Abstract

The Schrodinger equation in the effective mass approximation is commonly used to calculate the electronic states confined in low-dimensional semiconductor structures. Three-dimensional calculations are unavoidable in the general case of asymmetrical quantum structures and the solutions are not analytical, thus demanding resource-consuming numerical methods. In particular cases, the formalism may be simplified by several approaches: neglecting the gradient of the effective mass, approximating the confinement potentials by simple functions, and exploiting the symmetries in order to reduce the dimensionality of the equation. Particular approaches rarely lead to full analytical solutions, but often to more-convenient, semi-analytical or numerical calculations. We revisit the adiabatic approach for using the Schrodinger formalism in axisymmetric and asymmetrical quantum dots by discussing its reliability as compared with the direct finite element method. We discuss how the difference between the results obtained from the two methods depends on the shape and the symmetry of the quantum structures. We show that adiabatic approach and direct finite element calculation involve similar levels of complexity and computing resources for axisymmetric quantum dots, while providing larger relative differences for flatter structures. On the contrary, for asymmetrical quantum structures, the adiabatic approximation has clearly an advantage regarding the use of computing resources, yet maintaining a high degree of accuracy.