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

Автор: Группа авторов
Издательство: John Wiley & Sons Limited
Серия:
Жанр произведения: Техническая литература
Год издания: 0
isbn: 9781119763352
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      (1.14)image

      When in the intrinsic material we represent the Fermi level position Ei one can obtain from equations 1.5 and 1.9:

      (1.16)image

      The Fermi level Ei is nearby to the midgap; a minor alteration is due to the variance in the effective densities of conduction and valance and band.

      Also using Equation 1.15 and reference energy as Ei, we have for N-type materials the alternate equations given as:

      (1.17)image

      And for P-type materials:

      (1.18)image

      Donors and acceptors

      The number of holes and electrons in their bands respectively and therefore the conductivity of the semiconductor, may be regulated by adding different dopants or different types of impurities called acceptors and donors. The doped semiconductor, known as extrinsic material.

      A semiconductor has four kinds of charged species: holes, electrons, donor ions which are positive Nd, and acceptor ions which are negative Na. Generally, there is no net charge in all samples.

      1 Nd – Na ≫ ni (i.e., N-type material),(1.21)(1.22)If additionally, Nd ≫ Na, then(1.23)The Fermi energy can then be written as:(1.24)

      2 Na – Nd ≫ ni (i.e., P-type material)(1.25)(1.26)If furthermore, Na ≫ Nd, then(1.27)The Fermi energy can then be written as:(1.28)

      B. Nonequilibrium carrier concentration

      Many semiconductor devices work by producing charge carriers that exceed the thermal equilibrium values, such excess carriers can be generated either by optical excitation or by adding an electrical field.

      Through producing excess carriers (electrons and holes), thermal equilibrium in the semiconductor is no longer maintained, and the Fermi energy is no longer strictly specified. For the nonequilibrium semiconductor, we can outline two novel parameters: the quasi-Fermi energy for electrons and holes respectively.

      The electron and hole concentrations of for the nonequilibrium are then given by:

      (1.29)image

      (1.30)image

      When electrons and holes are at equilibrium, EFn and EFp coincide and this is known as EF.

      (II) Basic equations for semiconductor modeling

      The so-called equations of semiconductor devices could explain the activity of most of the devices made up of semiconductor materials, including solar cells.

      The elementary equations for the operation of semiconductor-based devices describe the static and dynamic carrier behavior in semiconductors under external factors, like optical excitation or applied field, both causing deviations from conditions of thermal equilibrium.

      Poisson’s Equation

      The electric potential is related to the density of the space-charge by Poisson equation:

      (1.31)image

      where ψ represents the electrostatic potential, the local permittivity is given by ε, and ρ represents the density of the local space charge.

      The total contribution from all charges which may be mobile or fixed, including holes, electrons and ionized impurities is expressed as local space charge density.

      (1.32)image

      Where the elementary charge is given by q, n gives the electron concentration, p represents the concentration of holes, Na is the concentration of ionized acceptors and Nd is the concentration of ionized donor.

      The electric field is obtained by the gradient of the potential as:

      (1.33)image

      Continuity