Proposed experiments to grow nanoscale $p-n$ junctions and modulation-doped quantum wires and dots

We propose and model several experiments where the field effect defined by split gates is used to restrict acceptors and donors to regions of a semiconductor layer. The nonlinear potential defined by split gates restricts positive donors to the center of the layer, whereas the negative acceptors localize near the edges. The Arrhenius equation modified to include effects of the external and internal fields is used to calculate time- and position-dependent impurity hopping probabilities for Monte Carlo simulations of the experiments. The results show that at high doping levels, the internal field resists high concentrations of net charge, and “flattens” the doping profile. In addition, we perform Monte Carlo simulations, where the split gates move relative to the semiconductor sample, to demonstrate how regions of a semiconductor layer can be cleared of unwanted impurities. Finally, we discuss how a “chessboard” arrangement of square gates can be employed to create modulation-doped quantum dot arrays.