sarkas.utilities.fdints.fermidirac_integral#

sarkas.utilities.fdints.fermidirac_integral(p, eta)[source]#

Wrapper function to calculate the Fermi-Dirac integral using approximation found in Ref. [Fukushima, 2015].

Parameters

  • p (float) – Order of the unnormalized Fermi-Dirac integral.

  • eta (float) – Value of the normalized chemical potential \(\mu/(k_BT)\).

Return type

float

Returns

fd (float) – Value of the Fermi-Dirac integral.

Raises

SarkasError – If the order of the integral is not supported.

Examples

>>> from numpy import pi, sqrt
>>> # Electron density
>>> eta = -0.2860
>>> I = fermidirac_integral(p = 0.5, eta = eta)
>>> lambda_deB = 1.957093e-11 # [m]
>>> ne = 4.0/( sqrt(pi) * lambda_deB**3 ) * I
>>> f"{ne:.4e}"
    '1.6201e+32'