Energy-Dependent Effective Mass Approximation in One-Dimensional Quantum Dots

We extend the effective mass approximation by taking into account the energy dependence of the effective mass. The effective Hamiltonian with an energy-dependent effective mass is applied to one-dimensional quantum dots. The eigenvalues of the effective Hamiltonian agree well with the energy levels of confined states in the dots, even in the energy region where the usual effective mass approximation is not useful. The energy dependence of the effective mass, which is common to any size of quantum dot, is derived from the nonparabolic conduction band of bulk materials.