A computational method for energy level spin splitting simulation in InAs/GaAs semiconductor quantum dots

An impact of the spin-orbit interaction on the electron quantum confinement is considered theoretically for narrow gap semiconductor cylindrical quantum dots. To study the phenomena for InAs quantum dot embedded into GaAs semiconductor matrix, the effective one electronic band Hamiltonian, the energy position dependent electron effective mass approximation, and the spin-dependent Ben Daniel-Duke boundary conditions are considered, formulated and solved numerically. To solve the nonlinear Schrödinger equation, we propose a nonlinear iterative algorithm. This calculation algorithm not only converges for all simulation cases but also has a good convergent rate. With the developed quantum dot simulator, we study the effect of the spin-orbit interaction for narrow gap InAs/GaAs semiconductor cylindrical quantum dots. From the numerical calculations, it has been observed that the spin-orbit interaction leads to a sizeable spin-splitting of the electron energy states with nonzero angular momentum. Numerical evidence is presented to show the splitting result is strongly dependent on the quantum dot size.