Journal of Computational Electronics 2: 269–273, 2003 c  2003 Kluwer Academic Publishers. Manufactured in The Netherlands. Efficient Computational Method for Ballistic Currents and Application to Single Quantum Dots M. SABATHIL AND S. BIRNER Walter Schottky Institute, Technische Universit¨ at M ¨ unchen, Am Coulombwall 3, 85748 Garching, Germany D. MAMALUY Department of Electrical Engineering, Arizona State University, Tempe, AZ 85287-5706, USA P. VOGL Walter Schottky Institute, Technische Universit¨ at M ¨ unchen, Am Coulombwall 3, 85748 Garching, Germany Abstract. We present an efficient method for the calculation of the ballistic transmission function and current through an arbitrarily shaped, multi-terminal two- or three-dimensional open device. The method is applicable to cases where a ballistic current model is meaningful and charge self-consistency is not relevant, such as quantum dot devices, quantum wires, or interferometer type of structures. As a concrete example, we study the electron escape rate in self-assembled GaAs/InGaAs single quantum dots as a function of applied bias, as measured by photocurrent experiments. Keywords: ballistic transport, quantum dots, nanometer device simulation 1. Introduction In recent years, zero dimensional heterostructures such as quantum dots (QD) became a subject of increas- ing attention experimentally as well as theoretically. So far, most theoretical studies have focused on the static electronic and optical properties of these atom- like structures. On the other hand, many experimen- tal groups investigate the transport properties of open quantum dot devices either by resonant tunneling ex- periments [1–5] or in photocurrent experiments [6–8]. The calculation of the tunneling transport of electrons and holes through a realistic QD coupled to external leads is extremely difficult and is basically out of reach with present-day methods. Thus, the transport calcula- tions that have been published so far either considered simplified geometries [9–11] or very small structures [12]. Recently, we have developed an efficient method to calculate the ballistic transmission function and current through an arbitrarily shaped, multi-terminal two- or three-dimensional open device [13]. This method, that we have termed contact block reduction (CBR) method, allows us to study the transport properties of realis- tic quantum dot structures. It is applicable to all cases where the current is sufficiently small so that a ballis- tic model is meaningful and charge self-consistency is not relevant. This is the case for many quantum dot devices, quantum wires, or interferometer type of structures. With the widely used QTBM [14,15] method, the computational effort for the calculation of the ballis- tic current through a 3D device of complex geometry scales with the third power of the number of nodes or grid points covering the entire device. This requires the repeated inversion of matrices of typical size 10 5 –10 6 for each energy step. In the CBR method, on the other hand, this effort can be reduced to a single calculation of a small percentage of the stationary states in the iso- lated device plus the inversion of a small matrix that is