# Diffusion Length

### Overview

1. Diffusion length is the average length a carrier moves between generation and recombination.
2. Semiconductor materials that are heavily doped have greater recombination rates and consequently, have shorter diffusion lengths.
3. Higher diffusion lengths are indicative of materials with longer lifetimes and are, therefore, an important quality to consider with semiconductor materials.

The second related parameter to recombination rate, the "minority carrier diffusion length," is the average distance a carrier can move from point of generation until it recombines. As we shall see in the next chapter, the diffusion length is closely related to the collection probability.

The minority carrier lifetime and the diffusion length depend strongly on the type and magnitude of recombination processes in the semiconductor. For many types of silicon solar cells, SRH recombination is the dominant recombination mechanism. The recombination rate will depend on the number of defects present in the material so that as doping the semiconductor increases the defects in the solar cell. Doping will also increase the rate of SRH recombination. In addition, since Auger recombination is more likely in heavily doped and excited material, the recombination process is itself enhanced as the doping increases. The method used to fabricate the semiconductor wafer and the processing also have a major impact on the diffusion length.

Color chart of a high-efficiency multicrystalline PERL solar cell. The percentage refers to the fraction of light-generated carrier and the variations between one region and another are due to variations in the diffusion length in the solar cell caused by the grain boundaries in the multicrystalline material.

In silicon, the lifetime can be as high as 1 msec. For a single crystalline silicon solar cell, the diffusion length is typically 100-300 µm. These two parameters give an indication of material quality and suitability for solar cell use.

The diffusion length is related to the carrier lifetime by the diffusivity according to the following formula:

$$L=\sqrt{D \tau}$$,

where:
L is the diffusion length;
D is the diffusivity and
τ is the lifetime in seconds.

The diffusivity is a measure of how quickly a group of particles fill a space and it is described in more detail on the diffusion page The diffusivity is typically given in cm2/s and the lifetime is in seconds so the above formula will give the diffusion length in cm. However, a diffusion length in a silicon solar cell will typically be quoted in microns (µm). Multiply the result by 10,000 (104) to convert from cm to µm

The following calculator provides a way of converting between lifetime and diffusion length using more familiar units. The diffusivity can be found in the appendices.