Читать книгу Perovskite Materials for Energy and Environmental Applications - Группа авторов - Страница 22

Derivations focused on the transport theory given by Boltzmann have depicted that the current densities can be approximated in the continuity equations by the drift-diffusion model. In the present case, of the quasi Fermi levels EFn and EFp express the current densities:

(1.36)

(1.37)

Where μn and μp are the mobilities of the electrons and holes. The quasi-Fermi levels are linked to the carrier concentrations and the potential through the two Boltzmann approximations as follows:

(1.38)

(1.39)

To describe the quasi-Fermi levels these two equations may then be rewritten as:

(1.40)

(1.41)

By putting these equations into the expression for current density, the following current relationships can be attained:

(1.42)

(1.43)

Where Dn and Dp represent the electron and hole diffusion constants, respectively:

(1.44)

(1.45)

The final term in (1.42) and (1.43) reflects the difference in the effective concentration of the intrinsic carriers, taking into account the decreasing influence of the band-gap. Defining active electrical fields:

(1.46)

(1.47)

The drift-diffusion equations can then be written in more conventional form as.

(1.48)

(1.49)