Doping Dependence of Hole Lifetime in <i>n</i>-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 n&amp;lt;1.5×1018 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&amp;gt;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&amp;gt;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.