Accumulation, inversion, and depletion layers in SrTiO${}_3$

Abstract

We study potential and electron density depth profiles in accumulation, inversion and depletion layers in crystals with large and nonlinear dielectric response such as $\mathrm{SrTi}{\mathrm{O}}_3$. We describe the lattice dielectric response using the Landau-Ginzburg free energy expansion. In accumulation and inversion layers we arrive at new nonlinear dependencies of the width $d$ of the electron gas on applied electric field $D_0$. Particularly important is the predicted electron density profile of accumulation layers (including the $\mathrm{LaAl}{\mathrm{O}}_3/SrTi{\mathrm{O}}_3$ interface) $n(x)\propto (x+d{)}^{-12/7}$, where $d\propto D_0^{-7/5}$ . We compare this profile with available data and find satifactory agreement. For a depletion layer we find an unconventional nonlinear dependence of capacitance on voltage. We also evaluate the role of spatial dispersion in the dielectric response by adding a gradient term to the Landau-Ginzburg free energy.

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