# carrier_statistics¶

Calling sequence

classical{ carrier_statistics }

Properties
• using: $$\mathrm{\textcolor{ForestGreen}{optional}}$$

• type: $$\mathrm{choice}$$

• values: $$\mathrm{maxwell\_boltzmann}$$ or $$\mathrm{fermi\_dirac}$$

• default: $$\mathrm{fermi\_dirac}$$

Functionality

Attribute to chose carrier statistics.

If set to maxwell_boltzmann, then Maxwell-Boltzmann statistics is used for the classical densities. If set to fermi_dirac, then Fermi-Dirac statistics is used for the classical densities. It is not recommended as this is only an approximation which is only applicable in certain cases.

In order to maintain consistency, also the (integrated) energy distribution (density_vs_energy) and the classical emission spectra and densities are computed using the same statistics. Use together with quantum regions is possible but not recommended, and convergence of the current-Poisson or quantum-current-Poisson equation may become worse (please readjust convergence parameters accordingly).

Note

• $$n=N_c\ \mathcal{F}_{1/2}\left(\frac{E_F-E_c}{k_BT}\right)$$ (electron density for fermi_dirac)

• $$p=N_c\ \mathcal{F}_{1/2}\left(\frac{E_v-E_F}{k_BT}\right)$$ (hole density for fermi_dirac)

• $$n=N_c\exp\left(\frac{E_F-E_c}{k_BT}\right)$$ (electron density for maxwell_boltzmann)

• $$p=N_c\exp\left(\frac{E_v-E_F}{k_BT}\right)$$ (hole density for maxwell_boltzmann)

• where $$\mathcal{F}_n(E)$$ is a Fermi-Dirac integral of the order $$n$$.

Example
classical{
carrier_statistics = maxwell_boltzmann

Gamma{}
HH{}
}