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Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

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Taken together, the hexagonal lattice structure, crystal shape asymmetry,and the electron–hole-exchange interaction split the original ‘‘spherical’’eightfold degenerate exciton into five levels. The levels are labeled <strong>by</strong> themagnitude of the exciton total angular momentum projection, F = M + s z :one level with F = F2, two with F = F1, and two with F = 0. The levelenergies, e jFj , are determined <strong>by</strong> solving the secular equation det(Eˆ e jFj ) = 0,where the matrix Eˆ consists of matrix elements of the asymmetry perturbationsand the exchange interaction, Hˆexch, taken between the exciton wavefunctions C a,M (r e , r h ) = w a (r e )w M (r h ):z; 3=2 z; 1=2 z; 1=2 z; 3=2 #; 3=2 #; 1=2 #; 1=2 #; 3=2z; 3=23g2z; 1=2 0D2g20 0 0 0 0 0 0D2pffiffiffi0 0 i 3 g 0 0 0gz; 1=2 0 02 þ D 0 0 i2g 0 023g Dpffiffiffiz; 3=2 0 0 00 0 i 3 g 02 2pffiffi3g D#; 3=2 0 i 3 g 0 0 0 0 02 2g#; 1=2 0 0 i2g 0 02 þ D 0 02pffiffiffig#; 1=2 0 0 0 i 3 g 0 02 þ D 023g#; 3=2 0 0 0 0 0 0 02D2ð14Þwhere g = (a ex /a) 3 tx ST v(b), and the dimensionless function v(b) is writtenin terms of the electron and hole radial wave functions:vðbÞ ¼ 1 Z aa 2 dr sin 2 ðpr=aÞ½R 2 06ðrÞ þ 0:2R2 2 ðrÞŠ0ð15ÞThe dependence of v on the parameter b is shown in Fig. 1d.Solution of the secular equation yields five exciton levels. The energyof the exciton with total angular momentum projection jFj = 2 and itsdependence on the crystal size is given <strong>by</strong> [3]e 2 ¼3g2D2ð16Þ<strong>Copyright</strong> <strong>2004</strong> <strong>by</strong> <strong>Marcel</strong> <strong>Dekker</strong>, <strong>Inc</strong>. <strong>All</strong> <strong>Rights</strong> <strong>Reserved</strong>.

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