Christoph Jungemann

Hierarchical 2-D DD and HD noise simulations of Si and SiGe devices II. Results

For pt. I see ibid., vol. 49, pp. 1250-1257 (2002). Terminal current noise is investigated with Langevin-type drift-diffusion (DD) and hydrodynamic (HD) noise models for one-dimensional (1-D) N/sup +/ NN/sup +/ and P/sup +/ PP/sup +/ structures and a realistic two-dimensional (2-D) SiGe NPN HBT. The new noise models, which are suitable for technology computer aided design (TCAD), are validated by comparison with Monte Carlo (MC) device simulations for the 1-D structures including noise due to particle scattering and generation of secondary particles by impact ionization (II). It is shown that the accuracy of the usual approach based on the DD model in conjunction with the Einstein relation degrades under nonequilibrium conditions. 2-D MC noise simulations are found to be feasible only if the current correlation functions decay on a subpicosecond scale, what is not always the case.

Comparative study of electron transit times evaluated by DD, HD, and MC device simulation for a SiGe HBT

Transit times of a silicon/germanium heterojunction 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.

Analysis of the stochastic error of stationary Monte Carlo device simulations

Without proper analysis of the stochastic error, it is not possible to assess the accuracy or efficiency of Monte Carlo device simulations, and misleading results might be obtained. This is demonstrated for the so-called variance-minimizing estimator for the steady-state terminal currents which turns out to be not more efficient than a standard estimator. Self-consistent (with respect to the electric field) and non self-consistent device simulations are analyzed. In contrast to previously published results both methods have the same efficiency with respect to terminal currents, but in the case of internal distributions, like the particle density, self-consistent simulations are much more efficient. In addition, it is shown that non self-consistency increases the relaxation times of fluctuations by orders of magnitude necessitating extremely long simulation times. The efficiency of statistical enhancement is found to be degraded by strong interparticle correlation due to particle splitting.

On the applicability of nonself-consistent Monte Carlo device simulations

Recently, nonself-consistent (with respect to the electric field) Monte Carlo (NSC-MC) simulations have been proposed for the estimation of the noise and expected value of stationary terminal currents without examining the accuracy of the NSC approximation for these kinds of simulations. Comparison with self-consistent (SC) simulations reveals that NSC simulations of quantities like the drain current of a MOSFET or collector current of a BJT tend to reproduce the results of the momentum-based model used to calculate the electric field without improving the accuracy. In case of terminal current noise it is found that under nonequilibrium conditions the NSC results can substantially overestimate the SC results.

Hall factors of Si NMOS inversion layers for MAGFET modeling

Hall factors of Si NMOS inversion layers for the modeling of CMOS MAGFETs are given for a wide range of effective fields, temperatures and doping concentrations. The Hall factors are simulated with a microscopic transport model of the quasi-two-dimensional electron gas (2DEG). The model is verified by measured data of different MOS Hall plates.

Hierarchical 2D RF noise simulation of Si and SiGe devices by Langevin-type DD and, HD models based on MC generated noise parameters

2D RF noise models based on Langevin-type drift-diffusion (DD) and hydrodynamic (HD) models for Si and SiGe devices are presented, where all transport and noise parameters are generated by full-band Monte Carlo (MC) bulk simulations. The DD and HD model are validated by comparison with MC device simulations. It is shown that the usual approach based on the DD model in conjunction with the Einstein relation fails under nonequilibrium conditions. Considering the full-band structure a remarkably strong dependence of noise on crystal orientation is found.

Stochastic Properties of Monte-Carlo Device Simulations

The relative stochastic error of a quantity evaluated by stationary MC simulation is proportional to its variance, which can be evaluated with the corresponding autocorrelation function (cf. Sec. 3.4).

Full-band Monte Carlo device simulation of a Si/SiGe-HBT with a realistic Ge profile

In this paper we present full-band Monte Carlo simulations of an advanced Silicon/Silicon-Germanium Heterojunction Bipolar Transistor. In addition to this 2D MC simulations we performed simulations with a 1D MC model and a hydrodynamic model. For main internal distributions good consistency is found. We conclude with a microscopic investigation of the full-band Monte Carlo results.

MC simulation of strained Si/SiGe devices

Transport in strained Si N- and PMOSFETs with gate lengths from 250 to 50 nm is investigated by full-band MC (Monte Carlo) device simulation. Performance improvement by strain is found for both device types, and even for the shortest gate length the on-current is enhanced by about 30% compared to the unstrained case. Thus, these simulations predict that the performance advantage of strained Si MOSFETs will scale well into the deca-nanometer gate length range. This seems to be due to the reduction in scattering by strain, leading to quasi-ballistic transport and enhanced charge carrier velocities at the source side injection point of the inversion channel.

Accuracy assessment of compact RF noise models for SiGe HBTs by hydrodynamic device simulation

The accuracy of the SPICE and unified compact noise models is assessed in the RF range by comparison with the hydrodynamic device model for a state-of-the-art SiGe HBT with a low base resistance. Despite the low base resistance, as a general result, it turns out that the noise is dominated by the thermal fluctuations of the holes within the base and the exact determination of the base noise resistance is a prerequisite for accurate compact noise modeling. It is shown that the base noise resistance equals the base resistance and can be evaluated with standard parameter extraction schemes. Based on an accurate base resistance the SPICE model yields good results as long as the frequency is considerably below the peak cutoff frequency. The unified model, on the other hand, is found to yield good results even at frequencies comparable to the peak cutoff frequency. But this is achieved at the expense of an additional parameter which is difficult to determine without physics-based numerical noise simulation. Moreover, it is shown that the drift-diffusion model should not be used to assess the accuracy of compact noise models, because it yields erroneous noise results for state-of-the-art SiGe HBTs.