Doping Dependence of Hole Lifetime in n-Type GaAs

Abstract

The bulk hole lifetimes τ at 300 and 77°K are determined by a phase‐shift technique for several Te‐doped melt‐grown GaAs crystals with electron concentrations n ranging from 2×10¹⁶ to 6.5×10¹⁸ cm⁻³. The phase‐shift technique measures the phase lag φ of band‐to‐band photoluminescence relative to the excitation which is intensity modulated at some radio frequency ω. An expression relating τ and φ is derived taking into account hole diffusion and the reabsorption of emitted radiation. If the diffusion length is greater than the absorption length, the the usual simplified relation φ=tan⁻¹ ωτ yields a poor approximation. It is also shown that the reabsorption can cause a wavelength‐dependent phase shift along the spectrum of the band‐to‐band recombination. Apparatus used to measure φ is described. Values of τ are obtained from the measured φ using the previously determined diffusion length. At 300°K, τ=1.9×10⁻⁸ sec and is constant for n18 cm⁻³, indicating that recombination processes other than the band‐to‐band transitions are dominant in these lightly doped crystals. The hole lifetime begins to decrease at n=1.5×10¹⁸ cm⁻³ but decreases more rapidly for n>3×10¹⁸ cm⁻³. This shows that the band‐to‐band process is competitive with other processes beginning at n=1.5×10¹⁸ cm⁻³ and that additional hole‐capturing processes exist in crystals with n>3×10¹⁸ cm⁻³. At 77°K, the behavior is similar, but the decrease from a constant lifetime of 1×10⁻⁹ sec for lightly doped crystals now occurs at n=8×10¹⁷ cm⁻³.