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J. Semicond. > 2021, Volume 42?>?Issue 5?> 052401

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A complete small-signal HBT model including AC current crowding effect

Jinjing Huang and Jun Liu

+ Author Affiliations

 Corresponding author: Jun Liu, ljun77@hdu.edu.cn

DOI: 10.1088/1674-4926/42/5/052401

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Abstract: An improved small-signal equivalent circuit of HBT concerning the AC current crowding effect is proposed in this paper. AC current crowding effect is modeled as a parallel RC circuit composed of Cbi and Rbi, with distributed base-collector junction capacitance also taken into account. The intrinsic portion is taken as a whole and extracted directly from the measured S-parameters in the whole frequency range of operation without any special test structures. An HBT device with a 2 × 20 μm2 emitter-area under three different biases were used to demonstrate the extraction and verify the accuracy of the equivalent circuit.

Key words: small-signal model, HBT, AC current crowding effect



[1]
Zhang J, Liu M, Wang J, et al. Modeling of InP HBTs with an improved keysight HBT model. Microw J, 2019, 62(7), 56
[2]
Shivan T, Weimann N, Hossain M, et al. A highly efficient ultrawideband traveling-wave amplifier in InP DHBT technology. IEEE Microw Wirel Compon Lett, 2018, 28(11), 1029 doi: 10.1109/LMWC.2018.2871336
[3]
Griffith Z, Urteaga M, Rowell P. A 190-GHz high-gain, 3-dBm OP1dB low DC-power amplifier in 250-nm InP HBT. IEEE Microw Wirel Compon Lett, 2017, 27(12), 1128 doi: 10.1109/LMWC.2017.2764739
[4]
Lin Q, Wu H, Chen Y J, et al. A 0.5 to 4.0 GHz low-cost broadband GaAs HBT low noise amplifier. 2019 IEEE MTT-S International Wireless Symposium (IWS), 2019
[5]
Huang S C, Tang W B, Hsin Y M. High-frequency noise modeling of InGaP/GaAs HBT with base-contact capacitance and AC current crowding effect. IEEE Electron Device Lett, 2009, 30(11), 1125 doi: 10.1109/LED.2009.2031132
[6]
Yadav S, Chakravorty A, Schroter M. Modeling of the lateral emitter-current crowding effect in SiGe HBTs. IEEE Trans Electron Devices, 2016, 63(11), 4160 doi: 10.1109/TED.2016.2606652
[7]
Yapei C, Yong Z, Yuehang X, et al. Investigation of terahertz 3D EM simulation on device modeling and a new InP HBT dispersive inter-electrode impedance extraction method. IEEE Access, 2018, 6, 45772 doi: 10.1109/ACCESS.2018.2865929
[8]
Gloria, Daniel, Danneville, et al. Small-signal characterization and modelling of 55 nm SiGe BiCMOS HBT up to 325 GHz. Solid State Electron, 2017, 129, 150 doi: 10.1016/j.sse.2016.11.012
[9]
Sun Y, Fu J, Wang Y, et al. Direct analytical parameter extraction for SiGe HBTs T-topology small-signal equivalent circuit. Superlattices Microstruct, 2016, 94, 223 doi: 10.1016/j.spmi.2016.03.046
[10]
Rhee H S, Lee S, Kim B R. D. c. and a. c. current crowding effects model analysis in bipolar junction transistors using a new extraction method. Solid-State Electron, 1995, 38(1), 31 doi: 10.1016/0038-1101(94)E0062-J
[11]
Tang W B, Wang C M, Hsin Y M. A new extraction technique for the complete small-signal equivalent-circuit model of InGaP/GaAs HBT including base contact impedance and AC current crowding effect. IEEE Trans Microw Theory Tech, 2006, 54, 3641 doi: 10.1109/TMTT.2006.882411
[12]
Lee K, Choi K, Kook S H, et al. Direct parameter extraction of SiGeHBTs for the VBIC bipolar compact model. IEEE Trans Electron Devices, 2005, 52(3), 375 doi: 10.1109/TED.2005.843906
[13]
Dousset D, Issaoun A, Ghannouchi F M, et al. Wideband closed-form expressions for direct extraction of HBT small-signal parameters for all amplifier bias classes. IEEE Proceedings - Circuits, Devices and Systems, 2005, 152(5), 441 doi: 10.1049/ip-cds:20045077
[14]
Johansen T K, Leblanc R, Poulain J, et al. Direct extraction of InP/GaAsSb/InP DHBT equivalent-circuit elements from S-parameters measured at cut-off and normal bias conditions. IEEE Trans Microw Theory Tech, 2016, 64(1), 115 doi: 10.1109/TMTT.2015.2503769
[15]
Zhang J C, Liu B, Zhang L M, et al. A rigorous peeling algorithm for diret parameter extraction procedure of HBT small-signal equivalent circuit. Analog Integr Circuits Signal Process, 2015, 85(3), 405 doi: 10.1007/s10470-015-0586-z
[16]
Bousnina S, Mandeville P, Kouki A B, et al. Direct parameter-extraction method for HBT small-signal model. IEEE Trans Microw Theory Tech, 2002, 50(2), 529 doi: 10.1109/22.982232
[17]
Degachi L, Ghannouchi F M. Systematic and rigorous extraction method of HBT small-signal model parameters. IEEE Trans Microw Theory Tech, 2006, 54(2), 682 doi: 10.1109/TMTT.2005.862661
[18]
Degachi L, Ghannouchi F M. An augmented small-signal HBT model with its analytical based parameter extraction technique. IEEE Trans Electron Devices, 2008, 55(4), 968 doi: 10.1109/TED.2008.917539
[19]
Zhou W, Sun L, Liu J, et al. Extraction and verification of the small-signal model for InP DHBTs in the 0.2–325 GHz frequency range. ICE Electron Express, 2018, 15(13), 20180244 doi: 10.1587/elex.15.20180244
[20]
Zhang A, Gao J, Wang H. Direct parameter extraction method for InP heterojunction bipolar transistors based on the combination of T- and π-models up to 110 GHz. Semicond Sci Technol, 2019, 35(2), 025001 doi: 10.1088/1361-6641/ab5917
[21]
Zhang A, Gao J. A direct extraction method to determine the extrinsic resistances for InP HBT device based on S-parameters measurement up to 110 GHz. Semicond Sci Technol, 2020, 35(7), 075025 doi: 10.1088/1361-6641/ab8b1e
Fig. 1.  Complete small-signal equivalent circuit of HBT device including ${C_{{\rm{bi}}}} $. $ {{{g}}_{\rm{m}}}{\rm{ = }}{g_{{\rm{m0}}}}{{\rm{e}}^{-j\omega \tau }}$.

Fig. 2.  Small-signal equivalent circuit after de-embedding the extrinsic parameters.

Fig. 3.  Final circuit after T-π transformation.

Fig. 4.  Frequency of F0 versus ω2.

Fig. 5.  S-parameters comparisons in the frequency range from 100 MHz to 20 GHz under the biasing condition: (a) Bias1 (Vce = 1 V, Ib = 15 μA), (b) Bias2 (Vce = 1 V, Ib = 30 μA), (c) Bias3 (Vce = 3 V, Ib = 17.5 μA).

Fig. 6.  (a) Plot of Cbi versus Ib. (b) Plot of Cbi versus Vce.

Table 1.   The initial extraction and optimization results of the HBT under Bias1 (Vce = 1 V, Ib = 15 μA) and Bias3 (Vce = 3 V, Ib = 17.5 μA). Error = |Extracted – Optimized| / Extracted × 100%.

ParameterExtractedOptimizedError (%)
Rbx (Ω) Bias1 6.897 7.723 11.98
Bias3 6.897 8.65 25.42
Rcx (Ω) Bias1 1.281 1.591 24.20
Bias3 1.281 1.271 0.781
Rci (Ω) Bias1 1.281 0.970 24.28
Bias3 1.281 0.961 24.98
Re (Ω) Bias1 6.526 5.289 18.95
Bias3 6.526 8.417 28.98
Rbcx (kΩ) Bias1 239.9 246.1 2.584
Bias3 571.6 569.3 0.402
Cbcx (fF) Bias1 34.92 34.82 0.286
Bias3 30.32 28.58 5.739
Rbex (kΩ) Bias1 2.093 5.500 162.8
Bias3 1.590 2.621 64.84
Cbex (fF) Bias1 208.5 127.6 38.80
Bias3 639.5 208.6 67.38
Rbi (Ω) Bias1 306.7 309.0 0.750
Bias3 627.9 541.4 13.78
Cbi (pF) Bias1 2.058 2.033 1.215
Bias3 1.271 1.203 5.350
Rbci (kΩ) Bias1 140.4 139.1 0.926
Bias3 271.5 296.8 9.319
Cbci (fF) Bias1 1.764 1.773 0.510
Bias3 1.069 1.088 1.777
Rbei (Ω) Bias1 2.093 1.490 28.81
Bias3 1.590 0.553 65.22
Cbei (fF) Bias1 208.5 289.9 39.04
Bias3 639.5 1,049 64.03
Ro (kΩ) Bias1 12.54 12.84 2.390
Bias3 6.666 5.244 21.33
Co (fF) Bias1 23.48 20.43 12.99
Bias3 17.61 17.63 0.114
gm0 (mS) Bias1 79.77 80.03 0.326
Bias3 227.5 227.9 0.176
τ (ps) Bias1 2.317 2.821 21.75
Bias3 2.834 3.179 12.17
DownLoad: CSV

Table 2.   The accuracy of S-parameters versus frequency.

BiasS-parameterWithout Cbi (%)With Cbi (%)
Bias1S1185.1389.31
S1291.7894.65
S2188.3792.63
S2297.0698.39
Bias2S1191.6291.68
S1295.0695.86
S2192.3593.44
S2297.7098.21
Bias3S1191.1692.51
S1293.4996.71
S2193.1793.82
S2296.3899.12
DownLoad: CSV
[1]
Zhang J, Liu M, Wang J, et al. Modeling of InP HBTs with an improved keysight HBT model. Microw J, 2019, 62(7), 56
[2]
Shivan T, Weimann N, Hossain M, et al. A highly efficient ultrawideband traveling-wave amplifier in InP DHBT technology. IEEE Microw Wirel Compon Lett, 2018, 28(11), 1029 doi: 10.1109/LMWC.2018.2871336
[3]
Griffith Z, Urteaga M, Rowell P. A 190-GHz high-gain, 3-dBm OP1dB low DC-power amplifier in 250-nm InP HBT. IEEE Microw Wirel Compon Lett, 2017, 27(12), 1128 doi: 10.1109/LMWC.2017.2764739
[4]
Lin Q, Wu H, Chen Y J, et al. A 0.5 to 4.0 GHz low-cost broadband GaAs HBT low noise amplifier. 2019 IEEE MTT-S International Wireless Symposium (IWS), 2019
[5]
Huang S C, Tang W B, Hsin Y M. High-frequency noise modeling of InGaP/GaAs HBT with base-contact capacitance and AC current crowding effect. IEEE Electron Device Lett, 2009, 30(11), 1125 doi: 10.1109/LED.2009.2031132
[6]
Yadav S, Chakravorty A, Schroter M. Modeling of the lateral emitter-current crowding effect in SiGe HBTs. IEEE Trans Electron Devices, 2016, 63(11), 4160 doi: 10.1109/TED.2016.2606652
[7]
Yapei C, Yong Z, Yuehang X, et al. Investigation of terahertz 3D EM simulation on device modeling and a new InP HBT dispersive inter-electrode impedance extraction method. IEEE Access, 2018, 6, 45772 doi: 10.1109/ACCESS.2018.2865929
[8]
Gloria, Daniel, Danneville, et al. Small-signal characterization and modelling of 55 nm SiGe BiCMOS HBT up to 325 GHz. Solid State Electron, 2017, 129, 150 doi: 10.1016/j.sse.2016.11.012
[9]
Sun Y, Fu J, Wang Y, et al. Direct analytical parameter extraction for SiGe HBTs T-topology small-signal equivalent circuit. Superlattices Microstruct, 2016, 94, 223 doi: 10.1016/j.spmi.2016.03.046
[10]
Rhee H S, Lee S, Kim B R. D. c. and a. c. current crowding effects model analysis in bipolar junction transistors using a new extraction method. Solid-State Electron, 1995, 38(1), 31 doi: 10.1016/0038-1101(94)E0062-J
[11]
Tang W B, Wang C M, Hsin Y M. A new extraction technique for the complete small-signal equivalent-circuit model of InGaP/GaAs HBT including base contact impedance and AC current crowding effect. IEEE Trans Microw Theory Tech, 2006, 54, 3641 doi: 10.1109/TMTT.2006.882411
[12]
Lee K, Choi K, Kook S H, et al. Direct parameter extraction of SiGeHBTs for the VBIC bipolar compact model. IEEE Trans Electron Devices, 2005, 52(3), 375 doi: 10.1109/TED.2005.843906
[13]
Dousset D, Issaoun A, Ghannouchi F M, et al. Wideband closed-form expressions for direct extraction of HBT small-signal parameters for all amplifier bias classes. IEEE Proceedings - Circuits, Devices and Systems, 2005, 152(5), 441 doi: 10.1049/ip-cds:20045077
[14]
Johansen T K, Leblanc R, Poulain J, et al. Direct extraction of InP/GaAsSb/InP DHBT equivalent-circuit elements from S-parameters measured at cut-off and normal bias conditions. IEEE Trans Microw Theory Tech, 2016, 64(1), 115 doi: 10.1109/TMTT.2015.2503769
[15]
Zhang J C, Liu B, Zhang L M, et al. A rigorous peeling algorithm for diret parameter extraction procedure of HBT small-signal equivalent circuit. Analog Integr Circuits Signal Process, 2015, 85(3), 405 doi: 10.1007/s10470-015-0586-z
[16]
Bousnina S, Mandeville P, Kouki A B, et al. Direct parameter-extraction method for HBT small-signal model. IEEE Trans Microw Theory Tech, 2002, 50(2), 529 doi: 10.1109/22.982232
[17]
Degachi L, Ghannouchi F M. Systematic and rigorous extraction method of HBT small-signal model parameters. IEEE Trans Microw Theory Tech, 2006, 54(2), 682 doi: 10.1109/TMTT.2005.862661
[18]
Degachi L, Ghannouchi F M. An augmented small-signal HBT model with its analytical based parameter extraction technique. IEEE Trans Electron Devices, 2008, 55(4), 968 doi: 10.1109/TED.2008.917539
[19]
Zhou W, Sun L, Liu J, et al. Extraction and verification of the small-signal model for InP DHBTs in the 0.2–325 GHz frequency range. ICE Electron Express, 2018, 15(13), 20180244 doi: 10.1587/elex.15.20180244
[20]
Zhang A, Gao J, Wang H. Direct parameter extraction method for InP heterojunction bipolar transistors based on the combination of T- and π-models up to 110 GHz. Semicond Sci Technol, 2019, 35(2), 025001 doi: 10.1088/1361-6641/ab5917
[21]
Zhang A, Gao J. A direct extraction method to determine the extrinsic resistances for InP HBT device based on S-parameters measurement up to 110 GHz. Semicond Sci Technol, 2020, 35(7), 075025 doi: 10.1088/1361-6641/ab8b1e

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    Received: 27 August 2020 Revised: 08 January 2021 Online: Accepted Manuscript: 08 March 2021Uncorrected proof: 09 March 2021Published: 01 May 2021

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      Jinjing Huang, Jun Liu. A complete small-signal HBT model including AC current crowding effect[J]. Journal of Semiconductors, 2021, 42(5): 052401. doi: 10.1088/1674-4926/42/5/052401 ****J J Huang, J Liu, A complete small-signal HBT model including AC current crowding effect[J]. J. Semicond., 2021, 42(5): 052401. doi: 10.1088/1674-4926/42/5/052401.
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      Jinjing Huang, Jun Liu. A complete small-signal HBT model including AC current crowding effect[J]. Journal of Semiconductors, 2021, 42(5): 052401. doi: 10.1088/1674-4926/42/5/052401 ****
      J J Huang, J Liu, A complete small-signal HBT model including AC current crowding effect[J]. J. Semicond., 2021, 42(5): 052401. doi: 10.1088/1674-4926/42/5/052401.

      A complete small-signal HBT model including AC current crowding effect

      DOI: 10.1088/1674-4926/42/5/052401

      • Key Laboratory of RF Circuits and Systems, Ministry of Education, Hangzhou Dianzi University, Hangzhou 310018, China

      More Information
      • Jinjing Huang：is a MS student in Key Laboratory of RF Circuits and Systems in Hangzhou Dianzi University. She obtained her BS from Hangzhou Dianzi University in 2018. She focuses on the modeling of semiconductor devices
      • Jun Liu：received his master's degree from Hangzhou Dianzi University in 2006 and his doctor's degree from Dublin City University in 2011. He is now a professor at the School of Electronic Information, Hangzhou Dianzi University. His main research interest includes device equivalent circuit modeling, RF/MMIC design, CAD/EDA tool development
      • Corresponding author: ljun77@hdu.edu.cn
      • Received Date: 2020-08-27
      • Revised Date: 2021-01-08
      • Published Date: 2021-05-10

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