Properties of the ubiquitous p–n junction in semiconductor nanowires

Abstract

The properties of nanowires with built-in p–n junctions such as the energetic position of the one-dimensional sub-bands, charge distributions and band bending in equilibrium are determined by the self-consistent solution of the Poisson–Schrödinger equations in the effective mass approximation. The built-in potential Vbi of a GaAs nanowire with a radius of R = 500 Å and a symmetric built-in p–n junction are equal to Vbi = 1.4 V at T = 300 K, taking the donor and acceptor doping levels to be equal to ND = NA = 1 × 1018 cm−3. The radial depletion is governed by the position of the conduction-band edge relative to the Fermi level at the surface, i.e. eϕS = EC − EF, and is a ‘shell’ with a thickness of 250 Å for EC − EF = 0.7 eV while the depletion width along z is ≈0.15 µm which is three times larger than the value of the bulk p–n junction taking the same doping level. It is found that decreasing the radius leads to a reduction in Vbi from 1.4 V at R = 500 Å to Vbi = 0.02 V at R = 50 Å and also complete depletion of the nanowire across its diameter and all along its length. Similarly, a reduction in the doping level leads to a decrease in Vbi down to Vbi ≈ 0.02 V for ND = NA = 1 × 1016 cm−3 which is significantly lower than Vbi ≈ 1.1 V obtained for the bulk p–n junction. These findings are discussed in a practical context related to growth and devices like nanowire solar cells.