We have calculated the binding energy of a hydrogenic donor in a quantum well with potential shape proportional to I z as a function of the width of the quantum well and the barrier height under an applied uniform magnetic field along the z axis. As the well width decreases, the binding energy increases initially up to a critical well width (which is nearly the same for all magnetic fields) at which there is a turnover. The results are qualitatively similar to those of a hydrogenic donor in a rectangular well.
We have also calculated (p')'/' and (z')'/'for the donor electron.(p')'/' is found to be strongly dependent on the magnetic field for a given well width and weakly dependent on the well width and the barrier height, for a given value of magnetic field. (z')'~' is weakly dependent on the applied magnetic field. The probability of finding the donor electron inside the well shows a rapid decrease as the well width is reduced at nearly the well width at which the binding energy shows a maximum.
Surface quantum wells are seeking considerable attention due to their asymmetrical nature of polarized interface and its consequences. Their results with and without external perturbations are expected to be remarkably different from their counterparts in symmetrical quantum wells. Effect of electric field on binding energies of light hole and heavy hole exciton in surface quantum well composed of vacuum/GaAs/Ga 1-x Al x As are theoretically calculated as a function of well width and Al composition. Effect of image charges arising due to the mismatch of the dielectric constant at the vacuum/GaAs interface is considered. Stark shift and polarizability of exciton in this surface quantum well is also calculated for various strengths of electric field with different well width confinement as well as Al concentration. Our results show that: (1) exciton binding energy increases as the electric field applied along the growth axis increases; (2) stark shift in exciton energy decreases as electric field, Al composition and well width increase; and (3) polarizability of exciton decreases when the electric field increases, but increases when well width increases. Variation of our results with those for other symmetrical wells will provide a choice of the well for electric field applications.
The effect of a tilted magnetic field in a rectangular symmetrical quantum well formed by GaAs/AlxGa1-xAs is studied using perturbation theory. The single electron energystates and hence the resonance energies are calculated as functions of the magnetic field. The energies corresponding to the cyclotron resonance, intersubband and combined intersubband-cyclotron resonance in tilted magnetic fields are obtained. We have also calculated the oscillator strengths and cyclotron mass ratios for different magnetic fields. The cyclotron resonance and combined resonance are observed only in magnetic fields B ≥ 3T. The diamagnetic shift in the intersubband resonance and the depolarisation shift of the diamagnetically shifted intersubband resonance are calculated for various values of the tilted magnetic field. The depolarisation shift increases only for B ≥ 1T and the intersubband resonance oscillator strength starts decreasing for B ≥ 1T. The oscillator strengths are also calculated as functions of the well width and the tilt angle. While the intersubband resonance is possible in very narrow wells, the cyclotron resonance and the combined intersubband-cyclotron resonance appear only for well width L ≥ 300Å, when the tilt angle is 45° and the field strength is 3T.
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