The "collection probability" describes the probability that a carrier generated by light absorption in a certain region of the device will be collected by the *p-n* junction and therefore contribute to the light-generated current, but probability depends on the distance that a light-generated carrier must travel compared to the diffusion length. Collection probability also depends on the surface properties of the device. The collection probability of carriers generated in the depletion region is unity as the electron-hole pair are quickly swept apart by the electric field and are collected. Away from the junction, the collection probability drops. If the carrier is generated more than a diffusion length away from the junction, then the collection probability of this carrier is quite low. Similarly, if the carrier is generated closer to a region such as a surface with higher recombination than the junction, then the carrier will recombine. The impact of surface passivation and diffusion length on collection probability is illustrated below.

For a device with uniform doping and an abrupt junction, the collection probability is governed by the equation below:

$$CP = cosh\frac{x}{L} - \frac{\frac{SL}{D}\cosh\frac{W}{L} + \sinh\frac{W}{L}}{\frac{SL}{D}\sinh\frac{W}{L} + \cosh\frac{W}{L}} \sinh\frac{x}{L}$$

where: L is the minority carrier diffusion length in cm, S is the surface recombination velocity in cm/s, D is the minority carrier diffusivity in cm2/s and W is the width (thickness) of the layer. x is the distance from the junction, not the depth into the device. For the emitter, x starts at a maximum at the surface and drop to zero at the junction edge.

The above equation simplifies to:

$$CP = \exp\frac{-x}{L}$$

for a very short diffusion length (L << W) or when SL/D =1.

The collection probability in conjunction with the generation rate in the solar cell determine the light-generated current from the solar cell. The light-generated current is the integration over the entire device thickness of the generation rate at a particular point in the device, multiplied by the collection probability at that point. The equation for the light-generated current density (J_{L}), with an arbitrary generation rate (G(x))and collection probability (CP(x)), is shown below, as is the generation rate in silicon due to the AM1.5 solar spectrum:

$$J_{L}=q \int_{0}^{W} G(x) CP(x) d x$$

$$J_{L}=q \int_{0}^{W}\left[\int H_{0} \alpha(\lambda) e^{-\alpha(\lambda) x}d\lambda\right] CP(x) dx$$

where:

q is the electronic charge;

W is the thickness of the device;

α(λ) is the absorption coefficient;

H_{0} is the number of photons at each wavelength.

A non-uniform collection probability will cause a spectral dependence in the light-generated current. For example, at the surfaces, the collection probability is lower than in the bulk. Comparing the generation rates for blue, green and infrared light below, blue light is nearly completely absorbed in the first few tenths of a micron in silicon. Therefore, if the collection probability at the front surface is low, any blue light in the solar spectrum does not contribute to the light-generated current.