Chapter 2: Semiconductor fundamentals
3.1 Introduction

2.10 The drift-diffudion model

The drift-diffusion model of a semiconductor is frequently used to describe semiconductor devices. It contains all the features described in this chapter.

Starting with Chapter 3, we will apply the drift-diffusion model to a variety of different devices. To facilitate this analysis, we present here a simplified drift-diffusion model, which contains all the essential features. This model results in a set of ten variables and ten equations.

The assumptions of the simplified drift-diffusion model are:

Full ionization: all dopants are assumed to be ionized (shallow dopants)

Non-degenerate: the Fermi energy is assumed to be at least 3 kT below/above the conduction/valence band edge.

Steady state: All variables are independent of time.

Constant temperature: The temperature is constant throughout the device.

The ten variables are the following:

ρ, the charge density

n, the electron density

p, the hole density

, the electric field

φ, the potential

Ei, the intrinsic energy

Fn, the electron quasi-Fermi energy

Fp, the hole quasi-Fermi energy

Jn, the electron current density

Jp, the hole current density

The ten equations are:

Charge density equation

(2.10.1)

Electric field and potential equations

(2.10.2)
(2.10.3)
(2.10.4)

Carrier density equations

(2.10.5)
(2.10.6)

Drift and diffusion current equations

(2.10.7)
(2.10.8)

Continuity equation in steady state with SHR recombination

(2.10.9)
(2.10.10)

 

Boulder, 2022