Quantum dot defined in a two-dimensional electron gas at an−AlGaAs∕GaAsheterojunction: Simulation of electrostatic potential and charging properties

Abstract

We present a self-consistent Schr\"odinger--Poisson scheme for simulation of electrostatic quantum dots defined in gated two-dimensional electron gas formed at $n\text{\ensuremath{-}}\mathrm{Al}\mathrm{Ga}\mathrm{As}∕\mathrm{Ga}\mathrm{As}$ heterojunction. The computational method is applied to a quantitative description of transport properties studied experimentally by Elzermann et al. [Appl. Phys. Lett. 84, 4617 (2004)]. Our three-dimensional model describes the electrostatics of the entire device with a quantum dot that changes shape and floats inside a gated region when the applied voltages are varied. Our approach accounts for the metal electrodes of arbitrary geometry, includes magnetic field applied perpendicular to the growth direction, electron-electron correlation in the confined electron system, and its interaction with the electron reservoir surrounding the quantum dot. We calculate the electric field, the space charge distribution, and energies as well as wave functions of confined electrons to describe opening of two transport channels between the reservoir and the confined charge puddle. We determine the voltages for charging the dot with up to four electrons. The results are in qualitative and quantitative agreement with the experimental data.