Transport equations are derived for particles, momentum, and energy of electrons in a semiconductor with two distinct valleys in the conduction band, such as GaAs. Care is taken to state and discuss the assumptions which are made in the derivation. The collision processes are expressed in terms of relaxation times. The accuracy is improved by considering these to depend on the average kinetic energy rather than the electron temperature. Other transport equations used in the literature are discussed, and shown to be incomplete and inaccurate in many cases. In particular, the usual assumption that the mobility and diffusion constant depend locally on the electric field strength is shown to be incorrect. Rather, these quantities should be taken as functions of the local average velocity of electrons in the lower valley.

Transport equations for electrons in two-valley semiconductors

Following our previous work, the Meshless Local Petrov-Galerin method based on Rankine source solution (MLPG_R) will be extended in this paper to deal with breaking waves. For this purpose, the governing equation for pressure is improved and a new technique called Mixed Particle Number Density and Auxiliary Function Method (MPAM) is suggested for identifying the free surface particles. Due to complexity of the problem, two dimensional (2D) breaking waves are only concerned here. Various cases are investigated and some numerical results are compared with experimental data available in literature to show the newly developed method is robust.

MLPG_R Method for Numerical Simulation of 2D Breaking Waves

A numerical method for solving the Boltzmann equation for electrons in a semiconductor under spatially varying conditions has been used to investigate the characteristics of instabilities due to the transferred electron effect. For both accumulation layers and dipole domains the main features are in overall qualitative agreement with the predictions of existing theories, but in both cases electron relaxation effects are quantitatively significant in determining the velocities of the instabilities and their growth and decay characteristics.

https://iopscience.iop.org/article/10.1088/0022-3719/6/10/012/pdf

A reappraisal of instabilities due to the transferred electron effect

Multivariable process control - A survey

Publisher Summary This chapter describes the numerical physics of micron-length and submicron-length semiconductor devices. Numerical simulations are routinely used (1) when the device transport is nonlinear and the device differential equations do not admit to exact solutions, (2) as surrogates for laboratory measurements that are costly and/or not feasible, and (3) in computer-aided device design. The numerical ability, coupled with heightened interest in device physics and generated in large measure by the VLSI and very high speed integrated circuit (VHSIC) programs, is also forcing a long-needed reassessment of the assumptions used in device simulations. The chapter discusses semiconductor equations and the picture they provide for the numerical simulation of GaAs and Si devices. The analysis of semiconductor devices relies on the assumption that current flow is by drift and diffusion. Diffusion is related to the spatial spreading of an ensemble of carriers with time, as the ensemble responds to both applied drift forces and random forces such as are generated by collisions. Semiconductor device physics separates into three overlapping categories, identified by a particular type of equation: (1) the semiconductor mobility equation, (2) the Boltzmann transport equation, and (3) the quantum transport equation.

The Numerical Physics of Micron-Length and Submicron-Length Semiconductor Devices

The efficiency of the l.s.a. mode is calculated for galliumarsenide diodes taking account of all the electron-lattice relaxation processes. The efficiency falls off with increasing frequency and typically becomes negative above 100GHz.

Theoretical efficiency of the l.s.a. mode for gallium arsenide at frequencies above 10GHz

Domains are simulated using a new model in which the electron transport and relaxation coefficients depend on the mean energies of the electrons in the valleys, which are deduced from the energy balance within the domain. In GaAs, the accumulation layers are narrowed by cooling effects.

C.J. Hearn

Papers

Theoretical efficiency of the l.s.a. mode for gallium arsenide at frequencies above 10GHz

Energy-balance model for Gunn domains