Donor states in modulation-doped Si/SiGe heterostructures

Abstract

We present a unified approach for calculating the properties of shallow donors inside or outside heterostructure quantum wells. The method allows us to obtain not only the binding energies of all localized states of any symmetry, but also the energy width of the resonant states which may appear when a localized state becomes degenerate with the continuous quantum well subbands. The approach is non-variational, and we are therefore also able to evaluate the wave functions. This is used to calculate the optical absorption spectrum, which is strongly non-isotropic due to the selection rules. The results obtained from calculations for Si/Si$_{1-x}$Ge$_x$ quantum wells allow us to present the general behavior of the impurity states, as the donor position is varied from the center of the well to deep inside the barrier. The influence on the donor ground state from both the central-cell effect and the strain arising from the lattice mismatch is carefully considered.Comment: 17 pages, 10 figure

Effect of resonant impurity scattering on the carrier dynamics in Si∕SiGe quantum wells

“…This expectation is correct if only the CCS channel contributes, but it is no longer so when the RSS channel is included because the width of the resonant level ⌫͑z 0 ͒ depends on the position z 0 in a complicated way. 7 In fact, in the present sample structure, ⌫͑z 0 ͒ attains its maximum value when z 0 is in the quantum well and about 8 Å from one interface. Such behavior of the broadening of the resonant level also introduces a weak dependence of the interface roughness scattering on the position of the ␦-doping layer.…”

“…The first channel which we call conventional Coulomb scattering ͑CCS͒ will be treated as conventional potential scattering, while the second resonant state scattering ͑RSS͒ channel will be analyzed in more details in the next section. As an approximation, which typically is well justified, 4,7 we can ignore the cross term ͑see below͒ and treat the two scattering channels independently.…”

“…14͒ and in 2D electron gases. 7,15 The complicated theory of resonant scattering in quantum wells can be much simplified if intersubband transitions are ignored. This will be the case to be studied in the present work.…”

“…18 The details of the calculation can be found in Ref. 7. With these eigensolutions one can calculate all the relevant scattering rates given in the preceding section, and the Monte Carlo calculation can then be performed.…”

“…In connection to the possible THz radiation from Si/ SiGe quantum wells, such resonant states were studied in detail very recently. 7 It was found that the width of the resonant level is very sensitive to the position of the impurity when the impurity is moved from the center of the well into the barrier. Therefore, in a ␦-doped quantum well sample, the electron transport parallel to the interfaces will depend on the position of the ␦-doping.…”