We have performed simulations for the design and optimization of a qubit system for use as a component in a quantum phonon repeater. The device structure consists of two planar quantum wells whose structure is manipulated by control of the voltage on gates at the top. System design parameters include the thickness of all of the layers and the size of the gates. In addition there are delta-doped layers, whose position and doping level can be used to affect the voltage profile. A negative voltage is applied to two planar, side gates in order to pinch the electron gas into a quantum wire in the bottom well. A positive voltage is applied to a central circular gate to form a quantum dot in the upper well. The qubit system design is successful, i.e. "pinchoff" is achieved, if there is a single trapped electron in the quantum dot and a single (or small number of) conduction states in the quantum wire.
Two simulation methods have been developed for this problem. The first is a semi-analytic approximation that allows rapid solution, so that parameter space can be quickly searched for successful designs. The second is a direct numerical solution of the Poisson equation for the electrostatic potential and a single particle Schrodinger equation for the electronic wave function in the dot and the wire. Using the semi-analytic method, we found a set of successful designs, establishing the "existence" of double pinchoff (at least in simulation). Then we optimized the system to find a robust design; i.e. a design which is likely to be successful even in the presence of perturbations in the system parameters due to limited fabrication precision. These results from the semi-analytic method were validated by comparison to the direct numerical solution.
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