carrier_statistics¶
- Calling sequence
classical{ carrier_statistics }
- Properties
using: \(\mathrm{\textcolor{ForestGreen}{optional\;within\;the\;scope}}\)
type: \(\mathrm{choice}\)
values:
maxwell_boltzmann
;fermi_dirac
default:
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 tofermi_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{} }