Theoretical model for polarization superlattices: Energy levels and intersubband transitions

A theoretical model for stress-free polarization superlattices composed of wurtzite semiconductors is described, which exploits Airy function solutions of the Schrödinger equation for a superlattice in the absence of free carriers. The theory is applied to several stress-free structures consisting of AlN barriers and GaN wells. The part played by the crystal-field splitting of the valence band and its dependence on biaxial elastic strain in determining the conduction-band offset is fully taken into account. Electric fields were determined from the spontaneous and nonlinear piezoelectric polarization. Energy bands, transition energies between subbands 1 and 2, and associated eigenfunctions are calculated, and the sensitivity to the conduction-band discontinuity explored. Intersubband radiative and nonradiative transition rates are estimated taking into account the Bloch-function overlap integrals and the role of intervalley scattering. Upper limits to technologically useful subband separations set by conduction-band offsets and the energy of conduction-band valleys are discussed. An upper limit of around 1.5 eV for the energy of the second subband is indicated.