2014 Fourth International Conference on Advanced Computing & Communication Technologies
TCAD Simulation, Small-Signal and Noise Modeling of Si Based Bandgap Engineered Semiconductor Device for Near THz Applications Pradeep Kumar
R. K. Chauhan
Monika Gupta
Department of ECE ABES Engineering College Ghaziabad, India
[email protected]
Department of ECE M.M.M. University of Technology Gorakhpur, India
[email protected]
Department of EIE K.I.E.T. Ghaziabad, India
[email protected]
SiGe HBT performance with record fT / fmax values of 300 GHz and 500GHz respectively [2].
Abstract— In this paper high frequency small-signal model is presented for optimization of device parameters of SiGe HBT with 0.1µm base-width which is based on the technique of direct parameter extraction. For this purpose, we use process simulator ATHENA and device simulator ATLAS from SILAVCO International. Further, a model is proposed to portray the noise in SiGe HBT with uniform Ge concentration in base. The results of the SiGe HBTs are advanced to those of III–V semiconductor devices.
Numerous methods are used to characterize the high frequency devices. These methods include the scattering parameter measurement by means of a network analyzer. Sparameter measurement is a mean of a small signal measurement. The main issue in this measurement is the calibration with accurately de-embedding the parasitic. The load-pull measurement which is a very useful technique can be used for power measurements, albeit it is expensive and time consuming. A set of two-port parameters for instance Z-, Y-, H-, and S- parameters] are used to describe the small signal RF performance of SiGe HBT. The Y-parameters are frequently most appropriate for equivalent circuit based analysis whereas the S-parameters are almost absolutely used for RF as well as microwave measurements due to practical reasons [3].
Keywords- Si, Ge, SiGe HBT, noise figure, cut-off frequency
I.
INTRODUCTION
THz technology is an emerging field which has exhibited an ample ranging potential. During the last years wide research has recognized many attractive application areas, and covered the technological pathways in the direction of broadly usable THz systems. At present, THz technology is in a essential phase and will soon be in a position to radically expand our analytical capabilities via its intrinsic benefits. One of the most pressing challenges of THz applications is the development of cost effective, compact & efficient THz signal sources and receivers for everyday applications. In this context, SiGe Technology is offering fully integrated cost efficient electronic THz solutions. The use of the related high-performance circuits and systems in commercial other non-military markets is driven mainly by cost and energyefficiency.
While working at frequencies in the GHz range, noisy transistors degrade the performance of mobile wireless receivers and thwart the amplifiers and oscillators from meeting the rigorous requirements imposed on them. Small noise improvements at the device level can have a large impact on overall system performance. For example, a degradation of the low-noise amplifier noise figure by even 0.2 dB can be detrimental to the RF link performance. Various analytical equations were used to determine the minimum noise figure Nfmin of a bipolar transistor as a function of bias conditions and transistor parameters [4].
The International Technology Roadmap for Semiconductors (ITRS) [ITRS 06] predicts target performances of SiGe HBTs for fulfill the future need of emerging applications. Figure 1 shows the fT and fmax ITRS targets for SiGe HBTs together with an area indicating the best experimental frequency performance achieved so far. The ITRS longer term roadmap calls for HBTs operating at fT /fmax of 460/500 GHz in 2015 and 570/610 GHz in 2020 with yet unknown manufacturing solutions. The present objective (for Infineon) is to drive the existing performance of 200 GHz to higher frequencies close to 500 GHz by the year 2011 in order to enable circuits for target applications (e.g. 77 GHz and 140 GHz radar sensors) with much lower power consumption, less temperature sensitivity, higher gain, lower noise figure and yield [1] . The successful EC IP DOTFIVE [DOT5] has established new benchmarks for
978-1-4799-4910-6/14 $31.00 © 2014 IEEE DOI 10.1109/ACCT.2014.47
The constantly increasing computational power of computer systems permits the use of technology computer aided design (TCAD) tools on a very large scale. A number of commercial device simulators, company-developed simulators and university developed simulators maintain the potential to handle SiGe devices. These simulators differ significantly in dimensionality (one-, /quasi-/two-, or /quasi/three-dimensional), in the alternative of carrier transport model (drift-diffusion, energy- transport, or Monte Carlo statistical solution of the Boltzmann equation), and in the capability of including electrothermal effects [5]. In this paper, an accurate high frequency small-signal model and noise modeling of high speed SiGe HBT are presented. Following this motivation, Small-signal π- model 144
and direct parameter extraction method are presented in the section II. Section III describes the noise modeling and device physics. The simulation results are discussed in the section IV. Finally, we concluded in last section with common projections. II.
MODEL PROPOSED AND DEVICE PARAMETER INVESTIGATION
In this work a small-signal π-model is proposed as shown in figure.2 where the elements inside the square are the intrinsic part, whereas parameters outside the square represent the extrinsic part (parasitic elements due to contacts and pads).
Figure 2. a small-signal Π equivalent circuit of an HBT device (a) contains intrinsic and extrinsic circuit elements. The intrinsic elements (b) can be determined from the admittance parameters of the device at a number of different bias points [ref.3].
An uncomplicated extraction method is depicted for discussing the transistor high frequency performance along with procedures to find out the parameters of SiGe HBT by means of small-signal Π topology equivalent circuits of this HBT. The algorithm is helpful for extracting both intrinsic plus extrinsic (parasitic) elements. If we determine formerly the extrinsic elements of the HBT then conventional procedures or methods derived from simple bias measurements work very sound. Through different procedures for example DC, cut-off measurements, or optimization can be used for this approach. Since the typical DC and cut-off techniques present poor performance for Silicon Germanium HBT devices that’s why it is frequently very hard to precisely determine the values of parasitic elements of the HBT. An innovative technique has been developed to circumvent this problem and in this technique only scattering (S)-parameters at different biases are measured [3]. For fitting the measured S-parameters appropriately, linear models by way of a Π topology have been experienced. We have neglected emitter resistance, the collector resistance, along with the output resistance due to Early effect for simplicity [3]. S-parameters obtained from ac analysis are simply converted into Y-, Z- or Hparameters using ATLAS. Power Gains for example MSG (maximum stable gain) is used for analysis. Due to simplicity of measurement, these quantities are calculated from the measured small-signal scattering parameters at high frequencies. The maximum stable gain is calculated by y21 and y12 as [6],
Figure 1. ITRS fT and fmax targets for SiGe HBTs together with the region showing best SiGe HBTs available [Ref 1].
MSG =
145
y 21 y12
(1)
frequencies smaller than fT. Thus it can be ignored for simplicity, even though it is noteworthy as a noise voltage generator.
Where k is ‘Rollett stability factor’ and extracted by this equation as [3],
k=
2 Re( y 11) Re( y 22) − Re( y 12 y 21)
y 12 y 21
As power gain with no impedance transformation is achieved by common-emitter microwave transistors. This is the reason why these transistors may comprise useful gain when inserted into a system with 50 Ω [3]. The intrinsic and extrinsic parameters in Figure.2 can be extracted by the following method: The junction capacitances is calculated by the equations as follow [7],
I m ⎡⎣Y 11⎤⎦ + I m ⎡⎣Y 12 ⎤⎦ ωi − I m ⎡⎣Y 12 ⎤⎦ C BC = ωi I m ⎡⎣Y 22 ⎤⎦ + I m ⎡⎣Y 12 ⎤⎦ C CE = ωi C BE =
(2)
(3)
(4)
The junction resistances is calculated by the equations as follow [7],
−1
R BC = Re ⎡ ⎤ ⎣Y 12 ⎦
Figure.3 Noisy and noiseless two port representations
(5)
1
R CE = Re ⎡ ⎤ + Re ⎡ ⎤ ⎣Y 12 ⎦ ⎣Y 22 ⎦ 1
R BE = Re ⎡ ⎤ + Re ⎡ ⎤ ⎣Y 11⎦ ⎣Y 12 ⎦
(6)
(7)
In this method CBE are intrinsic junction capacitances and RBC, RCE and RBE are intrinsic junction resistances. As the device dimension shrink, the parameters RB and the parasitic capacitances start to measure the high frequency behaviour of the device and have to be taken into account in the equivalent circuit to improve the transistor model accuracy in the broad frequency range from Y parameters under the reverse-bias condition. The extrinsic resistance is obtained by the equation as follow [3], = 11 − 12 (8) B
R
Z
Z
III.
Figure 4: Equivalent circuit for the y-parameter derivation used in analytical noise modeling [9].
NOISE MODELING The Y-parameters can be obtained as [10],
At RF and high frequencies, the main noise sources are the base resistance thermal noise and the terminal current shot noises. Figure 3 shows the noisy and noiseless two-port model [8]. The analytical expressions for noise parameters are advantageous for gaining additional intuitive insight into device optimization for noise. This can be accomplished using analytical Y-parameter equations. The small-signal equivalent circuit in simplified is shown in figure 4 [9]. The base resistance is not important for the input impedance at
y
11
g
,m
β
+ jω C i
12
= − jω C bc
21
=g
y y
146
=
m
(9) (10) (11)
y
12
= jω C bc g m = qkT
Where
4.3 Minimum Noise Figure
(12)
Ic
, and
The minimum noise figure is obtained as [9],
C i = C be + C bc . The C be
consists of the EB diffusion capacitance
( )
2 ⎡ ⎤ 1 ⎢2gm Rn 2Rn ωCi 1 ⎥ = + + + − ) 1 ( 1 NFmin β ⎢ β 2g Rn ⎥ gm m ⎣ ⎦
Si1− xGe x τ
( C be = C te + g mτ ), with τ being the transit time, and any other EB parasitic capacitances.
C i is related to f T and
(18)
C bc is the total CB junction capacitance, through [3], gm fT = (13) 2π C i
⎡ ⎢1 ⎛ 1 1 2 = + + g ⎢ +⎜ NF min m rb β ⎢β ⎜ ⎝ ⎣
The oscillation frequency is expressed as [3],
f
=
max
f 8π C R T
CB
⎤ f ⎞⎥ ⎟⎥ f T ⎟⎠ ⎥ 2
⎦ (19)
NF min, increases with frequency. At a given frequency, the NF min, has a minimum at a J C much smaller than the peak f T , J C .
(14) B
4.1 Noise Resistance IV.
The noise resistance can be determined as [9],
R
n
S
=
vn
4kT
= rb +
1 2g
(15) m
This equation indicates that R n is directly proportional to the base resistance. Thus at a given biasing current, it is independent of frequency. R n is also declines with J C at lower
J C , and then stays constant.
4.2 Optimum Source Admittance The optimum source admittance can be expressed as [10],
G
s, opt
=
(
)
2 ⎡ g ⎤ ω 1 1 C i m ⎢ + (1 − )⎥ ⎢ 2 Rn β 2 g R 2 g Rn ⎥ n m m ⎣ ⎦
ATLAS simulation of SiGe HBT is performed to prove precision. All important physical effects, such as impact ionization (II), monte-carlo model are appropriately accounted for the simulation for obtaining admirable pact with characteristics. The impact ionization results in a strong improvement of collector-current. AC simulation needs apposite DC calibration which is an important prerequisite for it [3]. For this simulation, it is compulsory to take the complete device composition into account with the aim of considering the capacitance between substrate and collector (CCS) as well as capacitance between base and collector (CBC). The simulated SiGe device is presented in figure 5. Based on above model, the cut-off frequency is obtained 1THz at 28% germanium concentration. The calculated base-collector junction capacitance and collector-emitter junction capacitance are 2 fF and 0.98 fF respectively. The Gummel plot and current-voltage characteristic of this HBT is depicted in figure 6.
(16)
− I ⎛⎜ S * ⎞⎟ ⎝ i nv n ⎠ = − ω C i (17) Bs,opt = 2 g Rn S vn m G Sopt increases with IC in general. G Sopt increases with frequency. In the case when diffusion capacitance leads the C i , then B Sopt becomes independent of I c , as C i is proportional to
SIMULATION RESULTS AND DISCUSSION
On the basis of above models and physics the values of many performance parameters such as electrical parameters and device high frequency parameters which junction capacitances and resistances, current-gain (β), collector current, base resistance, maximum oscillation frequency fmax, cut-off frequency fT, are calculated for n-p-n SiGe HBT with uniform Ge doping in the base. The HBT considered in this paper has the base width of 0.1µm. Average Ge concentration in this base region considered in our calculations is varied from 10%-28% as higher to this are not supported by present epitaxial technologies and beyond it the improvement associated with Ge seizes may be due to lattice constant mismatch [3].
g m . The absolute value of B Sopt enhances
with frequency.
147
4 3.5
N fm in (d B )
3 2.5 2 1.5 1 0.5 0 0
200
400
600
800
1000
1200
Frequency (GHz)
Figure 7. Minimum Noise Figure vs. Frequency plot
As the emitter regions of both a Si BJT and a SiGe HBT are essentially the same, implying an identical base current IB. The net result is that adding Ge increases the current gain of the transistor. In testing, the maximum current-gain is found about 912 at 28% Ge content. This plot indicates that the important ac and DC consequence of adding Ge into the base, however, lies with the collector current density. Figure 6 shows the variation of IC & IB of SiGe HBT at various bias points. Based on above analytical noise model, the important observations can be made from figures 7, 8, 9. These are the plots of noise parameters vs. frequency. These plots demonstrate that the NFmin increases with frequency. At 2 GHz, simulated NFmin is only 2.6 dB. This is an excellent result. Noise Resistance Rn is weakly frequency dependent. The GSopt and | BSopt | increase with frequency and collector current.
Figure5- SiGe HBT device with 0.1 µm base width from TCAD simulation
A very important consequence of adding Ge into the base of a transistor is its effect on the collector current. With Ge in the base, electron injection at the emitter base junction is made easier, and thus more charge can flow from the emitter to the collector with a resultant increase in IC. Also, because of the Ge-induced band offset, there is a decrease in intrinsic carrier density in the base which also increases IC [6].
10 9
R n / 5 0 (o h m )
8 7 6 5 4 3 2 1 0 0
200
400
600
800
1000
1200
Frequency (GHz)
Figure.6 The Gummel plot (on log scale) and I-V characteristic (on linear scale)
Figure 8. Noise Resistance vs. Frequency plot
148
also calculated. Low base resistance for SiGe HBTs is realized by the appositely optimized base-region with a high Ge content of appropriate form. This model can be used for building the completely integrated receivers and for realizing microwave power amplification at high frequencies which has been demonstrated to be practicable. The proposed device with such frequency may be helpful in the realm of medicine, chemical spectroscopy and other space applications. REFERENCES [1]
[2]
[3]
Figure 9. GSopt vs. Frequency plot
This HBT in near THz frequencies can be useful in high speed communications such as broadband ADCs, 100 Gb/s wireless data transmission and radar applications like higher GHz industrial sensors and automation systems as well as millimeter-wave, THz imaging and sensing used in medical equipments. In addition, these noise parameters are extremely valuable for designing the low-signal RF amplifier which results in the high power gain and stable function of the amplifier as well as low noise level in wide frequency range. Such consequences are viable contender for fabricating analog/mixed-signal/RF and high-speed digital circuit design as well as completely integrated Receivers at higher frequencies. V.
[4] [5]
[6]
[7]
[8]
CONCLUSION
[9]
In this paper, simple device physics, accurate models and methods of electrical parameter calculation and high frequency parameter extraction are presented for SiGe HBT with uniform Ge doping in the base. This is performed by simulated Z- and Y- and S-parameters of proposed device and small signal π-equivalent circuit model. With the help of these parameters we calculated device parameters. We found the fine value of base resistance and base-collector junction capacitance which are 20Ω and 2 fF respectively. These two values are very helpful for figuring out the high frequency response of proposed device. The cut-off frequency is calculated 1 THz. After 28% Ge concentration, these are not supported by present epitaxial technologies and beyond it the improvement associated with Ge seizes may be due to lattice constant mismatch. A comprehensive analysis has also been made and noise parameters based on equivalent noise model are extracted. It is concluded on the basis of above noise analysis that NFmin increases with frequency. An excellent value of simulated NFmin i.e.2.6dB at 2 GHz is achieved. While the Noise Resistance Rn is weakly depend on frequency. On the other hand, GSopt and | BSopt | increase with frequency and collector current. Some foundations for the noise modeling which include the intrinsic and extrinsic parameters based on π-topology are
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