Calculation of the optical absorption between surface states of silicon

A detailed calculation of the optical absorption between surface states on silicon is reported and the results compared with the observed absorption. Actually the observations relate to the (111) surface whereas the calculations involved the better understood (110) surface, but arguments are advanced to suggest that similar results should be obtained for both and a simulated (111) calculation presented. A model, which accurately reproduces the results of complete theoretical calculations, is used to obtain the surface state energies throughout the two-dimensional Brillouin zone, and to obtain the momentum matrix elements at each k point by utilising the effective mass sum rule. The formation of a band gap between the surface state bands, arising from surface rearrangement, is incorporated into the model in a physically sensible manner. There is very good agreement in both shape and absolute magnitude between the calculated and observed absorption clearly indicating that the measured absorption does arise from surface states. The (1, 1, 0) calculations show large polarisation effects which should be observable on reconstructed (1, 1, 0) silicon surfaces or on the III–V compounds.