(Color online) Strain dependence of free-exciton resonance energies. The symbols distinguish the growth technique: open squares, open circles, and closed diamonds corresponding to data for the AlN epilayers grown by -MBE, MOVPE (series I), and MOVPE (series II), respectively. The green (upper), black (middle), and red (lower) solid curves are the best fit curves for the experimental data.
(Color online) Valence band ordering (a), transition probability from each valence band to the conduction band for ordinary and extraordinary light (b), and strain dependence of free-exciton binding energy (c). (a) Relative valence band ordering of (upper red curve) and (lower green curve) against the (flat black line) band. Anticrossing between the red and green bands occurs at . For , the valence band ordering is , , and from the top to the bottom. (b) The transition from the valence band to the conduction band with symmetry is allowed only for ordinary light (dashed line) independent of strain. Depending on the anticrossing nature of the valence bands the transition probabilities vary with strain for ordinary (dashed curves) and extraordinary (solid curves) light. (c) The binding energy at is fitted to the experimental data. The difference in the binding energy is at most 3 meV.
(Color online) Valence band ordering in bulk . (a) dependence of relative valence band energies against the band with symmetry (flat black solid line) in strain-free bulk . The red (lower) and green (upper) solid curves with negative slope represent the relative energies of and , respectively. The symmetry of the uppermost valence band changes from to at . (b) The black solid curve with positive slope indicates a boundary curve satisfying , in the upper half plane of which the valence band ordering is , , and in the lower half plane of which the ordering is , , . The red (lower) solid curve with negative slope is the relation of and in bulk grown on a strain-free GaN substrate. The red solid curve crosses the black solid curve at . This means that the valence band ordering is , , for . The green (upper) solid curve with negative slope represents the relation of and when the deviation parameters of are taken into account. The crossing point of the green and black solid curves gives .
Comparison of valence band parameters obtained in the present work with those reported previously.
Transition probability from each valence band to the conduction band for ordinary and extraordinary light.
Dielectric constants of AlN. In the present work, the dielectric constants were calculated using the values of , 0.868 and 0.833.
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