Effect of shape and size on electron transition energies of inas semiconductor quantum dots

We present a theoretical study of the electron energy states in three-dimensional narrow gap semiconductor quantum dots with different shapes under an external magnetic field. The problem is solved by using the effective one-electronic-band Hamiltonian, the energy- and position-dependent electron effective mass approximation, and the Ben Daniel-Duke boundary condition. We investigate small InAs/GaAs quantum dots with disk, lenticular, and conical shapes. Electron energy dependence on volume is expressed as V ^-γ where the exponent γ depends on the dot shapes and can vary over a wide range. The most stable against the dot size deviations (among dots of the same base radius) is the energy spectra of the conical dots. In addition, this type of dot also has the weakest diamagnetic shift. Contrarily, quantum dots with cylindrical shapes show a wide deviation in energy and a relatively strong diamagnetic shift.