Infrared Spectra at Surfaces and Interfaces from First Principles: Evolution of the Spectra across the $\mathrm{Si}(100)\mathrm{\text{−}}{\mathrm{SiO}}_2$ Interface

We introduce a general scheme for calculating from first principles both the transverse-optical and longitudinal-optical infrared absorption spectra at surfaces or interfaces. A spatial decomposition of the spectra gives the evolution of the infrared activity across the considered system. Application to ultrathin oxides on silicon yields infrared spectra which reproduce the observed redshift of the high-frequency peaks for decreasing oxide thicknesses. This effect is shown to arise from the lengthening of the Si-O bonds in the substoichiometric oxide at the interface.

Figure 1

Local TO (left) and LO (right) infrared absorption spectra calculated at various distances from the Si substrate. The indicated distances (in Å) are referred to the first O atom of the oxide. The principal spectral features are indicated.

Figure 2

Position of the high-frequency TO (top) and LO (bottom) peaks of the $\mathrm{Si}(100)\mathrm{\text{−}}{\mathrm{SiO}}_2$ interface vs oxide thickness (solid lines). Experimental data are taken from the indicated references. To facilitate the comparison, the theoretical frequencies were rescaled to match the experimental peaks of bulk ${\mathrm{SiO}}_2$ in the limit of thick oxides.

Figure 3

Principal TO stretching frequencies associated to individual Si-O bonds plotted against their bond length. The different oxidation states of Si are indicated separately. A linear regression (dashed line) gives a redshift of $43{\mathrm{cm}}^{-1}$ for a bond length increase of 0.01 Å.