Estimation of electrical bandgap narrowing in heavily doped p-gallium arsenide

For device modeling, the effect of heavy doping can be described by relating the effective intrinsic carrier concentration n_ie to the intrinsic carrier concentration in lightly doped material n_io with a nonphysical apparent bandgap shrinkage. The electrical measurements on bipolar devices provide the value of the equilibrium minority-carrier concentration and cannot directly give the amount of bandgap narrowing. The aim of this work is to extract this nonphysical, apparent bandgap shrinkage from the measurement of the minority-carrier transport parameters in p⁺-n GaAs diodes with the p⁺-layer hole density in the range from 6.3×10¹⁷ to 1.3×10 ¹⁹ cm^-3. The recombination velocity at the surface of the p⁺ layer is calculated and compared with the available experimental data