# Generation Rate

### Overview

1. The generation of an electron-hole pair can be calculated at any location within the solar cell, at any wavelength of light, or for the entire standard solar spectrum.
2. Generation is the greatest at the surface of the material, where the majority of the light is absorbed.
3. Because the light used in PV applications contains many different wavelengths, many different generation rates must be taken into account when designing a solar cell.

The generation rate gives the number of electrons generated at each point in the device due to the absorption of photons. Generation is an important parameter in solar cell operation.

Neglecting reflection, the amount of light which is absorbed by a material depends on the absorption coefficient (α in cm-1) and the thickness of the absorbing material. The intensity of light at any point in the device can be calculated according to the equation:

$$I=I_{0} e^{-\alpha x}$$

where α is the absorption coefficient typically in cm-1;
x is the distance into the material at which the light intensity is being calculated; and
I0 is the light intensity at the top surface.

The above equation can be used to calculate the number of electron-hole pairs being generated in a solar cell. Assuming that the loss in light intensity (i.e., the absorption of photons) directly causes the generation of an electron-hole pair, then the generation G in a thin slice of material is determined by finding the change in light intensity across this slice. Consequently, differentiating the above equation will give the generation at any point in the device. Hence:

$$G=\alpha N_{0} e^{-\alpha x}$$

where N0 = photon flux at the surface (photons/unit-area/sec.);
α = absorption coefficient; and
x = distance into the material.

The above equations show that the light intensity exponentially decreases throughout the material and further that the generation is highest at the surface of the material.

For photovoltaic applications, the incident light consists of a combination of many different wavelengths, and therefore the generation rate at each wavelength is different. The generation rate at different wavelengths in silicon is shown below.

wavelength =

3001100

Changing the slider in the graph above changes the wavelength of the incoming light. The changing absorption coefficient causes the light to be absorbed at different depths. The generation rate has been normalized.

To calculate the generation for a collection of different wavelengths, the net generation is the sum of the generation for each wavelength. The generation as a function of distance for a standard solar spectrum (AM 1.5) incident on a piece of silicon is shown below. The y-axis scale is logarithmic showing that there is an enormously greater generation of electron-hole pairs near the front surface of the cell, while further into the solar cell the generation rate becomes nearly constant.

Generation rate of electron-hole pairs in a piece of silicon as a function of distance into the cell. The cell front surface is at 0 µ m and is where most of the high energy blue light is absorbed.

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