By Peter W. Hawkes (Ed.)
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Extra resources for Advances in Electronics and Electron Physics, Vol. 72
We are interested in selecting the a which renders the energy levels the more sensitive to the offset V,. B. method we obtain the approximate quantization rule: where m* is the carrier effective mass, assumed to be position-independent for simplicity. Thus, qualitatively, we get: Equation (59) shows that the smaller a makes the EN'S to be the more sensitive to V,. This is why band offset determinations are easier in nonrectangular quantum well structures. The pseudo-parabolic wells are multiple quantum wells whose thicknesses are adjusted to mimic a parabolic band edge profile.
Loo), xl(z) is the ground quantum well bound state wavefunction and II is the variational parameter. The acceptor problem is more difficult to handle but symmetry considerations help to reduce the difficulties for on-center acceptors. Masselink et al. (1983, 1985) have used the 50 G. BASTARD, C. DELALANDE, Y. GULDNER A N D P. VOISIN trial wavefunction: 7 C nr;l/Z 1 Cn(i)exp- a i ( x Z+ y 2 + pzz) n=O 4 $(r) = i=l (101) when T;‘I2is a five component basis whose elements displays or d symmetry,, Cn(i)and p are variational parameters and a, fixed lengths chosen to cover a large physical range.
It may be remarked that Eq. (43) is non-linear upon the eigenvalue E, as a result of the projection technique. The boundary conditions which have to be fulfilled across the interfaces are that: x(z) and (45) OPTJCAL CHARACTERIZATION OF SEMICONDUCTOR HETEROLAYERS 19 are both continuous. The continuity condition for dX/dz can be written: in complete analogy with the heavy hole case. In Eq. (47), P(E,z) is a positionand energy-dependent effective mass which appears in the implicit formulation of the dispersion relations in the Kane model for each host layer: The continuity condition of Eq.