A consistent model for carrier transport in heavily doped semiconductor devices

A self-consistent model for describing carrier transport in heavily doped semiconductor devices has been developed. The proposed model allows convenient treatment of non-uniform semiconductors in a manner that is both thermodynamically consistent and consistent with the transport equations, the steady-state continuity equations and the electrostatic potential with explicit boundary conditions at the contacts. The complex problems are reduced to determining two types of quantities: the reference electrostatic potential and the activity coefficient of the carriers. In order to find the simple working equations for the model, two choices of reference for the electrostatic potential are discussed. The presented transport equations are written in a simple Shockley-like form, in which the effects associated with the non-uniform band structure and the influence of Fermi-Dirac statistics are described by a thermodynamic property, the activity coefficient of the carriers, which is expressed in terms of two band model parameters, the effective band-gap shrinkage, Delta E_g, and the effective asymmetry factor, A. In this form they are convenient for use in computer-aided analysis and the design of heavily doped semiconductor devices.