 remains at 8.57Ω and f n shifts from ≈142Hz to ≈138Hz. Comparison of Figure 6.11(a) with (b)

! reveals that the larger dc blocking capacitor (2.35F) shifts the 3dB contour well below 1Hz. Once this effect was ! understood the 15mF capacitor was replaced with a 2.35F capacitor (two 4.7F polarized capacitors back to back in series) in the measurement system, see Figure 6.4.


6-13

Figure 6.9: (a) Amplitude density as a function of frequency for the equivalent circuit shown in Figure 6.8, (b) calculated output spectral density and (c) calculated input spectral density for a 15mF blocking capacitor in series with source resistances 0Ω, 0.1Ω, 1Ω, 10Ω, 100Ω and 1000Ω.


6-14

Figure 6.10: (a) Amplitude density as a function of frequency, (b) calculated output spectral density and (c) calculated input spectral density for a 2.35F blocking capacitor in series with source resistances 0Ω, 0.1Ω, 1Ω, 10Ω, 100Ω and 1000Ω.


6-15

Figure 6.11: Noise figure of PARC Transformer in series with (a) 15mF capacitor and (b) 2.35F capacitor.

6.4.3 Low-noise amplifier An Ithaco model 1201 low-noise amplifier is used in the experimental set-up, see Figure 6.4. At the optimum frequency, f n,amp " 100 Hz, the amplifier has an input resistance of 1GΩ and voltage and current noise source values of Vn,amp " 9 nV/√Hz and I n,amp " 3.2 fA/√Hz respectively, resulting in a noise resistance value of

! Rn,amp " 2.8 MΩ. Using equation (F.58), the amplifier minimum noise factor is Fmin,amp = 1.00348 (or ! ! NFmin,amp = 0.01507dB. According to equation (F.63), the 3dB range of the input resistance is between ! ! !

!

Rn(min),amp " 5kΩ and Rn(max),amp " 1.6GΩ.

The noise factor F of the amplifier at optimum frequency is defined by equation (F.61), in which the

! , R and R are replaced by F variables Fmin g min,amp , Rn,amp and Ros , from equation (F.64), respectively. Also, n

! F can be cited as a composite function of Rg , through equation (F.64), such that F (Rg ) = F [ Ros (Rg )] . Figure !

!

!

!

! !

!

!

!


6-16

6.12 shows both of these functions converted into noise figures, see Appendix F. For the NF (Ros ) curve the minimum at point “1” on the x " axis indicates Ros = 2.8 MΩ, whereas for the NF (Rg ) curve the minimum at

! the x " axis point is Rg = 2.74" . The noise factor shown in Figure 6.12 is well below the limit of 3dB for all !

!

Rg . ! !

! With Ros and Fmin values known, three noise voltages are of interest, (i) thermal noise,

4k BTRos = 215.9 nV/√Hz, (ii) total amplifier input noise, ! ! internal noise of the amplifier,

!

!

4k BTRosFmin,amp = 216.2 nV/√Hz and (iii) the

4k BTRos ( Fmin " 1) = 12.73 nV/√Hz. In this example, 100 Fmin,amp " 1 # 5.9 %

! of the total noise is from the amplifier’s own contribution. The input noise due to Rg = 2.74 Ω can be ! ! approximated by dividing the thermal noise by the turns ratio, n , giving 0.215nV/√Hz (1.3% error since ! noise voltage applied to the transformers internal noises are not included). From the above it is shown that the ! input is ≈17 times larger than that produced by the amplifier itself. The above calculations were for a source resistance giving the minimum noise factor. However, for the transformer example, see Figure F.11 in Appendix F, where it was shown that an optimum transformer input source resistance is

Rg = Rn = 8.6 Ω. This gives

Ros " 8.68 MΩ and by inspecting Figure 6.11 at

Ros Rn,amp = 3.08 gives the noise figure for the amplifier, NF = 0.02566 (or F = 1.00593 ). With these values,

! 4k BTRos = 379.14 nV/√Hz, the total amplifier input noise is 4k BTRosF = 380.26 ! ! nV/√Hz and the internal noise of the amplifier is 4k BTRos (F " 1) = 29.19 nV/√Hz ( 100 F " 1 # 7.7 % ! the thermal noise is

!

! ! contribution to the total input noise). In this case, the applied noise voltage is 13 times larger than the internal noise.

!

!


6-17

Figure 6.12: Noise Figures for the Ithaco 1201 low-noise amplifier.

6.4.4 Spectrum analyzer The low-noise measurement system uses a Hewlett Packard (HP) spectrum analyzer model HP3567A under GPIB control using PC software. It has the capability of simultaneously measuring eight channels of analogue data into 1MΩ/10pF input impedances. It has a dynamic range of 15nV/√Hz to 40V/√Hz and a frequency range of 61µHz to 102.4kHz. Low frequency measurements ( f < 1.6 kHz) were made on all input channels, for the quietest channel an equivalent noise voltage source of Vn,sp " 18 nV/√Hz and an equivalent current noise source of

! I n,sp " 0.81fA/√Hz at 100Hz ( Vn,sp " 22 nV/√Hz and I n,sp " 0.15fA/√Hz at 10Hz). This implies an optimum ! noise resistance of Rn,sp " 22 MΩ (≈150MΩ at 10Hz) with a minimum noise figure of Fmin,sp " 1.00181 !

(≈1.00044 at 10Hz).

!

!

! most low-noise amplifiers the Ithaco has two outputs to select, a 50Ω ! Like or 600Ω impedance output port, obviously these fall extremely short of the 22MΩ noise resistance of the HP spectrum analyzer. The difference between using either port is slight, the attenuation ratio of both is about one and assuming the


6-18

amplifier has zero output except for thermal noise due to its output resistance, for 50Ω the noise figure of the HP spectrum analyzer is NF = 26 dB ( F = 401.8 ) and for 600Ω the noise figure is NF = 15.4 dB ( F = 34.4 ), both at 100Hz. At 290K for both port impedances, the internal noise voltages ( 4k BTRo,sp (NF " 1) ) are 18.36nV/√Hz

! ! ! ! for the 50Ω output port and 18.22nV/√Hz for the 600Ω output port, a very small difference. These internal noises nevertheless contribute to the overall noise measured. It!is very important that the gains prior to the HP spectrum analyzer be such that the measured noise power exceeds that generated internally. Moreover, the first amplification gain (the transformer) should have the highest gain in order to enhance the total SNR in the entire measurement chain.

6.5

Noise power density measurement system calibration

The noise measurement system described in §6.4 consists of a high impedance low-noise transformer connected to the bolometer through a transformer with 1:1000 turns ratio. The noise voltage is read out through a spectrum analyzer, see Figure 6.4, in an experimental set-up like this it is necessary to calibrate the instrumentation.

6.5.1 Noise voltage gain The gain of the transformer-preamplifier combination was calibrated by applying an ac signal from a frequency generator across a calibration resistance that is roughly the same value as the bolometer. The ratio of the magnitude of the input signal from the source to that of the output signal from the amplifier will then give the voltage gain of the system. The HP3567A spectrum analyzer has a programmable internal sine sweep generator, the output source can be fed directly into one of the channels (reference channel 2) of the analyzer while the signal across the calibration resistor can be fed into another discrete channel (measurement channel 1). Since the channels are synchronized, the ratio of the two voltages measured in each channel gives the voltage gain. This is shown in Figure 6.15(a), (b) and (c) that shows the voltage gain for a 0.1Ω, 1Ω and 5Ω resistor (the range of values expected within the superconducting transition) respectively for a 2mV peak-to-peak voltage source that has been attenuated until there is no saturation in the spectrum analyzer measurement channel. Table 6.4 gives the voltage gain for a number of resistance values at various spot frequencies and highlights the fact that the gain


6-19

can change significantly as a function of frequency so this must be taken into consideration when evaluating the noise voltage.

Figure 6.15: Frequency response of noise measurement system for input source resistance a) 0.1Ω, b) 1Ω and c) 5Ω: raw data processed with median filter windows r1 = 243, r2 = 29 and r3 = 9.

!

!

!


6-20

6.5.2 Noise spectra roll-off frequency In the experimental set-up shown in Figure 6.4, the transformer will increase the equivalent series impedance and if this value becomes comparable, at the measurement frequency, to the shunt capacitive reactance of the low-noise preamplifier then this will not give a true noise voltage reading (will be reduced). To check the system noise spectra roll off frequency standard resistors were substituted for the bolometer. Since the HTS bolometer resistance in the transition region is typically a few ohms the voltage noise spectral density spectra for 0Ω (short), 0.1Ω, and 1Ω standard resistors were measured at room temperature to establish if any serious frequency roll-off effects come into play. Figure 6.13(a), (b) and (c) shows the raw data divided by the gain of the measurement system, G = 1 " 10 6 V/V (120dB), determined from the frequency response, see section, §6.5.1. Superimposed on the raw data (shown in red) is the filtered (using a median filter, r1 = 13 ) data (shown in blue).

! The noise voltage spectra are seen to be fairly flat between 2Hz and 100Hz. The shorted (0Ω) case noise voltage ! frequency bin this value must be spectra represents the noise baseline of the measurement system for each subtracted in quadrature (see equation F.30) from the values obtained for the 0.1Ω and 1Ω resistors to obtain the corrected noise voltage spectral densities these smoothed spectra are shown in Figure 6.14(a) and (b). At 10Hz the noise voltage baseline is Sv = 0.0574 nV resistor at 10Hz is Sv = 0.042 nV

Hz (c.f.

Hz , then the corrected voltage noise spectral density for the 0.1Ω 4k BTR"f = 0.040 nV

Hz at T = 290K and "f = 1Hz ) and

! similarly for the 1Ω resistor the corrected voltage noise spectral density at 10Hz is Sv = 0.130 nV Hz (c.f. ! ! ! ! 4k B RT"f = 0.1265nV Hz ). The measured noise voltage reading at 10Hz for the 0.1Ω resistor is about 2.5% ! higher than the calculated value and for the 1Ω resistor is about 0.6% higher. Since the resistor value tolerance is !

±1% it is safe to assume a measurement system error of ±2%. The noise voltage spectra for the standard test resistors 0.1Ω and 1Ω are fairly flat between 3Hz and 100Hz. The roll off frequency for the 0.1Ω resistor is 1600Hz (10% deviation from average between 3Hz and 100Hz) and the roll off frequency for the 1Ω resistor is at 147Hz using the same criteria. If noise measurements need to be made at these frequencies (for comparable source resistance values) or higher then a lower transformer turns ratio should be used. Table 6.3 gives the noise voltage values for the two calibration resistors for spot frequencies between 1Hz and 1kHz.


Figure 6.13: Noise voltage spectral density for (a) short, (b) 0.1Ω and (c) 1Ω input source resistance to measurement system.

6-21


6-22

Figure 6.14: Corrected noise voltage as a function of frequency for a) 0.1Ω and b) 1Ω.

f (Hz) 1

!

!

4

Sv (short)

Sv (0.1Ω)

Sv (1Ω)

(nV/√Hz)

(nV/√Hz)

(nV/√Hz)

0.696

0.559

0.594

!

!

0.061

0.041

0.126

10

0.057

0.042

0.130

40

0.057

0.041

0.128

100

0.055

0.042

0.124

400

0.046

0.046

0.078

1000

0.024

0.045

0.044

Table 6.3: Corrected noise voltages for system calibration resistors.


6-23

References [1]

G. W. C. Kaye, T. H. Laby, Tables of Physical and Chemical Constants, 14th Ed., 1973.

[2]

P. Horowitz and W. Hill, The art of Electronics, pp. 22, 2nd edition, Cambridge University Press, New York, NY, 1989.

[3]

Y. Netzer, “The Design of Low-Noise Amplifiers,” Proceedings of the IEEE, pp. 728-741, vol. 69, no. 6, June 1981.

Chapter 7

Excess noise measurements

7-1

Chapter 7. Excess noise measurements

7.1

7-2

Introduction

In §1.2, see equation (1.6), it was shown that temperature fluctuations are a limiting factor for bolometric detection. Since the HTS bolometer detection principle relies on operation in a highly sensitive temperature domain, see Figure 1.2, it would be instructive to understand the excessive strength and behaviour of resistance noise in the normal-superconducting transition region. Khrebtov et al. [1] have studied the low frequency 1/ f noise as a function of both deposition conditions and microstructure in HTS thin films at 300K. However such

! since at the physical correlations are more difficult to address in the normal-superconducting transition region, mid-point of transition the TCR, " = 1/ R(dR / dT ) , can be a few K"1 and temperature fluctuations caused by heating power instabilities can significantly contribute to the measured noise.

! In Chapter 6 a !system was described for precisely controlling and measuring the temperature of the HTS film, see §6.2.1, and further an experimental set-up, see Figure 6.4, was described to properly study the intrinsic excess noise of the HTS films within the superconducting transition region. In this Chapter, using the experimental set-up described in Chapter 6, results are presented for the voltage noise spectral density for a YBCO and a MgB2 thin film device. For the YBCO device the contribution of phonon and Johnson noise to the excess noise is assessed. The measured noise voltage spectral density is used to derive the NEP of the YBCO device and the temperature noise for the MgB2 device, both figures of merit give a measure of the sensitivity that can be expected from such thermistor materials, since the lower the NEP or temperature noise value then the better the signal to noise ratio.

7.2

Temperature coefficient of resistance for YBCO thin film thermistor

Using the experimental set-up described in §6.3, the resistance of a YBCO film used in the construction of bolometer device no. 6036-3-#A1 was measured as a function of temperature for bias current levels of I bias = 1mA and 4mA. For each bias level, data was collected as the film warmed from the superconducting state to the normal state and as the sample cooled from the normal to superconducting state. The curves, for!each bias level, for the warm up and cool-down cycles coincided. However, the transition curves are offset for the two different bias levels as seen in Figure 7.1(a), where the resistance is plotted as a function of the “substrate” temperature. The offset is due to the bias current self-heating. The corrected YBCO film temperature is found from


(

7-3

)

2 T " = T s # I bias R G , see §2.2. The thermal conductance of the membrane can be estimated by making the two

curves in Figure 7.1(a) coincide at the mid-point of transition. The offset for the two curves at mid-point of

!

2 transition ( "T = T s # T $ = I bias R G ) was found to be ≈ 0.3K. From this the thermal conductance of the

membrane supporting the YBCO film is calculated to be G " 1.3# 10$5 W/K .

!

The mid-point of transition for the curves was found by fitting a modified Boltzmann-type function to

! the raw data in the interval range T " [89,96] K,

!

R(T ) =

!

1 dR ! = R dT

mT + c

(

1+ e" # (T "Tc )

)

n

+ Rc

(7.1a)

# " (T #Tc ) dR n" ( mT + c ) e = n +1 dT 1 + e# " (T #Tc )

(

(1+ e

" (T #Tc )

(7.1b)

)

n" (mT + c) n $ ' & mT + c + 1+ e# " (T #Tc ) Rc ) % (

)

(

)

(7.1c)

where, T c is the centre of the transition, m is the slope and c is the intercept of the normal part, Rc is the ! residual resistance, " and n are constants. Using equation (7.1a) with the parameters m = 0.12 , c = "8.11,

! ! T = 89.8 , " = 2.91, n = 85 and !R = 0.01 a curve fit to the raw data, to better than 0.5% ! error, was obtained c c ! ! ! ! near the centre of the transition. Figure 7.1(b) shows the approximated resistance as a function of the “corrected”

!

! ! ! temperature for a film biased with 4mA, superimposed on this curve is the calculated dR / dT and 1/ R(dR / dT ) curves. The maximum value of dR / dT (found by setting d 2 R / dT 2 = 0 ) gives the mid-point of transition,

! ! T m = 91.45K (0.98Ω). The temperature coefficient of resistance at mid-point of transition, " = 1 R ( dR dT ) , is ! then calculated to be 2.95K-1. !

!

! are first identified using a In order to determine the superconducting transition width, the knee-points curvature function defined as,

" d 2R % K (T ) = $ 2 ' # dT &

!

( " dR %2 +3 / 2 *1 + $ ' *) # dT & -,

(7.2)


7-4

and the local maximum points are found by setting the derivative function to zero i.e., dK / dT = 0 , see Figure 7.2. Thus the maximum rate of curvature occurs at the lowest knee, T = 90.8 K, and the upper knee, T = 92.3K,

!

giving a transition width of "T = 1.5 K.

!

!

!

Figure 7.1: (a) Resistance as a function of substrate temperature for YBCO film for 1mA and 4mA bias and (b) transition fit and dR / dT , R "1dR / dT curves [device no: 6036-3-#A-1].

!


7-5

Figure 7.2: Curvature function and its derivative for fitted transition curve.

7.3

System noise for YBCO thin film measurements

In section §6.5.2 the system voltage noise baseline was measured using standard low-noise resistors (short, 0.1Ω and 1Ω) at the input of the blocking capacitor, this gives the ultimate capability of the system with “ideal” inputs. However, the system voltage noise baseline for a bolometer in a cold dewar has additional noise sources, e.g. contact resistances at the device and at connectors and resistances of wiring. Therefore, a voltage noise baseline measurement was made with the YBCO film in the superconducting state with zero current bias this essentially represents a short at the input of the blocking capacitor but additionally gives contributions from other noise sources (known and not known). This baseline noise voltage spectral density must be subtracted in quadrature, see equation F.30, from the raw data collected from all subsequent measurements. Figure 7.3 shows the voltage noise spectral density for a YBCO film bolometer (device # 6036-3-#A1) in the superconducting state at a temperature of 79.9K, superimposed on the raw data is the smoothed data using running median filters r1 = 9 , r2 = 49 and r3 = 243. The noise voltage spectrum shown is averaged over 1024 measurements. At 10Hz the total peak noise voltage of the read-electronic system is Sv,10Hz = 0.107 nV

! ! ! (c.f. 0.057nV/√Hz using a short at input, see Table 6.3).

!

Hz


7-6

Figure 7.3: Noise voltage spectral density of measurement system with YBCO film in superconducting state (79.9K).

7.4

Temperature dependence of YBCO film noise voltage

Figures 7.4 (a)-(i) shows the raw noise voltage data spanning a frequency range 10mHz to 1.6kHz for a YBCO film (device no. 6036-3-#A1) corrected for the measurement system gain ( G = 10 5 ) for temperatures through the superconducting transition (90.8K to 92.6K) with a current bias of 2mA. Figures 7.5 (a)-(l) shows the raw noise

! voltage data with gain correction for the same device but biased at 4mA again through the superconducting transition in the temperature range 90.3 to 92.2K. The noise voltage spectral density after subtracting out the noise voltage contribution from the measurement system (see §7.3) for the device biased at 2mA is given in Figure 7.6 and biased at 4mA in Figure 7.7. Table 2 numerically tabulates the excess noise for the 2mA and 4mA biased device for different spot frequencies at the mid-point of transition at 91.45K (0.98Ω).

f (Hz)

!

1 4 10 40 100

2mA bias Measured Excess (nV/√Hz) (nV/√Hz) 9.422 9.342 2.727 2.646 1.436 1.355 0.217 0.137 0.165 0.084

4mA bias Measured Excess (nV/Hz) (nV/√Hz) 27.134 27.054 26.409 26.329 20.607 20.526 8.356 8.276 3.722 3.641

Table 2: Excess noise voltage above an ideal resistor (0.98Ω) at midpoint of transition (91.45K) for device no: 6036-3-#A1.


7.5

7-7

YBCO noise voltage correlation with dR / dT

Figure 7.8 shows the temperature dependence of the excess noise voltage at 1Hz, 4Hz and 10Hz for two bias current levels 2mA and 4mA. In Figure 7.9 the dR / dT curve for the device is superimposed on the 4Hz data to

!

highlight the fact that the noise voltage peak corresponds to the maximum slope of the transition, this is clearly seen for the 2mA bias data where the ! peak is at 2.6 nV√Hz at 91.45K. The highest noise level recorded for the 4mA (not shown on Figure 7.9) case is 26.3 nV/√Hz at 91.5K (which is near the midpoint of transition 91.45K), this is 10x greater than the 2mA data near the mid-point of transition. The Johnson noise voltage (see §2.6.3) should scale linearly with the current so the remainder of the excess noise measured in the superconducting transition region is most likely due to the phonon noise of the YBCO film connected to the heat sink via the thermal conductance, see §2.6.2, this is the topic of the next section §7.6.

7.6

Noise voltage correlation with phonon noise

Figure 7.10 shows the voltage noise spectral density of the YBCO bolometer near the midpoint of the superconducting transition at 91.6K measured at 4mA bias. Superimposed on the spectra is the theoretical noise spectra due to phonon noise of the thermal conductance, G , (equation (2.42)) and Johnson noise of the HTS film resistance (equation (2.43)) and 1/ f noise (equation (2.44)). These contributions have been calculated

! using the relationship NEPi2 = Sv " v , where " v is the responsivity defined in equation (2.13) and using the ! following parameters: L0 = 0.5; " = 2.95 K -1 ; G = 2 " 10#5 W/K ; Rm = 0.98 " and I bias = 4mA . The plot ! ! shows that the frequency dependence of the spectrum is well described by the sum of phonon, Johnson and 1/ f

! ! noise contributions of the film.

!

!

!

! From the noise voltage spectra collected at different temperatures through the YBCO superconducting transition, the noise voltage data at 10Hz has been determined. This data is plotted normalized by the voltage across the bolometer in Figure 7.11. Superimposed on the measured noise voltage data is the calculated contribution from phonon and Johnson noise using equations (2.29) and (2.33) respectively. It is seen that in the superconducting transition regime the phonon noise is dominating the calculated noise. The measured noise voltage is close to the theoretical minimum set by the phonon and Johnson noise indicating that any contribution to the excess noise arising from the superconducting film itself is very low.


7-8

Figure 7.4: Voltage noise spectral density for YBCO film [device 6036-3-#A1] biased at 2mA and at “substrate” temperature (a) 90.8K, (b) 91K, (c) 91.2K


Figure 7.4: cont. (d) 91.4K, (e) 91.6K, (f) 91.8K

7-9


Figure 7.4 cont. (g) 92K, (h) 92.2K, (i) 92.6K

7-10


Figure 7.5: Voltage noise spectral density for YBCO film [device 6036-3-#A1] biased at 4mA and at “substrate” temperature (a) 90.3K, (b) 90.4K, (c) 90.5K

7-11


Figure 7.5: cont. (d) 90.6K, (e) 90.8K, (f) 91K

7-12


Figure 7.5: cont. (g) 91.2K, (h) 91.4K, (i) 91.6K

7-13


Figure 7.5: cont. (j) 91.8K, (k) 92K, (l) 92.2K.

7-14


7-15

Figure 7.6: Noise spectral density corrected for system noise for device no: 6036-3-#A1 biased at 2mA and at substrate temperature (a) 90.8K-91.6K and (b) 91.8K to 92.6K.


7-16

Figure 7.7: Noise spectral density corrected for system noise for device no: 6036-3-#A1 biased at 4mA and at substrate temperature (a) 90.4K-91.6K and (b) 91.8K to 92.2K.


7-17

Figure 7.8: Excess noise voltage as a function of temperature for YBCO film (device no: 6036-3-#A1) biased at 2mA and 4mA.

Figure 7.9: Excess noise correlation with dR / dT .

!


7-18

Figure 7.10: Noise voltage spectrum near mid-point of transition (91.6K), I bias = 4mA and Rm = 0.98" and calculated contributions from phonon, Johnson and 1/ f noise of the film.

!

!

!

Figure 7.11: Normalized noise voltage at 10Hz on YBCO device with 2mA and 4mA bias and calculated contributions from phonon and Johnson noise at mid-point of transition.


7-19

Figure 7.12(a) shows the calculated voltage responsivity at 10Hz, using equation (2.12) and the measured parameters given earlier, for the two current bias cases, 2mA and 4mA. The responsivity peaks to a maximum at 2138V/W with 4mA bias and 1071V/W for 2mA bias, the peaks coincide with the maximum of

(

dR / dT as expected. Figure 7.12(b) shows the electrical NEP = Sv2 " 2

1/ 2

)

for measured noise voltage data in

the transition. A third order polynomial curve fit to both sets of data is also shown on Figure 7.12(b), data point

!

(a) on this plot was excluded from the analysis.!The minimum electrical NEPe derived from the polynomial fit 1/ 2

is 3.2 " 10#12 W/ Hz (c.f. NEPphonon = ( 4k BT m G )

!

= 3.0 " 10#12 W/ Hz ). This NEPe value translates to a

! specific detectivity of D" = 3.2 # 1010 cm Hz /W , calculated using a 1mm square detector receiving area. ! ! ! !

Figure 7.12: (a) Voltage responsivity and (b) NEPe as a function of corrected temperature (data was fitted using a third order polynomial fit: NEPe = "4.237 #10 6 + 140705#T " 1557.42 #T 2 + 5.745#T 3 ).

!

!


7.7

7-20

Temperature coefficient of resistance for MgB2 thin film thermistor

For the MgB2 film studied, the normalized resistance as a function of temperature through the superconducting transition is shown in Figure 7.13.

Figure 7.13: (a) R , dR / dT and (1 R) dR dT as a function of temperature for MgB2 thin film and (b) curvature function and its derivative for fitted transition curve.

! !

!

The experimental raw data was fitted using the closed form functional equation described in equation (7.1). This gave a fit to the raw data down to 38.2K to better than 0.2%. Below 38.2K (bottom knee of the transition) the error to the curve fit was better than 5%. This functional equation was used to calculate the


7-21

(1 R) dR

dT curves shown in Figure 7.13(a). The film has an onset of

superimposed dR / dT and

superconductivity at 38.44K. Calculating the curvature function, see equation (7.2) and Figure 7.13(b), and

! ! finding the local maximum points accurately determined the transition width, which gives "T = 0.23K . The film showed a zero resistance at 38.16K. The peak of the dR / dT (12.4Ω/K) curve, i.e. the mid-point of

!

transition, is at 38.24K.

!

7.8

Temperature dependence of MgB2 thin film noise voltage

The system noise baseline for noise measurements on MgB2 films is given in Figure 7.14. This is the noise voltage measured while the film is superconducting at 9.6K and with a current bias of 4mA. In the measurement set-up, a 15mF blocking capacitor was initially used, see §6.4.2, the effect is seen as a resonant peak at 4Hz. This was clearly due to the blocking capacitor since removing it from the measurement instrumentation (with zero bias) removed the peak. This peak was subtracted to give the amplitude spectrally corrected spectrum in Figure 7.14(c). This represents the system noise baseline that is subtracted in quadrature to correct measurements for system noise. The temperature dependence of the noise voltage through the superconducting transition region is shown in Figure 7.15 to Figure 7.19. The MgB2 is current biased at 4mA. Table 3 gives the amplitude spectrally corrected noise voltage values for 1Hz, 4Hz, 10Hz, 100Hz and 1000Hz.

T (K) 1Hz

!

9.6 5.062 38.05 !7.049 38.15 7.271 38.2 5.891 38.26 7.031 38.27 7.115 38.34 7.382

S v (nV/ Hz) @ 4mA bias 4Hz 10Hz 100Hz 1000Hz 0.132 0.1 0.89 1.912 0.26 0.435 0.84

0.083 0.097 0.889 1.515 0.342 0.433 0.816

0.067 0.074 0.577 0.721 0.126 0.153 0.186

0.032 0.029 0.1 0.092 0.024 0.024 0.02

Table 3: Amplitude spectrally corrected noise voltages.


1Hz Sv = 0.4 2?1 1 .10

8

1 .10

9

7-22

4Hz nV

Sv

= 0.23

10Hz

nV

= 0.079

Sv

100Hz nV

Sv

= 0.062

1000Hz nV

Sv

2?4 as a function 2?100 for gain; 2?1000 Hz S v (V/ Hz) Hz Hz Avg=64; (a) of 2f?10 data corrected (Hz) raw Hz

nV

= 0.058

Hz

!

!

Sv 1 .10

10

1 .10

11

1

10

1Hz = 0.4

F2

2?1

1 .10

4Hz

nV

F2

2?4

Hz

= 0.23

nV

F2

1 .10

100

10Hz = 0.078

100Hz

f

nV

F2

= 0.061

3

1000Hz nV

?10 100 (b) median filter2x2 (window Hz Hzsize: r12?= Hz ) 33, r2 = 99

F2

2?1000

= 0.046

nV Hz

8

! 1 .10

9

F2 1 .10

10

1 .10

11

1

1Hz F1

2?1

nV = 5.062 ! " Hz # 1 .10

8

1 .10

9

4Hz F1

2?4

10

10Hz

3

1 .10

100

f

100Hz

nV nV !nV = 0.132 ! F1 = 0.067 ! " F12?10 = 0.083 " " 2?100 Hz #(c) amplitude Hz Hz # # spectrally corrected

1000Hz F1

2?1000

nV = 0.032 ! " Hz #

F1 1 .10

10

1 .10

11

1

10

100 f

Figure 7.14: System noise voltage baseline for MgB2 thin film noise measurements (9.6K).

1 .10

3

Chapter 7. Excess noise measurements 1Hz Sv 1 .10

2?1

7-23

4Hz

= 0.53

nV

S

10Hz nV

= 0.242

S

= 0.104

100Hz nV

= 0.066

S

1000Hz nV

S

v2?4 v2?100 v2?1000 Hz Hz Avg=64; (a) HzSv (V/ Hz) as a function of v2f?10 data corrected for gain; (Hz) raw Hz

= 0.035

nV Hz

8

!

! 9 1 .10

Sv 1 .10

10

1 .10

11

1

10

1Hz F2

2?1

= 0.53

nV

F2

2?4

Hz

= 0.242

nV

3

1 .10

100

4Hz

10Hz = 0.105

F2

100Hz

f

nV

F2

1000Hz

nV

= 0.068

F2

?10 Hz filter 2x2 Hzsize: r21?100 (b) median (window = 57, r2 = Hz 41)

2?1000

= 0.036

nV Hz

1 .10

8

(c)

! 9

1 .10

Figure 7.12. Superconducting at T = 28K

F2

(a)

1 .10

10

1 .10

11

1

1Hz

Sv = 7.049 2?1 1 .10

8

1 .10

9

4Hz nV Hz

Sv = 0.1 2?4

10

nV Hz (c)

Sv

= 0.097

3

100

10Hz f

100Hz

nV

Sv

2?10 2?100 Hz corrected amplitude spectrally

= 0.074

1000Hz nV Hz

Sv = 0.029 2?1000

1 .10

nV Hz

F1 1 .10

10

1 .10

11

1

10

100

3

1 .10

f

Figure 7.15: Noise voltage spectral density of MgB2 thin film thermistor at 28K (superconducting).

Chapter 7. Excess noise measurements 1Hz Sv

4Hz

nV = 0.547 Sv (V/ HzHz)

2(a) ?1

1 .10

8

1 .10

9

S

10Hz nV

= 2.051

S

= 0.937

100Hz nV

= 0.519

S

1000Hz nV

nV

= 0.122

S

v2?100 10 data corrected ?1000 Hz Hz Rv2= 20m" asv2a?4functionHz of f (Hz)v2?raw for gain; Avg=64;

Hz

!

!

!

(c)

7-24

Sv 1 .10

10

1 .10

11

1

10

1Hz = 0.547

F2

2?1

1 .10

nV

F2

2?4

Hz

= 2.051

10Hz

nV

3

1 .10

100

4Hz

f

nV

= 0.937

F2

100Hz F2

1000Hz nV

= 0.544

F2

?10 100 Hz filter 2x2 Hz size r12?= Hz ) (b) median (window 47, r2 = 99

2?1000

= 0.127

nV Hz

8

! 1 .10

9

F2 1 .10

10

1 .10

11

1

Sv

2?1

1 .10

8

1 .10

9

1Hz

= 7.271

10

4Hz nV Hz

Sv = 0.89 2?4

nV

Sv

= 0.889

3

100

10Hz f

100Hz

nV

Sv

2?10spectrally 2?100 Hz amplitude Hz corrected (c)

= 0.577

1000Hz nV Hz

Sv

2?1000

= 0.1

1 .10

nV Hz

F1 1 .10

10

1 .10

11

1

10

3

1 .10

100 f

Figure 7.16: Noise voltage spectral density of MgB2 thin film thermistor at 38.15K ( R = 20m" ).

!


1Hz

4Hz nV

Sv

2?1 (a)

1 .10

8

1 .10

9

7-25

= 0.528 Sv (V/ HzHz)

10Hz nV

Sv = 0.452 2?4

Sv

as a function Hz of f (Hz)

= 0.334

2raw ?10

100Hz nV

Sv = 0.117 2?100

= 0.031

Sv

nV

R 2=?1000 0.509"

Hz Hz data corrected for gain; Avg=64;

Hz

!

!

!

1000Hz nV

Sv 1 .10

10

1 .10

11

1

10

1Hz = 0.528

F2

2?1

nV

F2

2?4

Hz

1 .10

8

1 .10

9

= 0.452

10Hz

nV

3

1 .10

100

4Hz

nV

= 0.334

F2

100Hz

f

F2

1000Hz nV

= 0.118

F2

?10 100 Hz filter2x2 Hz size r12?= Hz ) (b) median (window 45, r2 = 99

2?1000

= 0.029

nV Hz

!

F2 1 .10

10

1 .10

11

1

Sv

2?1

1 .10

8

1 .10

9

1Hz

= 7.031

10

4Hz nV Hz

Sv = 0.26 2?4

100Hz

f

nV

Sv

= 0.342

3

100

10Hz nV

Sv


= 0.126

1000Hz nV Hz

Sv

2?1000

= 0.024

1 .10

nV Hz

F1 1 .10

10

1 .10

11

1

10

3

1 .10

100 f

Figure 7.17: Noise voltage spectral density of MgB2 thin film thermistor at 38.26K ( R = 0.509" ).

!


7-26

4Hz

= 0.535

nV

S

10Hz nV

= 0.654

S

= 0.45

100Hz nV

S

= 0.145

1000Hz nV

S

= 0.032

v2?100 2?1 S (V/ HzHz) as va2?function 4 ?10 data corrected Hz Hz Hz Rv2=?1000 0.721" (a) of f (Hz)v2raw for gain; Avg=64; v

1 .10

8

1 .10

9

Hz

!

!

!

nV

Sv 1 .10

10

1 .10

11

1

10

1Hz = 0.535

F2

2?1

nV

F2

2?4

Hz

= 0.654

10Hz

nV

3

1 .10

100

4Hz F2

2?10

Hz filter x2 (b) median

f

100Hz

1000Hz

nV

nV F2 = 0.145 2 ? 100 Hz size r1 = 33, r2 = 73 Hz ) (window

= 0.505

F2

2?1000

= 0.03

nV Hz

8 1 .10

! 9

1 .10 F2 1 .10

10

1 .10

11

1

10

3

1 .10

100 f

1Hz Sv

2?1

1 .10

8

1 .10

9

= 7.115

4Hz nV Hz

10Hz

100Hz

nV (c)

nV corrected nV amplitude Sv = 0.435 Sv spectrally = 0.433 Sv = 0.153 2?4 2?10 2?100 Hz Hz Hz

1000Hz Sv

2?1000

= 0.024

nV Hz

F1 1 .10

10

1 .10

11

1

10

3

1 .10

100 f


!


7-27

4Hz nV

= 0.583

S

10Hz nV

= 1.033

S

= 0.799

100Hz nV

S

= 0.181

1000Hz nV

S

nV

= 0.032

v ?10 v2?100 2?1 S (V/ Hz 4 Hz f (Hz) 2raw Hz Hz Rv2=?1000 1.194" (a) of data corrected for gain; Avg=64; Hz) as va2?function v

1 .10

Hz

8

!

!

! 9 1 .10

Sv 1 .10

10

1 .10

11

1

10

1Hz F2

2?1

1 .10

= 0.583

4Hz nV

F2

2?4

Hz

= 0.898

10Hz

nV

3

1 .10

100

F2

= 0.764

100Hz

f

nV

F2

1000Hz nV

= 0.169

F2

?10 Hz filter 2x2 Hz size: r21?100 (b) median (window = 17, r2 = Hz 73)

2?1000

= 0.03

nV Hz

8

! 1 .10

9

F2 1 .10

10

1 .10

11

1

1Hz

Sv = 7.382 2?1 1 .10

8

1 .10

9

10

4Hz nV Hz

Sv = 0.84 2?4

nV

Sv

= 0.816

3

100

10Hz f

100Hz

nV

Sv


= 0.186

1000Hz nV Hz

Sv = 0.02 2?1000

1 .10

nV Hz

F1 1 .10

10

1 .10

11

1

10

3

1 .10

100 f


!


7-28

Table 4 gives the excess noise voltage near the mid-point of transition at 38.26K ( R = 0.509Ω). The noise voltage increased as the film was heated from the superconducting state to the mid-point of transition and then to

! the noise voltage at 10Hz is the top of the superconducting transition. In the superconducting regime (9.6K), Sv = 0.083 nV/ Hz , while near the mid-point of transition (38.26K) the noise voltage is Sv = 0.342 nV/ Hz . The mid-point noise level is ≈ 59x lower than that of the YBCO thin film reported in §7.4.

!

! Excess noise (nV/

Hz ) @ 4mA bias

T (K) 1Hz

!

38.26 (near mid-transition)

4Hz

10Hz

100Hz

7.031 ! 0.258

0.340

0.122

Table 4: Excess noise near mid-transition of MgB2 thin film device.

7.9

MgB2 noise voltage correlation with dR / dT

Figure 7.20(a) gives a plot of the measured noise voltage spectral density data as a function of temperature at a frequency of 10Hz and a bias current of 4mA. Unlike the YBCO noise data, see §7.6, the largest measured noise

!

voltage appears not at the mid-point of transition but between the peaks of (1 R)( dR dT ) and ( dR dT ) . From visual examination, the measured noise data could correlate with either of these peaks if the noise data is shifted

! test to be made to show by about 0.1K in either direction. There is insufficient data for any ! statistical confidence which peak the noise data may correlate with. More data has to be gathered before any conclusions can be made. Also, a very careful examination of the temperature sensor and its mounting needs to be carried out, since a small error in the sensor (silicon diode) reading could account for an offset in either direction. However, it can be stated that the largest noise appears between the bottom knee of the transition (38.15K) and the mid-point of transition (38.26K) a temperature difference of 0.06K. To highlight what effect this temperature difference offset can make, the measured noise data has been shifted in the positive temperature direction by 0.06K to align more with the dR / dT curve, see Figure 7.20(b), on a first examination it looks as if the noise data follows this curve however this may not be necessarily true.

!


7-29

Another anomaly is that at the top of the transition, 38.34K (1.194Ω), the noise level is

Sv = 0.81 nV/ Hz (c.f. 0.05 nV/√Hz for an ideal 1.194Ω resistor), this is higher than the mid-point noise level when one would expect it to be somewhat lower. It may well be that even though the dR / dT and the

!

responsivity are smaller at the top of the transition, the large values of thermal capacity and thermal conductance

! noise sources, Johnson, to the sink of the device under test contribute significantly. It is a case where all three phonon and 1/ f noise have comparable contributions (see §2.7) and add up to 0.81nV/√Hz. Once a bolometer is built using a MgB2 thin film thermistor then a better insight into the noise at the top of the transition will be

! established.

7.10 MgB2 thin film temperature noise The MgB2 thin film thermistor studied here was not suspended on a thermally isolating membrane, so it is inappropriate to carry out an analysis to derive the NEP in the manner that was carried out for the YBCO device reported in §7.7. However, the Noise Equivalent Temperature Difference, NETD (K/√Hz), is the temperature difference that would produce a signal-to-noise ratio of unity. This figure-of-merit can be used to assess (with some caution) the suitability of the film as a thermistor material in a bolometer construction. The NETD is defined as,

NETD =

"T

(

V p Sv

)

=

Sv dT I bias dR

(7.3)

where V p is the peak voltage signal and Sv is the rms noise voltage and the other parameters are as defined ! earlier. Table 5 gives the temperature noise at 10Hz for the MgB2 film thermistor at mid-point of transition. To

!

! the authors knowledge no reported values of D" , NEP or NETD values are given in the literature to date for MgB2 thin film but for comparison the best reported values for YBCO and GdBaCuO are given, together with

! the measured values for YBCO reported in §7.4.


7-30

Figure 7.20: (a) Measured noise spectral density at 10Hz plotted as a function of temperature and (b) noise data shifted on temperature axis by 0.06K to show a possible correlation with dR / dT .

! HTS

Tm (K)

MgB2 38.27 (this work) ! ! YBCO* 90 YBCO 91.3 (this work) GBaCuO**

90.2

dR / dT (Ω/K)

I bias (mA)

Sv (nV/√Hz)

NETD at 10Hz (nK/√Hz)

12.4 ! 2.5

4

0.34 ! 0.8

6.8

! 6.35

2.95

2

1.35

229

3414

50 " 10#3

21

123

50

Table 5: Temperature noise at mid-point of transition of MgB2 film and comparison with other HTS materials; *YBCO on sapphire [2], **GdBCuO on SiN [3]. !


7-31

References

[1]

I. A. Khrebtov et al., Proc. 14th Int. Conf. on Noise in Physical Systems and 1/ f fluctuations, 313, 1997.

[2]

B. Lakew et al., Sensors and Actuators A, 114, 2004.

[3]

M. J. de Nivelle et al., Appl. Supercond., 9(2), 1999.

!

Chapter 8

Conclusions

8-1

Chapter 8. Conclusions

8.1

8-2

Introduction

Two main achievements have been accomplished through the work carried out for this thesis, the first is that a prototype HTS bolometer has been fabricated that shows promise for future applications in planetary FIR spectrometer experiments and the second is that a new class of material, MgB2 thin film, has been identified as a good candidate for a thermometer in bolometer design and construction. The HTS bolometer structure consists of a YBCO thin film thermometer suspended on a Si:B membrane. Infrared radiation incident on the bolometer receiving area heats the YBCO film, whose resistance is a strong function of temperature. A bias current through the YBCO film creates a voltage drop across the device, which is then measured/amplified for detection. The construction of a highly sensitive device requires a minimization of both the thermal capacity of the detecting area and the structurally coupled thermal conductance while maintaining an acceptable time constant. From the work carried out in this study a number of issues have arisen that need to be addressed before the future role of HTS bolometers can be fully assessed as FIR detectors. Before remarking on these issues, a summary of the results obtained on the YBCO bolometer and the MgB2 thin film is given.

8.2

Summary of results

8.2.1 YBCO bolometer A HTS YBCO bolometer based on a Si:B membrane has been fabricated with an output noise level that is dominated by the fundamental phonon noise. Based on spectral noise voltage density measurements, the electrical NEPe is 3.2 " 10#12 W

Hz at a measurement frequency of 10Hz. This value corresponds to a

specific detectivity of D" = 3.2 # 1010 cm Hz/W . By micromachining spider legs into the membrane to reduce

! ! the thermal conductance even further and by adding an optimized absorption layer it is expected that the same ! detection of FIR with a wavelength of 84.4µm will be achieved. Preliminary optical response NEP value for measurements indicate a time constant of 14ms. Such a detector will satisfy the demands, for example, of a space borne FT spectrometer for observation of OH lines and would exceed the sensitivity of HgCdTe detectors operating at 77K, which to date is typically 2 " 1010 cm Hz/W with a cut-off wavelength of 12µm (see §1.4).

!


8-3

8.2.2 MgB2 thin film on SiN Good quality MgB2 thin film was successfully grown on a SiN/Si substrate. The film showed a zero resistance at 38.16K and a sharp superconducting transition width of 0.23K. The peak of the dR / dT curve, i.e. the mid-point of superconducting transition is at 38.24K. The maximum measured value of dR / dT is 12.4Ω/K. From spectral

! nV/√Hz, this clearly shows that MgB noise voltage density measurements the NETD was evaluated to be 6.8 2 ! films grown on SiN can provide better signal-to-noise ratio than current cuprate-based HTS bolometers. The substrate material, SiN/Si, is ideally suited for micromachining low thermal capacity membranes with optimal thermal conductance. This is very encouraging news for the development of a highly sensitive MgB2 based bolometer for integration into space instrumentation that can meet the cooling requirements of 30K.

8.3

Improvements

8.3.1 Choice of supporting membrane In this work, several approaches were taken to fabricate membranes, namely membranes based on Si:B, SiN, SOI and sapphire. It was shown that thinned membranes, in all four materials, can be fabricated with varying degrees of difficulty. The first three approaches are preferred since these materials are fully compatible with silicon micromachining processes. However, in this work due to practical realities only the Si:B membranes manufactured at Southampton were used for bolometer construction. It is unclear whether there would be a clear difference in the quality of the HTS film/buffer layer growth if deposited on a different membrane material e.g. SiN. For instance, would the crystal defects caused by B implantation in the silicon influence the epitaxial growth of the YSZ/CeO2 buffer layer? This question is important since the quality of the YBCO thin film relies on good heteroepitaxy to the buffer layer.

8.3.2 Reduction of the thermal capacity For a given time constant, if the thermal capacity of the membrane and its connecting thermal conductance is reduced, then the phonon noise and low frequency current noise also reduces (see §2.6); the voltage responsivity also increases. Table 4.2 gave the contributions to the total thermal capacity of a bolometer due to the individual layers that make up the device structure. For the bolometer device fabricated the thickness of the membrane was


8-4

≈ 10x larger than the design, so there is a large margin for improvement. Future efforts should be directed at depositing good quality films on ≈1µm thick membranes.

8.3.3 Reduction of the thermal conductance From §7.6 it was seen that the NEP is dominated by the phonon noise that scales with G1/ 2 (see §2.6.2). In the fabricated bolometer the main contribution to the thermal conductance is the supporting silicon membrane this at

! the present time has not been micromachined into a spider leg type structure, see Figure 4.2.1. A 40x lowering of thermal conductance should be possible if 50µm wide legs of length 500µm are micromachined, see §4.4. The thermal conductance can be further reduced through innovative freestanding suspension designs. Much work still needs to be done to optimize these types of structures.

8.3.4 Application of an absorber In §7.6 the reported electrical NEPe is within the requirements set by the initial design but this will scale with the absorption efficiency according to NEPe / " . At the present time, the constructed bolometer does not have an

! optimized radiation absorber (see 4.2.3) so spectral response measurements in the FIR have not yet seriously been undertaken. However, ! a quick optical response measurement (first light on the YBCO bolometer!) was performed with an order filtered grating monochromator at a blazing wavelength of 3.5µm and a Si optical window with cut-off at 1.2µm, see Appendix G. A voltage response was seen in the band-pass, 1.2µm-3.5µm, however, based on the reflectivity spectra of YBCO (see §4.2.3) the optical absorption is estimated at ≈10% at 6µm and decreasing further with increasing wavelength. In order to get high absorption efficiency, a gold black or impedance matched coating has to be applied.

8.4

Prospects for HTS bolometers

A fuzzy but slowly focusing picture is beginning to emerge of future HTS bolometers for utilization in space. There are many problems to solve but three main factors need to be addressed. The first is HTS thin film quality; the goal of future bolometer development should be the minimization of the noise contributions from the film (and from other sources). The results reported here showed that the noise voltage measured was close to the fundamental limit of the phonon noise but this was only because the film was not patterned into a high resistance


8-5

meander. In new bolometer designs, it is anticipated that the HTS film will be etched into meanders to increase the resistance of the film; although not fully discussed, the problems encountered in this thesis related to the degradation of the HTS film superconducting transition and the increase in noise voltage after photolithographic processing and wet etching. The wet etching of HTS may never solve these problems so alternative approaches have to be found. An avenue for exploration is depositing directly onto meander structures micromachined into the membrane. This may be the best route for the future until a thin film transfer technology has evolved using surrogate single crystals. Second, is the optimization of a high efficiency radiation absorber. Black gold coatings show the highest absorbtivity but they are an “art” to deposit and have a high electrical conductivity that can short out electrical connections, so new ways of depositing this material onto the prescribed areas of the device have to be found. In the design presented here the HTS is deposited over the front side of a 1mm "1mm area and the absorber is deposited on the same area of the back of the membrane and is the radiation receiver. A new design could incorporate the absorber and HTS on the same side of the membrane, ! the absorber area would remain the same but this time with a thin width HTS peripheral ring around this area that would act as the thermometer, this would also have the added advantage of creating a higher HTS resistance. This idea would be realizable today with Bi impedance space matched coatings but black gold coatings are a little bit more problematic, so the processing procedures need to be fully developed. It is predicted that a gold black layer will have an absorption efficiency of 80-90% at a wavelength of 84.4 µm (emission line of OH) and would be far superior to space matched coatings at that wavelength. Third, considerable improvement in bolometer performance can be attained by voltage biasing the bolometer. In the present design, a large bias current is chosen to get a large responsivity. However, the current cannot be larger than the critical current of the HTS to avoid destroying the superconductivity of the film and a further limitation on the bias current is that the effective thermal conductance, see equation (2.3), must be kept positive in order to avoid thermal runaway. It was pointed out in §2.4 that this problem can be avoided by voltage biasing the bolometer; an added advantage is that bolometer time constant is reduced. So future work should address how best to read out small currents, it is recommended here that low-noise HTS thin film superconducting quantum interference device (SQUID) current meters or transistor based transimpedance amplifiers be developed for this purpose.

Appendix A: Detector figures of merit A.1

Introduction

In this Appendix, figures of merit are presented which give a measure of the performance of detectors. Although figures of merit are widely accepted and used to compare relative performance between detectors caution must be exercised since many assumptions are hidden in the definition of these parameters. It is useful to introduce the notion of signal chopping and to define the output signal from the detector that will be used in defining these figures of merit. In most instrument design, the input radiant power (flux) is chopped to allow for ac amplification of the output voltage signal and to subtract out any dc power level that may contribute to the signal from the background or from the system itself. For example, if cold apertures are not incorporated into the focal plane design, the temperature of the optics and their housing is high enough to radiate a steady but significant amount of flux onto the bolometer. If the input flux from the source, " , is modulated with a sinusoidal wave chopper then the flux on the bolometer is, using the n -harmonic Fourier series approximation,

! !

"(t) = " 0 +

%

&

n=1

" n cos(n# 0 t + $ n )

(A.1)

where each Fourier component in the series has amplitude coefficients " n (non-negative) and radian phase ! angles " n ( 0 " # n " 2$ ). The modulated voltage output from the detector is then,

! !

!

V (t) = V0 +

$

%

n=1

Vn cos(n" 0 t + # n )

(A.2)

If the dc gain of the associated electronics is zero then, !

Vrms =

Vmax 2

This relationship is used to define the spectral responsivity. !

A-1

(A.3)

Appendix A

A.2

A-2

Responsivity

The spectral responsivity, "(# , f ) , of a detector quantifies the amount of output current or voltage seen per watt of monochromatic radiation. The nomenclature is " V (# , f ) for voltage spectral responsivity and " I (# , f ) for

! current spectral responsivity, i.e., !

" V (# , f ) =

!

Vrms $(# , f ) rms

and

" I (# , f ) =

I rms $(# , f ) rms

(A.4)

Responsivity is a function of wavelength, chopping frequency, temperature and bias voltage. The units of ! responsivity are V/W. The blackbody responsivity " BB can similarly be defined as,

! " = BB

Vrms (# BB ) rms

(A.5)

where the incident radiant power is the integral over all wavelengths of the spectral power distribution from a ! blackbody.

A.3

Responsive time constant

The time constant, " , of a detector is a measure of its speed of response. If f is the chopping frequency for which the responsivity falls to 1

2 then the time constant is defined as,

!

!

!

"=

1 (s) 2#f

(A.6)

If the detector is exposed instantaneously to a different irradiance level then " is the time required for the output ! voltage to reach 1 " (e"1 ) or 0.63 of its asymptotic value. The responsivity, chopping frequency and time

!

constant are related by,

!

"(# , f ) =

"(# , 0) 1 + (2$f% ) 2

(A.7)

(V W)

where "(# , f ) and "(# , 0) are the spectral responsivities at a chopping frequency f and under dc conditions ! respectively.

!

!

!

Appendix A

A.4

A-3

Blackbody Noise Equivalent Power, NEPBB

The blackbody Noise Equivalent Power, NEPBB , is the level of incident rms flux required to produce a signalto-noise ratio of unity. In quoting a value for NEPBB , the chopping frequency, detector area, electrical

!

! bandwidth and in some measurements the solid angle of view and background temperature should be specified. ! of unity is, The defining equation for signal-to-noise ratio

NEPBB =

A.5

Vrms (W) " BB

(A.8)

! Blackbody detectivity, DBB

The blackbody detectivity, DBB , is the reciprocal of NEPBB . It is a figure of merit that increases in magnitude with improvement in performance,

!

!

!

DBB =

A.6

1 (W -1) NEPBB

(A.9)

"

Blackbody D-star,! DBB

" The blackbody DBB is a normalization of the blackbody detectivity to take account of the detector area, A , and

the electrical bandwidth ! dependence, "f . The electrical bandwidth is normally taken as 1Hz. The defining

!

! is, equation ! " DBB =

!

A #f = DBB A #f (cm Hz / W) NEPBB

(A.10)

Appendix B: Square-wave chopped incident radiation If the input radiant power, " , is modulated with a square wave chopper then,

0 < $t < # # < $t < 2 #

{0

"(t) = "

!

(B.1)

"(t) can be transformed into the Fourier series, ! % ' * 1 2sin(2n + 1)#t , "(t) = " 0 ) + )( 2 n= 0 (2n + 1) $ ,+

!

&

(B.2)

" 2" 0 2" 0 sin 3#t 2" 0 sin 5#t = 0+ sin #t + + + ... 2 $ $ 3 $ 5 if the first two terms of equation (B.2) are considered, then, !

# d"T1 & )* 0 C% ( + G e "T1 = $ dt ' 2

(B.3)

and,

!

For

# d"T 2 & 2)* 0 C% sin ,t ( + G e "T 2 = $ dt ' +

(B.4)

t >> " ! the solutions of equations (B.3) and (B.4) are, !

"T1 =

#$ 0 2G e

( ( &C ++ 2#$ 0 "T 2 = ! sin**&t + tan'1 * --) G e ,, ) % (&C) 2 + G e2

(B.5)

(B.6)

Therefore the total temperature rise is, !

"T total = "T bias + "T1 + "T 2

! B-1

(B.7)

Appendix B

B-2

"T total =

( ( &C ++ I 2 R #$ 0 2#$ 0 + + sin**&t + tan'1 * -G 2G e % (&C) 2 + G 2 G e ,-, ) ) e

(B.8)

The voltage output from the bolometer is, !

V = I"R = I (Ri # Rb )

where,

Ri

is the resistance when !

T i = T + "T bias + "T1 + "T 2

and

Rb

is the resistance when

T b = T + "T bias + "T1 therefore the change in resistance "R = Ri # Rb is due to a temperature change "T 2 , the ! ! voltage output of the bolometer then can be expressed as, !

!

!

V =I

!

dR "T dT

2

=

2#$IR% 0

& ('C) 2 + G e2

(B.9)

the definition of responsivity (see Appendix A) is given by, !

"=

where, Vrms =

Vrms # rms V 2 2%

& #(t)d ($t) and

# rms =

0

2%

=

2 #0 %

The responsivity is therefore, !

"=

#$IR (%C) 2 + G e2

and is identical to that derived from sinusoidal chopping, see equation (2.12). !

(B.10)

Appendix C: Normalized responsivity The expression in equation (2.24) in Chapter 2 is derived in the following manner. The normalized responsivity

Sn is defined as,

Sn = !

S# "

(C.1)

S0

where S0 is the responsivity with zero power loading and S# " is the responsivity with loading " = " # . The effect ! of radiant power loading on the dissipated power in the HTS resistance when the bolometer is biased in a

!

constant current mode can be described by,

!

!

( I R) ( I R) 2

"=0

2

=

" =" #

P" = 0

(C.2)

P" = " #

Using equation (2.20) together with equation (2.16) and the expression for the normalized temperature i.e. ! equation (2.19), gives,

[

]

[ (

) ]

" 0n (" 0 % 1) " 0n = "$n# "$&# "$ # % 1 % $

which reduces to,

(C.3)

!

[ (

)] [

]

" = #"n$ #" $ % 1 % # 0& %n#"n$ (# 0 % 1)

(C.4)

Then from equation (C.2) and equation (2.23), the normalized responsivity is, ! 1/ 2

"$n# ("$%# ("$ # & 1) + " 0% &n"$n# (" 0 & 1) & "$%# ("$ # & 1))] [ (% + 1)" 0% +1 & %" 0% & n(" 0% (" 0 & 1))] [ Sn = 1/ 2 [" 0n (" 0% (" 0 & 1))] [(% + 1)"$%# +1 & %"$%# & n("$%# ("$ # & 1) + " 0% &n"$n# (" 0 & 1) & "$%# ("$ # & 1))]

!

C-1

(C.5)

Appendix D: Photolithographic masks The following details the mask layers required for the photolithography steps in the fabrication of crystalline silicon membranes (see §5.1.1).

D.1

Chip alignment patterns

The chip alignment scheme consists of a 120µm square frame, 20µm wide, positioned in each corner of each chip. Within each frame are nine positions for alignment target squares 20µm and 16µm squares, see Figure D1.1. The 16µm squares fit concentrically within the 20µm squares. Different combinations of squares are used for each mask level; see Figures D1.3 (a)-D1.3 (f).

(0.0)

(20,20) (27,27)

(52,27)

(43,43)

(68,43)

(50,75)

(77,77)

(70,95)

(93,93) (100,100)

(120,120)

Figure D1.1. Relative co-ordinates of alignment patterns in microns

D.2

Double-side aligning specification

The double-sided alignment targets are in the form of 100µm x 20µm wide cross on wafer side 1 that fits inside a larger light-field (LF) cross on wafer side 2, see Figure D1.2. Large search arrows point towards the alignment mark at the centre of the chip, see Figure 5.3(a) and (b).

D-1

Appendix D

D-2

area not available

5mm

(a)

n x 5mm and > 50mm pitch

(b)

Figure D1.2. Double-side alignment specification: (a) area not available for devices and (b) pitch of LF crosses on front-side of wafer

(a)

(b)

Figure D1.3 Double-side alignment marks on wafer (a) DF cross on side 1 and (b) LF cross on side 2

D.3

Mask Levels

The mask set number (K550) appears in exactly the same position on each mask level, this is seen in the lower left hand corner of the chip. Mask level identification and etch patterns are included along the lower edge of the chip. These patterns do not overlay and are not obstructed by any other part of the chip design. To maintain the strength of the wafer after membrane etching, an annulus of unpatterned silicon is left around the edge of the wafer. Single sided alignment patterns are positioned in the corners of both alignment and device chip. The mask levels are: (1) Mask AL (Alignment) has the side 1 double-sided alignment targets in the target chips and the first level single sided alignment marks. See Figure D1.4 (a).

Appendix D

D-3

(2) Mask P1 (Polysilicon) this has the heater pattern on the device chips, the side 2 double sided alignment targets on the alignment chips and the first level single sided alignment marks. See Figure D1.4 (b). (3) Mask BE (Back-Etch) has the back-etch pattern and the single sided alignment marks on AL. See Figure D1.4(c). (4) Mask HS (High Superconductor) is a dark field (DF) mask for a LF lift-off pattern. It contains single sided alignment marks to align to the marks on mask P1. See Figure D1.4 (d). (5) Mask CW (Contact Window) is a DF mask with the single sided alignment marks to align with the marks on mask P1. See Figure D1.4 (e)

(6) Mask M1 (Metallization) is a DF mask for a LF lift-off pattern. It contains the single sided alignment marks on CW. See Figure D1.4 (f). Both heater and superconductor contacts are made at this stage.

(a)

(b)

(c)

(d)

Figure D1.4. Alignment marks for (a) Mask AL, (b) Mask P1 (c) Mask BE and (d) Mask

Appendix D

D-4

(e)

(f)

Figure D1.4 cont. (e) Mask CW and (f) Mask M1

Appendix E: Deposition of YSZ barrier layer and HTS In 1991, GEC had already developed thin film growth techniques and assessment facilities for the characterization of YBCO, GdBaCuO and BiSCCO on MgO substrates. However HTS and YSZ deposition on thin SiO2-SiN-SiO2 membranes was a new area of development. Work was therefore carried to DC sputter deposit thin films of YSZ and YBCO onto oxidized Si wafers SiO2-SiN-SiO2 over a wide range of temperatures in order to establish the feasibility of the process and to establish the deposition parameters.

E.1

YSZ and YBCO deposition on oxidized Si wafers

A 0.5 mm thick, 100mm diameter Si (100) wafer with 3000Å of thermally grown oxide was diced into 5 mm square samples. The samples were cleaned in acetone and methanol to remove organic material and particulates on the surface. Thin films of YSZ and YBCO were deposited using DC magnetron sputtering system from single stoichiometric targets. Both YSZ and YBCO thin films are deposited at 800°C. In order to establish good thermal transfer between the inconel heater and the silicon substrate, a gold foil was used as intermediate layer. After the first deposition it was apparent that the gold reacted with the silicon and heater. As a result it was impossible to remove the silicon chip undamaged. The surface of the heater had to be ground flat in the workshop to restore it to its original condition. A second experiment was carried out with a copper shim replacing the gold foil. It was easier to remove the sample but the difference was only marginal and again the silicon chip broke. Finally the silicon chip was clamped directly onto the inconel heater. No reaction or bonding occurred between the heater and the sample but the thermal contact was unsatisfactory, the temperature of the silicon chip was approximately 150-200°C lower than the temperature inside the heater. Unfortunately, the heater temperature could not be increased to above 1000°C to compensate for the temperature gradient between the heater and the silicon chip. None of the films showed superconductivity because the growth temperature was too low. This work motivated the group to develop a new heater technology that avoided any reaction of siliconbased materials to the heater surface. Using the new heater design (proprietary), the desired deposition temperature was attainable and the samples could be removed without damage. Five samples were prepared all with a 30nm YSZ barrier layer and YBCO thin film thickness nominally varying from 500nm to 900nm, in steps of 100nm. The samples with YBCO film thickness 500nm and 600nm showed superconductivity, thickness’

E-1

Appendix E

E-2

greater than this showed severe cracking of the YBCO and no superconductivity was observed. Figure E1.1 shows a plot of inductance as a function of resistance for the superconducting 500nm thick YBCO film sample.

E.2

YSZ and YBCO deposition on SiO2-SiN-SiO2 membranes

A wafer with micromachined SiO2-SiN-SiO2 membranes was kindly provided by Dr. F. Volklein (Akademie der Wissenschaften der DDR., Physikalisch-Technisches Institut, DDR-6900 Jena, Helmholtzweg 4, Germany) for the experiments. The wafer was diced into 10mm x 10mm chips using a diamond saw. During this operation some of the membranes were damaged (< 5%). Each chip contained an array of nine 0.5mm square membranes. After the depositions the chips showed serious damage. On some chips one or two corners were broken out and most of the membranes were fractured. This is believed to be due to the combination of the highly strained nature of the silicon nitride layer (not optimized for stress, see §5.1.3) that makes up the membrane sandwich structure and the thermal stress generated due to the CTE mismatch of the materials deposited (see Table 3.5 in §3.2.7). Due to the extensive damage that was induced by thermal stress due to the YSZ deposition at 800°C, only one sample was selected for the HTS growth. Only two of the membranes were intact after the YBCO deposition. During the characterization one of those broke when cooled using a dip stick inserted into a He dewar. However, the sample even with broken membranes showed superconductivity and a transition width of approximately 2K, see Figure E1.2.

Figure E1: Superconducting transition of 500nm thick YBCO film on oxidized silicon.

Appendix E

Figure E2: Superconducting transition of 500nm thick YBCO film on SiO2-SiN-SiO2 membrane.

E-3

Appendix F: Low noise transformer measurements F.1

Introduction

For thin films with resistances > Rs and that RL " RL + Rs .

! Equation (F.10) is a second-order bandpass expression that can be re-arranged in a more familiar form as,

!

!

!

H (s) =

!

a1s # " & s 2 + % m (s + " m2 $ Q '

(F.11)

where, " m is the natural frequency, Q is the quality factor, both these quantities are regarded as a function of !

Rg . The coefficient in the denominator of (F.11) is the bandwidth i.e. " B = " m Q . The coefficients of s in

!

!

equation (F.11) are,

!

!

!

" m (Rg ) =

( Rg + R p ) RL

(L L # M ) p s

2

!

!

(L L # M )

RL M L p Ls # M 2

Amax (Rg ) = a1 " B , and lower 3dB cutoff frequency,

RL M

(F.13)

( Rg + R p ) L s + RL L p

2 2 $ '1/ 2 2 2 2 ! R + R L + R L # 2R R + R 2M # 3L L g p s L p L g p s p )( # Rg + R p Ls + RL L p %&

(

)

(F.12)

!

Amax (Rg ) =

" L (Rg ) =

a1 =

2

p s

From the relationship for maximum gain, !

$ ' " L = 1 / 2& 4 " m2 + " B2 # " B ), % (

( Rg + R p ) L s + RL L p

" B (Rg ) =

)(

(

(

2 Ls L p # M 2

)

(

)

)

(F.14)

The high frequency cutoff is " H = " B # " L , typically " L < " H # " B . The magnitude density and the phase angle function are found from, A(" , Rg ) = H (s,Rg )

! !

s= j"

!

!

[

] s= j# giving,

and " (# ,Rg ) = arg H (s,Rg )

Appendix F

A(" , Rg ) =

F-6

RL M" 2 4 $ * 2 2 2 2 2 ,+ M # L p Ls " + &% 2M Rg + R p RL + L p RL + Ls Rg + R p

(

)

(

)

(

)

2'

(

2

)" + Rg + R p (

% ( M 2 $ L p L s # 2 + Rg + R p RL * ' " (# , Rg ) = arctan ' * L p RL + L s Rg + R p # & )

(

)

(

!

F.3

(

)

-1/ 2 RL2 /

(F.15)

.

(F.16)

))

(

)

2

! Transformer noise

The available noise power in any conductor is Pt = k BT"f , where k B is the Boltzmann constant ( 1.38 " 10#23 J/K ), T is the absolute temperature in K and "f is the noise bandwidth in Hz of the measurement

! ! system [4,5]. For a given temperature, the available power contained within a given interval "f is the same

!

! ! value ( k BT = 4 " 10#21 W at 290K) for any conductor despite the resistance. “Available” implies the maximum !

power measured under conjugate matched conditions only.

!

Zt

Zt

*

Vt

Vt

*

(a)

Vo

Vt

Z *t

(b)

Figure F.2: (a) Noise source and (b) conjugate matched circuit.

Consider a noisy voltage source such as a resistance member of an element Z t as shown in Figure F.2(a), where

Vt represents the noise voltage generated by the element. Given that Z t consists of a series equivalent resistive ! and reactance members such that Z t (" ) = Rt (" ) + jX t (" ) , to extract the available power a conjugate load, !

! Z t (" ) = Rt (" ) # jX t (" ) is placed at the terminals as shown in Figure F.2(b). The reactances cancel and the real ! parts form a voltage divider such that V0 = Vt / 2 , where V0 is the actual voltage measured at the load. The

!

power dissipated at the load is,

!

!

V02 Vt2 = = k BT#f Re[ Z t (" )] 4 [ Rt (" )]

!

(F.17)

Appendix F

F-7

Re-arranging gives the thermal generated rms voltage, Vt across any element Z ,

Vt = 4k BT Re(Z)"f ! !

(F.18)

Dividing both sides by the square root of the measurement bandwidth gives, the root normalized spectral density ! [6],

St ( f ) =

Vt "f

= 4k BT Re[Z ( f )]

(F.19)

Equation F.19 shows that the spectral density is only as flat in frequency as the real part of the source impedance ! producing the noise. The best one can hope for is that St ( f ) is flat up to, if not past, the bandwidth of the measurement system.

! Consider an amplifier with transfer function H (s) that measures the externally applied noise. The noise content in interval "f is not the same as the –3dB bandwidth used in describing signal transfer. The power

! frequency span, B , between half power points, B = f " f , e.g. content of a signal is considered to lie in the H L ! for a low-pass filter, B = f c , from 0Hz to the cutoff point.

! ! The equivalent noise bandwidth (ENB) is the power content i.e. the area under the power gain curve throughout!its frequency span divided by its maximum. Since the power gain is equal to the square magnitude of the transfer function, see equations (F.13 and F.15), then,

"f =

1 2 Amax

$

# 0

A 2 (2%f )df

(F.20)

The ENB is relative to the –3dB bandwidth, B . Except for a few filters, such as a Chebyshev or Legendre with ! orders > 3, the ENB is larger than B , e.g. applying equation (F.20) to a first order low-pass filter reduces to

! (1/ 2n ) f c . The ENB for the "f = (# / 2) f c . For any n th -order low-pass filters with n > 1 , the ENB is "f = ( # / 2) ! transformer can be written as, !

!

! "f (Rg ) =

!

! 1 2 Amax (Rg )

$

# 0

A 2 (2%f ,Rg )df

(F.21)

Appendix F

F-8

To understand the use of equation (F.21) in the amplification of noise, assume that a single resistor Rg is connected to the primary input terminals of the transformer network described in Figure F.1. Also, assume that the transformer element values are the same as those used for calculating the transfer function for!the PAR 1900 low-noise transformer, see §6.4.1. Consider the setup shown in Figure F.3, the rms output voltage with a given input resistance is,

v no (Rg ) =

$

# 0

St2 ( f )A 2 (2 "f , Rg )df

(F.22)

! Rg

Vt

*

A

Vo

Vno

METER

r.m.s meter

Figure F.3: Rg noise source applied to transformer.

Neglecting any reactive element ! associated with Rg , then,

2 v no (Rg ) = 4k BTRg

#

" 0

% ! 1 2 A 2 (2$f ,Rg )df = 4k BTRg Amax (Rg )' 2 '& Amax (Rg )

#

" 0

( A 2 (2$f ,Rg )df * *)

(F.23)

Equation (F.23) reduces to, !

v no (Rg ) = St Amax (Rg ) "f (Rg )

(F.24)

Dividing both sides by the square-root of the ENB results in the spectral noise voltage Sno at the output, !

v no (Rg ) "f (Rg )

= St Amax (Rg ) = Sno (Rg ) !

(F.25)

and with St constant, Sno is also constant as a function of frequency. Substituting F.13 into F.19 gives the ! output maximum noise spectral density in terms of the transformer elements,

!

!

Sno (Rg ) =

!

RL M 4k BTRg (Rg + R p )Ls + RL L p

"

Sno (Rg )

R L #$

% n 4k BTRg

(F.26)

Appendix F

F-9

where, n is the turn’s ratio. Equations (F.23) – (F.26) are considered ideal and treated in a forward manner, i.e. the output noise is calculated from the knowledge of the input noise. In practical noise measurements the

!

purpose of the transformer voltage gain is to raise the input noise above the noise floor of the device being measured. The measured output is referred to the input by dividing through with the gain A(" ) . The referred to input (RTI) noise spectral density is,

Sni ( f ,Rg ) =

!

Sno ( f ) A(2"f ,Rg )

(F.27)

In actual measurements, the noise response is not spectrally flat. With a bandpass type frequency response, the ! input spectral density, Sni will have a U-shaped response, moreover, 1/ f noise and other factors can affect the resulting distribution.

! passive devices, the output spectral density is ! To obtain Sni , Nyquists theory is invoked, i.e. for proportional to the real part of the output impedance. Thus in equation (F.19), Z represents the impedance

! the secondary terminals. Since the transformer shares a parallel connection with Z , then the output looking into L

! (F.5). In the model developed here, impedance is Z o = Z s Z L , where Z s has been defined in equations (F.4) and ! approximated by, Z L = RL and RL >> Rs , then the resistance member of the output impedance is closely !

! !

!

Ro (" ,Rg ) = RL

(M

2

2 2 $ ' # L p Ls " 4 + & R p + Rg ( 2Rs + RL ) M 2 + RsRL L2p + R p + Rg L2s )" 2 + RsRL R p + Rg % ( 2 4 $ 2 2' 2 2 2 2 2 2 M # L p Ls " + & 2RL R p + Rg M + RL L p + R p + Rg Ls )" + RL2 R p + Rg % (

)

(

(

)

)

(

(

)

(

)

(

)

(

)

2

)

(F.28)

!

Substituting (F.28) into (F.19) gives the calculated output noise voltage spectral density,

Sno ( f ,Rg ) = 4k BTRo (2"f ,Rg )

(F.29)

Figure F.4(a) shows the calculated output noise spectral density and Figure F.4(b) shows the calculated RTI ! spectral density, using the PAR 1900 transformer values given §6.4.1, as a function of frequency and for decade values of Rg for each trace. Both graphs show that the noise levels of the example 1:1000 port transformer circuit rise as expected, but the frequency responses are quite varied as the input source resistance Rg increases.

! Zero ohms at the input does not give a zero noise output. There is inherent noise that is independent of Rg and ! represents the limit of noise measurement with this transformer. For example in Figure F.4(b) at f = 100Hz , as !

!

Appendix F

F-10

Rg " 0, Sv " 0.035nV

Hz such that the noise generated by Rg is indistinguishable from the transformers

inherent noise.

!

! The baseline spectral density Sni ( f , Rg = 0) , see Figure F.4(b), should be subtracted from the other Sni ( f , Rg " 0) plots to give a corrected value, i.e. one that equals the thermal noise of Rg under measurement. ! Since the thermal noise of Rg and the inherent noise of the transformer are uncorrelated, the corrected spectral

!

!

density is,

!

Sv ( f , Rg ) = Sni ( f , Rg ) 2 " Sni ( f , 0) 2

(F.30)

The corrected plots are shown in Figure F.5. As the frequency for each plot increases the spectral density ! becomes flat. The spectral density due to Rg = 1k" is also shown to highlight the increased noise effect. Table F.1 compares the corrected and actual spectral densities at 100Hz and gives the relative errors. It is evident that

! before R = 100" . At 1kΩ, the error approaches 50%! Hence it is advisable an extra noise source is introduced g to maintain the source resistance as low as possible but greater than the equivalent resistance calculated from the baseline spectral density. As seen!from Figure F.5 this is 0.074Ω. In order to see where these extra noise sources come from, consider Figure F.1(b) without the input and output devices and consider each port in turn as a connection to a one-port network with the other port left open circuit [6]. By Thevenin’s theorem, the real network port is seen as an ideal noise-less network that responds similar to signal input but has two noise generators placed at each port, see schematic in Figure F.6(a). The noise generator spectral densities are considered to be equal to that measured at each port with the opposite port open. To represent this, the primary and secondary noise voltage generators V p and Vs are inserted into the voltage vector matrix equation (F.1), i.e.,

!

!

!

R g (")

S ni (100Hz), nV Hz

S v (100Hz), nV Hz

error (%)

0.1

0.0407

0.0407

0.012

1

0.1288

0.1287

0.058

10

0.4091

0.407

0.508

100

1.35

1.287

4.91

1000

5.763

4.070

41.6

!

!

Table F.1: Percentage error between input spectral density and corrected spectral density.

Appendix F

F-11

Figure F.4: Calculated (a) output noise voltage spectral density and (b) RTI noise voltage spectral density.

Figure F.5: Corrected input spectral density.

Appendix F

F-12

V1 + V p = z11I1 + z12 I 2

;

V2 + Vs = z 21I1 + z 22 I 2

(F.31)

Noise generators V p and Vs are partially correlated since they represent different fractions of the same internal ! noise mechanisms [6]. Now consider the arrangement of voltage and current noise generators ( Vn and I n ) only

! ! at the primary port, see Figure F.6(b), then the relationship between the noise generators of Figure F.6(a) and !

F.6(b), using equation (F.1) are,

V = z11I + z12 I 2

!

I1

;

I2

V2 = z 21I + z 22 I 2

I1

*

*

*

Vp

Vs

Vn

Z

V1

V2

!

V1

(F.32)

I2

I

In

*

Z

V

V2

(b)

(a)

Figure F.6: (a) Two-port noise source and (b) Equivalent noise source network.

Figure F.6(b) reveals that, V = V1 + Vn and I = I1 + I n , substituting into (F.32),

V1 + (Vn " z11I n ) = z11I1 + z12 I 2 !

!

;

V2 " z11I n = z 21I1 + z 22 I 2

(F.33)

Comparing (F.33) and (F.31) reveals, !

V p = Vn " z11I n

Extending (F.34) to the complex !

!

;

Vs = "z 21I n

(F.34)

z -parameter functions given in (F.3) for the transformer gives, V p = Vn " (R p + sL p )I n

;

Vs = "sMI n

(F.35)

Since, Vs and V p are partially correlated, then in general by (F.34), Vn and I n are also partially correlated. For ! the following analysis, to make the calculations easy, it is assumed that Vn and I n are uncorrelated and that they

!

! ! ! adequately represent the noise. The noise sources in Figure F.6 have been described independent of Rg . Figure !

! !

Appendix F

F-13

F.7 shows the equivalent circuit with signal source Vg and its input resistance at the terminals. Recalling equations (F.8) and (F.9), the relationship between the system and network gains is found to be,

!

H=

Assuming Vg =0,

Zp % V2 " ' = $T Vg $# Z p + Rg '&

(F.36

! 2

2

Vno2 = T Vi2 = H Vni2

!

(F.37)

! Rg Zs

*

*

Vt

Vn

+ -

Vg ,V ni

In

*

Z

Zp

V, Vi

Figure F.7: Equivalent noise sources

V2 ,Vno

ZL

Vn ,In with Vg and Vt .

Then,

! 2

Vi =

2

(Vt + Vn2 )

!

! 2

Zp Z p + Rg

+ I n2

Z p Rg

2

(F.38)

Z p + Rg

The noise at the output is,

! 2 Vno

=

2 (Vt + Vn2 )T 2

Zp Z p + Rg

2 2 + I n2 T

Z p Rg Z p + Rg

2

(F.39)

Also the RTI noise is, !

Vni2 = Vt2 + Vn2 + I n2 Rg2

(F.40)

It was assumed that the quantities En and I n are uncorrelated, if there is some correlation between the voltage ! and current noise generators then (F.40) can be stated as,

!

!

Appendix F

F-14

Vni2 = Vt2 + Vn2 + I n2 Rg2 + 2CVn I n Rg

(F.41)

where C is the correlation factor, C = 1 for total correlation between the voltage and current noise source. The ! last term can be seen as a voltage noise source (2CVn I n Rg )1/ 2 placed in series with Vn or as a current noise

!

! source (2CVn I n / Rg )1/ 2 in parallel with I n . ! ! Equation (F.40) shows that the RTI noise generator is composed of the sum-square of three noise

! sources, i.e. the thermal noise ! from Rg and two internal (voltage and current) noise generators. Since Vni and Vt are usually known, solving for Vn and I n is easy. If Rg = 0 , then Vn = Vni . As Rg " # , I n2 Rg2 dominates in

! ! ! equation (F.40), giving I n = Vni Rg . There is a middle range of Rg in which thermal noise Vt dominates. ! ! ! ! ! ! However if both Vn and I n are considerably high then their ranges of dominance overlap and Vt is swamped by ! internal noise sources.

!

!

! The spectral ! ! current are respectively, densities of the internal noise sources due to voltage and

SVn ( f ) = Vn / "f V/√Hz and SI n ( f ) = I n / "f A/√Hz. Applying these to equation (F.40) and using equation (F.27) gives,

!

! SVn ( f ) = Sni ( f , Rg )

Rg = 0

;

SI n ( f ) =

Sni ( f , Rg ) Rg

(F.42) R g "#

Figure F.8 shows the resulting spectral density curves for the PAR 1900 transformer example in §6.4.1. The Vn ! curve has a minimum spectral density of 0.035 nV/√Hz in the frequency span 0.5 to 1.3kHz, whereas above 10Hz, I n has a spectral density value of 4.075 pA/√Hz. The graph shows that Vn increases without ! bound at the extreme frequencies, while I n increases without bound only as the frequency tends to zero.

!

! Now that the two internal noise sources that contribute and can dominate the thermal noise source have ! been identified, equation (F.30) can be modified using (F.42), i.e.,

Appendix F

F-15

Figure F.8: Equivalent voltage and current sources.

Figure F.9: Corrected input spectral density.

(

Sv ( f ,Rg ) = Sni ( f ,Rg ) 2 " SVn ( f ) 2 + SI n ( f ) 2 Rg2

)

(F.43)

This function is plotted in Figure F.9, once again using the values given in §6.4.1. Comparison of the family of ! curves with Figure F.5, shows that these are spectrally flat for f > 0.1 Hz. Also it is noted that that spectral density values given on the graph are equal to the Sv values given in Table F.1, giving an error of 0%. However,

! !

Appendix F

F-16

Figure F.6.9 raises the question of why does the spectral density of each curve grow unbounded as f approaches zero? This is due to the fact that I n is approximated. To obtain totally flat curves as f " 0 , I n must be calculated for each individual Rg . Any study of 1/ f characterization must take this into ! consideration.

!

!

F.4

!

!

!

Effect of load resistance on internal noise

The relationship between the internal voltage noise source, Vn , and the transformer elements can be found by examining equations (F.15), (F.28) and (F.29), after setting Rg = 0 , the ratio, Sno / A , reduces to,

! ! ! *$ 2 2' R p2 2 ' 2 ,& L p L s # M / ) 4 $ 2 2 2 4k BT ,& )" + && R p M + RsL p + R Ls ))" + RsR p / R ) L L % ( ,+&% /. ( "M

(

SVn (" , RL ) =

)

(F.44)

The internal current noise, I n , also has the same ratio, Sno / A , but taking the limit Rg " # gives, !

!

!

SI n (" ,RL ) =

# L2 & 4k BT % s " 2 + Rs ( $ RL ' "M

! (F.45)

Equations (F.44) and (F.45) are plotted in Figures F.10(a) and F.10(b) respectively for varying values of load ! resistance. The plots show that significant changes of RL effects the magnitude and frequency distribution of Vn and I n considerably. In Figure F.10(a), the black dashed curve represents the spectral density of a hypothetical

! ! load resistance, RL = 1G" for the PAR 1900 transformer. The blue curves give the spectral density for load !

resistance values 1MΩ, 100MΩ, 1GΩ and 1TΩ and the red curve indicates the limit of Vn as RL " # . In

! Figure F.10(b), the black dotted curve is the current spectral density for a load resistance, RL = 1G" . The red ! ! curves show how the spectral density changes with load resistance and the blue line indicates the limit of I n as ! RL " # . The curves in Figure F.10 highlight that the loading effect on the input noise must be considered very ! carefully in selecting the passband, choosing a high value of load resistance results in a lower overall input!

related noise. It would be useful to simplify Equations (F.44) and (F.45) to get an idea of the possible spectral density values within a passband for acceptable Rg and RL values. Figures F.8 and F.10 reveal that Vn and I n have

!

!

!

!

Appendix F

F-17

minimum values within the midrange of frequencies, this makes it possible to provide simpler equations to state the internal noise spectral densities. The minimum value of Vn or SVmin is derived by taking the polynomial of " in the RHS term in the n radical of equation (F.44) over " 2 M 2 to become an equivalent resistance. Taking the first derivative and setting ! ! ! to zero leads to,

! ( " L2 % R 2 " L2 %+ ( " R %" L p Ls %+ p p s RVn = * R p + Rs $$ 2 '' + ''$1 . $ s2 '- . * 2R p $$ 'R R *) M M M 2 &-, &, *) # L &# L # # &

(F.46)

usually the last term in (F.46) is insignificant leaving the first two terms dominant. Substituting this into ! equation (F.29) the spectral density of the incoherent noise source Vn is obtained. In most cases since RL >> R p2 then the approximation Rv n " R p + Rs n 2 is valid within the pass band of interest without any loss of generality and can state the minimum spectral density of Vn as,

!

!

! !

# R & SVn (min) " 4k bT % R p + 2s ( $ n '

then SVn (min) " 0.035nV/ Hz within the frequency bandwidth !

(F.47)

" 0.1Hz to 1kHz.

The minimum spectral density expected from the I n noise generator is found by inspecting Figure

!

F.10(b) and taking the limit of equation (F.45) as ! f " # . This leads to the inherent current noise generator as,

!

!

#M 2 & R RI n " %% 2 ((RL " L n $ Lp '

(F.48)

The approximated minimum spectral density of the inherent current source is then, !

SI n (min) " 4k BT

n2 RL

(F.49)

Using the intersection of equation (F.45) and the “ideal” I n in Figure F.10(b), less than 5% error is obtained for !

f > RsRL "Ls . At frequencies below this i.e. when f " # , then the ideal case of equation (F.45), ! 4k BTRs "M , is used to determine the spot frequency spectral density, i.e., the noise content within a unit

! !

!

Appendix F

F-18

bandwidth centred at f . For the PAR transformer, RI n " 1kΩ and SI n (min) " 4.07 pA/√Hz for f > 5.15 Hz. Applying equation (F.47) to the PAR transformer that is used in the experimental setup, i.e., RVn " 0.074# .

!

!

!

! !

Figure F.10: The effect load resistance on (a) input voltage spectral density and (b) input current spectral density.

F.5

Effect of source resistance on input noise

The spectral density version of equation (F.40) is given by,

Sni ( f ,Rg ) = St (Rg ) 2 + SVn ( f ) 2 + SI n ( f ) 2 Rg2

(F.50)

Figure F.11(a), (b) and ! (c) show the individual noise sources that make up this equation plotted as a function of frequency, i.e., Vt , Vn and I n for three values of Rg (100kΩ, 8.6Ω and 0.01Ω). Each graph shows the

!

!

!

!

Appendix F

F-19

relationship of Vn with the other noise sources. In Figure F.11(a) as Rg " 0 , for all f the spectral density is

Vni " Vn . Note that Vt and I n Rg fall well below the Vn curve for this situation. At Rg = Rn = 8.6" in Figure

! ! ! F.11(b) there are three distinct regions, (i) f < f a when Vni " I n Rg ; (ii) f a " f # f b for Vni " Vt and (iii) f > f b !

! ! ! ! for Vni " Vn where the frequency points f a and f b are defined at the intersection of Vt with I n Rg and Vn ! ! ! ! ! respectively. Setting the product of equation (F.44) and Rn to 4k BTRn and solving for " , repeating the same !

for equation (F.45) leads to,

!

!

! !

fa =

1 2"

RL Rs Rn RL M 2 # Rn L2s

(a)

!

! fb =

!

!

RL [ Rn # R p ] M 2 # RsL2p

1 2"

L p Ls # M 2

(b)

(F.51)

Applying these equations to the PAR transformer gives f a = 0.48 Hz and f b = 42 kHz. From Figure F.11(b) the ! optimum frequency, f n , occurs at the centre of the condition Vn = I n Rg , i.e., f n =

f a f b = 142 Hz. In Figure

! ! F.11(c) because of the Rg2 term in equation (F.50), the I n Rg term increases faster than Vt as Rg " larger. Thus, ! ! ! I n is the dominant source such that the noise input is approximately, Vn " I n Rg for all f . ! ! ! ! The spectral voltage density contributions from Vni , Vn and I n Rg as a function of source resistance is

! ! given in Figure F.12 and shows that for the optimum frequency of 142Hz the value of source resistance can be

!

! ! ! between 0.074Ω " Rg " 1kΩ. The optimum source resistance value, Rn " RVn RI n " 8.6Ω, is given by the intersection of Vn and I n Rg plots.

!

F.6

!

! !

Noise matching

Since Rn occurs at the intersection of Vn and I n Rg plots, the optimum noise resistance can be stated as

Rn = Vn I n . Substituting the spectral densities of equations (F.44) and (F.45) and after some manipulation !

!

gives,

!

!

(L L # M ) p s

Rn (" ,RL ) =

!

RL

2

2

$ R p2 2 ' 2 " 4 + && R p M 2 + RsL2p + Ls ))" + RsR p2 R L % ( 2 Ls 2 " + Rs RL

(F.52)

Appendix F

F-20

Figure F.13 shows the optimum noise resistance as a function frequency for load resistances RL = 1MΩ, 100MΩ, 1GΩ, 10GΩ, 1TΩ and ∞. These curves can be used to noise match at a given frequency of interest. With higher load resistance the optimum frequency plateau shifts to higher frequencies and ! shows a wider range. If the load is removed i.e., RL = " , there is no plateau and there is no discernable optimum frequency point and Rn is uniquely defined at all frequencies. For a 1 : n turns ratio transformer, the middle band value of

! Rn can approximated by the ratio of (F.47) and (F.49) giving,

!

! !

Rn(mid ) "

# 1 R & RL % Rs + 2s ( $ n n '

(F.53)

Then, for the PAR transformer, using the values given in §6.4.1, Rn(mid ) = 8.6" . !

F.7

!

Noise Figure

The noise factor [7], F , of a two port device is the ratio of the available output noise power per unit bandwidth to the portion of that noise caused by the actual source connected to the input terminals of the device, measured

! temperature of 290K (IEEE definition). The total available noise power, P , and the available at the standard noa noise output power arising from the source, Ptoa , can be obtained by examining the circuit shown in Figure F.1(b)

under

a

conjugate

matched

condition,

Z L = Z s" .

The

!

available

power

gain

is

! 2 z11 + Z g Re( Z s ) and can be used to show that the ratio of the available powers at the input is ! also identical to F ,

( )

2 G a = z 21 Re Z g

!

F=

!

where Pnia = Vg

2

Pnoa G a Pnia Pnia = = Ptoa G a Pta Pta

(F.54)

( )

4 Re Z g is ! the available power of the total input noise and Pta is the available power due to

( )

!

Re Z g . Substituting Vni " Vg and using equation (F.17) to define Vt , then, ! ! " % 2 $ Vni ' ! $ 4 Re Z g!' # & Vni2 F= = " % Vt2 2 $ Vt ' $ 4 Re Z g ' # &

( ) ( )

!

(F.55)

Appendix F

F-21

Figure F.11: Input spectral voltage density resulting from Vin , Vn and I n Rg for (a) 0.01Ω, (b) Rg = 8.6Ω and (c) Rg = 100kΩ.

! !

!

!

!

Appendix F

F-22

Figure F.12: Spectral voltage density contributions from Vni , Vn and I n Rg as a function of source resistance at the optimum frequency of 142Hz.

!

!

!

Figure F.13: Optimum noise resistance for different load values.

Appendix F

F-23

Substituting equation (F.40) yields,

F = 1+

Vn2 + I n2 Rg2 Vt2

(F.56)

Since Rg appears in the equation and that the internal noise generators are frequency dependent equation (F.56) ! covers both the frequency and source resistance and also distinguishes between the internal noises and the source

! thermal noise. This noise factor is useful in indicating the closeness to an ideal noiseless network. To aid examination, a noise figure NF = 10 log10 (F) is defined in dB. In this form an ideal network will give

NF = 0 dB. At NF = 10 dB, the excess noise power of Vn and I n are ten times the source thermal noise power. ! At NF = 3 dB, the source resistance noise equals the internal noise, so for NF > 3 dB it is futile to attempt noise

!

! ! reduction. In practice the best performance is ! found between 0.5dB and 3dB. !

Multiplying both sides of equation (F.56) by "f allows ! the spectral densities of F.42 or equations F.44 and F.45 to be used to define F ,

!

!

F (" ,Rg ) = 1+

SV2n (" ) + SI2n (" )Rg2 St2 (Rg )

(F.57)

where St (Rg ) = 4k BTRg . The noise figure contour map for the PAR transformer (see §6.4.1) is shown in ! Figure F.14. The contours are essentially the loci of points of constant noise figure as a function of source

! resistance and operating frequency. The choice of source resistance and frequency operation should be ideally kept within the 3dB contour. The centre point of the contour map is a local minimum and agrees with the above calculations for the optimum noise resistance (8.6Ω) and frequency (142Hz).

Figure F.14: PAR 1900 transformer noise figure: (a) 2D contour plot and (b) 3D plot for visualizing noise minima.

Appendix F

F-24

Taking the derivative of equation (F.56) and setting this to zero gives the minimum noise factor,

Fmin = 1+

Vn I n 2k BT

(F.58)

Converting Vn " SVn and I n " SI n the minimum noise factor can be expressed with spectral densities of ! equation (F.42) or equations (F.44) and (F.45),

!

! Fmin (" ,RL ) = 1+

SVn (" ,RL )SI n (" ,RL )

(F.59)

2k BT

Equation (F.59) is plotted in Figure F.15 for RL = 1GΩ. The source resistance as a function of frequency is also ! shown, i.e. equation (F.52). NFmin (solid line) has a minimum in the same frequency regime under the plateau of

! Rn (dashed line) spanning ≈8Hz to ≈3kHz. At the points f n = 142Hz and Rn = 8.57Ω, NFmin = 0.074dB or ! Fmin = 1.017. The thermal noise generated by Rg when identical to Rn is Vt = 0.377 nV/√Hz. Thus the internal ! !

noise

mechanisms

added

together

! is

at

a

! minimum

!

and

found

to

be

! ! ! Vt 10 NF 10 " 1 = Vn2 + I n2 Rn2 = 2Vn = 0.0496 nV/√Hz. Root two appears since under noise matching condition, Vn = I n Rg .

! !

Figure F.15: Minimum noise factor and source resistance as a function of frequency RL = 1GΩ.

!

Appendix F

F-25

The effect of load resistance is shown in Figure F.16. The minimum noise factor, Fmin , decreases with increasing load resistance, where noise matching is assumed at all frequencies. Large RL values have an

! advantage in frequency width before the 3dB points ( Fmin = 2 ) are reached. Equation (F.56) can be written as, !

F = 1+

Vn2 +!I n Rg2 4k BTRg

1"V I = 1+ $ n n 2 # 2k BT

%" V I n Rg % ' '$$ n + Vn '& &# I n Rg

(F.60)

!

Figure F.16: Minimum noise factor as a function of frequency for varying load resistance.

From (F.58) and with Rn = Vn I n , equation (F.60) becomes,

# F " 1 &# Rn Rg & ( F = 1+ % min + (% $ 2 '%$ Rg Rn ('

!

(F.61)

With Fmin and Rn as known quantities, the above equation gives the value of F at an optimum frequency. ! Setting F = 2 (3dB) and rearranging equation (F.61) gives the quadratic relationship,

!

!

!

" Rg %2 2 ( $ ' ( R F # n& min ( 1

!

1

( Fmin ( 1)

2

(1 +1 = 0

(F.62)

The two solutions of equation (F.62) indicate the crossing points of the ratio Rg Rn for Fmin " 2 . Multiplying ! both sides of the solutions by Rn yields inequality statement in which to maintain Rg ,

!

!

!

!

Appendix F

F-26

# 1 Rn % " % ( Fmin " 1) $

1

( Fmin " 1)

2

& # 1 " 1 ( ) Rg * Rn % + ( % ( Fmin " 1) ' $

1

( Fmin " 1)

2

& "1( ( '

(F.63)

! as Rg is between these two extremes the source resistance noise is equal or greater than the internal As long noise power.

!

F.8

Transformer output resistance

In cases where the applied noise power is much greater that the inherent noise of the amplifier ( > 2 ), then the noise matching to the low-noise transformer is not too critical since the result will be chiefly from the applied

! noise, i.e., the internal noise from the amplifier is negligible. However, for low-noise measurements, ideally the input of the transformer operating at Rn conditions with the output impedance matched to the noise resistance of the amplifier. With reference to Figure F.1(b) removing the load, RL , and evaluating z s , from equation (F.5) as

! the real part of the secondary winding impedance, then the output resistance is, !

Ros (" ,Rg ) =

!

[(R

g

!

]

)

(

+ R p M 2 + RsL2p " 2 + Rs Rg + R p

(

L2p " 2 + Rg + R p

)

2

)

(F.64)

Appendix F

F-27

References [1]

C.D. Motchenbacher and J. A. Conelly, Low-noise Electronic System Design, John Wiley & Sons, Inc., New York, NY, 1993.

[2]

J. W. Nilsson, Electric Circuits, 4th Ed., Addison-Wesley Publishing Company Inc., Reading, Mass., 1993.

[3]

W-K Chen, Active Network Analysis, World Scientific Publishing Co. Pte. Ltd, Singapore, 1991.

[4]

J. B. Johnson, “Thermal Agitation of Electricity in Conductors,” Physical Review, p. 97, vol. 32, 1928.

[5]

H. Nyquest, “Thermal Agitation of Electric Charge in Conductors,” Physical Review, p. 110, vol. 32, 1928.

[6]

P. J. Fish, Noise and Low-noise Design, McGraw-Hill Inc., New York, NY, 1994.

[7]

H. A. Haus et al., “IRE Standards on Methods of Measuring Noise in Linear Two-ports,” Proceeding of the IRE, 32(1), 60-68, 1960.

Appendix G: Preliminary results on YBCO bolometer G.1

Optical response

One of the YBCO bolometer devices (6036-3-#A3) was subject to a spectral response test using the experimental set-up in the planetary experiments laboratory at the DAOPP, Oxford. The experimental arrangement is described in Chapter 4 of Dr. Neil Bowles doctoral thesis (“Infrared Spectroscopy to Support Measurement of the Atmosphere of the Planet Jupiter,” DAOPP, Oxford University) and consists basically of a Bentham TM300 triple grating monochromator with order sorting filters acting as optical band pass filters. By cutting off wavelengths below the insertion wavelengths the filter dramatically reduced the contribution of shorter wavelengths to the spectrum in the first order of the grating. A dual light source is attached at the variable input slit to the monochromator to provide the radiation. A quartz halogen bulb using a UV grade fused silica lens is useful for the visible to 2µm and a Nernst glow-bar that uses a silicon lens is suitable for wavelengths from 1.2µm to the MIR. Both this source and the halogen lamp have a continuous spectrum. The source is switchable so that the halogen lamp can be used for alignment purposes; this was very useful in setting up the bolometer in the cold optics chamber.

Figure G.1: Optical response from a Nernst source blazed at 3.5µm

G-1

Appendix G

G-2

With the YBCO bolometer at near mid-point of transition (91.5K) operating at a 2mA bias current and using the Nernst source, the grating blazed at 3.6µm and an order sorting filter to 7µm an optical response was seen to a 10Hz radiation chopped signal, see Figure G.1. Note the cold chamber also has a 3mm silicon window, setting a wavelength cut-off at 1.2µm. The signal recovery was achieved using a Stanford Research SR830 DSP lock-in amplifier operated in differential mode (across the bolometer resistance). The NIR response trace and the chopper voltage reference signal were captured on a Tektronix TDS 3054 oscilloscope.

G.2

Frequency response measurement

Using the optical set-up described above, the frequency response for the bolometer operating at 2mA and 4mA bias current was measured by varying the chopper frequency, see Figure G.2. The response time constant, " , is found by examining when the optical response voltage reaches ( 1" e"1) or 0.603 of the asymptotic value, see

! Appendix A. For the 2mA current bias the response time constant is 14.2ms and for the bolometer biased at

! 4mA the time constant is 13.8ms. This bolometer has a time constant of 14ms.

Figure G.2 Frequency response of Nernst glow-bar radiation blazed at 3.5µm