Formulation of Macroscopic Transport Models for Numerical Simulation of Semiconductor Devices

Edwin C Kan,Umberto Ravaioli,Datong Chen,Yu Zhang ,R.w Dutton

doi:10.1155/1995/12686

Abstract

According to different assumptions in deriving carrier and energy flux equations, macroscopic semiconductor transport models from the moments of the Boltzmann transport equation (BTE) can be divided into two main categories: the hydrodynamic (HD) model which basically follows Bløtekjer's approach [1, 2], and the Energy Transport (ET) model which originates from Strattton's approximation [3, 4]. The formulation, discretization, parametrization and numerical properties of the HD and ET models are carefully examined and compared. The well-known spurious velocity spike of the HD model in simple nin structures can then be understood from its formulation and parametrization of the thermoelectric current components. Recent progress in treating negative differential resistances with the ET model and extending the model to thermoelectric simulation is summarized. Finally, we propose a new model denoted by DUET (Dual ET)which accounts for all thermoelectric effects in most modern devices and demonstrates very good numerical properties. The new advances in applicability and computational efficiency of the ET model, as well as its easy implementation by modifying the conventional drift-diffusion (DD) model, indicate its attractiveness for numerical simulation of advanced semiconductor devices

Highlights

He semi-classical Boltzmann Transport Equaion (BTE), together with the Poisson equation, has been regarded basic and sufficient to model the electrical behaviors of modern semiconductor devices in spite of its inability to account for quantum
The Monte Carlo (MC) method has many practical problems which limit its applications, such as, the need for extremely large computational resources, slow convergence in seeking self-consistent solutions with the Poisson equation in lowfield and barrier regions, lack of rigorous calibration denote this approach as the energy transport (ET)
The fluxes, as odd moments of the BTE, only explic- tions, which are used as subscripts for other itly depend on the odd part of the distribution terms to denote the electron and hole parts, U is the function, fodd

Summary

INTRODUCTION

He semi-classical Boltzmann Transport Equaion (BTE), together with the Poisson equation, has been regarded basic and sufficient to model the electrical behaviors of modern semiconductor devices in spite of its inability to account for quantum. The even-order (zeroth and second) moment equations directly result in the continuity equations and the energy balance equations for electrons and holes: some phenomenological laws We denote this approach as the hydrodynamic (HD) model [1, 2]. The fluxes, as odd moments of the BTE, only explic- tions, which are used as subscripts for other itly depend on the odd part of the distribution terms to denote the electron and hole parts, U is the function, fodd, (the parts with the even part, feven, net carrier recombination rate, and Wn and Wp are vanish in integration due to symmetry). To obtain closed forms of J and S, there are mainly two approaches, namely, the HD and ET models

Carrier and Energy Flux Equations in the HD Model

The second moment is a scalar

Lattice Temperature Variations

CONCLUSIONS