Electronic Raman scattering and the metal-insulator transition in doped silicon

Abstract

We have systematically studied the valley-orbit Raman spectrum of phosphorus-doped silicon for donor concentrations on both sides of the metal-insulator transition. As the impurity concentration $n_d$ increases, the $1s\left(A_1\right)\to 1s\left(E\right)\mathrm{}$ valley-orbit line broadens rapidly and asymmetrically. The valley-orbit line broadens beyond recognition before $n_d$ reaches $n_c$, the critical value for the metal-insulator transition. A continuum due to intervalley fluctuations starts appearing as a background as $n_d$ approaches $n_c$. This continuum becomes stronger with increasing $n_d$, and above $n_c$ it completely dominates the spectrum. We have also observed some of the above features in antimony- and arsenic-doped silicon. To understand the broadening of the valley-orbit line and to calculate the resulting line shape, we have applied the notion that molecular bonding alters the valley-orbit splitting by estimating the occupancy of donor sites in a two-donor "molecule" treated in the Heitler-London approximation. The continuum starts at zero excitation energy and may be understood as single-particle excitations within a single, partially occupied energy band superimposed on a quasielastic Rayleigh line. The observed temperature dependence of the continuum can be qualitatively understood in terms of temperature-dependent occupation probabilities. For $n_d$ just below $n_c$ the remnant of the valley-orbit line shows a temperature dependence that can be explained by thermal depopulation of the $1s\left(A_1\right)$ ground-state orbitals. A sum rule valid for all concentrations has been derived for an integral of the intensity. It shows that the gross features of the spectrum are dominated by the short-range, or intervalley, part of the donor potential. Spectra taken on silicon crystals with arsenic and antimony donors gave results similar to those with phosphorus donors. We have also studied the Raman spectra of several $p$-type silicon crystals. A low-frequency continuum was observed from boron, gallium, and aluminum impurities, but only boron showed the sharp acceptor line of the $B$ type seen previously.