Accumulation, inversion, and depletion layers in SrTiO3

We study potential and electron density depth profiles in accumulation, inversion, and depletion layers in crystals with a large and nonlinear dielectric response such as SrTiO3. 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 an applied electric field D0. Particularly important is the predicted electron density profile of accumulation layers (including the LaAlO3/SrTiO3 interface) n(x) (x+d)-12/7, where d D0-7/5. We compare this profile with available data and find satisfactory agreement. For a depletion layer we find an unconventional nonlinear dependence of the 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.