**Branch :**Computer Science and Engineering

**Subject :**Fundamental of Electronic Devices

## Diffusion of carriers :Diffusion Processes

When excess carriers are created nonuniformly in a semiconductor, the electron and hole concentrations vary with position in the sample. Any such spatial variation (gradient) in n and p calls for a net motion of the carriers from regions of high carrier concentration to regions of low carrier concentration.

This type of motion is called diffusion and represents an important charge transport process in semiconductors.

**Diffusion Processes:**

Carriers in a semiconductor diffuse in a carrier gradient by random thermal motion and scattering from the lattice and impurities. For example, a pulse of excess electrons injected at x = 0 at time t = 0 will spread out in time as shown in Fig. Initially, the excess electrons are concentrated at

x = 0; as time passes, however, electrons diffuse to regions of low electron concentration until finally n(x) is constant.

We can calculate the rate at which the electrons diffuse in a onedimensional problem by considering an arbitrary distribution n(x) such as Fig.(a) given below. Since the mean free path l between collisions is a small incremental distance, we can divide x into segments l wide, with n(x) evaluated at the center of each segment (Fig.b).

The electrons in segment (1) to the left of x_{0} in Fig.b have equal chances of moving left or right, and in a mean free time t one-half of them will move into segment (2).The same is true of electrons within one mean free path of x_{0} to the right; one-half of these electrons will move through x_{0} from right to left in a mean free time. Therefore, the net number of electrons passing x_{0} from left to right in one mean free time is , where the area perpendicular to x is A. The rate of electron flow in the x direction per unit area (the electron flux density (Φ_{n}) is given by

Since the mean free path I is a small differential length, the difference in electron concentration {n_{1} - n_{2}) can be written as