Non-stationary transport models and their application in gallium arsenide MESFETs.

摘要

The study of carrier transport in semiconductors requires solving the Boltzmann transport equation which yields a distribution function that describes the relevant transport properties of carriers. Based on the distribution function, macroscopic transport models can be extracted to take into account non-stationary phenomena which become important at short time scales and small spatial dimensions. By coupling a macroscopic transport model with other relevant equations, a device simulator is realized which allows the study of the terminal behavior of devices. With appropriate, physically motivated assumptions, a CAD-oriented device simulator can be developed which is computationally efficient and physically accurate.;The Boltzmann transport equation is solved for GaAs using a path integral method originally proposed by Rees. In order to simulate high field phenomena, a multi-valley, parabolic band model is assumed. An iterative scheme is implemented to obtain true transient behavior. Transient simulations are performed to reveal non-stationary transport in the time domain. The iterative scheme is simulated to steady-state in order to obtain steady-state transport parameters. Steady-state results in each valley are also obtained from the transient Boltzmann solver. Results obtained from the path integral method are in excellent agreement with results from Monte Carlo simulations. However, unlike the Monte Carlo method, in which it is difficult to tabulate the distribution function, the path integral method yields the distribution function directly. Steady-state results reveal significant anisotropy of the distribution in the Gamma valley; the Lambda valley distribution remains fairly isotropic even at high fields.;Based on the distribution function, macroscopic transport models are obtained using the balance equations method. Transport parameters for the macroscopic models are obtained from the aforementioned Boltzmann solver. The drift-diffusion (DD) model is obtained as a special case of the balance equations. Although drift-diffusion is a purely local model, retaining an additional term in the balance equation derivation results in the augmented drift-diffusion (ADD) model. The ADD contains a transport parameter (length coefficient) which accounts for some non-local phenomena. The length coefficient obtained in this work is in reasonable agreement with reported results. The drifted-Maxwellian (DM) non-stationary model is also developed and discussed.;A CAD-oriented device simulator is implemented for GaAs MESFETs using a quasi-two-dimensional (Q-2D) scheme. The Q-2D scheme exploits the behavior of sub-micron GaAs MESFETs to recast the relevant equations in one dimension while retaining some two-dimensional effects. The Q-2D approximation represents a compromise between physical accuracy and computational efficiency. Different transport models are coupled with the Q-2D method to assess their utility in actual devices. Results show that the DD model underestimates the drain current for sub-micron gate lengths. The ADD transport model, with proper choice of length coefficient, yields results comparable to those obtained from a more sophisticated DM model. The ADD approach, because of its inherent simplicity, is computationally very efficient while retaining the effects of non-stationary transport. The ADD model is subsequently used to compare modeled and measured results. Reasonable agreement is obtained given the lack of device details which are required for the device simulator, and the inherent approximations of the Q-2D scheme.