Diffusion of charge carriers into semiconductors

As we have seen, the drift current appears in semiconductors under the action of potential difference. There is also a diffusion current in semiconductors, which appears under the action of difference between carriers density.

If the charge carriers spread evenly into a semiconductor, their concentration will be in balance. Concentration of charge carriers in different parts of a semiconductor can change under the action of some outer effects. For example, if the radiation acts on a part of a semiconductor, generation of carriers will arise. The additional concentration of carriers is called an excess concentration.

The carriers always travel from a place with higher concentration to a place with lower one, because they have their own kinetic energy, i.e. they seek a balance concentration. The diffusion motion of charge carriers (electrons, holes) is called a diffusion current (I_df). This current can be produced by electrons or holes as well as a drift one.

The diffusion current is defined as:

, ,

where D_n and D_p – factors of diffusion, and - gradients of carriers concentration.

The gradient of carriers concentration is defined as changes of electrons (n) or holes (p) concentration per unit length. If there is no difference between carriers concentration ( or ) in a semiconductor structure, the diffusion current will not arise. The diffusion current will grow if changes of the concentration or grow in the given section .

The factor of diffusion (D_p or D_n) characterizes the intensity of diffusion process. This factor is proportional to mobility of carriers and depends on temperature. Each material has its own factor of diffusion which is distinguished from other materials one. The unit of diffusion factor is cm² per second. The electrons diffusion factor is always more than the holes one. For example, at room temperature germanium has D_n=98 cm²/sec and D_p=34 cm²/sec, and the silicon has D_p=12 cm²/sec and D_n=34 cm²/sec. The sign “minus” in the formula for holes current density means that the holes current flows in the direction of reducing the holes concentration.

The excess concentration of carriers is formed under the action of some outer effects on a semiconductor section. But, if this action stops, the excess carriers will recombine and spread over the entire semiconductor due to diffusion. The excess concentration will come down by the exponential low. The period of time when an excess concentration reduces 2.7 times (equal to 0.37 of the earlier concentration) is called excess-carrier life τ_n.

During the diffusion movement of unbalanced carriers along a semiconductor, their concentration also reduces under the exponential law due to recombination. The excess concentration of unbalanced carriers reducing 2.7 times along the distance L_n is called the diffusion distance.

Thus, the decrease in excess concentration occurs in space and for a definite period of time. τ_n and L_n are related to each other by the function: .