Here is the Fermi-Dirac distribution function, and is the probability that the finial site is empty. The Gaussian DOS is rewritten as

(3.5) |

where is the normalized energy , is the Gaussian center, is the effective DOS and is defined as , where is the standard deviation of the Gaussian distribution. If we let be the normalized Fermi-Dirac distribution function, then the carrier concentration can be written as

(3.6) |

Considering the distribution function, will be calculated as

Substituting (3.7) into (3.3), we obtain

where

is the new transport energy and can be calculated by solving (3.9) numerically.

Ling Li: Charge Transport in Organic Semiconductor Materials and Devices