Intersubband spectroscopy and valley degeneracy of Si(110) and Si(111)n-type inversion layers

Abstract

Detailed far-infrared frequency domain intersubband spectroscopy has been carried out on Si(110) and Si(111) $n$-type inversion layers at 4.2 K. Studies of the polarization dependence of the spectra of the (110) samples are consistent with a fourfold valley degeneracy for these samples and with recent calculations of Yi and Quinn. However, measured transition energies are consistently lower than those calculated. Both normally processed and specially Ar-annealed (111) samples were investigated. Normally processed samples exhibited twofold valley degeneracy as determined by Shubnikov---de Haas measurements, and polarization dependences were again in good agreement with the calculations for twofold degeneracy. However, transition energies were substantially lower than those calculated. Ar-annealed samples were found to have a valley degeneracy of 6, in agreement with previous work. Transition energies for these samples were 9-10 meV below those for the twofold samples, and very small shifts to higher energy were observed for the infrared electric field polarized perpendicular to the interface compared with the parallel polarization. The apparent disagreement of the latter result with calculations appears to be due to the lack of substantial depletion charge in the perpendicular polarization samples. The large discrepancy in transition energies for these samples is attributed in part to interface degradation. The (111) optical results are internally consistent with built-in stress or built-in stress modified by many-body effects as the underlying mechanism producing the twofold valley degeneracy; however, the present results do not establish this unambiguously.