Characterization of excitons in wurtzite GaN quantum wells under valence band mixing, strain, and piezoelectric field

Low-dimensional excitons in general, and quantum-well (QW) excitons in particular, are important for linear and nonlinear semiconductor optics applications. The recent observation of the high binding energy of bulk excitons in gallium nitride samples being the main impetus, we undertake a theoretical work to characterize QW excitons in wurtzite semiconductors. In our formulation, we take into account valence band mixing, strain, and piezoelectric field effects. The in-plane behavior of excitons is treated variationally, whereas the finite-element method is used for the dependence along the growth direction. The formulation is applied to GaN-Al/sub x/ Ga/sub 1-x/N QW's. The presence of the piezoelectric field leads to the well-known quantum-confined Stark effect. We deduce from an oscillator strength analysis that the quantum-confined Franz-Keldysh effect is operational for QW's of width around 45 /spl Aring/ for an aluminum content of x=0.15. Our results further indicate that, for very clean samples, QW excitons should not ionize at room temperature even in the presence of the piezoelectric field for sufficiently narrow QW's. We determine the fractional dimensionality of the QW excitons in the absence of the piezoelectric field, which can in principle be cancelled by introducing delta-doped ionized layers on either side of the QW. The absorption spectra associated with the low-lying 1s excitons are also presented for several well widths.