Resonant interaction of acceptor states with optical phonons in silicon

This paper presents a study of the broadening and splittings of bound-hole excitation lines in silicon when the excitation energy is comparable to that of optical phonons. The approach utilized is a generalization of a similar study for donors in which the degeneracies of the ground and excited states do not play an essential role. However, the specific excitation considered in this work is a ${\Gamma }_8\to {\Gamma }_8$ transition which is in resonance with the ${\Gamma }_5^{+}$ zone-center optical phonon of frequency ${\omega }_0$, a situation which obtains for line 2 of Si(Ga). The hole-phonon interaction gives rise to a mixing of the ${\Gamma }_8$ excited states of the acceptor with the states in which the acceptor is in its ${\Gamma }_8$ ground state and the optical phonons are excited. The mixing of these states is governed by matrix elements which are linear functions of two phenomenological constants. The experimental observation that the expected line 2 of Si(Ga) is replaced with a broad feature and a sharp spike on the high-frequency side of ${\omega }_0$ can be explained using this model. Further, the model accounts for the striking sharpening of spectral features observed under uniaxial stress as well as the differences in this behavior when this stress is applied along different crystallographic directions. In the theory, the nonlinear stress dependence of the stress-induced components, the "pinning" of some components to $\hslash {\omega }_0$, and the possibility of observing the otherwise infrared-inactive zone-center optical phonons find a natural explanation.