Evolution of domain structure with electron doping in ferroelectric thin films

To minimize their electrostatic energy, insulating ferroelectric films tend to break up into nanoscale ``Kittel'' domains of opposite polarization that are separated by uncharged 180$^\circ$ domain walls. Here, I report on self-consistent solutions coupled Landau-Ginzburg-Devonshire and Schr\"odinger equations for an electron-doped thin film. The model is based LaAlO$_3$/SrTiO$_3$ interfaces in which the SrTiO$_3$ substrate made cation substitution or strain. find electron doping destabilizes Kittel domains. As two-dimensional density $n_\mathrm{2D}$ increases, there a smooth crossover zigzag wall configuration. positively charged, but compensated gas, attaches itself screens depolarizing fields. approaches flat head-to-head configuration limit perfect screening. profile may be manipulated external bias voltage gas switched between surfaces