Spin relaxation of photoelectrons inp-type gallium arsenide

Abstract

We have measured by optical-pumping methods the spin-relaxation time $T_1$ of photocreated conduction electrons in $p$-type GaAs ($N_A=4\mathrm{}\times {10}^{18}$ ${\mathrm{cm}}^{-3\mathrm{}}$) as a function of temperature. To analyze our results we present a detailed discussion of the possible relaxation mechanisms in $p$-type semiconductors. The electronic spin relaxation may originate from: (i) the splitting of the conduction band, (ii) the spin-orbit interaction, (iii) the hyperfine interaction with nuclei of the host crystal, and (iv) the exchange interaction between electrons and holes. The spin-relaxation time is given in each case as a function of experimentally attainable parameters and permits one to obtain a numerical result for all usual III-V compounds. It is established that in doped $p$-type GaAs the exchange interaction with the holes is the dominant relaxation mechanism at low temperatures, the other mechanisms being too weak by several orders of magnitude. For higher temperatures ($T\ge 100$ °K), the relaxation due to the $k^3$ splitting of the conduction band may become predominant for $N_A\lesssim {10}^{+7\mathrm{}}$ ${\mathrm{cm}}^{-3\mathrm{}}$. The theory is compared with experimental data available in the literature and with our experiments. From our measurements we obtain in GaAs the value of the exchange splitting of $1s$ exciton ${\Delta }_{x.\mathrm{}1s}\simeq 0.1$ meV. We also show that the observed spin depolarization at high kinetic energy (200-300 meV) can be explained by the splitting of the conduction band, taking into account the energy relaxation by optical-phonon scattering.