“…The absorption coefficient α[ E , N , T ] (Figure a) is calculated as a function of carrier density and temperature through α [ E , N , T ] = π 2 c 2 h 3 n 2 E 2 false( 2 π false) 3 B ∫ 0 E − E g ρ c false[ E false′ false] × ρ V [ E ′ − Ε ] × ( f l false[ E − Ε g − E ′ false] − f u false[ E ′ false] ) normald E ′ where n is the average index of refraction; B is the radiative bimolecular coefficient which depends on the transition matrix element; ρ i [ E ] is the 3D density of states in the conduction/valence band; f i [ E ] = (1/(1 + exp[( E – E F )/( k B T )])) is the Fermi–Dirac distribution probability that upper/lower states involved in the transition are occupied by electrons, with the quasi-Fermi energy E F [ N , T ] related to both the carrier density N and temperature T ; E ′ is the upper state energy above the conduction band minimum. For n and B , we use the average values from the literature − because only the relative change of the absorption coefficient is critical, not its absolute value. Using the Kramers–Kronig relation, we transform the calculated absorption coefficient α[ E , N , T ] to obtain the index of refraction n [ E , N , T ] as a function of carrier density and temperature.…”