By Peter W. Hawkes (Ed.)
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Additional resources for Advances in Electronics and Electron Physics, Vol. 72
In heterostructures with wide gap hosts like GaAs-Gal -,AI,As, the r6related states are well energy-separated from the r,-related ones. The Landau levels of the r,-related subbands are complicated (see Fig. 24 for an example). In a given manifold they are unevenly spaced in n and exhibit a pronounced non-linearity upon B. This is a mere consequence of the complexity of the T, in-plane dispersion relations. The associated wavefunctions display a large mixing of m, = k3/2 and m, = & 1/2 components.
OPTICAL CHARACTERIZATION OF SEMICONDUCTOR HETEROLAYERS 43 and f2 envelopes is: where the + sign refers to fi. One readily obtains the eigen-energies: where: eB w, = m *c and v labels the eigenstates of the z motion. The wavefunction associated with E,, n, a, is: with The interesting point is that the Landau level spectrum is entirely discrete (for the bound states of the z motion). For a given bound state v one can write the density of states as: where gB is the universal degeneracy factor associated with the center of the cyclotron orbit: The discreteness of the B # 0 spectrum is in marked contrast with the continuous spectrum which prevails at B = 0: p;u;o(&) = L,L m* Y2& ~ Y(E - Ev) (93) The imperfections and defects round off the 6 singularities of the B # 0 density of states (Fig.
BASTARD, C. DELALANDE, Y. GULDNER AND P. 18. In-plane dispersion relations of the valence subbands of a GaAs-Ga,,,AIo,,As quantum well ( L = 100 A) subjected to an external electric field F//z ( F = lo’ Vjcm). The twofold Kramers degeneracy prevailing at k, = 0 is lifted at k, # 0. After Bastard and Brum (1986). f 1/2 (or f (k 3/2, f (f 1/2)). This is illustrated in Fig. 19 for the two wells whose subbands dispersions where shown in Fig. 17. , 1985; Chang and Schulman, 1983, 1985; Altarelli, 1983, 1985, 1986; Bastard and Brum (1986) influences the optical spectra (see Section 111).
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