### Overview

- Intrinsic carriers are the electrons and holes that participate in conduction.
- The concentration of these carriers is contingent upon the temperature and band gap of the material, thus affecting a material's conductivity.
- Knowledge of intrinsic carrier concentration is linked to our understanding of solar cell efficiency, and how to maximize it.

The thermal excitation of a carrier from the valence band to the conduction band creates free carriers in both bands. The concentration of these carriers is called the intrinsic carrier concentration, denoted by n_{i}. Semiconductor material which has not had impurities added to it in order to change the carrier concentrations is called intrinsic material. The intrinsic carrier concentration is the number of electrons in the conduction band or the number of holes in the valence band in intrinsic material. This number of carriers depends on the band gap of the material and on the temperature of the material. A large band gap will make it more difficult for a carrier to be thermally excited across the band gap, and therefore the intrinsic carrier concentration is lower in higher band gap materials. Alternatively, increasing the temperature makes it more likely that an electron will be excited into the conduction band, which will increase the intrinsic carrier concentration. This translates directly to solar cell efficiency.

### Intrinsic Carrier Concentration of Silicon as a Function of Temperature

The exact value of the intrinsic carrier concentration in silicon has been extensively studied due to its importance in modeling. At 300 K the generally accepted value for the intrinsic carrier concentration of silicon, n_{i}, is 9.65 x 10^{9} cm^{-3} as measured by Altermatt[1], which is an update to the previously accepted value given by Sproul[2]. A formula for the intrinsic carrier concentration in silicon as a function of temperature is given by Misiakos[3]:

The small difference in the values of Altermatt and Misiakos is within the bounds of experimental error. While the intrinsic carrier concentration is normally quoted at 300 K, solar cells are usually measured at 25 °C where the intrinsic carrier concentration is 8.3 x 10^{9} cm^{-3}. The above equation is implemented in the mini-calculator below:

- 1. , “Reassessment of the intrinsic carrier density in crystalline silicon in view of band-gap narrowing”, Journal of Applied Physics, vol. 93, no. 3, p. 1598, 2003.
- 2. , “Improved value for the silicon intrinsic carrier concentration from 275 to 375 K”, Journal of Applied Physics, vol. 70, pp. 846-854, 1991.
- 3. , “Accurate measurements of the silicon intrinsic carrier density from 78 to 340 K”, Journal of Applied Physics, vol. 74, no. 5, p. 3293, 1993.