Effects of a staircase on minigaps in Si inversion layers

Abstract

Effects of one-dimensional periodic staircases on minigaps are theoretically investigated. Various cases are classified according to the step height. Observed positions of minigaps can be explained by a staircase model whose step height is half a lattice constant. In this case (i) the minigaps are assigned from the lowest as $E_0$, $E_1$, $A_1$, $E_{-1\mathrm{}}$, $E_2$, $A_2$, $E_{-2\mathrm{}}$, and so on, where $E_r$ stands for an intervalley minigap and $A_r$ for an intravalley one; (ii) $E_r$ observed in dc conduction are approximately given by $E_r\approx 23\left(\frac{\theta }{\alpha }\right)\exp [-(\frac{1}{4}\left)r^2{W}^2\right]sin\left(2\mathrm{}\phi \right)N_{\mathrm{eff}}$ (meV) for $\mathrm{}\left|r\right|\mathrm{}\pi \alpha \theta <1\mathrm{}$, where $\theta$ and $\phi$ are polar and azimuthal angles of tilting, $\alpha$ is a parameter expressing a step structure and of the order of one, $W$ is a parameter specifying the disorder of staircase, and $N_{\mathrm{eff}}=\frac{(N_{\mathrm{inv}}+3\mathrm{}{N}_{\mathrm{depl}})}{{10}^{12}}$ ${\mathrm{cm}}^{-2\mathrm{}}$; (iii) $A_r\approx {[{\left(\frac{0.46}{r}\right)}^2+{83}^2{(\frac{\theta }{\alpha }-2\mathrm{}{\theta }^2)}^2{N}_{\mathrm{eff}}^{\frac{-2\mathrm{}}{3}}]}^{\frac{1}{2}}\exp [-(\frac{1}{4}\left)r^2{W}^2\right]N_{\mathrm{eff}}$ (meV); (iv) uniaxial stress along [110] or [$1\overline{1}0$] has an effect on $E_r$.