Polarization of gain and symmetry breaking by interband coupling in quantum well lasers

Abstract

We have studied the influence of conduction band-valence band coupling on the polarization of gain in quantum well ͑QW͒ lasers. As a reference we used the eight-band k • p description of the gain polarization. Our eight-band k • p model accounts for the crystal orientation, lack of inversion symmetry, strain induced deformation potentials, and piezoelectricity. We have studied both strained and unstrained ͑001͒ and ͑111͒ QWs. The results are compared with the transition dipole model of the gain polarization ͓M. Asada et al., IEEE J. Quantum Electron. 20, 745 ͑1984͔͒, which is based on a phenomenological generalization of Kane's ͓J. Phys. Chem. Solids 1, 249 ͑1957͔͒ linear k • p model of bulk crystals. We found a quantitative difference between our multiband model and the transition dipole model of Asada et al. The difference is addressed to lack of orthogonality between the transition dipole and the electron wave vectors. The orthogonality is broken outside the ⌫ point by both the QW heterostructure geometry and the interband coupling. Results obtained by the complete eight-band model are also compared with restricted multiband models excluding the conduction band.

Choosing a basis that eliminates spurious solutions ink∙ptheory

“…4 Today this model is still used frequently for the study of mediumand narrow-gap nanostructures. 5,6,7,8,9,10,11,12,13 Kane's theory has a notorious pitfall: spurious solutions with large crystal momentum k, which arise from small Hamiltonian matrix elements of order k 2 . 14,15,16,17,18,19,20,21,22 23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46 7,8,9,11,12,13,47 Spurious propagating waves pose a serious problem, since their presence within the energy gap changes the physical character of the model system from semiconducting to metallic.…”

“…4 Today this model is still used frequently for the study of medium-and narrow-gap nanostructures. [5][6][7][8][9][10][11][12][13] Kane's theory has a notorious pitfall: spurious solutions with large crystal momentum k, which arise from small Hamiltonian matrix elements of order k 2 .…”

Theory of the electronic structure and carrier dynamics of strain-induced (Ga, In)As quantum dots

“…The EFA model is consequently accurate for calculations of confined states close to bandedges. It has, nevertheless, permitted the successful modelling of a wide variety of III-V compound semiconductor QW [45,49,56], QWR [35,57,58] and QD [8,[59][60][61][62][63].…”

“…The faceted geometry of the stressor islands gives rise to an angle-dependent confinement potential which has the same symmetry as that of the stressor island. An even greater deviation from the axisymmetric geometry is induced by the PEP [44,45]. We have computed the strain of SIQD using CE and the FEM.…”