LA phonon assisted transition

As a further test of the calculation, we have evaluated the polarization dependent intensities of the LA phonon assisted transitions in the strained crystal for stresses along fOOll and [ill] This was accomplished through the use of the equations listed in Table V along with Eqs. (41) - (43). The results of this calculation along with the experimental values of Ref. 4 are presented in Table XI. The agreement between experiment and heor is quite good for both of the stresses for E H X and E 1 X. 

Table XI. Theoretical and experimental values for the intensities of the LA-phonon assisted transition in Ge for stress, X, along fill and fool for the electric field vector, E, of the incident light polarized parallel and perpendicular to X.

Although in Ge a piezospectroscopy experiment has been performed on the LA phonon-assisted transition its interpretation is more complex due to the fact that there are two intermediate electron states. However, from this work as well as the WMA spectrum of the TO-phonon assisted transition at zero stress valuable information about Sg pjj and S -ph both these transitions was obtained. 

Table I. Theoretical expressions for the "oscillator strengths" of the LA, LO, TA, and TO phonon-assisted transitions in indirect materials. The subscript I refers to the phonon branch being considered. The spin orbit split band, is considered.

Table V. Polarization dependent relative intensities of the LA phonon assisted r-L transition for X Ij [ill] and X COOl]... 

Fig. 10. Wavelength-modulated absorption spectra of the LA-phonon assisted indirect transition in Ge at 77K for X = 0 and 3.73 x 10 dyn-cm along [ lll for E 1 X and E X It. For the X = 0 spectra the TO-phonon assisted peak is also observed as marked.

For Ge reliable experimental data exists for Af A snd the polarization dependent relative intensities of the LA phonon in the strained crystal, as shown in Fig. 10. Reference 41 could not resolve the TO transition and thus there is no known value for the quantity Af pQ The lack of data for the TO phonon can be remedied by making use of the WMA spectra of Fig. 10 at zero stress. A line is found approximately 9 meV higher in energy than the strong LA peak and is a result of TO phonon assisted indirect transitions. This conclusion is based on the fact that at L the LA and TO phonons differ in energy by 9 meV. 

Piezospectroscopy experiments in Si and GaP have made it possible to determine the ratio of Se-ph/Sh-ph for the I-A (X) transitions for several intervalley phonons, i.e. TO in Si and LA and TA in GaP. Comparing these results with experimental values and theoretical expressions for the absorption coefficient related to these phonon-assisted processes we have been able to... 

Germanium, just like Si, is a diamond type material and thus Eq. (37) can be used to calculate its EP and HP matrix elements. However, in Ge, the fundamental absorption results from F-L indirect processes assisted by LA and TO phonons. The LA transition has two intermediate conduction band states, V2, c... 

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