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

TL;DR

This paper investigates the nonlinear dielectric response and electron density profiles in SrTiO₃, revealing new dependencies of electron gas width on electric field and comparing theoretical predictions with experimental data.

Contribution

It introduces a nonlinear model for accumulation, inversion, and depletion layers in SrTiO₃ using Landau-Ginzburg theory, predicting novel electron density profiles and capacitance behavior.

Findings

Electron density profile in accumulation layers follows n(x) ∝ (x+d)^{-12/7}

Width of electron gas scales as d ∝ D₀^{-7/5}

Capacitance exhibits nonlinear dependence on voltage in depletion layers

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 $\mathrm{SrTiO_3}$. 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 $\mathrm{LaAlO_3/SrTiO_3}$ 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.