Electronic structure of piezoelectric double-barrier InAs/InP/InAs/InP/InAs (111) nanowires

We present a theoretical study of an n-type InAs nanowire with built-in InAs/InP heterojunctions in the effective-mass approximation via self-consistent Poisson–Schrödinger calculations in cylindrical coordinates. Rapid convergence and efficiency are achieved by (i) a suitable transformation of the radial part of the Hamiltonian matrix thereby maintaining symmetry (ii) using quantum mechanical perturbation theory to derive an expression for the change in electron density with electrostatic potential. We calculate the energy levels in a 150 Å long InAs quantum dot surrounded by 50 Å long InP barriers within an InAs quantum wire of radius 200 Å, having a doping level of 3×1016 cm−3 and conduction-band discontinuities of ΔECB=0.6 eV. In equilibrium, the lowest quantum dot state is at 15 meV above the Fermi level and we find that upon variation of the applied collector–emitter voltage VCE, resonance occurs at VCE=88 mV. This is in good agreement with an experimental study of resonant tunneling in a nominally undoped InAs/InP nanowire of similar dimensions grown in the [111] direction, where resonance was detected at VCE=80 mV, and a small shift (<5 mV) in its position occurred upon inverting the voltage polarity. We rule out barrier asymmetry, bandbending due to impurities or defects, and contact effects as being the origin of the resonant-voltage shift, and attribute it to the strain-induced charges at the InP/InAs interfaces. Both InAs and InP segments are shown to be under in-plane compression giving a piezoelectric field of 0.155 meV/Å in the InAs quantum dot while resonant tunneling, as calculated, occurs at 84 mV for VCE<0 and at 87 mV for VCE>0. This is in contrast to two-dimensional pseudomorphic heteroepitaxy, where the InP is under in-plane tensile strain yielding a very strong resonance-voltage shift (≫5 mV). The small magnitude of the measured shift indicates that in nanowires any strain at the heterointerfaces relaxes within a few atomic layers.