We report experiments and theory on the effects of electric fields on the optical absorption near the band edge in GaAs/AlGaAs quantum-well structures. We find distinct physical effects for fields parallel and perpendicular to the quantum-well layers. In both cases, we observe large changes in the absorption near the exciton peaks. In the parallel-field case, the excitons broaden with field, disappearing at fields \ensuremath{\sim}${10}^{4}$ V/cm; this behavior is in qualitative agreement with previous theory and in order-of-magnitude agreement with direct theoretical calculations of field ionization rates reported in this paper. This behavior is also qualitatively similar to that seen with three-dimensional semiconductors. For the perpendicular-field case, we see shifts of the exciton peaks to lower energies by up to 2.5 times the zero-field binding energy with the excitons remaining resolved at up to \ensuremath{\sim}${10}^{5}$ V/cm: This behavior is qualitatively different from that of bulk semiconductors and is explained through a mechanism previously briefly described by us [D. A. B. Miller et al., Phys. Rev. Lett. 53, 2173 (1984)] called the quantum-confined Stark effect. In this mechanism the quantum confinement of carriers inhibits the exciton field ionization. To support this mechanism we present detailed calculations of the shift of exciton peaks including (i) exact solutions for single particles in infinite wells, (ii) tunneling resonance calculations for finite wells, and (iii) variational calculations of exciton binding energy in a field. We also calculate the tunneling lifetimes of particles in the wells to check the inhibition of field ionization. The calculations are performed using both the 85:15 split of band-gap discontinuity between conduction and valence bands and the recently proposed 57:43 split. Although the detailed calculations differ in the two cases, the overall shift of the exciton peaks is not very sensitive to split ratio. We find excellent agreement with experiment with no fitted parameters.

Electric field dependence of optical absorption near the band gap of quantum-well structures.

Using nonlocal empirical pseudopotentials, we compute the band structure and shear deformation potentials of strained Si, Ge, and SiGe alloys. Fitting the theoretical results to experimental data on the phonon‐limited carrier mobilities in bulk Si and Ge, the dilatation deformation potential Ξd is found to be 1.1 eV for the Si Δ minima, −4.4 eV for the Ge L minima, corresponding to a value for the valence band dilatation deformation potential a of approximately 2 eV for both Si and Ge. The optical deformation potential d0 is found to be 41.45 and 41.75 eV for Si and Ge, respectively. Carrier mobilities in strained Si and Ge are then evaluated. The results show a large enhancement of the hole mobility for both tensile and compressive strain along the [001] direction, but only a modest enhancement (approximately 60%) of the electron mobility for tensile biaxial strain in Si. Finally, from a fit to carrier mobilities in relaxed SiGe alloys, the effective alloy scattering potential is determined to be about 0...

Band structure, deformation potentials, and carrier mobility in strained Si, Ge, and SiGe alloys

This review is concerned with quantum confinement effects in low-dimensional semiconductor systems. The emphasis is on the optical properties, including luminescence, of nanometre-sized microcrysta...

Low-dimensional systems: quantum size effects and electronic properties of semiconductor microcrystallites (zero-dimensional systems) and some quasi-two-dimensional systems

https://deepblue.lib.umich.edu/bitstream/handle/2027.42/28081/0000527.pdf;sequence=1

On the stability of surfaces of stressed solids

In this article we review the experimental and theoretical investigations of the linear and nonlinear optical properties of semiconductor quantum well structures, including the effects of electrostatic fields, extrinsic carriers and real or virtual photocarriers.

Linear and nonlinear optical properties of semiconductor quantum wells

Energy levels of hydrogenic impurity states in GaAs-Ga1−xAlxAs quantum well structures

Theoretical and experimental studies are presented to understand the initial stages of growth of InGaAs on GaAs. Thermodynamic considerations show that, as strain increases, the free‐energy minimum surface of the epilayer is not atomically flat, but three‐dimensional in form. Since by altering growth conditions the strained epilayer can be grown near equilibrium or far from equilibrium, the effect of strain on growth modes can be studied. In situ reflection high‐energy electron diffraction studies are carried out to study the growth modes and surface lattice spacing before the onset of dislocations. The surface lattice constant does not change abruptly from that of the substrate to that of the epilayer at the critical thickness, but changes monotonically. These observations are consistent with the simple thermodynamic considerations presented.

https://deepblue.lib.umich.edu/bitstream/handle/2027.42/70448/APPLAB-53-8-684-1.pdf?sequence=2

Role of strain and growth conditions on the growth front profile of InxGa1−xAs on GaAs during the pseudomorphic growth regime

We have calculated the binding energies of the ground (1s-like) and excited (2${p}_{\ifmmode\pm\else\textpm\fi{}}$-like) states of a hydrogenic donor associated with the first subband in a GaAs quantum well, sandwiched between two semi-infinite layers of ${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$${\mathrm{Al}}_{\mathrm{x}}$As. Results have been obtained as a function of the potential-barrier height (or equivalently of Al concentration x) and the size of the quantum well in the presence of an arbitrary magnetic field. We have considered the two cases of donor at the center and at the edge of the well. The applied magnetic field is taken to be parallel to the axis of growth of the quantum-well structure. We have used a variational approach in which the trial wave functions are expanded in terms of appropriate Gaussian basis sets. For a given value of the magnetic field, the binding energies are found to be larger than their values in a zero magnetic field.

Effect of magnetic field on the energy levels of a hydrogenic impurity center in GaAs/Ga1-xAlxAs quantum-well structures.

A formalism to study the effect of alloy disorder and interface roughness on the linewidths of excitonic emission spectra in quantum‐well structures is developed. The study includes the cases where the alloy forms (a) the barrier region, (b) the well region, and (c) both the barrier and well regions of the quantum‐well structures, and demonstrates the importance of alloy quality in all three cases. The relative importance of the effects of alloy disorder and interface roughness on the excitonic linewidths is discussed. As an illustration, the formalism is applied to AlGaAs/GaAs, InP/InGaAs, and InAlAs/InGaAs quantum‐well structures and the results compared with the available experimental data.

Role of interface roughness and alloy disorder in photoluminescence in quantum‐well structures

We have developed a simple theory to understand the role of interfacial quality in the line shape of photoluminescence spectra in quantum wells. The interface is described in terms of microscopic fluctuations δ1 and δ2, where δ1 is the local fluctuation in the well width and δ2 is the lateral correlated extent of the fluctuation. We make use of Lifshitz theory of disordered alloys to determine the probability of distribution of fluctuations in the well size over the extent of the optical probe, i.e., the exciton. The line shape is then calculated from this probability distribution. Both δ1 and δ2 are found to be important in controlling the linewidths in quantum wells. The use of this quantitative theory to characterize the microscopic nature of interfaces is discussed.

K. K. Bajaj

Papers

Energy levels of hydrogenic impurity states in GaAs-Ga1−xAlxAs quantum well structures

Role of strain and growth conditions on the growth front profile of InxGa1−xAs on GaAs during the pseudomorphic growth regime

Effect of magnetic field on the energy levels of a hydrogenic impurity center in GaAs/Ga1-xAlxAs quantum-well structures.

Role of interface roughness and alloy disorder in photoluminescence in quantum‐well structures

Theory of photoluminescence line shape due to interfacial quality in quantum well structures