Perovskite Materials for Energy and Environmental Applications. Группа авторов. Читать онлайн. Newlib. NEWLIB.NET

Автор: Группа авторов
Издательство: John Wiley & Sons Limited
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Жанр произведения: Техническая литература
Год издания: 0
isbn: 9781119763352
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      When the electric fields and density gradients are present, the equation of continuity describes the behavior of excess carriers with time and in space:

      (1.34)image

      (1.35)image

      In steady state image and image.

      Current density equations

      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)image

      (1.37)image

      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)image

      (1.39)image

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

      (1.40)image

      (1.41)image

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

      (1.44)image

      (1.45)image

      (1.46)image

      (1.47)image

      (1.48)image

      (1.49)image

      Optical generation of electron-hole pairs

      It is necessary to the operation of solar cells to produce electron-hole pairs by absorbing sunlight. Holes and electrons lead to the transition of energy carried by the photons of light into electrical energy.

      The number of incident photons S0 (ν) (per unit area, per unit time and per unit energy) determine the number of generated electron-hole pairs. The photon flux S (x, ν) decreases inside the semiconductor exponentially as:

      (1.50)image

      where ν is the frequency. The absorption process in the semiconductor determines the absorption coefficient α(ν).

      At x distance from the surface of the semiconductor the generation rate G(x, ν) of electron-hole pairs can be obtained as:

      (1.51)image

      Where R is the reflectance.

      Here an assumption is made that one electron-hole pair is generated by each absorbed photon.

      (III) Recombination phenomenon in semiconductors

      Recombination is a course of annihilation or destruction of holes and electrons.

Schematic illustration of the different recombination processes in semiconductors.

      Radiative recombination may be understood as the opposite of optical generation. This recombination takes place if a free electron drops out of the conduction band and recombine with a free hole in the valance band and a photon of energy equivalent to the difference in starting and ending energy states is released. For direct bandgap semiconductors, radiative recombination is very significant, but not as relevant for indirect semiconductors such as silicon, since a photon must also be absorbed or expelled for an electron to complete the transmission.

      Due to radiative processes the net recombination rate is expressed as:

      (1.52)image

      Where B is a material constant.

      For n-type semiconductors under low injection (p0pn0) the net rate of recombination can be given as:

      (1.53)image