Envelope-function equation and motion of wave packet in a semiconductor superlattice structure

We present a new description of envelope-function equation of the superlatt ice (SL). The SL wave function and corresponding effective-mass equation ar e formulated in terms of a linear combination of Bloch states of the consti tuent material with smaller band gap. In this envelope-function formalism, we review the fundamental concept on the motion of a wave packet in the SL structure subjected to steady and uniform electric fields F. The review con firms that the average of SL crystal momentums K = (k(X),k(Y),q), where (k( x), ky) are bulk inplane wave vectors and q SL wave vector, included in a w ave packet satisfies the equation of motion (K)= (K)(0) + Ft/(h) over bar; and that the velocity and acceleration theorems provide the same type of gr oup velocity and definition of the effective mass tensor, respectively, as in the Bulk. Finally, Schlosser and Marcus's method for the band theory of metals has been used by Altarelli to include the interface-matching conditi on in the variational calculation for the SL structure in the multi-band en velope-function approximation. We re-examine this procedure more thoroughly and present variational equations in both general and reduced forms for SL s, which agrees in form with the proposed envelope-function formalism. As a n illustration of the application of the present work and also for a brief investigation of effects of band-parameter difference on the subband energy structure, we calculate by the proposed variational method energies of non -strained GaAs/Al0.32Ga0.68As and strained In0.63Ga0.37As/In(0.73)Ga(0.27)A s(0.58)P(0.42)SLs With well/barrier widths of 60 Angstrom/500 and 30 Angstr om/30 Angstrom, respectively.