IEEE Transactions on Electron Devices, Vol. 41, No. 4, pp. 484-490, April 1994.

(Manuscript received August 7, 1993; revised November 19, 1993)

Copyright Notice

© 1994 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.

Steady-state electron transport in graded-base heterojunction bipolar transistors is investigated using a regional ensemble Monte Carlo approach. Besides the graded band and scattering parameters already incorporated in the particle model, emitter-base and collector-base junctions are also considered in the boundary conditions for carrier injection/absorption. It is shown that optimum base transit times are directly related to the maximum average velocities, which occur at different base width-composition combinations. It also illustrates a general approach to studying electron transport in graded-band devices.

• [1] H. Kroemer, "Heterostructure bipolar transistors: What should we build?" J. Vac. Sci. Technol., vol. B1, pp. 126-130, 1983.
• [2] D. L. Miller, R. M. Asbeck, R. J. Anderson, and F. H. Eisen, "GaAlAs/GaAs heterojunction bipolar transistors with graded composition in the base," Electron. Lett., vol. 19, pp. 367-386, 1983.
• [3] J. R. Hayes, F. Capasso, A. C. Gossard, R. J. Malik, and W. Wiegmann, "Bipolar trnasistor with graded band-gap base," Electron. Lett., vol. 19, pp. 410-411, 1983.
• [4] R. J. Malik, F. Capasso, R. A. Stall, R. A. Kiehl, R. W. Ryan, R. Wunder, and C. G. Bethea, "High-gain, high-frequency AlGaAs/GaAs graded band-gap base bipolar transistors with a Be diffusion setback layer in the base," Appl. Phys. Lett., vol. 46, pp. 600-602, 1985.
• [5] M. Kurata and J. Yoshida, "Modeling and characterization for high-speed GaAlAs-GaAs n-p-n heterojunction bipolar transistors," IEEE Trans. Electron Devices, vol. ED-31, pp. 467-473, July 1984.
• [6] K. Tomizawa, Y. Awano, and H. Hashizume, "Monte Carlo simulation of AlGaAs/GaAs heterojunction bipolar transistors," IEEE Electron Device Lett., vol. EDL-5, pp. 362-364, 1984.
• [7] C. M. Maziar, M. E. Klausmeier-Brown, S. Bandyopadhyay, M. S. Lundstrom, and S. Datta, "Monte Carlo evaluation of electron trnasport in heterojunction bipolar transistor base structures," IEEE Trans. Electron Devices, vol. 33, pp. 881-888, July 1986.
• [8] M. A. "Osman, "Minority electron transport across p+ doped submicron layer of GaAs," J. Appl. Phys., vol. 71, pp. 308-313, 1992.
• [9] R. Katoh and M. Kurata, "Self-consistent particle simulation for (AlGa)As/GaAs HBT's under high bias conditions," IEEE Trans. Electron Devices, vol. 36, pp. 2122-2128, 1989.
• [10] J. Hu, K. Tomizawa, and D. Pavlidis, "Transient Monte Carlo analysis and application to heterojunction bipolar transistor switching," IEEE Trans. Electron Devices, vol. 36, ppl. 2138-2145, 1989.
• [11] J. Hu, D. Pavlidis, and K. Tomizawa, "Monte Carlo studies of the effect of emitter junction grading on the electron transport in "InAlAs/InGaAs heterojunction bipolar transistors," IEEE Trans. Electron Devices, vol. 39, pp. 1273-1281, 1992.
• [12] H.-F. Chau, J. Hu, D. Pavlidis, and K. Tomizawa, "Breakdown-speed considerations in AlGaAs/GaAs heterojunction bipolar transistors with special collector designs," IEEE Trans. Electron Devices, vol. 39, pp. 2711-2719, 1992.
• [13] R. Katoh and M. Kurata, "A model-based comparison of AlInAs/GaInAs and InP/GaInAs HBT's: A Monte Carlo study," IEEE Trans. Electron Devices, vol. 37, pp. 1245-1252, 1990.
• [14] X. Zhou, "Electron transport in grade-band devices: Interplay of field, composition, and length dependencies," to be published in Solid-State Electron..
• [15] A. K. Saxena, "The conduction band structure and deep levels in Ga_1-xAl_xAs alloys from a high-pressure experiment," J. Phys. C, vol. 13, pp. 4323-4334, 1980.
• [16] S. Adachi, GaAs, AlAs, and Ga_1-xAl_xAs: Material parameters for use in research and device applications," J. Appl. Phys., vol. 40, pp. R1-R29, 1985.
• [17] M. A. Littlejohn, J. R. Hauser, and T. H. Glisson, "Velocity-field characteristics of GaAs with G₆^c-L₆^c-X₆^c conduction-band ordering," J. Appl. Phys., vol. 48, pp. 4587-4590, 1977.
• [18] M. E. Klausmeier-Brown, "Monte Carlo studies of electron transport in III-V semiconductor heterostructures," M.S. Thesis, Purdue Univ., 1986.
• [19] H. C. Casey, Jr. and M. B. Panish, Heterostructure Lasers, New York: Academic, 1978, chap. 4.
• [20] X. Zhou, T. Y. Hsiang, and R. J. D. Miller, "Monte Carlo study of photogenerated carrier transport in GaAs surface space-charge fields," J. Appl. Phys., vol. 66, pp. 3066-3073, 1989.
• [21] X. Zhou, "Ensemble Monte Carlo modeling of high-field transport and ultrafast phemonena in compound semiconductors," Ph.D. thesis, Univ. Rochester, 1990.
• [22] W. Fawcett, D. A. Boardman, and S. Swain, "Monte Carlo determination of electron transport properties in gallium arsenide," J. Phys. Chem. Solids, vol. 31, pp. 1963-1990, 1970.
• [23] J. G. Ruch and W. Fawcett, "Temperature dependence of the transport properties of gallium arsenide determined by a Monte Carlo method," J. Appl. Phys., vol. 41, pp,. 3843-3829, 1970.
• [24] X. Zhou and T. Y. Hsiang, "Monte Carlo determination of femtosecond dynamics of hot-carrier relaxation and scattering processes in bulk GaAs," J. Appl. Phys., vol. 67, pp. 7399-7403, 1990.
• [25] M. A. Littlejohn, J. R. Hauser, T. H. Glisson, D. K. Ferry, and J. W. Harrison, "Alloy scattering and high field transport in ternary and quaternary III-V semiconductors," Solid-State Electron., vol. 21, pp. 107-114, 1978.
• [26] A. G. Milnes, "Heterojunctions" Some knowns and unknowns," Solid-State Electron., vol. 30, pp. 1099-1105, 1987.
• [27] H. Unlu and A. Nussbaum, "A review of models for heterojunction band offset," Solid-State Electron., vol. 30, pp. 1095-1098, 1987.
• [28] K. Taira, C. Takano, H. Kawai, and M. "Arai, "Band offset effect on transport in Al_xGa_1-xAs/GaAs heterojunction bipolar transistors grown by metalorganic chemical vapor deposition," IEEE Trans. Electron Devices, vol. 34, pp. 2040-2042, 1987.
• [29] C. M. Maziar and M. S. Lundstrom, "On the estimation of base transit time in AlGaAs/GaAs bipolar transistors," IEEE Electron Device Lett., vol. 8, pp. 90-92, 1987.
• [30] X. Zhou, "Monte Carlo calculation of base transit times in ballistic-base versus graded-base HBT's," Proc. 5th Int. Symp. IC Technology Sys. & Appl. (ISIC-93), Singapore, 1993, pp. 717-721.
• [31] J. Weng, "Transit time of fast bipolar transistors at high collector-current densities," Solid-State Electron., vol. 35, pp. 599-610, 1992.
• [32] K. Suzuki, "Analytical base transit time model of uniformly-doped-base bipolar transistors for high-injection regions," Solid-State Electron., vol. 36, pp. 109-110, 1993.
• [33] W. Liu, D. Costa, and J. S. Harris, Jr., "Derivation of the emitter-collector transit time of heterojunction bipolar transistors," Solid-State Electron., vol. 35, pp. 541-545, 1992.
• [34] W. Liu, D. Costa, and J. S. Harris, Jr., "Current gain of graded AlGaAs/GaAs heterojunction bipolar transistors with and without a base quasi-electric field," IEEE Trans. Electron Devices, vol. 39, pp. 2422-2429, 1992.
• [35] A. A. "Grinberg and S. Luryi, "On the therminonic-diffusion theory of minority transport in heterostructure bipolar transistors," IEEE Trans. Electron Devices, vol. 40, pp. 8590866, 1993.
• [36] Z. Yu and R. W. Dutton, "SEDAN III--A generalized electronic material device analysis program," Tech. Rep., Stanford Electronics Lab., Stanford, CA, 1985.
• [37] Q. M. Zhang, G. L. Tan, J. M. Xu, and D. J. Day, "Current gain and transit-time effects in HBT's with graded emitter and base regions," IEEE Elecron Device Lett., vol 11, pp. 508-510, 1990.
• [38] Q. M. Zhang, G. L. Tan, W. T. Moore, and J. M. Xu, "Effects of displaced p-n junction of heterojunction bipolar transistors," IEEE Trans. Electron Devices, vol. 39, pp. 2430-2437, 1992.
• [39] S. E. Laux and W. Lee, "Collector signal delay in the presence of velocity overshoot," IEEE Electron Device Lett., vol. 11, pp. 174-176, 1990.
• [40] F. Berz, "Diffusion near an absorbing boundary," Solid-State Electron., vol. 17, pp. 1245-1255, 1974.
• [41] F. Berz, "The Bethe condition for thermionic emission near an absorbing boundary," Solid-State Electron., vol. 28, pp. 1007-1013, 1985.

1. [10] X. Zhou, "Electron transport in graded-band devices: Interplay of field, composition and length dependencies," Solid-State Electron., Vol. 37, No. 11, pp. 1888-1890, Nov. 1994.
2. [1] X. Zhou and H. S. Tan, "Monte Carlo formulation of field-dependent mobility for Al_xGa_1-xAs," Solid-State Electron., Vol. 38, No. 6, pp. 1264-1266, June 1995.
3. [9] T. Kumar, M. Cahay, S. Shi, and K. Roenker, and W. E. Stanchina, "Limit of validity of the thermionic-field-emission treatment of electron injection across emitter-base junctions in abrupt heterojunction bipolar transistors," J. Appl. Phys., vol. 77, no. 11, pp. 5786-5792, June 1995. 
4. [3] T. Kumar, M. Cahay, S. Shi, and K. Roenker, "Influence of quantum-mechan!cal reflection at the emitter-base spike on the base transit time through abrupt heterojunction bipolar transistors," J. Appl. Phys., vol. 78, no. 11, pp. 6814-6817, Dec. 1995. 
5. [9] T. Kumar, M. Cahay, and K. Roenker, "Trends in the emitter-base bias dependence of the average base transit time through abrupt heterojunction bipolar transistors," J. Appl. Phys., vol. 80, no. 9, pp. 5478-5482 Nov. 1996. 
6. [15] O. Qasaimeh and Y. Zebda, "Effect of bandgap discontinuity on the cut-off frequency, base transit time and junction capacitance of npn AlGaAs/GaAs heterojunction bipolar transistors," Int. J. Electron., vol. 84, no. 1, pp. 25-35, Jan. 1998. 
7. [12] A. Agrawal, A. Goswami, S. Sen, and R. S. Gupta, "Current-voltage characteristics and field distribution of pseudomorphic (AlGaAs/InGaAs) modulation-doped field-effect transistor for microwave circuit applications," Microwave Opt. Technol. Lett., vol. 24, no. 6, pp. 407-412, Mar. 2000. 
8. K. Y. Xu, X. F. Lu, G. Wang, and A. M. Song, "Strong spatial dependence of electron velocity, density, and intervalley scattering in an asymmetric nanodevice in the nonlinear transport regime," IEEE Trans. Nanotech., vol. 7, no. 4, pp. 451-457, Jul. 2008.

IEEE Citation
IEL Citation