Performance comparison of state-of-the-art heterojunction bipolar ...
Microelectronics Journal 35 (2004) 901–908 www.elsevier.com/locate/mejo
Performance comparison of state-of-the-art heterojunction bipolar devices (HBT) based on AlGaAs/GaAs, Si/SiGe and InGaAs/InP Onur Esame, Yasar Gurbuz*, Ibrahim Tekin, Ayhan Bozkurt Faculty of Engineering and Natural Sciences, Sabanci University, Orhanli, Tuzla, 34956 Istanbul, Turkey Received 10 June 2004; received in revised form 12 July 2004; accepted 14 July 2004 Available online 12 September 2004
Abstract This paper presents a comprehensive comparison of three state-of-the-art heterojunction bipolar transistors (HBTs); the AlGaAs/GaAs HBT, the Si/SiGe HBT and the InGaAs/InP HBT. Our aim in this paper is to find the potentials and limitations of these devices and analyze them under common Figure of Merit (FOM) definitions as well as to make a meaningful comparison which is necessary for a technology choice especially in RF-circuit and system level applications such as power amplifier, low noise amplifier circuits and transceiver/receiver systems. Simulation of an HBT device with an HBT model instead of traditional BJT models is also presented for the AlGaAs/GaAs HBT. To the best of our knowledge, this work covers the most extensive FOM analysis for these devices such as I–V behavior, stability, power gain analysis, characteristic frequencies and minimum noise figure. DC and bias point simulations of the devices are performed using Agilent’s ADS design tool and a comparison is given for a wide range of FOM specifications. Based on our literature survey and simulation results, we have concluded that GaAs based HBTs are suitable for high-power applications due to their high-breakdown voltages, SiGe based HBTs are promising for low noise applications due to their low noise figures and InP will be the choice if very high-data rates is of primary importance since InP based HBT transistors have superior material properties leading to Terahertz frequency operation. q 2004 Elsevier Ltd. All rights reserved. Keywords: RF device; SiGe; GaAs; InP; HBT; Modeling; III–V Devices
1. Introduction Besides Si based VLSI there are other fields such as RF electronics with RF transistors as its basic building blocks. One of the main differences between Si based VLSI and RF electronics is the choice of semiconductor materials and transistor types. While Si is the only semiconductor and CMOS is the dominant device used in VLSI, a wide range of alternative materials and devices are present in RF electronics. A common definition of Figure of Merits (FOMs) is necessary to be able to choose the right device or material type. A comprehensive study is already done which is taken as reference in this work for the definition of FOMs for RF heterojunction bipolar transistors (HBTs) [1]. HBTs have attained enough maturity as RF power devices due to their intrinsic high-power density, linearity and * Corresponding author. Tel.: C90-216-483-9533; fax: C90-216-4839550. E-mail address: [email protected] (Y. Gurbuz). 0026-2692/$ - see front matter q 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.mejo.2004.07.003
efficiency. Compared with field-effect devices, bipolar transistors employ vertical current transport, which offer better utilization of wafer area and thus lead to higher power density. The bipolar approach also offers higher linearity at higher power levels, superior power-added-efficiency, and smaller frequency noise as necessary for RF circuits and systems. A typical HBT cross-section is given in Fig. 1. For a common terminology we have used the name ‘AlGaAs/GaAs HBT’ for a device with GaAs as the base material and AlGaAs as the emitter. This is also the same for SiGe and InP based devices. However, a variety of terminology is used when different materials (Sb for example) are used in different layers. The base material is of primary importance since base resistance and base doping directly effects the characteristic frequencies of the device as will be discussed in Sections 2.4 and 2.5. HBTs based on AlGaAs/GaAs, InGaAs/InP and Si/SiGe have shown superior material properties compared to Si BJTs. Much of this improvement is due to the high-base doping achievable through the use of wide band-gap emitters as well as superior material
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power consumption at optimal bias and DC to RF efficiency. † AC frequency sweep and S-parameter simulations for ft, fmax, NFmin and stability factor (k) calculations.
Fig. 1. Cross-section of a HBT.
properties of the state-of-the-art HBTs due to band-gap engineering techniques and epitaxial growth developments. For example, by varying Al content in AlGaAs/GaAs HBT, a graded band-gap can be engineered. The resulting accelerating field decreases the time that the electrons needed to transport across the base and thus increases ft. Furthermore, using MBE, it is possible to grow extremely thin layers with a thickness of only a few nanometers and sharp interfaces between adjacent layers. AlGaAs/GaAs HBTs are commercially available today and commonly used in RF power amplifiers due to higher power densities and higher ft and fmax without the limitation of photolithography. This means better device matchings when compared to III–V FETs. GaAs based HBTs with 171 GHz ft and 275 GHz fmax are reported in Refs. [2,3]. SiGe HBTs with ftO200 GHz are becoming more promising each day and threatening the GaAs market due to competitive material properties, yield, cost and integration potentials [4–6]. Although brittle and expensive, InP based HBTs show even higher speed performance due to superior material properties of the InP material. An InP HBT with 370 GHz ft and 459 GHz fmax is recently fabricated [7]. Rodwell group in UCSD demonstrated an InP based HBT with fmax of 1.08 THz with a transferred substrate method [8]. Also, UIUC group has reported a single HBT with 506 GHz ft [9]. All these devices especially the InP based HBT show aggressive characteristic frequencies when compared to traditional homojunction Si BJTs, where 100 GHz fmax and 84 GHz ft are available from experimental devices [10]. For characterization, simulation and comparison, we first chose three HBTs; AlGaAs/GaAs HBT as the most matured technology, Si/SiGe HBT and InGaAs/InP HBT as two promising devices in RF applications. We used the model parameters from previous works for Si/SiGe HBT [11], AlGaAs/GaAs HBT [12] and InGaAs/InP HBT [13]. Then, we integrated these model parameters into Agilent’s ADSe environment with the model parameters given in Appendix A. During simulations, we ignored the packaging parasitic capacitances and inductances. The simulations we have carried out for an extensive comparisons are as follows: † DC operating point and parameter sweep simulations for extracting the device I–V curves, output power and DC
In AlGaAs/GaAs HBT simulations, we used Agilent’s new HBT model. Most of the previous works about HBT comparison were based on the traditional homojunction bipolar transistor models. The Agilent HBT model leverages the essential compound-semiconductor physics based model introduced in the DARPA/UCSD HBT model, widely referred to as the UCSD model [12,14]. Detailed information is given in Ref. [15] for this model. For the Si/SiGe HBT, Vertical Bipolar Inter Company (VBIC) model is used. The VBIC model is the direct extension of SPICE Gummel-Poon (SGP) model proposed by a group of researchers from widely representative industries [16]. It eliminates the deficiencies of the industry standard SGP model such as Early effect model, parasitic substrate transistor action, avalanche multiplication and self-heating. Finally, for the InGaAs/InP HBT we used SGP model [17,18].
2. Simulation results For accomplishing true DC and bias point comparison in a simulation environment, a common definition for all of the FOMs must be given. To characterize AlGaAs/GaAs HBT, Si/SiGe HBT and InGaAs/InP HBT, device I–V curves, ft, fmax, NFmin and stability behavior vs bias were extracted using the model parameters in Appendix A. The derivation of FOM equations were based on Schwierz’s work for a common definition [1]. An extensive comparison of AlGaAs/GaAs, Si/SiGe and InGaAs/InP devices based on our surveys and simulations are given in this section. 2.1. Device I–V curves For device I–V curve families VCE is swept from 0 to 5 V and IB from 10 to 100 mA. As seen from Fig. 2, for 70 mA base current the AlGaAs/GaAs device’s collector current is 6 mA, while it is 11 mA for the Si/SiGe device and 4 mA for the InGaAs/InP HBT at their optimal VCE for class A operation. The meaning of optimal VCE for class A operation is described in Section 2.2. The difference in currents mainly stems from the current gain b values of devices. b is related to the device design as bz
NE wE DB expðDEG =kTÞ NB wB DE
(1)
where NE and NB are the emitter and base doping concentrations, wE and wB, the emitter base widths DE and DB, the minority carrier diffusion constants in emitter and base, k, the Boltzmann constant and T, the absolute temperature (K) in the device. Different design parameters
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design a double heterojunction bipolar transistors, which provides high-breakdown voltages owing to the use of a wide-gap material in the collectors. 2.2. Power calculations Power calculations are accomplished by setting (i) the maximum allowed VCE, VCEmax to 5 V and (ii) the maximum allowed DC power dissipation, PDmax to 50 mW to set a common reference point. The optimal VCE is calculated from the load line between the knee of the I–V curve (the value of VCE for maximum IC at AC operation) and ICZ0 (VCEmax) point. These VCE values are 2.9 V for AlGaAs/GaAs device, 2.6 V for the Si/SiGe devices and 2.65 V for the InGaAs/InP HBT. The output powers of devices at optimum bias points are again calculated from this load line as all the other power calculations. Pout is computed from the peak values of the collector current (Ip) and the collector–emitter voltage (Vp) as Pout Z 0:5IP VP
(2)
for class A operation. The DC power consumption values are obtained for the optimal bias points and this calculation neglects the power consumed due to the base current. Finally, the DC to RF efficiency is the ratio of Pout to PDC in percent hDC;RF Z 100 !ðPout =PDC Þ
(3)
where PDC Z IC;opt VCE;opt
(4)
The DC to RF efficiencies of the analyzed HBTs are hDC;RF;GaAs Z 100 !ð3:022=8:347Þ Z 36:21 hDC;RF;SiGe Z 100 !ð5:753=12:47Þ Z 46:15 hDC;RF;InP Z 100 !ð2:835=6:394Þ Z 44:34
Fig. 2. IC vs VCE curves of (a) AlGaAs/GaAs HBT, (b) Si/SiGe HBT, (c) InGaAs/InP HBT.
lead to different current gains in model parameters explaining the collector current (IC) differences. Since the breakdown voltage phenomena were not modeled for the AlGaAs/GaAs and InGaAs/InP devices, no collector–base breakdown can be seen in Fig. 2a and c. However, for the Si/SiGe device, this breakdown can be seen at around 5 V of collector–emitter voltage (Fig. 2b). This low BVCB is the main problem for the SiGe based heterojunction transistors and limits their use in some application areas such as base stations of cellular networks, where supply voltages exceed 10 V. A solution may be to
where the calculated Pout and PDC parameters are summarized in Table 1. With approximately 46% efficiency, SiGe based device is observed to be more power efficient than the other two HBTs. The efficiency of InP based HBT is also comparable Table 1 Power calculations for AlGaAs/GaAs HBT, Si/SiGe HBT and InGaAs/InP HBT Device
Optimal VCE (V)
Pout at optimal bias (mW)
DC to RF efficiency (%)
AlGaAs/GaAs HBT Si/SiGe HBT InGaAs/InP HBT
2.90
3.022
36.21
8.347
2.60 2.65
5.753 2.835
46.15 44.34
12.47 6.394
DC power consumption at optimal bias (mW)
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to Si/SiGe HBT, but it is lower when compared with the GaAs based device. Table 1 summarizes all the power related parameters for the devices. 2.3. Stability factor ‘k’ RF transistors, as all other active devices are unconditionally stable at any operating frequency above a critical frequency, fk. At operating frequencies below fk, the transistor is conditionally stable and certain termination conditions can cause oscillations. As discussed in Ref. [19], stability measure ‘BO0’ and stability factor ‘kO1’ are the necessary and sufficient conditions for stability. k and B are defined as 1 K js11 j2 K js22 j2 C jDj2 2ðs12 s21 Þ
(5)
B Z 1 C js11 j2 K js22 j2 K jDj2
(6)
kZ
where jDj Z js11 s22 K s12 s21 j
(7)
These sets of expressions reduce to ‘kO1’ since in our case B is positive for all the devices. In Fig. 3, stability factor k vs frequency curves for 70 mA base current is given and ‘kZ1’ points are marked. The AlGaAs/GaAs device is unconditionally stable over 12.3 GHz while fk is 31.7 GHz for the Si/SiGe HBT and 56.5 GHz for InGaAs/InP HBT. Collector voltages are set to optimum values for class A operation (seen in Table 1) during stability analysis. 2.4. Transition frequency, ‘ft’ The transition frequency, ft, of a device is defined as the frequency at which the magnitude of the short-circuit current gain decreases to 1 (or 0 dB). This current gain is defined as ratio of the small signal output current to input current of the transistor with the output short-circuited. ft is directly related to emitter to collector transit time as tEC Z ttot Z 1=2pft Z tE C tB C tRC C tC;SCR
(8)
where tE, tB, tRC and tC,SCR are the emitter charging time, the time required to discharge the excess electrons in the base through the collector junction, collector charging time and the space charge transit time, respectively. They are defined as tE Z ðCje C Cjc Þ
nkT qIC
(9)
tB Z XB2 =2D
(10)
tRC Z ðRE C RC ÞCjc
(11)
tC;SCR Z Xdep =2vsat
(12)
Fig. 3. Stability factor k vs frequency curves for (a) AlGaAs/GaAs HBT, (b) Si/SiGe HBT, (c) InGaAs/InP HBT.
where n is a current ideality factor, XB is the base width, Xdep is the depletion region width, Cje and Cjc are the collector and emitter junction capacitances, RE and RC are the collector and emitter resistances, D is the diffusion constant of electrons and vsat is the saturation velocity. For ft calculation, we set VCE to optimal value for class A operation for each device, and select different base current values over a wide range of frequency spectrum. The ft values can be read from Fig. 4, where the short current gain vs frequency curves can be easily obtained. Table 2 summarizes the ft and b values for the corresponding devices at specific bias points. For all devices, IB is swept from 10 to 100 mA with 10 mA steps. 2.5. fmax and MAG fmax, the maximum oscillation frequency, is defined as the frequency at which the transistor still provides a power
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Table 3 fmax and b values for the HBTs Device
fmax (GHz)
IB (mA)
b at IBZ100 mA
AlGaAs/GaAs HBT SiGe HBT InGaAs/InP HBT
151.7 134.6 416.6
100 100 100
25 51 40
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ft fmax Z 8pRB CjBC
(13)
where RB is the base resistance and CjBC is the collector– emitter junction capacitance.
Fig. 4. Short-circuit current gain vs frequency curves for (a) AlGaAs/GaAs HBT, (b) Si/SiGe HBT, (c) InGaAs/InP HBT.
gain MAG is the maximum available gain if the stability factor kO1; it is equal to the maximum stable gain, js21j/js12j, if k!1 and it is the maximum unilateral gain if s12Z0. It can be expressed as Table 2 ft and b values for the HBTs Device
ft (GHz)
IB (mA)
b at IBZ100 mA
AlGaAs/GaAs HBT SiGe HBT InGaAs/InP HBT
95.70 278 302.6
100 100 100
25 51 40
Fig. 5. MAG vs frequency curves for (a) AlGaAs/GaAs HBT, (b) Si/SiGe HBT, (c) InGaAs/InP HBT.
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Si/SiGe, and InGaAs/InP HBTs, respectively. Si/SiGe HBTs show better noise performance than their AlGaAs/ GaAs and InGaAs/InP counterparts as seen from Fig. 6. NFmin is about 5 dB for the GaAs based device at its optimum bias for class A operation. It is about 1.5 dB for the SiGe based device and 2.735 dB for the InP based HBT for a wide range of VCE values. This advantage makes SiGe attractive for applications such as low noise amplifiers (LNAs), where minimum noise figure is the critical FOM. Another interesting point to emphasize for the AlGaAs/ GaAs and InGaAs/InP HBT is the hump seen in the NFmin curves at low VCE voltages. This is mainly due to the change of device’s operating region from saturation to forward active mode. 2.7. Discussion of simulation results
Fig. 6. NFmin vs VCE curve of (a) AlGaAs/GaAs HBT, (b) Si/SiGe HBT, (c) InGaAs/InP HBT.
Table 3 summarizes the fmax and b values for the corresponding devices at specific bias points. Also, MAG vs frequency curves are illustrated in Fig. 5. Again, IB is swept for MAG curves from 10 to 100 mA with 10 mA steps. 2.6. Minimum noise figure, NFmin vs bias Minimum noise figure, NFmin, is calculated at a specific frequency point (at 10 GHz in this work) for different values of IB. VCE is set to 2.9, 2.6 and 2.65 V for AlGaAs/GaAs,
A summary of simulation results is given in Table 4. From power perspective SiGe, GaAs and InP based devices shows slightly different DC power consumption and output power values at 10 GHz. InGaAs/InP HBT is the least power consuming one since its output current is smaller. Si/SiGe HBT maintains output power nearly twice as its counterparts and it is relatively more power efficient. Three of the devices are competitive and there is a comparable difference between them from power viewpoint. Nevertheless, GaAs is yet the stronger candidate for power applications due to large collector–base breakdown voltages. The characteristic frequencies ft and fmax depend on material properties, device model parameters, device geometry and bias. The difference between ft values of the two HBTs mainly stems from the material properties along with the transistor design leading to different model parameters. Optimized SiGe based HBTs show better (O200 GHz) characteristic frequency values when compared to traditional GaAs based HBTs. Nevertheless, speed related FOMs are comparable for the two material systems. InP based HBT is the most promising among them due to superior properties of InP material system. To conclude, ‘if speed is the case, InP will be the choice.’ The question of ‘Which is important: ft or fmax?’ does not have an unequivocal answer, but the commonly cited statement is that ft is more important for digital circuits, while for analog applications fmax is more significant. Manufacturers of RF transistors often strive for ftzfmax so that the devices are useful for a large number of different applications.
Table 4 Comparison of AlGaAs/GaAs HBT, Si/SiGe HBT and InGaAs/InP HBT for different FOMs Device
DC power consumption (mW)
Output power (mW)
ft (GHz)
fmax (GHz)
NFmin (dB)
AlGaAs/GaAs HBT Si/SiGe HBT InGaAs/InP HBT
8.347 12.47 6.394
3.022 5.753 2.835
95.70 278 302.6
151.7 134.6 416.6
5.026 1.748 2.735
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One more discussion point is the characteristic frequencies of Si/SiGe HBT. As provided in Table 4, ft value of SiGe based transistor is greater than its fmax. This may seem as a conflict to the recorded frequency values, where ft is smaller than fmax. However, it should be noted that a bipolar transistor designed and optimized for maximum ft can show relatively low fmax values. This brings the trade-off that the analyzed Si/SiGe HBT with its given parameters in this study may not be used as a power amplifier between the frequency range from fmax to ft. Another significant FOM difference between AlGaAs/ GaAs HBT, Si/SiGe HBT and InGaAs/InP HBT is their noise behavior. Unlike III–V HBTs, the noise figure of SiGe based HBTs are quite low at high frequencies. This is one of the most prominent features of SiGe. So, we can conclude that for low noise applications SiGe would be a better choice. Finally, considering the breakdown voltages SiGe based single HBTs’, BVCB values are relatively low due to their smaller band-gap of the collector material. This makes it more difficult to use them for high-power applications. However, this problem can be reduced by the double HBT approach since designing the collector–base junction as a heterojunction allows to use a wide band-gap material as the collector material leading to high-breakdown values.
3. Conclusion Three different heterojunction bipolar devices (AlGaAs/ GaAs HBT and SiGe HBT) are studied in this work. All of the simulations are performed in Agilent’s Advanced Design System environment. For the AlGaAs/GaAs HBT we used the HBT model of ADS, for the Si/SiGe device our simulations were based on the VBIC model and for the InGaAs/InP HBT we used the SGP model. There are several discussion points for a technology choice such as power related concepts, characteristic frequencies and noise behavior. The question of ‘which device is most suitable for RF circuit/systems applications’ is a rather complex situation and depends strongly on the application. However, the general tendency is to use SiGe based devices for low noise applications such as LNAs due to better noise behavior, GaAs based devices for high-power applications due to higher breakdown voltages and InP based devices for high-speed applications. This is mainly parallel to our study, where SiGe based device has the best noise performance as its NFmin is as low as 1.5 dB and InP based device has the highest ft and fmax of 302.6 and 416.6 GHz, respectively. However, when it comes to power concepts, SiGe device would not be a suitable choice because of its relatively low breakdown voltage (5 V). SiGe also has the advantage of low cost, high yield and integration potential, while GaAs is technologically more mature, where InP suffers from cost, integration and maturity problems.
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Acknowledgements This work was performed in the context of the network TARGET—‘Top Amplifier Research Groups in a European Team’ and supported by the Information Society Technologies Programme of the EU under contract IST-1-507893NOE, www.target-org.net.
Appendix A. Model parameters The following parameters describe AlGaAs/GaAs HBT, Si/SiGe HBT and InP HBT model at room temperature. AlGaAs/GaAs HBT (after Ref. [11]) TNOMZ25, ISZ8.36!10K26, NFZ1, NRZ1, ISAZ 2.18!10K18, NAZ4.51, ISBZ1!1010, NBZ2, VAFZ 300, VARZ100, IKZ0.1, BFZ500, BRZ1000, ISEZ 2.7!10K18, NEZ1.8, ISEXZ4!10K24, NEXZ1.3, ISCZ1.2!10K14, NCZ2, ISCXZ5.2!10K14, NCXZ2, FAZ0.995, BVCZ28, NBCZ6, ICSZ1!10K30, NCSZ 2, REZ16, REXZ2000, RBXZ55, RBIZ20, RCXZ10, RCIZ20, CJEZ14 fF, VJEZ1.384, MJEZ0.5, CEMINZ 3 fF, FCEZ0.975, CJCZ8 fF, VJCZ1.077, MJCZ0.514, CCMINZ3 fF, FCZ0.8, CJCXZ7 fF, VJCXZ1.4, MJCXZ0.514, CXMINZ4 fF, XCJCZ1, CJSZ0.05 fF, VJSZ1.4, MJSZ0.01, TFBZ0.3 ps, TBEXSZ0.1 ps, TBCXSZ0, TFC0Z1 ps, ICRIT0Z12 mA, ITCZ6 mA, ITC2Z30 mA, VTCZ10, TKRKZ0.5 ps, VKRKZ10, IKRKZ12 mA, TRZ350 ps, TRXZ350 ps, FEXZ0.25, RTHZ2200 C/W, CTHZ3!10K10 C/J, KFNZ0, AFNZ 1.5, BFNZ1, XTIZ2, XTBZK2.8, TNEZ0, TNCZ0, TNEXZ0, EGZ1.645, EAAZK0.495, EABZK0.1, EAEZ0.105, EAEZ0.105, EABZ0, EAXZ0, XREZ 0.5, XREXZ0.5, XRBZ0.5, XRCZ0.5, TVJEZK1.5! 10K3, TVJCXZK1.5!10K3, TVJCIZK1.5!10K3 , TVJSZK1.5!10K3, XTITCZ0, XTITC2Z0, XTTFZ 0.75, XTTKRKZ0.6, XTVKRKZ0.6, XTIKRKZ0.6, XRTZ1.2, XRTZ1.2, DTMAXZ1000 Si/SiGe HBT (after Ref. [12]) ISZ4:10589!10K15, NFZ1.01, IBEIZ1.748!10K17, NEIZ1.0, WBEZ1, IBENZ1.5433!10K13, NENZ2, IBCIZ1.031!10K16, NCIZ1.02, IBCNZ1.4127!10K12, NCNZ1.5, IKFZ8.55!10K2, NRZ1.01, IKRZ0.35! 10K2, VEFZ45, VERZ39, RCIZ3.24, RCXZ0.24, RBXZ5.26, RSZ0.001, RBIZ10, RBPZ0.001, REZ1.1, CJEZ105!10K15, PEZ0.76, MEZ0.36, AJEZ0.5, CJEPZ76!1015, CJCZ3.0!1015, PCZ0.72, MCZ0.42, AJCZ0.5, GAMMZ2.5!1011, HRCFZ2, VOZ1, RTHZ 400, CTHZ10!1014, FCZ0.9, AVC2Z21.5, AVC1Z 6.515, TNOMZ300 ISZ5.2621!1015, QP0Z20.25!1014, ICHZ5.5036!102, HFEZ1.0, HFCZ1.0, HJEIZ1.0, HJCIZ1.0, IBEISZ3.65433!1017, MBEIZ1.0249, IREISZ1.4573!1013, MREIZ2.0, IBCISZ0.543!1016, MBCIZ1.057, IBCXSZ2.7!1020 , MBCXZ1.005, IBETSZ0, ABETZ40, FAVLZ1.0286, QAVLZ 11.1!105, ALFAVZ8.25!105, ALQAVZ1.96!104,
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RBI0Z25.01, RBXZ2.03, FGEOZ0.6557, FQIZ0.9055, REZ1.3470, RCXZ8.624, CJEI0Z105!1015, VDEIZ 0.75, ZEIZ0.35, ALJEIZ1.8, CJCI0Z79!1015, VDCIZ 0.71, ZCIZ0.38, VPTCIZ416, RCI0Z5.2, VLIMZ0.70, VCESZ0.05, VPTZ1, RTHZ400.0, CTHZ10.0!1014, TNOMZ300 InP HBT (after Ref. [13]) ISZ6!10K13, BFZ50, NFZ1, VAFZ12, IKFZ0, ISEZ6!10K40, NEZ1, BRZ3, NRZ1, VARZ100, ISCZ1!10K30, NCZ1, RBZ54, IRBZ0, RBMZ54, REZ10, RCZ0, CJEZ4 fF, VJEZ0.9, MJEZ0.5, CJCZ2.5 fF, VJCZ20, MJCZ0.01, XCJCZ0.5, CJSZ0, VJSZ0.75, MJSZ0.5, FCZ0.8, XTFZ0, TFZ0.44 ps, VTFZ0, ITFZ0, PTFZ43, TRZ1 ns, KFZ0, AfZ1, KBZ0, ABZ1, FBZ1, ISSZ0, NSZ1, NKZ0.5, FFEZ1, TNOMZ25, EGZ1.11, XTBZ0, XTIZ35.
References [1] F. Schwierz, J.J. Liou, Microelectron. Reliab. 41 (2001) 145–168. [2] T. Ishibashi, et al., Suppressed base widening in AlGaAs/GaAs ballistic collection transistors, Dev. Res. Conf. (1990). [3] T. Oka, et al., InGaP/GaP HBTs with high speed and low current operation fabricated using WSi/Ti as the base electrode and burying SiO2 in the extrinsic collector, IEDM Tech. Dig. 1997; 739–742.
[4] B. Jagannathan, et al., Self-aligned SiGe NPN transistors with 285 GHz fmax and 207 GHz ft in a manufacturable technology, IEEE Electron. Device Lett. 23 (2002) 258–260. [5] J.S. Rieh, et al., SiGe HBTs with cutoff frequency of 350 Ghz, 2002 International Electron Devices Meeting Technical Digest, San Fransisco, USA, December 8–11, 2002, pp. 771–774. [6] S. Rieh, et al., SiGe HBTs with cutoff frequency of 350 Ghz, IEDM Tech. Dig. (2002); 771–774. [7] Z. Griffith, et al., IEEE Electron. Device Lett. 25 (5) (2004). [8] M. Rodwell, et al., Submicron lateral scaling of HBTs and other vertical transport devices: towards Thz bandwidths, European Gallium Arsenide IC Symposium, Paris, October 2000. [9] Electronics Material Update 17 (11) (2003) 1–16. [10] E. Ohue, 100 Ghz ft Si homojunction bipolar technology, Dig. Symp. VLSI Tech. (1996); 106–107. [11] A. Chakravorty, R. Garg, C.K. Maiti, Appl. Surf. Sci. 224 (2004) 354–360. [12] http:\\hbt.ucsd.edu. [13] www.ece.usb.edu/Faculty/rodwell/Classes/ECE594A/. [14] L.H. Camnitz, S. Kofol, T.S. Low, S.R. Bahl, An accurate large signal high frequency model for GaAs HBTs, GaAs IC Symposium Technical Digest, 1996, pp. 303–306. [15] http://eesof.tm.agilent.com. [16] C. McAndrew, et al., VBIC95: an improved vertical, IC bipolar transistor model, Proceedings of the BiCMOS Circuits and Technology Meeting, Mineapolis, 1995, pp. 170–177. [17] H.K. Gummel, H.C. Poon, An integrated charge control model of bipolar transistors, Bell Syst. Tech. J. 49 (1970) 827–850. [18] L.W. Nagel, SPICE2: a computer program to simulate semiconductor circuits, Memo. No. Erl-520, Electronics Research Labratory, University of California, Berkeley, May 1975. [19] G. Gonzales, Microwave Transistor Amplifiers, Prentice-Hall, Englewood Cliffs, NJ, 1984.
Performance comparison of state-of-the-art heterojunction bipolar devices (HBT) based on AlGaAs/GaAs, Si/SiGe and InGaAs/InP Onur Esame, Yasar Gurbuz*, Ibrahim Tekin, Ayhan Bozkurt Faculty of Engineering and Natural Sciences, Sabanci University, Orhanli, Tuzla, 34956 Istanbul, Turkey Received 10 June 2004; received in revised form 12 July 2004; accepted 14 July 2004 Available online 12 September 2004
Abstract This paper presents a comprehensive comparison of three state-of-the-art heterojunction bipolar transistors (HBTs); the AlGaAs/GaAs HBT, the Si/SiGe HBT and the InGaAs/InP HBT. Our aim in this paper is to find the potentials and limitations of these devices and analyze them under common Figure of Merit (FOM) definitions as well as to make a meaningful comparison which is necessary for a technology choice especially in RF-circuit and system level applications such as power amplifier, low noise amplifier circuits and transceiver/receiver systems. Simulation of an HBT device with an HBT model instead of traditional BJT models is also presented for the AlGaAs/GaAs HBT. To the best of our knowledge, this work covers the most extensive FOM analysis for these devices such as I–V behavior, stability, power gain analysis, characteristic frequencies and minimum noise figure. DC and bias point simulations of the devices are performed using Agilent’s ADS design tool and a comparison is given for a wide range of FOM specifications. Based on our literature survey and simulation results, we have concluded that GaAs based HBTs are suitable for high-power applications due to their high-breakdown voltages, SiGe based HBTs are promising for low noise applications due to their low noise figures and InP will be the choice if very high-data rates is of primary importance since InP based HBT transistors have superior material properties leading to Terahertz frequency operation. q 2004 Elsevier Ltd. All rights reserved. Keywords: RF device; SiGe; GaAs; InP; HBT; Modeling; III–V Devices
1. Introduction Besides Si based VLSI there are other fields such as RF electronics with RF transistors as its basic building blocks. One of the main differences between Si based VLSI and RF electronics is the choice of semiconductor materials and transistor types. While Si is the only semiconductor and CMOS is the dominant device used in VLSI, a wide range of alternative materials and devices are present in RF electronics. A common definition of Figure of Merits (FOMs) is necessary to be able to choose the right device or material type. A comprehensive study is already done which is taken as reference in this work for the definition of FOMs for RF heterojunction bipolar transistors (HBTs) [1]. HBTs have attained enough maturity as RF power devices due to their intrinsic high-power density, linearity and * Corresponding author. Tel.: C90-216-483-9533; fax: C90-216-4839550. E-mail address: [email protected] (Y. Gurbuz). 0026-2692/$ - see front matter q 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.mejo.2004.07.003
efficiency. Compared with field-effect devices, bipolar transistors employ vertical current transport, which offer better utilization of wafer area and thus lead to higher power density. The bipolar approach also offers higher linearity at higher power levels, superior power-added-efficiency, and smaller frequency noise as necessary for RF circuits and systems. A typical HBT cross-section is given in Fig. 1. For a common terminology we have used the name ‘AlGaAs/GaAs HBT’ for a device with GaAs as the base material and AlGaAs as the emitter. This is also the same for SiGe and InP based devices. However, a variety of terminology is used when different materials (Sb for example) are used in different layers. The base material is of primary importance since base resistance and base doping directly effects the characteristic frequencies of the device as will be discussed in Sections 2.4 and 2.5. HBTs based on AlGaAs/GaAs, InGaAs/InP and Si/SiGe have shown superior material properties compared to Si BJTs. Much of this improvement is due to the high-base doping achievable through the use of wide band-gap emitters as well as superior material
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power consumption at optimal bias and DC to RF efficiency. † AC frequency sweep and S-parameter simulations for ft, fmax, NFmin and stability factor (k) calculations.
Fig. 1. Cross-section of a HBT.
properties of the state-of-the-art HBTs due to band-gap engineering techniques and epitaxial growth developments. For example, by varying Al content in AlGaAs/GaAs HBT, a graded band-gap can be engineered. The resulting accelerating field decreases the time that the electrons needed to transport across the base and thus increases ft. Furthermore, using MBE, it is possible to grow extremely thin layers with a thickness of only a few nanometers and sharp interfaces between adjacent layers. AlGaAs/GaAs HBTs are commercially available today and commonly used in RF power amplifiers due to higher power densities and higher ft and fmax without the limitation of photolithography. This means better device matchings when compared to III–V FETs. GaAs based HBTs with 171 GHz ft and 275 GHz fmax are reported in Refs. [2,3]. SiGe HBTs with ftO200 GHz are becoming more promising each day and threatening the GaAs market due to competitive material properties, yield, cost and integration potentials [4–6]. Although brittle and expensive, InP based HBTs show even higher speed performance due to superior material properties of the InP material. An InP HBT with 370 GHz ft and 459 GHz fmax is recently fabricated [7]. Rodwell group in UCSD demonstrated an InP based HBT with fmax of 1.08 THz with a transferred substrate method [8]. Also, UIUC group has reported a single HBT with 506 GHz ft [9]. All these devices especially the InP based HBT show aggressive characteristic frequencies when compared to traditional homojunction Si BJTs, where 100 GHz fmax and 84 GHz ft are available from experimental devices [10]. For characterization, simulation and comparison, we first chose three HBTs; AlGaAs/GaAs HBT as the most matured technology, Si/SiGe HBT and InGaAs/InP HBT as two promising devices in RF applications. We used the model parameters from previous works for Si/SiGe HBT [11], AlGaAs/GaAs HBT [12] and InGaAs/InP HBT [13]. Then, we integrated these model parameters into Agilent’s ADSe environment with the model parameters given in Appendix A. During simulations, we ignored the packaging parasitic capacitances and inductances. The simulations we have carried out for an extensive comparisons are as follows: † DC operating point and parameter sweep simulations for extracting the device I–V curves, output power and DC
In AlGaAs/GaAs HBT simulations, we used Agilent’s new HBT model. Most of the previous works about HBT comparison were based on the traditional homojunction bipolar transistor models. The Agilent HBT model leverages the essential compound-semiconductor physics based model introduced in the DARPA/UCSD HBT model, widely referred to as the UCSD model [12,14]. Detailed information is given in Ref. [15] for this model. For the Si/SiGe HBT, Vertical Bipolar Inter Company (VBIC) model is used. The VBIC model is the direct extension of SPICE Gummel-Poon (SGP) model proposed by a group of researchers from widely representative industries [16]. It eliminates the deficiencies of the industry standard SGP model such as Early effect model, parasitic substrate transistor action, avalanche multiplication and self-heating. Finally, for the InGaAs/InP HBT we used SGP model [17,18].
2. Simulation results For accomplishing true DC and bias point comparison in a simulation environment, a common definition for all of the FOMs must be given. To characterize AlGaAs/GaAs HBT, Si/SiGe HBT and InGaAs/InP HBT, device I–V curves, ft, fmax, NFmin and stability behavior vs bias were extracted using the model parameters in Appendix A. The derivation of FOM equations were based on Schwierz’s work for a common definition [1]. An extensive comparison of AlGaAs/GaAs, Si/SiGe and InGaAs/InP devices based on our surveys and simulations are given in this section. 2.1. Device I–V curves For device I–V curve families VCE is swept from 0 to 5 V and IB from 10 to 100 mA. As seen from Fig. 2, for 70 mA base current the AlGaAs/GaAs device’s collector current is 6 mA, while it is 11 mA for the Si/SiGe device and 4 mA for the InGaAs/InP HBT at their optimal VCE for class A operation. The meaning of optimal VCE for class A operation is described in Section 2.2. The difference in currents mainly stems from the current gain b values of devices. b is related to the device design as bz
NE wE DB expðDEG =kTÞ NB wB DE
(1)
where NE and NB are the emitter and base doping concentrations, wE and wB, the emitter base widths DE and DB, the minority carrier diffusion constants in emitter and base, k, the Boltzmann constant and T, the absolute temperature (K) in the device. Different design parameters
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design a double heterojunction bipolar transistors, which provides high-breakdown voltages owing to the use of a wide-gap material in the collectors. 2.2. Power calculations Power calculations are accomplished by setting (i) the maximum allowed VCE, VCEmax to 5 V and (ii) the maximum allowed DC power dissipation, PDmax to 50 mW to set a common reference point. The optimal VCE is calculated from the load line between the knee of the I–V curve (the value of VCE for maximum IC at AC operation) and ICZ0 (VCEmax) point. These VCE values are 2.9 V for AlGaAs/GaAs device, 2.6 V for the Si/SiGe devices and 2.65 V for the InGaAs/InP HBT. The output powers of devices at optimum bias points are again calculated from this load line as all the other power calculations. Pout is computed from the peak values of the collector current (Ip) and the collector–emitter voltage (Vp) as Pout Z 0:5IP VP
(2)
for class A operation. The DC power consumption values are obtained for the optimal bias points and this calculation neglects the power consumed due to the base current. Finally, the DC to RF efficiency is the ratio of Pout to PDC in percent hDC;RF Z 100 !ðPout =PDC Þ
(3)
where PDC Z IC;opt VCE;opt
(4)
The DC to RF efficiencies of the analyzed HBTs are hDC;RF;GaAs Z 100 !ð3:022=8:347Þ Z 36:21 hDC;RF;SiGe Z 100 !ð5:753=12:47Þ Z 46:15 hDC;RF;InP Z 100 !ð2:835=6:394Þ Z 44:34
Fig. 2. IC vs VCE curves of (a) AlGaAs/GaAs HBT, (b) Si/SiGe HBT, (c) InGaAs/InP HBT.
lead to different current gains in model parameters explaining the collector current (IC) differences. Since the breakdown voltage phenomena were not modeled for the AlGaAs/GaAs and InGaAs/InP devices, no collector–base breakdown can be seen in Fig. 2a and c. However, for the Si/SiGe device, this breakdown can be seen at around 5 V of collector–emitter voltage (Fig. 2b). This low BVCB is the main problem for the SiGe based heterojunction transistors and limits their use in some application areas such as base stations of cellular networks, where supply voltages exceed 10 V. A solution may be to
where the calculated Pout and PDC parameters are summarized in Table 1. With approximately 46% efficiency, SiGe based device is observed to be more power efficient than the other two HBTs. The efficiency of InP based HBT is also comparable Table 1 Power calculations for AlGaAs/GaAs HBT, Si/SiGe HBT and InGaAs/InP HBT Device
Optimal VCE (V)
Pout at optimal bias (mW)
DC to RF efficiency (%)
AlGaAs/GaAs HBT Si/SiGe HBT InGaAs/InP HBT
2.90
3.022
36.21
8.347
2.60 2.65
5.753 2.835
46.15 44.34
12.47 6.394
DC power consumption at optimal bias (mW)
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to Si/SiGe HBT, but it is lower when compared with the GaAs based device. Table 1 summarizes all the power related parameters for the devices. 2.3. Stability factor ‘k’ RF transistors, as all other active devices are unconditionally stable at any operating frequency above a critical frequency, fk. At operating frequencies below fk, the transistor is conditionally stable and certain termination conditions can cause oscillations. As discussed in Ref. [19], stability measure ‘BO0’ and stability factor ‘kO1’ are the necessary and sufficient conditions for stability. k and B are defined as 1 K js11 j2 K js22 j2 C jDj2 2ðs12 s21 Þ
(5)
B Z 1 C js11 j2 K js22 j2 K jDj2
(6)
kZ
where jDj Z js11 s22 K s12 s21 j
(7)
These sets of expressions reduce to ‘kO1’ since in our case B is positive for all the devices. In Fig. 3, stability factor k vs frequency curves for 70 mA base current is given and ‘kZ1’ points are marked. The AlGaAs/GaAs device is unconditionally stable over 12.3 GHz while fk is 31.7 GHz for the Si/SiGe HBT and 56.5 GHz for InGaAs/InP HBT. Collector voltages are set to optimum values for class A operation (seen in Table 1) during stability analysis. 2.4. Transition frequency, ‘ft’ The transition frequency, ft, of a device is defined as the frequency at which the magnitude of the short-circuit current gain decreases to 1 (or 0 dB). This current gain is defined as ratio of the small signal output current to input current of the transistor with the output short-circuited. ft is directly related to emitter to collector transit time as tEC Z ttot Z 1=2pft Z tE C tB C tRC C tC;SCR
(8)
where tE, tB, tRC and tC,SCR are the emitter charging time, the time required to discharge the excess electrons in the base through the collector junction, collector charging time and the space charge transit time, respectively. They are defined as tE Z ðCje C Cjc Þ
nkT qIC
(9)
tB Z XB2 =2D
(10)
tRC Z ðRE C RC ÞCjc
(11)
tC;SCR Z Xdep =2vsat
(12)
Fig. 3. Stability factor k vs frequency curves for (a) AlGaAs/GaAs HBT, (b) Si/SiGe HBT, (c) InGaAs/InP HBT.
where n is a current ideality factor, XB is the base width, Xdep is the depletion region width, Cje and Cjc are the collector and emitter junction capacitances, RE and RC are the collector and emitter resistances, D is the diffusion constant of electrons and vsat is the saturation velocity. For ft calculation, we set VCE to optimal value for class A operation for each device, and select different base current values over a wide range of frequency spectrum. The ft values can be read from Fig. 4, where the short current gain vs frequency curves can be easily obtained. Table 2 summarizes the ft and b values for the corresponding devices at specific bias points. For all devices, IB is swept from 10 to 100 mA with 10 mA steps. 2.5. fmax and MAG fmax, the maximum oscillation frequency, is defined as the frequency at which the transistor still provides a power
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Table 3 fmax and b values for the HBTs Device
fmax (GHz)
IB (mA)
b at IBZ100 mA
AlGaAs/GaAs HBT SiGe HBT InGaAs/InP HBT
151.7 134.6 416.6
100 100 100
25 51 40
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ft fmax Z 8pRB CjBC
(13)
where RB is the base resistance and CjBC is the collector– emitter junction capacitance.
Fig. 4. Short-circuit current gain vs frequency curves for (a) AlGaAs/GaAs HBT, (b) Si/SiGe HBT, (c) InGaAs/InP HBT.
gain MAG is the maximum available gain if the stability factor kO1; it is equal to the maximum stable gain, js21j/js12j, if k!1 and it is the maximum unilateral gain if s12Z0. It can be expressed as Table 2 ft and b values for the HBTs Device
ft (GHz)
IB (mA)
b at IBZ100 mA
AlGaAs/GaAs HBT SiGe HBT InGaAs/InP HBT
95.70 278 302.6
100 100 100
25 51 40
Fig. 5. MAG vs frequency curves for (a) AlGaAs/GaAs HBT, (b) Si/SiGe HBT, (c) InGaAs/InP HBT.
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Si/SiGe, and InGaAs/InP HBTs, respectively. Si/SiGe HBTs show better noise performance than their AlGaAs/ GaAs and InGaAs/InP counterparts as seen from Fig. 6. NFmin is about 5 dB for the GaAs based device at its optimum bias for class A operation. It is about 1.5 dB for the SiGe based device and 2.735 dB for the InP based HBT for a wide range of VCE values. This advantage makes SiGe attractive for applications such as low noise amplifiers (LNAs), where minimum noise figure is the critical FOM. Another interesting point to emphasize for the AlGaAs/ GaAs and InGaAs/InP HBT is the hump seen in the NFmin curves at low VCE voltages. This is mainly due to the change of device’s operating region from saturation to forward active mode. 2.7. Discussion of simulation results
Fig. 6. NFmin vs VCE curve of (a) AlGaAs/GaAs HBT, (b) Si/SiGe HBT, (c) InGaAs/InP HBT.
Table 3 summarizes the fmax and b values for the corresponding devices at specific bias points. Also, MAG vs frequency curves are illustrated in Fig. 5. Again, IB is swept for MAG curves from 10 to 100 mA with 10 mA steps. 2.6. Minimum noise figure, NFmin vs bias Minimum noise figure, NFmin, is calculated at a specific frequency point (at 10 GHz in this work) for different values of IB. VCE is set to 2.9, 2.6 and 2.65 V for AlGaAs/GaAs,
A summary of simulation results is given in Table 4. From power perspective SiGe, GaAs and InP based devices shows slightly different DC power consumption and output power values at 10 GHz. InGaAs/InP HBT is the least power consuming one since its output current is smaller. Si/SiGe HBT maintains output power nearly twice as its counterparts and it is relatively more power efficient. Three of the devices are competitive and there is a comparable difference between them from power viewpoint. Nevertheless, GaAs is yet the stronger candidate for power applications due to large collector–base breakdown voltages. The characteristic frequencies ft and fmax depend on material properties, device model parameters, device geometry and bias. The difference between ft values of the two HBTs mainly stems from the material properties along with the transistor design leading to different model parameters. Optimized SiGe based HBTs show better (O200 GHz) characteristic frequency values when compared to traditional GaAs based HBTs. Nevertheless, speed related FOMs are comparable for the two material systems. InP based HBT is the most promising among them due to superior properties of InP material system. To conclude, ‘if speed is the case, InP will be the choice.’ The question of ‘Which is important: ft or fmax?’ does not have an unequivocal answer, but the commonly cited statement is that ft is more important for digital circuits, while for analog applications fmax is more significant. Manufacturers of RF transistors often strive for ftzfmax so that the devices are useful for a large number of different applications.
Table 4 Comparison of AlGaAs/GaAs HBT, Si/SiGe HBT and InGaAs/InP HBT for different FOMs Device
DC power consumption (mW)
Output power (mW)
ft (GHz)
fmax (GHz)
NFmin (dB)
AlGaAs/GaAs HBT Si/SiGe HBT InGaAs/InP HBT
8.347 12.47 6.394
3.022 5.753 2.835
95.70 278 302.6
151.7 134.6 416.6
5.026 1.748 2.735
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One more discussion point is the characteristic frequencies of Si/SiGe HBT. As provided in Table 4, ft value of SiGe based transistor is greater than its fmax. This may seem as a conflict to the recorded frequency values, where ft is smaller than fmax. However, it should be noted that a bipolar transistor designed and optimized for maximum ft can show relatively low fmax values. This brings the trade-off that the analyzed Si/SiGe HBT with its given parameters in this study may not be used as a power amplifier between the frequency range from fmax to ft. Another significant FOM difference between AlGaAs/ GaAs HBT, Si/SiGe HBT and InGaAs/InP HBT is their noise behavior. Unlike III–V HBTs, the noise figure of SiGe based HBTs are quite low at high frequencies. This is one of the most prominent features of SiGe. So, we can conclude that for low noise applications SiGe would be a better choice. Finally, considering the breakdown voltages SiGe based single HBTs’, BVCB values are relatively low due to their smaller band-gap of the collector material. This makes it more difficult to use them for high-power applications. However, this problem can be reduced by the double HBT approach since designing the collector–base junction as a heterojunction allows to use a wide band-gap material as the collector material leading to high-breakdown values.
3. Conclusion Three different heterojunction bipolar devices (AlGaAs/ GaAs HBT and SiGe HBT) are studied in this work. All of the simulations are performed in Agilent’s Advanced Design System environment. For the AlGaAs/GaAs HBT we used the HBT model of ADS, for the Si/SiGe device our simulations were based on the VBIC model and for the InGaAs/InP HBT we used the SGP model. There are several discussion points for a technology choice such as power related concepts, characteristic frequencies and noise behavior. The question of ‘which device is most suitable for RF circuit/systems applications’ is a rather complex situation and depends strongly on the application. However, the general tendency is to use SiGe based devices for low noise applications such as LNAs due to better noise behavior, GaAs based devices for high-power applications due to higher breakdown voltages and InP based devices for high-speed applications. This is mainly parallel to our study, where SiGe based device has the best noise performance as its NFmin is as low as 1.5 dB and InP based device has the highest ft and fmax of 302.6 and 416.6 GHz, respectively. However, when it comes to power concepts, SiGe device would not be a suitable choice because of its relatively low breakdown voltage (5 V). SiGe also has the advantage of low cost, high yield and integration potential, while GaAs is technologically more mature, where InP suffers from cost, integration and maturity problems.
907
Acknowledgements This work was performed in the context of the network TARGET—‘Top Amplifier Research Groups in a European Team’ and supported by the Information Society Technologies Programme of the EU under contract IST-1-507893NOE, www.target-org.net.
Appendix A. Model parameters The following parameters describe AlGaAs/GaAs HBT, Si/SiGe HBT and InP HBT model at room temperature. AlGaAs/GaAs HBT (after Ref. [11]) TNOMZ25, ISZ8.36!10K26, NFZ1, NRZ1, ISAZ 2.18!10K18, NAZ4.51, ISBZ1!1010, NBZ2, VAFZ 300, VARZ100, IKZ0.1, BFZ500, BRZ1000, ISEZ 2.7!10K18, NEZ1.8, ISEXZ4!10K24, NEXZ1.3, ISCZ1.2!10K14, NCZ2, ISCXZ5.2!10K14, NCXZ2, FAZ0.995, BVCZ28, NBCZ6, ICSZ1!10K30, NCSZ 2, REZ16, REXZ2000, RBXZ55, RBIZ20, RCXZ10, RCIZ20, CJEZ14 fF, VJEZ1.384, MJEZ0.5, CEMINZ 3 fF, FCEZ0.975, CJCZ8 fF, VJCZ1.077, MJCZ0.514, CCMINZ3 fF, FCZ0.8, CJCXZ7 fF, VJCXZ1.4, MJCXZ0.514, CXMINZ4 fF, XCJCZ1, CJSZ0.05 fF, VJSZ1.4, MJSZ0.01, TFBZ0.3 ps, TBEXSZ0.1 ps, TBCXSZ0, TFC0Z1 ps, ICRIT0Z12 mA, ITCZ6 mA, ITC2Z30 mA, VTCZ10, TKRKZ0.5 ps, VKRKZ10, IKRKZ12 mA, TRZ350 ps, TRXZ350 ps, FEXZ0.25, RTHZ2200 C/W, CTHZ3!10K10 C/J, KFNZ0, AFNZ 1.5, BFNZ1, XTIZ2, XTBZK2.8, TNEZ0, TNCZ0, TNEXZ0, EGZ1.645, EAAZK0.495, EABZK0.1, EAEZ0.105, EAEZ0.105, EABZ0, EAXZ0, XREZ 0.5, XREXZ0.5, XRBZ0.5, XRCZ0.5, TVJEZK1.5! 10K3, TVJCXZK1.5!10K3, TVJCIZK1.5!10K3 , TVJSZK1.5!10K3, XTITCZ0, XTITC2Z0, XTTFZ 0.75, XTTKRKZ0.6, XTVKRKZ0.6, XTIKRKZ0.6, XRTZ1.2, XRTZ1.2, DTMAXZ1000 Si/SiGe HBT (after Ref. [12]) ISZ4:10589!10K15, NFZ1.01, IBEIZ1.748!10K17, NEIZ1.0, WBEZ1, IBENZ1.5433!10K13, NENZ2, IBCIZ1.031!10K16, NCIZ1.02, IBCNZ1.4127!10K12, NCNZ1.5, IKFZ8.55!10K2, NRZ1.01, IKRZ0.35! 10K2, VEFZ45, VERZ39, RCIZ3.24, RCXZ0.24, RBXZ5.26, RSZ0.001, RBIZ10, RBPZ0.001, REZ1.1, CJEZ105!10K15, PEZ0.76, MEZ0.36, AJEZ0.5, CJEPZ76!1015, CJCZ3.0!1015, PCZ0.72, MCZ0.42, AJCZ0.5, GAMMZ2.5!1011, HRCFZ2, VOZ1, RTHZ 400, CTHZ10!1014, FCZ0.9, AVC2Z21.5, AVC1Z 6.515, TNOMZ300 ISZ5.2621!1015, QP0Z20.25!1014, ICHZ5.5036!102, HFEZ1.0, HFCZ1.0, HJEIZ1.0, HJCIZ1.0, IBEISZ3.65433!1017, MBEIZ1.0249, IREISZ1.4573!1013, MREIZ2.0, IBCISZ0.543!1016, MBCIZ1.057, IBCXSZ2.7!1020 , MBCXZ1.005, IBETSZ0, ABETZ40, FAVLZ1.0286, QAVLZ 11.1!105, ALFAVZ8.25!105, ALQAVZ1.96!104,
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RBI0Z25.01, RBXZ2.03, FGEOZ0.6557, FQIZ0.9055, REZ1.3470, RCXZ8.624, CJEI0Z105!1015, VDEIZ 0.75, ZEIZ0.35, ALJEIZ1.8, CJCI0Z79!1015, VDCIZ 0.71, ZCIZ0.38, VPTCIZ416, RCI0Z5.2, VLIMZ0.70, VCESZ0.05, VPTZ1, RTHZ400.0, CTHZ10.0!1014, TNOMZ300 InP HBT (after Ref. [13]) ISZ6!10K13, BFZ50, NFZ1, VAFZ12, IKFZ0, ISEZ6!10K40, NEZ1, BRZ3, NRZ1, VARZ100, ISCZ1!10K30, NCZ1, RBZ54, IRBZ0, RBMZ54, REZ10, RCZ0, CJEZ4 fF, VJEZ0.9, MJEZ0.5, CJCZ2.5 fF, VJCZ20, MJCZ0.01, XCJCZ0.5, CJSZ0, VJSZ0.75, MJSZ0.5, FCZ0.8, XTFZ0, TFZ0.44 ps, VTFZ0, ITFZ0, PTFZ43, TRZ1 ns, KFZ0, AfZ1, KBZ0, ABZ1, FBZ1, ISSZ0, NSZ1, NKZ0.5, FFEZ1, TNOMZ25, EGZ1.11, XTBZ0, XTIZ35.
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