Intrinsic density n i (T) in GaAs: Deduced from band gap and effective mass parameters and derived independently from Cr acceptor capture and emission coefficients

Abstract

Prior attempts at determination of the intrinsic density in GaAs are reviewed, and this quantity is then deduced anew from the temperature dependences of the intrinsic gap and of the valence and conduction band system statistical weights. The nonparabolicity of the lowest conduction band, and the effects of the next two conduction bands, are taken into account in deducing ni (T) for the range 250–1500 K. That procedure gives a room-temperature value ni (300) = 2.1×106 cm−3, which can be compared with prior values from various experimental methods. The magnitude and temperature dependence of ni are then calculated by a different and entirely new method, which utilizes experimental data of the electron and hole emission and capture coefficients associated with Cr2+?Cr3+ transitions of the substitutional CrGa deep-level impurity in GaAs. Recent data of Martin et al. concerning these coefficients permits a deduction of ni(T) = 1.05 ×1016 T3/2 exp(−0.802/kT) cm−3 for 300<T<475 K, a range in which ni increases from 2×106 cm−3 to 3×1011 cm−3. Throughout that range, the procedure gives ni lying within ±15% of that calculable ’’directly’’ from band gap and effective mass parameters.