Effects of interband excitations on Raman phonons in heavily dopedn−Si

Abstract

Raman-active inter-conduction-band transitions from the ${\Delta }_1$ to ${\Delta }_{2^{\prime }}$ bands in heavily doped $n-\mathrm{Si}$ ($n\simeq 1.5\times {10}^{20}$ ${\mathrm{cm}}^{-3\mathrm{}}$) interfere with the zone-center optical phonon to produce Fano-type asymmetric phonon line shapes typical of a discrete-continuum interaction. We have studied the line shapes as a function of exciting frequency and uniaxial stress along the [001] and [111] directions. The asymmetry is removed under [001] uniaxial stress for the doublet component of the phonon that couples to the stress-depleted doublet valley, and is enhanced for the singlet component that couples to the carrier-enhanced singlet valley. We have calculated from microscopic theory the parameters that describe the Fano interaction—the asymmetry parameter, the broadening, and the frequency shift due to the self-energy of the phonon deformation-potential interaction with the free electrons in the conduction-band valley. These parameters have been calculated for zero stress and a high stress and a high stress along the [001] direction, and are found to be in excellent agreement with experiment. We have also investigated the second-order acoustical-phonon scattering [$2\mathrm{TA}\mathrm{}\left(X\right)\mathrm{}$]; it shows no change in line shape for heavily doped $n-\mathrm{Si}$. Under uniaxial stress along the [001] and [111] directions, it exhibits only the hydrostatic shift, as does pure Si, which was measured for comparison.