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

a better description of the bulk bands must be incorporated into the theory.Although a variety of computational methods could be used, this route doesnot provide analytical expressions for the description of the bands. Thus, amore sophisticated effective mass approach, the k p method, is typically used[29]. In this case, bulk bands are expanded analytically around a particularpoint in k-space, typically k = 0. Around this point, the band energies andwave functions are then expressed in terms of the periodic functions u nk andtheir energies E nk .General expressions for u nk and E nk can be derived by considering theBloch functions in Eq. (6). These functions are solutions of the Schro¨dingerequation for the single-particle HamiltonianH 0 ¼ p22m 0þ VðxÞð17Þwhere V(x) is the periodic potential of the crystal lattice. Using Eqs. (6) and(17), it is simple to show that the periodic functions, u nk , satisfy the equationH 0 þ 1 ðk pÞ u nk ¼ E nk u nkð18Þm 0wherek 2E nk ¼ E nk2m 0ð19ÞBecause u n0 and E n0 are assumed known, Eq. (18) can be treated inperturbation theory around k = 0 withHV¼ k pð20Þm 0Then, using nondegenerate perturbation theory to second order, one obtainsthe energiesE nk ¼ E n0 þ k22m 0þ 1 m 2 0and functionswithu nk ¼ u n0 þ 1 m 0Xm p nu m0Xm p n ! k ! p nm 2E n0 E m0ð21Þ! k ! pnmE n0 E m0ð22Þ! pnm ¼ hu n0 ! pum0 i ð23ÞCopyright 2004 by Marcel Dekker, Inc. All Rights Reserved.