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Spontaneous emission of localized excitons in InGaN single and multiquantum well structures
1.For a review see, for example, S. Strite andH. Morkoc, J. Vac. Sci. Technol. B 10, 1237(1992).
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9.H. Tsutsui, T. Igarashi, T. Azuhata, T. Sota, S. Chichibu, and S. Nakamura (unpublished). The exciton binding energy in the N QW was calculated by the variational method according to G. Bastard, E. E. Mendez, L. L. Chang, and L. Esaki [Phys. Rev. B 26, 1974 (1982)]. In the calculation, we started from the Hamiltonian suitable to QWs including mass and dielectric constant anisotropy, assuming an infinite barrier height to simplify the calculation. After variable transformations for Z coordinates (perpendicular to the QW plane) that formally remove the mass anisotropy in the Hamiltonian, the exciton binding energy was calculated using the trial function for the excitonic relative motion given by considering the fact that the 3D exciton Bohr radius is as small as 3.4 nm. Here is the variational parameter, is the absolute value of the relative positions of the electron and the hole in the QW plane, and Z (Z is the transformed Z coordinate of the electron (hole).
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15.The piezoelectric field was calculated with the values of piezoelectric constants of GaN (see Ref.1) according to M. P. Halsall, J. E. Nicholls, J. J. Davies, B. Cockayne, and P. J. Wright [J. Appl. Phys. 71, 907 (1992)], and the Stark shift due to the electric field was calculated by the variational method neglecting exciton binding energy. Calculations are based on works by D. A. Miller, D. S. Chemla, T. C. Damen, A. C. Gross, W. Wiegmann, T. H. Wood, and C. A. Burrus [Phys. Rev. Lett. 53, 2173 (1981)] and [Phys. Rev. B 32, 1043 (1985)].
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