Electric field and charge density in the plane of a quasi-equilibrium asymmetric 2D $p$–$n$ junction with zero current

The problem of the distribution of potential and surface charge density in a thin layer containing a quasi-two-dimensional $p$–$n$ junction is reduced to the solution of an integral equation. Numerical solution of such an equation is obtained for an asymmetric 2D $p$–$n$ junction in the strong degeneracy and quasi-equilibrium conditions. The boundary conditions on the lines of intersection of the Fermi level and the thresholds of size-quantization subbands are used. The dependence of the width of the depletion region on the impurity concentration and bias voltage is analyzed.