Двухфононная релаксация возбужденных состояний акцепторов бора в алмазе

Abstract

The relaxation of holes in the excited states of boron acceptors in diamond is theoretically investigated when two optical phonons are emitted. An electron-like Hamiltonian with an isotropic effective mass was used to describe the wave function of the acceptor states. The wave function of the ground state was found by the quantum defect method. The transition probability was calculated in adiabatic approximation. The dispersion law of phonons was considered isotropic, and the frequency of phonons is quadratically dependent on the wave vector module, with the maximum value, omegamax, achieved in the center of the Brillouin zone, and the minimum, omegamin, at the edge of the Brillouin zone. The high sensitivity of the rates to the characteristic of phonon dispersion, omegamax-omegamin, especially for the transition energy, ET, in the 2homegamin≤ ET<homegamin +homegamax interval was revealed. Depending on the transition energy and dispersion of phonons, the rate of two-phonon relaxation in the low-temperature limit varies from ultra-low values (less than 108 s-1) near the threshold, ET=2homegamin, to ultra-high values (more than 1012 s-1) in the "resonance" region homegamin+homegamax≤ ET≤2homegamax.