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

摘要

Low-dimensional excitons in general, and quantum-well (QW)nexcitons in particular, are important for linear and nonlinearnsemiconductor optics applications. The recent observation of the highnbinding energy of bulk excitons in gallium nitride samples being thenmain impetus, we undertake a theoretical work to characterize QWnexcitons in wurtzite semiconductors. In our formulation, we take intonaccount valence band mixing, strain, and piezoelectric field effects.nThe in-plane behavior of excitons is treated variationally, whereas thenfinite-element method is used for the dependence along the growthndirection. The formulation is applied to GaN-Alx Ga1-xnN QW's. The presence of the piezoelectric field leads to thenwell-known quantum-confined Stark effect. We deduce from an oscillatornstrength analysis that the quantum-confined Franz-Keldysh effect isnoperational for QW's of width around 45 Å for an aluminum contentnof x=0.15. Our results further indicate that, for very clean samples, QWnexcitons should not ionize at room temperature even in the presence ofnthe piezoelectric field for sufficiently narrow QW's. We determine thenfractional dimensionality of the QW excitons in the absence of thenpiezoelectric field, which can in principle be cancelled by introducingndelta-doped ionized layers on either side of the QW. The absorptionnspectra associated with the low-lying 1s excitons are also presented fornseveral well widths