1

, „Jo J-v x Ypmp(6, 4)dQ- Iia)(V - 1,V; lp) Using Eq. (248) this expression is transformed to lQ\l' + 1, l; lp) = ^ 0 - I(n)(l' - 1, l'; lp)

VTZv

From the two last relations it immediately follows the phonon selection rule lp = 1. The other odd modes (lp = 3, 5,...) are forbidden in the scattering matrix element mFI- This lp = 1 selection rule breaks down when one considers configurations other than backscattering (i.e., when there is an angle between the incoming and scattered light directions). According to these selection rules the Raman cross-section for the Fröhlich interaction contribution in a spherical quantum dot or microcrystallite can be written as d2c dQ dws

[Hwi — Hms — 1iWp{^, lp)]2 + T2p where the 8 function in the calculation of the probability has been substituted by a Lorentzian in order to take into account the phonon linewidth Tp in the Raman shift spectrum. The coefficient S0 is equal to

Vl Ro

The dispersion relations and scattering intensities for electron, hole, and lattice for a CdS microcrystallite embedded in glass in Figures 1, 2, and 3 of [110] can be appreciated.

In this section the one phonon Raman scattering cross-section using the band structure and phonon dispersions described previously has been calculated. It is important to remember the phonon selection rules already derived for the electron-phonon Fröhlich interaction. For the dipole approximation, with the wavevector of the light considered to be zero, there exist only intrasubband transitions. Due to the symmetry of the initial and final carrier states the phonons must be even in lp and, furthermore, due to the degeneracy in energy for the carrier states of different m the only nonzero matrix element is for lp = 0 phonon modes. The interaction term which is proportional to the carrier states and a nonzero matrix element, when summing over the m of the electrons or holes, only arises when lp = 1 for the phonon modes.

In Figure 20 Raman scattering intensities as a function of frequency shift for different laser energies are shown.

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