2216 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 48, NO. 10, OCTOBER 2001 Comparative Study of Electron Transit Times Evaluated by DD, HD, and MC Device Simulation for a SiGe HBT Christoph Jungemann, Member, IEEE, Burkhard Neinhüs, and Bernd Meinerzhagen, Member, IEEE Abstract—Transit times of a silicon/germanium heterojunc- tion bipolar transistor (HBT) with a base width of 24 nm are investigated in the quasi–stationary limit for the first time by consistent drift-diffusion (DD), hydrodynamic (HD), and fullband Monte Carlo (MC) simulations. The quasi-ballistic transport in the base and collector leading to a strong velocity overshoot is well described by the HD model and corresponding transit times are in good agreement with the MC results. On the other hand, the DD model fails in this region and substantially overestimates the base transit time bearing the possibility of wrong guidelines for transistor design optimization. However, since the base transit time is no longer dominating the cutoff frequency of high-speed HBTs, the failure of the DD model leads to an underestimation of the peak cutoff frequency by only 10%. Close to high injection differences in the emitter transit times of the HD and MC model are observed which are mainly related to small differences in the Gummel plot. Index Terms—Bipolar transistor, cutoff frequency, device simu- lation, silicon. I. INTRODUCTION T HE silicon/germanium (SiGe) alloy has made bandgap–engineering possible based on more or less mainstream Si technologies retaining the cost advantage of Si over III/V materials [1], [2]. SiGe heterojunction bipolar tran- sistors (HBT) have been fabricated with a maximum oscillation frequency in the excess of 100 GHz [3], [4]. Due to the small base widths of less than 50 nm, the electron transport becomes more and more ballistic. This calls into question the validity of the standard simulation tools like the drift-diffusion (DD) or hydrodynamic (HD) model used to design high-frequency HBTs. In addition, the strain caused by the pseudomorphic growth of the epilayers results in a strong anisotropy of the band structure only captured in full detail by the fullband Monte Carlo (MC) model. In this paper, the impact of the quasi-ballistic transport and the anisotropic band structure on the accuracy of the DD and HD models are investigated by a comparison with the more accurate MC model for transit times and cutoff frequencies of an HBT. First, the simulation details, and then results for the HBT are presented. Manuscript received February 27, 2001; revised June 25, 2001. This work was supported in part by the Bundesministerium für Bildung, Wissenschaft, Forschung und Technologie under Contract 01M2416A. The review of this paper was arranged by Joachim Burghartz. The authors are with the University of Bremen, 28334 Bremen, Germany (e-mail: junge@item.uni-bremen.de). Publisher Item Identifier S 0018-9383(01)08357-5. II. THEORY The details of the MC model can be found in [5]. The band structure is calculated with the nonlocal empirical-pseudopoten- tial method [6]. The conduction and valence band edge are mod- eled similar to [1], [7], [19] and are the same for all three models. Apparent bandgap narrowing due to heavy doping is included as described in [8]. Further details of the DD and HD models are given in [9], [10]. All transport parameters of the DD and HD models are generated by MC bulk simulations to ensure consis- tency of the simulation models. The heat flux of the HD model is reduced to 25% compared to [9] as described in [11]. Using the three simulation models, transit times are evaluated for an HBT. In order to reduce the CPU time of the MC simu- lations, a one-dimensional (1-D)-device approximation is used. The missing base contact is simulated by setting the quasi-fermi potential of the holes in the center of the base to the value of the base voltage. The 1-D-device approximation works well as long as the device is not operated too far in the high-injection regime. In addition, generation/recombination processes are neglected, because they are difficult to include into an MC simulation. In the case of the MC model, no holes are simulated and their con- tribution to the space charge is calculated based on the DD hole quasi-fermi potential in conjunction with a nonlinear Poisson equation. These restrictions make it difficult to compare the re- sults to experimental data, but this is not the objective of this paper, which is the investigation of the approximations inherent to the DD and HD models by comparison with the more fun- damental MC model. Thus, a high degree of consistency of the models is more important here than a comparison with experi- ments. In the case of an 1-D-device approximation, the electron transit time for a region extending from to reads [12] (1) where electron charge; electron density; collector current per device area; collector/emitter voltage. The derivative is calculated by varying the base/emitter voltage. The total transit time is inversely proportional to the common emitter cutoff frequency: , where is the device length. The transit time and cutoff frequency are calcu- lated in the quasi–stationary approximation in accordance with 0018–9383/01$10.00 © 2001 IEEE