Fractional-dimensional calculation of exciton binding energies in semiconductor quantum wells and quantum-well wires

Abstract

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Spin dynamics of low-dimensional excitons due to acoustic phonons

“…In figure 2 we plot the spin relaxation time τ sp of the heavy-and light-hole excitons as functions of the exciton wavevector | K| in GaAs/Al 0.3 Ga 0.7 As quantum wells of well width 70Å and lattice temperature T lat = 10 K. We calculate τ sp corresponding to intraband scatterings of heavy-hole to heavy-hole (labelled HH → HH) due to the deformation potential interaction using equations (32), (35), (40), (44), (45) and (47) and integrating over both the in-plane ( q) and perpendicular (q z ) components of the phonon wavevector. A similar approach is used to calculate τ sp due to light-hole to light-hole scattering (LH → LH) via the deformation potential interaction.…”

“…Recently, Escorcia et al [46] used variationally determined envelope functions to calculate the wavefunctions of the exciton relative motion in quantum wires and disks. Like earlier approaches [45,47], the technique of evaluating α in reference [46] does not include valence band coupling effects between the heavyand light-hole bands. For our work, we improve on earlier methods [45]- [47] by utilizing realistic values of α that is evaluated by including valence band coupling effects through a 4 × 4 Baldereschi-Lipari Hamiltonian [20,21] which describes the relative motion of the exciton.…”

“…Ψ 1s ( k) yields the expected forms in the exact three dimensional and two dimensional limits. The dimensional parameter α characterizes the degree of "compression" of the confined exciton and can be calculated in several ways (see for instance references [45]- [47]). Once α is determined, many useful properties (see [38]- [42], [45]) can be determined by substituting its value into the appropriate equation that corresponds to a physical quantity.…”

“…The dimensional parameter α characterizes the degree of "compression" of the confined exciton and can be calculated in several ways (see for instance references [45]- [47]). Once α is determined, many useful properties (see [38]- [42], [45]) can be determined by substituting its value into the appropriate equation that corresponds to a physical quantity. Recently, Escorcia et al [46] used variationally determined envelope functions to calculate the wavefunctions of the exciton relative motion in quantum wires and disks.…”

“…These studies demonstrate the useful and important role of the dimensionality (denoted here by α, following [43]) which interpolates between zero in ideal quantum dots to three in an exact three dimensional system, such as an infinitely wide quantum well. The binding energy of a fractional dimensional exciton [45] is given by:…”