Electric-dipole transitions between group-III acceptor states in uniaxially compressed Ge

Abstract

We study the electric-dipole transitions between group-III acceptor states in Ge under stress along the [001] crystallographic direction in the effective mass approximation. We systematically investigate the cases of zero stress, infinitesimal stress, and finite stress including the low-stress and the high-stress regions. Our results show quantitative agreement with experimental data at zero stress and at infinitesimal stress. The relative intensities of infinitesimal-stress-induced components of transitions from the 1Γ(8)(+) state to the nΓ(8)(-) states do not correlate significantly with the species of acceptors except for the transition to the 1Γ(8)(-) state. The oscillator strengths of some transitions are susceptible to the stress in the low-stress region (<0.3 kbar), and could be zero at a specific stress. The behaviours of the stress dependence of oscillator strengths for different transition lines are explained in terms of the compositions of the wavefunctions and the dipole matrix elements. In the high-stress region (> or approximately equal3 kbar), the ground state is s-like, and only the transitions to the p-like states can have non-negligible oscillator strengths. The photon absorbed (emitted) and associated with each electric-dipole transition between the s-like and the p-like states is polarized either parallel or perpendicular to the stress direction. We also calculate the absorption spectra for Ge:Ga at liquid-helium temperature. The results are in good agreement with experiment.

Interface effects on acceptor qubits in silicon and germanium

“…The energy difference is enhanced as the acceptor gets closer to the interface. A decreasing splitting is found for distances d a 0.5 , min * ~smaller that the ones shown in the figures, probably signalling a qualitative change in symmetry similar to the one found in the limit of infinite strain, with extra degeneracies [23,24]. However, we do not expect the effective mass approximation used here to be valid for values d d .…”

“…This implies that close to an interface the four-fold degeneracy of the Γ 8 states is broken into two doubly degenerate states with symmetries Γ 6 and Γ 7 respectively. This effect of symmetry reduction by the interface is analogous to the effect of uniaxially strained silicon in the (001) direction [23,24,45].…”

“…However, the z projection of the atomic angular momentum is associated to the j coordinate so L z is not affected by the presence of the interface and, as F z is the sum of L z and J z , the selection rule equation (5) G respectively. This effect of symmetry reduction by the interface is analogous to the effect of uniaxially strained silicon in the 001 ( ) direction [23,24,45]. The barrier potentials usually considered are much larger than the typical binding energies and hence a hard-wall boundary condition z d 0 ( )  Y -= is assumed for the wave function.…”

“…This effect is more significant for the levels coming from the four-fold degenerate bulk groundstate than for the excited states leading to the compression of the full energy spectrum [46]. This compression also appears in bulk strained systems [23,24] due to the splitting of the heavy-hole and the light-hole bands.…”

“…Not only the energies but also the symmetry of the bound states may be modified. In the case of acceptors, the four-fold degeneracy of the ground state may be broken by strain [22][23][24], electric field [25,26] and/or magnetic fields. Characterisation of dopants embedded in nanostructures can be performed via transport measurements [2,27,28] while Scanning Tunnel Microscopy can give information of the wave-function of subsurface dopants [29][30][31][32].…”