Electrostatic modulation of the lateral carrier density profile in field effect devices with nonlinear dielectrics

The properties of two-dimensional (2D) electronic systems are often effectively controlled using electrostatic gating. geometry such field effect devices influences the effectiveness gate and carrier density profile in 2D device. Here, we analyze gate-induced spatial variations lateral patterned ${\mathrm{LaAlO}}_{3}/{\mathrm{SrTiO}}_{3}$ devices. We model electrostatics interface Thomas-Fermi approximation compute charge distribution at interface. show that electric lines generated by focused edges device, causing an increased depletion near its edges. This is accentuated due to large, nonlinear dielectric constant substrate, large distance between electrode experimentally demonstrate one consequence this directly imaging current distributions gated heterostructures, finding insulating regions nucleate device gate. Our results suggest choice materials control systems.