Using RSI format

REVIEW OF SCIENTIFIC INSTRUMENTS

VOLUME 71, NUMBER 11

NOVEMBER 2000

Static and dynamic calibration of thin-film thermocouples by means of a laser modulation technique B. Serio, Ph. Nika, and J. P. Prenela) Institut de Ge´nie Energe´tique-IMFC, Universite´ de Franche-Comte´, Parc Technologique, 2, Avenue Jean Moulin, 90000 Belfort, France

共Received 21 December 1999; accepted for publication 24 May 2000兲 This article presents static and dynamic calibration methods of thin-film thermocouples 共TFTCs兲 by means of a laser modulation technique. The static calibration is based on a combined analysis of theoretical and experimental results; knowing the experimental parameters 共incident laser power, beam waist radius兲, the temperature of the exposed junction is theoretically calculated using a thermal model and the sensor electromotive force 共emf兲 response is recorded. The ratio between the sensor emf and the corresponding temperature gives the TFTC sensitivity. The periodic method is used to determine both the frequency response and the 95% response time of the TFTC. Special test patterns with integrated Au/Pd thin-film thermocouples are developed and tested by these methods. Results of Au/Pd TFTC sensitivity are compared to the literature values and a good agreement is obtained. © 2000 American Institute of Physics. 关S0034-6748共00兲02410-2兴

I. INTRODUCTION

The aim of this article is to present an electro-optical laser modulation technique 共static and periodic兲 designed for calibrating thin-film thermocouples. The static calibration method is based on a combined analysis of experimental and theoretical results using the procedure described hereafter. The laser beam is first modulated and the relative temperature profile of the focused laser beam is recorded with the uncalibrated TFTC junction using a lock-in amplifier. The corresponding beam waist can thus be measured with high precision. The junction is subsequently placed at the maximum energy point of the laser spot and the thermal response of the sensor versus the total continuous incident laser power is recorded. A linear behavior of the static response is ‘‘observable’’ in a limited laser power range. Knowing the laser parameters 共total power, beam waist radius兲, the static junction temperature is theoretically computed with a thermal model solved by the Green’s function technique. Finally, the ratio between the experimental and theoretical response gives the sensor sensitivity. Following this method, we have calculated the mean sensitivity of specific gold–palladium thin-film thermocouples developed in our laboratory for testing laser beam profiles. In order to characterize the dynamic performances of TFTCs, we have also carried out a dynamic optical test bench. The time constant and the 95% response time have been measured for a TFTC junction of 8 ␮m⫻8 ␮m; a good agreement is obtained between these results and the computed theoretical values. The first two sections of this article give a presentation of the TFTC operation principle and a description of the analytical thermal model used to determine the steady-state and transient TFTC responses. The third section is devoted to the fabrication process of the tested TFTCs. The final

Measurements of rapid surface temperature changes are of crucial importance in many scientific fields. In particular, the control of polymer melting,1 laser processing,2 and the study of combustion chamber thermal behavior require such measurements. For instance, results have been reported in the literature for a single thin-film thermocouple 共TFTC兲 deposited directly onto a turbine blade, operating at 1000 °C.3 TFTCs are well adapted for these applications because they present excellent heat transfer characteristics for a precise surface temperature measurement without disturbing the heat transfer itself. In addition, they are interesting for mass production because their fabrication costs are rather low.4 In many applications, it is necessary to reduce the sensitive junction size of the sensor in order to achieve a short response time and a high spatial resolution; this is directly connected to the junction area while the temporal resolution depends not only on this parameter but also on the material properties.1,5 Thus, a dynamic calibration of these sensors is required for transient surface temperature measurements. It is also well established that the sensitivity of TFTCs deviates significantly from the bulk values.6 Therefore, a convenient and reliable static calibration is required before using these sensors to carry out absolute temperature measurements. Since the cold–hot junction distance and the junction size are generally small, it is difficult to create a well-known temperature difference between the TFTC junctions for calibration. The use of a focused laser beam as a point heat source is a good solution to this problem.7 a兲

Author to whom correspondence should be addressed; electronic mail: prenel@ ige.univ-fcomte.fr

0034-6748/2000/71(11)/4306/8/$17.00

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© 2000 American Institute of Physics

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Rev. Sci. Instrum., Vol. 71, No. 11, November 2000

Calibration of thermocouples

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TABLE I. Optical properties of gold–palladium thin films computed from Weaver values of n R and n I at 514 nm 共Ref. 8兲.

Real indice n R Imaginary indice n I Absorption coefficient ␣ 共cm⫺1 ) Transmittance I/I 0 , x⫽100 nm 共%兲 Reflectance Emissivity of total radiation 共Carefully polished兲 from Ref. 9

Gold

Palladium

0.55 1.82 444 957 1.2 0.62 0.02

1.46 3.59 877 690 0.015 0.69 ⬍0.1

section presents the TFTC calibration procedure proposed in this study and shows experimental and computed results. FIG. 1. Typical design of a thin-film thermocouple device assumed as an semi-infinite slab of uniform thickness, irradiated by a laser at perpendicular incidence.

II. BACKGROUND A. Optical absorption of metals

If a light wave passes through a metallic thin film, its intensity I 0 is reduced to a value I according to the equation I 共 x 兲 ⫽I 0 共 1⫺R 兲 exp共 ⫺ ␣ x 兲 ,

共1兲

where x is the depth, I 0 the irradiance at x⫽0, R the reflectance of the air–film boundary, and ␣ the absorption coefficient. The absorbed light fraction depends on the wavelength, the polarization, and the tilt angle of the incident beam. For a given wavelength ␭, the absorption coefficient ␣ and reflectance R 共under normal incidence兲 are computed with the following relations:

␣⫽ R⫽

4␲nI , ␭

共2兲

共 1⫺n R 兲 2 ⫹n I2 共 1⫹n R 兲

2

⫹n I2

,

共3兲

where n R and n I are, respectively, the real and imaginary components of the metal complex refraction index. Many investigations on optical properties of thin solid films are reported in the literature.8,9 We give, in Table I the optical properties of gold and palladium thin films at a 514 nm wavelength computed with relations 共2兲 and 共3兲. We can see that the penetration depth for these metals is extremely small. Then the transmittance of a few hundred angstro¨ms thick gold or palladium films can be neglected 共⬍1.2% percent after 100 nm兲. In this case, the whole radiation is reflected and absorbed. B. Illumination configuration

An argon laser (␭⫽514 nm兲 in the transmission electron microscope 关 TEM00兴 configuration 共Gaussian light distribution兲, linearly polarized, is used to test the TFTCs. Assuming an incident beam of total power P, the energy flux J(r) can be expressed as follows: J 共 r 兲 ⫽J 0 exp and

冉冊 ⫺2r 2 w2

共4兲

J 0⫽

2P

␲w2

共5兲

,

where J 0 is the maximum energy flux of the Gaussian laser beam, w the 1/e 2 beam radius, and r the radial position. Throughout this article, the laser power refers to the effective power incident on the substrate surface. In order to obtain a sharp focus, the laser beam is focused using a thin lens having a focal length f of positive sign. The propagation characteristics of the beam in the free space and its interaction behavior with the lens have been studied by Kogelnik and Li.10 The focusing function is the transformation of the cavity waist 共radius w 0 ) into a focused waist 共radius w兲 defined by the following equation: 1

1

w

w 20

⫽ 2

冉冊冉冊 1⫺

d0 f

2

⫹

1 ␲w0 f2 ␭

2

,

共6兲

where d 0 is the distance between the cavity waist and the lens position and ␭ is the beam wavelength.

III. THIN-FILM THERMOCOUPLES THEORETICAL THERMAL MODEL A. The boundary value problem

A typical thin-film thermocouple design is shown in Fig. 1. A theoretical model has been developed to predict the junction temperature response when it is exposed to a modulated laser beam. First of all, the thermal sensor structure is assumed as a semi-infinite medium. The laser beam focused onto the metallic junction increases the temperature proportionally to the local intensity of the incident laser beam. Since there is no absorption of light by the glass in the visible region of the spectrum, only the internal heat conduction around this point prevails. In our case, the contributions to the heat transport from the thin gold and palladium layers have been neglected because these have much smaller thermal mass in comparison with the glass substrate which constitutes the heat sink. For a concentrated heat flux, the local temperature increase can be calculated by solving the three-dimensional


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Serio, Nika, and Prenel

time-dependent heat-transport equation 共7兲, with proper initial and boundary conditions 共9兲, 共10兲, and 共11兲, 1 o´ T ⫺ⵜ 2 T⫽0, D o´ t

共7兲

where ⵜ is the Laplacian operator and D is the thermal diffusivity of the substrate D⫽

k . ␳C

共8兲

The initial and boundary conditions are T 共 x,y,z,0兲 ⫽T 0 ,

共9兲

x⫽0, ⫺k

共10兲

⳵ T 共 0,y,z,t 兲 ⫽ ␸ a 共 0,y,z,t 兲 o´ x ⫺h 关 T 共 0,y,z,t 兲 ⫺T g 共 0,y,z,t 兲兴 ,

T 共 x→⬁,y,z,t 兲 ⫽T 0 ,

x→⬁,

᭙t苸关 0,⬁ 关 ,

共11兲

T(x,y,z,t⫽0) is the initial temperature distribution assumed homogeneous, T(0,y,z,t) and T g (0,y,z,t) are the surface and gas 共air兲 temperatures, respectively, h is the linearized thermal loss coefficient 共radiation and convection兲, and ␸ a (0,y,z) is the surface heat flux absorbed by the thin-film thermocouple. This surface heat flux is defined as follows 共see Secs. III B and II C兲:

冋

␸ a 共 0,y,z 兲 ⫽ 共 1⫺R 兲 J 0 exp ⫺ ⫺L⬍y⬍L,

2 共 y 2 ⫹z 2 兲 w2

册

,

⫺⬁⬍z⬍⫹⬁,

共12兲

where L is the TFTC width and J 0 the total energy flux of the laser beam computed by the relation 共5兲.

FIG. 2. Difference of temperature between temperature distributions computed without and with heat losses 共TFTC width L⫽300 ␮ m, R⫽0.66, glass substrate, beam waist w⫽26 ␮ m, incident power P⫽0.1 W兲.

reflectances are quite similar at 514 nm wavelength 共Table I兲. If not, we use the reflectance of the exposed thin-film metal 共palladium兲 for the numerical calculation. C. Semi-infinite boundary value problem solution

The most suitable method to solve the boundary value problem described in the preceding section is the Green’s function technique.11 This one allows us to represent the temperature T(x,y,z,t), due to an instantaneous point source of strength unity, generated at the point (x ⬘ ,y ⬘ ,z ⬘ ) at time t ⬘. The general solution of the boundary value problem obtained with this method can be written as T 共 0,y,z,t 兲 ⫽T 0 ⫹

D k

冕冕冕 t

⬁

⬁

0

⫺⬁

⫺⬁

共兵 ␸ a 共 x ⬘ ⫽0,y ⬘ ,z ⬘ ,t ⬘ 兲

⫹h 关 T g 共 x ⬘ ⫽0,y ⬘ ,z ⬘ ,t ⬘ 兲 ⫺T 0 兴其 ⫻G 共 x,y,z,x ⬘ ⫽0,y ⬘ ,z ⬘ ,t⫺t ⬘ 兲兲 dy ⬘ dz ⬘ dt ⬘ ,

B. Hypothesis

共13兲

1. Thermal losses

Because the gold and palladium total emissivities are very small 共see Table I兲, radiation from the sensor can be neglected in a limited temperature range. So, the losses by thermal radiation are ignored. In addition, the convection losses are also neglected. Indeed, with a maximal convective heat transfer coefficient of 120 W/m2 K, we find a less than 3 °C difference of temperature computed from the second part of the solution 共16兲共see Fig. 2兲.

where G is the Green function. The Green function G including convection losses is given by11 G 共 x,y,z,x ⬘ ,y ⬘ ,z ⬘ ,t⫺t ⬘ 兲 ⫽

再

1

冑4 ␲ D 共 t⫺t ⬘ 兲

⫺

Although physical properties of materials are temperature dependent, the material properties involved in this study have been considered to be constant because the junction temperature level 共less than 250 °C兲 is always far from the thin-film melting points. If the junction area is smaller than the focused beam area, we assumed that the junction reflectance is an average of gold and palladium reflectances 共R⫽0.66兲 because their

⫻Erfc

⫻

冋

共 x⫺x ⬘ 兲 2 ⫹ 共 x⫹x ⬘ 兲 2

4D 共 t⫺t ⬘ 兲

h2 h h exp 2 D 共 t⫺t ⬘ 兲 ⫹ 共 x⫹x ⬘ 兲 k k k

冋

2. Material properties

冋

exp ⫺

x⫹x ⬘

冑4D 共 t⫺t ⬘ 兲 1

4 ␲ D 共 t⫺t ⬘ 兲

冋

exp

⫹

册

h 冑D 共 t⫺t ⬘ 兲 k

册冎

共 y⫺y ⬘ 兲 2 ⫹ 共 z⫺z ⬘ 兲 2

4D 共 t⫺t ⬘ 兲

册

,

册

共14兲

where Erfc共兲 is the complementary error function. Considering T g (0,y,z,t)⫽T 0 and according to Eqs. 共12兲 and 共13兲, the solution of the problem can be written as



T 共 x,y,z,t 兲 ⫽T 0 ⫹

D 共 1⫺R 兲 J 0 k

冕冕冕 t

L

⬁

0

⫺L

⫺⬁


再冋

exp ⫺

2 共 y ⬘ 2 ⫹z ⬘ 2 兲 w2

册

冎

G 共 x,y,z,x ⬘ ⫽0,y ⬘ ,z ⬘ ,t⫺t ⬘ 兲 dy ⬘ dz ⬘ dt ⬘ .

Introducing the variable u⫽ 冑4a(t⫺t ⬘ ) and integrating Eq. 共15兲 we get for the solution T 共 x,y,z,t 兲 ⫽T 0 ⫹

再冋

⫻ Erf

⫺

冊冋冉冊册冋冉冕冉冋册冋冉冊册冋冉冕

D 共 1⫺R 兲 J 0 w 冑8Dt/w 2 2k 冑2 ␲

0

冑2 共 1⫹u 2 兲 wu

L⫺

冉

2k

再冋

⫻ Erf

1⫹u

wu

y 2

u

1⫹u

0

冑2 共 1⫹u 2 兲

1⫹u 2

1

共 1⫺R 兲 J 0 hw 2 冑8Dt/w 2 2

1

L⫺

1

1⫹u

2

y 2

冉

exp ⫺

⫺Erf

exp ⫺

⫺Erf

2x 2

u 2w 2

exp ⫺


2 共 y 2 ⫹z 2 兲

w 共 1⫹u 兲 2

2

where Erf 共兲 is the error function. D. Theoretical results

To integrate Eq. 共16兲 we have used the numerical Simpson method;12 a specific C⫹⫹ program was carried out for this calculation. Figures 3共a兲 and 3共b兲 show density plot and three-dimensional 共3D兲 graph representations of the same steady-state temperature distribution, in both y and z directions. This distribution is calculated for a Au/Pd TFTC of 8 ␮ m width exposed to an argon laser beam 共total incident power of 100 mW兲 focused on the junction 共w⫽26 ␮m兲. Adopting a mean junction reflectance of 0.66, the corresponding central heat flux computed from Eq. 共12兲 is 3.2 kW/cm2 . In the direction of the sensor lead 共z兲, the temperature decreases by more than a factor of 10 at 50 ␮ m from the TFTC center. This justifies the assumption that the bond pad contacts are maintained at the room temperature. Figures 4共a兲 and 4共b兲 show steady-state temperature distributions in x and y directions for two TFTC widths 共L⫽8 ␮m and L ⫽300 ␮m兲. In both cases, the temperature decreases by more than a factor of 10 at 100 ␮ m from the TFTC surface center. This justifies the assumption that the 1 mm thick glass substrate can be assumed semi-infinite. The thermodynamic data used for these calculations are given in Table II. IV. TFTC DESIGN AND FABRICATION A. Thermoelectric considerations

Different combinations of thin-film conductors have been investigated in the literature for high-temperature applications. The thermoelectric characteristics of pure noblemetal thermocouples have been widely investigated because of their good compositional homogeneity, thermoelectric stability, and resistance to high temperatures oxidation.13 Since palladium has a high thermoelectric voltage when pairing with gold or platinum, it has been recently implemented as a new standard thermocouple material.14 Moreover, gold– palladium thermocouples have a relatively high Seebeck

w 2 共 1⫹u 2 兲

⫺L⫺

exp ⫺


2 共 y 2 ⫹z 2 兲

1 1⫹u 2

h 2w 2u 2

⫺L⫺

8k

2

1 1⫹u 2

册

y

冊册冎冊册冋冊册冎冊

共15兲

du

x 冑2 h huw ⫹ x Erfc ⫹ k uw 1 2 冑2k y

4309

du,

册共16兲

voltage compared to other pure noble-metal thermocouples. These merits suggest the possibility that the Au/Pd thermocouple is the most suited thermocouple in the temperature range 0 – 900 °C. Hence, it was decided to produce highpurity Au/Pd TFTCs suitable for static and dynamic calibration operations. B. Masking techniques

The two devices 共8 and 300 ␮ m width兲 have been patterned and delineated with two different masking techniques. The first one 共liftoff process兲 is fully compatible with standard microelectronic processes: a positive photoresist AZ 5214 is coated on a glass substrate and exposed to a 36 mJ/cm2 UV radiation flux, first with an optical mask and next without any 共flood exposure of 210 mJ/cm2 ). The photoresist is then developed in order to transfer the pattern from the mask to the photoresist layer. Afterwords, the first thermoelectric element 共gold兲 is deposited by magnetron sputtering and then the lift-off process must be started again in order to deposit the second thermoelectric element 共palladium兲. In this way, we built a miniature planar array with 16 individual Au/Pd TFTC junctions of 8 ␮ m width. The second process is an inexpensive mechanical masking technique, specially developed to make planar arrays with nine individual Au/Pd TFTC junctions of several large widths 共300–800 ␮ m兲. A special symmetrical mask has been made in stainless steel by micromachining. First of all, this mask is applied onto the glass substrate. The first thermoelectric element 共gold兲 is deposited by magnetron sputtering, then the mask is rotated by 180°. Now, the second one 共palladium兲 can be deposited. C. Thin-film technology

The metallic thin-film thickness has been chosen to be higher than 200 nm. With such a thickness, the substrate topography is fully covered, conductor lines are obtained without interruption, and the opacity of thin films to the UV–


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FIG. 4. Steady-state temperature distribution 共TFTC width L⫽8 ␮ m: R ⫽0.66, TFTC width L⫽300 ␮ m: R⫽0.69, glass substrate, beam waist w ⫽26 ␮ m, incident power P⫽0.1 W兲: 共a兲 in x direction and 共b兲 in y direction.

FIG. 3. Steady-state temperature distribution of the TFTC surface 共TFTC width L⫽8 ␮ m, R⫽0.66, glass substrate, beam waist w⫽26 ␮ m, incident power P⫽0,1 W兲: 共a兲 density plot and 共b兲 3D graph.

visible–IR light is total. The fabrication parameters for Au and Pd films obtained by magnetron sputtering are listed in Table III. V. CALIBRATION EXPERIMENTAL SETUP

The static and dynamic responses of a TFTC junction are studied by means of a radiative heat flux. An argon laser beam is focused onto the junction and the power is modulated by an electro-optical modulator to change the sensor temperature. The voltage input of a linear high-voltage amplifier TREK model 10/10 controls the electro-optical modu-

lator output response. This amplifier has a wide bandwidth 共dc to 25 kHz兲 and a voltage gain of 1000 V/V over the range 0–⫾10 kV. A digital oscilloscope 共TDS 340, Tektronix兲 is used for data acquisition. The incident laser beam power is measured by means of a pellicle beamsplitter which requires 10% of the total laser power measured by a laser power meter 共Field Master model LM-2兲. The sensor is fixed on a support which allows three independent rotations for the laser beam autocollimation. The device is mounted on a x, y, z micropositioner driven by a digital positioning system whose resolution is 0.5 ␮ m. This setup is designed to perform thermal measurements both in the dc mode and in the ac mode. In the dc mode, the TFTC junction is heated by a constant laser beam power. A stabilized power supply is used to provide a dc signal for the high voltage amplifier monitoring. Then, the energy flux of the incident laser beam is adjusted to change the mean temperature of the TFTC junction, and the dc thermal emf is detected by a digital voltmeter. In order to increase the measurement resolution, we used an instrumentation amplifier 共AD 624兲. In the ac mode, the laser beam is sine-wave modulated, and the ac thermal emf is detected by a lock-in amplifier 共SR




TABLE II. Thermodynamic data used to calculate the steady-state and dynamic TFTC responses.

Au

Pd

Au/Pd TFTC junction

Mean fraction of the 0.38 0.31 0.36 absorption light at 514 nm Thickness neglected neglected neglected Thermal conductivity ••• ••• ••• 共W/m K兲 Thermal diffusivity ••• ••• ••• 共m2 /s2 ) Mass density (kg/m3) ••• ••• ••• Specific heat 共J/kg K兲 ••• ••• •••

Glass substrate 0

semi-infinite 1.1

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TFTC sensitivity can be considered to be linear in both cases. Thus, the static sensitivity can be defined as the ratio between the experimental calibration measurement and its corresponding computed theoretical steady-state response. We computed, in this manner, a mean sensitivity of about 4.4 ⫾0.6 ␮ V/°C for the 8 ␮ m width TFTC and 4.6⫾0.1 ␮ V/°C for the 300 ␮ m width TFTC. The mean literature value of the thermal emf of Au/Pd thin-film thermocouples being about 5 ␮ V/°C,15 we can conclude that our calibration process is well validated.

5.87⫻10⫺7 2500 840

C. Dynamic calibration results

1. Frequency response

850, Stanford Research Systems兲. The experimental setup of the thin-film sensors characterization is shown in Fig. 5. A. Laser spot size measurement

The laser beam is focused with a lens of 160 mm focal length. The studied TFTC junction is placed at the maximum signal location corresponding to the focusing plane 关d 0 ⫽300⫾1 cm, Eq. 共6兲兴. At this location, the theoretical laser beam radius computed from relation 共6兲 is w(1/e 2 )⫽26.7 ⫾0.4 ␮ m. In order to get an unambiguous value of w, the uncalibrated TFTC is used to resolve the spatial ‘‘relative’’ temperature profile generated by the laser spot. To carry out this experiment, a digital signal processing 共DSP兲 lock-in amplifier is employed to increase the signal to noise ratio. A function generator is used to provide a sinusoidal signal to modulate the laser beam intensity at a frequency F⫽1 kHz, as well as to provide a reference for the lock-in amplifier. Then, the junction is translated across the focused laser beam and the amplitude is recorded with the DSP lock-in amplifier: the measured beam profile is presented in Fig. 6; the corresponding beam radius in the focal plane is w(1/e 2 ) ⫽26⫾0.5 ␮ m. A perfect concordance is obtained between the experimental and calculated values.

For this experiment, the lock-in amplifier has been used to measure the TFTC amplitude A, at the modulation frequency, in the range of 1 Hz–10 kHz. Figure 9 shows the TFTC frequency responses for two incident laser powers ( P⫽67 mW, P⫽45 mW兲. Throughout the range, the frequency responses are perfectly similar but shifted by a constant offset. This verifies the thermal response linearity over the investigated power range. In addition, the TFTC sensor frequency responses are not characteristic of a first-order system. Indeed, the amplitude does not follow the typical low and high asymptotes 共slope 0 and ⫺20 dB/decade兲 and the phase angle does not approach ⫺90° asymptotically. These deviations indicate a nonfirst-order behavior. Indeed the cut-off frequency of the substrate is about a few hertz against a few kilohertz for the TFTC. This suggests that the recorded frequency response does not correspond to the intrinsic TFTC response but to a combination between the sensor and the substrate responses. Consequently, the 95% time response t r seems to be more characteristic of the dynamic response of the complete sys-

B. Steady-state calibration results

The steady-state calibration consists of two steps. The steady-state TFTC response versus the total incident laser power is first recorded. Knowing the focused laser beam waist 共as indicated in Sec. V A兲, the steady-state mean temperature versus the total incident laser power is computed using the theoretical TFTC thermal model presented in Sec. III. In Figs. 7 and 8, we present experimental and theoretical steady-state responses obtained for two Au/Pd TFTC widths (L⫽8 ␮m and L⫽300 ␮m兲. For each sensor, we observed a linear behavior over the optical power range 0–100 mW: the TABLE III. Sputtering process parameters. Base pressure: Pressure 共Ar兲 during sputtering: Target material purity: Film thickness: 共a兲 Au film 共b兲 Pd film

1⫻10⫺6 mbar 3⫻10⫺2 mbar 99.99% ⬎200 nm ⬎200 nm FIG. 5. Experimental setup.


4312


FIG. 6. Laser beam profile measured with a 8 ␮ m width TFTC 共f ⫽160 mm, modulation frequency F⫽1 kHz, P⫽0.1 W兲.

FIG. 7. Theoretical and experimental steady-state responses of an Au/Pd TFTC 共TFTC width L⫽8 ␮ m, reflectance R⫽0.66, glass substrate, beam waist w⫽26 ␮ m兲.

FIG. 8. Theoretical and experimental steady-state responses of an Au/Pd TFTC 共TFTC width L⫽300 ␮ m, reflectance R⫽0.61, glass substrate, beam waist w⫽26 ␮ m兲.


FIG. 9. Experimental frequency-responses of an Au/Pd TFTC 共TFTC width L⫽8 ␮m, glass substrate, beam waist w⫽26 ␮m).

FIG. 10. Experimental Au/Pd TFTC step response 共TFTC width L⫽8 ␮ m, glass substrate, incident optical power P⫽52 mW, beam waist w⫽26 ␮ m, excitation frequency⫽200 Hz, sampling frequency⫽50 kHz兲.

FIG. 11. Experimental and theoretical Au/Pd TFTC step responses 共TFTC width L⫽8 ␮ m, reflectance R⫽0.66, glass substrate, incident power P ⫽52 mW, beam waist w⫽26 ␮ m兲.



tem. Presently, we are working to quantify the influence of the sensor substrate and the junction geometry on the dynamic characteristics. 2. Response time measurement

The experimental technique used to determine the dynamic TFTC characteristics is to study its step response. A typical step response of a Au/Pd TFTC 共L⫽8 ␮ m兲 is shown in Fig. 10. For this experiment, a function generator was used to provide a square wave laser signal modulation of 200 Hz, as well as to provide an external reference to the oscilloscope trigger. The signals are processed by numerical filtering 共oscilloscope averaging function兲 in order to reduce the noise level, in particular to suppress parasitic frequencies due to the optical modulator. We have measured 95% time response of about 1⫾0.1 ms. Figure 11 shows the experimental and computed TFTC step responses; a good agreement is observed between these results.


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1

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