Energy levels of and in graded quantum-well structures of GaAAs under magnetic fields

Energy levels of (Formula presented) and (Formula presented) confined in graded quantum wells of GaAs/(Formula presented)(Formula presented)As structures under magnetic fields are investigated in detail by the variational method. Binding energies as well as the 1s→2(Formula presented) transition energy for (Formula presented) and (Formula presented) in a square well calculated from the same trial wave functions are shown to be in good agreement with existing Monte Carlo calculations and with experimental data. An interesting quantum shape effect is revealed by studying the ratio of (Formula presented) transition energy to its binding energy. A detailed study of (Formula presented) and (Formula presented) states in graded quantum wells shows that (a) (Formula presented) binding energies first increase with the magnetic field and then decrease when the field increases further, (b) for a given well gradient, the singlet s-like state binding energy peaks at a much lower field strength than the triplet p-like states, producing the energy level crossing phenomenon, and (c) (Formula presented) will be dissociated into a (Formula presented) and an electron when either the field or the gradient increases.