Electron energy spectrum in cylindrical quantum dots and rods: approximation of separation of variables

A simple analytical method for electron energy spectrum calculations of cylindrical quantum dots (QDs) and quantum rods (QRs) is presented. The method is based on a replacement of an actual QD or QR hamiltonian with an approximate one, which allows for a separation of variables. Though this approach is known in the literature, it is essentially expanded in the present paper by taking into account a discontinuity of the effective mass, which is of importance in actual semiconductor heterostructures, e.g., InGaAs QDs or QRs embedded in GaAs matrix. Several examples of InGaAs QDs and QRs are considered—their energy spectrum calculations show that the suggested method yields reliable results both for the ground and excited states. The proposed analytical model is verified by numerical calculations, results of which coincide with an accuracy of ~1 meV.