Conductance in single electron transistors with quantum confinement

Single electron transistors are studied by self-consistent 3D quantum mechanical simulation. Computation of the linear-response conductance requires the calculation of thermal ensemble averages. The evaluation of these quantities can be substantially accelerated by means of Monte-Carlo sampling. 1 Introduction A single electron transistor (SET) is a three terminal device without a classically conducting path from source to drain: between source and drain resides a capacitatively gated island with tunnel junctions on either side (cf. Fig. 1). As long as the dimensions of the island regions are large compared with the electron thermal wavelength, an SET may be readily described in terms of the 'orthodox theory' [1]. For islands with dimensions comparable to the electron thermal wavelength, however, quantum confinement effects and energy-dependent tunnelling rates render the orthodox theory inapplicable. It is these quantum dot SETs that the present paper addresses. Computation of the conductance of such devices calls for a microscopic approach, that accounts correctly for both the quantum mechanics and the statistical mechanics of the quantum dot and its surroundings.