Theory of Raman Scattering in Solids

The Raman effect due to phonons, Landau levels, and Stark ladder levels is analyzed theoretically. For the phonons, three mechanisms are identified, and their orders of magnitude are estimated for both $\Delta n=1\mathrm{} \mathrm{and} 2$. The ratio of the intensities can be of order unity, especially when the crystal has only one narrow band gap. The resonance Raman effect is particularly strong in the band. For the electronic Raman effect from Landau levels, three similar mechanisms can be distinguished. The $\Delta n=1\mathrm{}$ transition can occur only in crystals without a center of symmetry, and has a strength comparable to the $\Delta n=2\mathrm{}$ process. It can also occur in case of broken symmetry, as in $n$-type Si. The Raman effect from a Stark ladder should in principle give the Fourier components of the $E-k$ curve. Finally, it is shown that effective-mass theory for donor levels is reliable only for materials with $\epsilon >5\mathrm{}$, irrespective of $m^{*}$.