Optical measurements of the minigaps in electron inversion layers on vicinal planes of Si(001)

Abstract

Measurements are reported of the far-infrared absorption of electron inversion layers at SiSi${\mathrm{O}}_2$ interfaces tilted a few degrees from (001). The lowest minigap $E_g$, as a function of electron density $N$ and tilt angle $\theta$, is found to be $E_g=(7.5\mathrm{}\pm 0.5)Nsin\left|\theta \right|+(0.15\mathrm{}\pm 0.02)N^2$ meV, where $N$ is in units of ${10}^{12}$ ${\mathrm{cm}}^{-2\mathrm{}}$. The first term is tentatively interpreted as arising from a term in the surface potential $V_Q{e}^{i\overrightarrow{\mathrm{Q}}·\overrightarrow{\mathrm{r}}}$, where $Q=\left(\frac{4\pi }{a}\right)sin\theta$ in the direction of tilt, and the second as coming from a kinetic energy term of the form $k_x{k}_y$. The second minigap has also been measured, for $N=3.1\mathrm{}\times {10}^{12}$ ${\mathrm{cm}}^{-2\mathrm{}}$ and $\theta =1.9\mathrm{}°$, to be 2.75±0.3 meV.