Energy Levels of a Hydrogenic Impurity in Gallium ARSENIDE/GALLIUM(1-X) Aluminum(x) Arsenide Multiple-Quantum Structures in a Magnetic Field

Energy levels of a hydrogenic impurity (Si) in the (GaAs/Ga_{1-x}Al_{x }As) quantum-well systems with and without an applied magnetic field perpendicular to the interfaces have been studied theoretically. A variational approach employing the envelope wavefunction approximation has been used. The envelope wavefunction is chosen to be a product of a combination (mixing) of one or more confined states of a free electron in the one dimensional quantum-well potential considered with Gaussian trial functions. First, the study is focused on a coupled double -quantum-well model which serves as a bridge between the single-, and multiple-quantum-well structures. It is found that the binding energies depend significantly upon the well width, the barrier width, the location of the impurity, and the magnetic field. A comparison with recent experiments demonstrates that intersubband mixing plus the difference in electron effective-masses in the two semiconductors should be included in the calculations. Next, the problem is extended to the cases of multiple-quantum-well model with narrow barriers. For the doped well at the center of the structure in zero field, the calculated binding energies do not change in any significant way beyond 15 periods for either of two structures investigated (with periodicities of 80A well-9A barrier and 40A well -9A barrier). Calculations are also performed for superlattices with 15 periods in the presence of the magnetic field. Very good agreement is obtained in comparing the results with recent measurements. For the doped well at various locations within the structure, the outer boundary of the finite superlattice (15 wells) has significant effect on the binding energies, especially when the doped well is less than 4 wells away from the boundary. Finally, in a departure from above approach, we have attempted to simplify the problem by subsumming the entire effect of the superlattice periodic potential in the electron effective-mass (miniband effective-mass-approximation). This gives anisotropic masses, which are used in variational calculations of energy levels as functions of the applied magnetic field. Remarkably, the results yield reasonable agreement with experiments for two superlattices considered (as mentioned in previous paragraph).