First-principles model for photoreflectance spectra from strained quantum wells
We present the most complete and accurate first-principles model of photoreflectance (PR) spectra from strained quantum wells currently in the field. We calculate the PR spectrum, [special characters omitted], by taking the difference between reflectivities as a function of quantum well absorption under electric fields representing the pump beam on and off. We calculate the band-to-band quantum well absorption using Fermi's Golden Rule, convolved with a Lorentzian lineshape. The Lorentzian broadened excitonic absorption includes variationally calculated binding energies. A 6 band Luttinger-Kohn k·p bandstructure calculation, including strain and valence-band mixing, provides dispersion relations, matrix elements, and wavefunctions.
We compared the calculated PR spectrum for a 100 Å In0.18 Ga0.82As/GaAs single quantum well with the experimental spectrum with excellent agreement. Our results agreed very well with experimental photoluminescence and photoluminescence excitation spectroscopy data and with another group's empirical fit evaluation of the experimental PR spectrum from a similar sample. They identified one heavy-hole state in a particular energy region where we identified two closely spaced heavy-hole states. Our theoretical PR spectra compared favorably with the experimental spectra for two AlxGa 1-xAs/GaAs single quantum wells in the literature.
Three other models exist for calculating the PR spectrum from quantum wells. The first PR model was a semi-empirical first derivative calculation. The second calculated the PR spectrum from an excitonic dielectric constant first derivative. Our model calculates both the excitonic and band-to-band absorption for two fields without assuming a derivative form. Our theoretical PR spectra matched these experimental spectra better than their theoretical models did. The third PR model used the band-to-band absorption derivative to calculate the spectrum for a superlattice, which our model was not designed to handle. The agreement between their experimental and theoretical spectra was poor.
We determined sensitivity of the PR spectrum to various parameters. The excitonic contribution dominated, but the band-to-band contribution provided a significant background spectrum. The spectrum was fairly sensitive to quantum well width, composition, and conduction band offset. The spectrum was very sensitive to the high electric field (10 kV/cm). This first principles model provides a deeper understanding of the physics of photoreflectance spectroscopy.