Chapter 2: Semiconductor Fundamentals

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2.10. The drift-diffusion 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:

r, the charge density

n, the electron density

p, the hole density

, the electric field

f, 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


Electric field and potential equations


Carrier density equations


Drift and diffusion current equations


Continuity equation in steady state with SHR recombination


Boulder, December 2004