A self-consistent Poisson-Schrödinger solution showing the HH (red solid line) and LH bands (blue solid line) as a function of vertical distance along with the carrier density (dashed green line) at 300 K.
Reciprocal space maps around the (004) and (224) Si-substrate Bragg peak for the center of the design 1 wafer. In addition to the substrate peak, superlattice oscillations are observed. The dashed line in the (004) map corresponds to the position of the radial scan used for dynamical scattering theory simulations. The dashed triangle in the (224) map corresponds to the relaxation triangle, spanned by the Si and theoretical Ge (fully relaxed and pseudomorph) Bragg peaks. It can be seen that the 0th-order superlattice peak (SL0) lies exactly on the relaxed line, confirming strain symmetrization.
Radial scan (red) together with fully dynamical Takagi-Taupin simulation (blue) for the parameter set with the best fit to the measurement, for the sample piece at the centre of the design 1 wafer.
Intensity of satellite peaks as a function of their position along Qz for several parameter sets (colored lines and symbols) compared to the experimental data (black circles). The series shows a variation of the barrier composition , the relative thicknesses of barrier and quantum well are adjusted to keep the superlattice period and the average Ge composition constant. All data are normalized to the zero-order satellite peak SL0.
The thicknesses (solid symbols) and Ge content (open symbols) across the design 1 wafer.
The layer thickness characterization in the top part of the design 1 superlattice demonstrates a high interface quality and a low roughness on a scale of 50 nm. The faint blue frame in the image indicates where the extracted intensity profile, shown in the inset, was taken. (b) and (c) A high TDD can be recognized in bright field TEM images in the (220) Bragg condition using only the undiffracted beam for imaging. Dislocations are not restricted to the bottom part of the layers but reach the surface with high density. (d) High angle annular dark field scanning transmission electron microscopy image in (110) zone axis orientation shows that in the vicinity of dislocations the QWs (bright contrast) are clearly thinner. This is partly compensated by a corresponding increase in thickness of the next barrier layer.
A SEM image of a free standing Hall bar device with heaters, electrical contacts, and thermometers.
An optical microscope image of the free standing Hall bar shown in Fig. 7 .
The electrical conductivity as measured by 4 terminal methods on Hall bar samples versus the QW width of the samples at 300 K. for design 1 (blue squares) and design 2 (red circles).
The Hall mobility (solid symbols) and carrier density (open symbols) versus the QW width of the samples at 300 K for design 1 (blue squares) and design 2 (red circles).
At high temperatures (>100 K) the Hall mobility (left, measured up to 1 T) decreases with a behaviour typical of optical phonon scattering. Maximum mobilities are generally reached in the region of 30 K, and the mobility then decreases with decreasing temperature, indicating ionized impurity scattering. The Hall sheet density per QW is about cm−2 for the 10 and 50 QW structures, but the 1 and 3 QW structures show some increase in density with temperature as dopants are ionized.
The Shubnikov de Haas oscillations in the 50 QW sample indicate a sheet carrier density of cm−2 (as compared to the Hall sheet density of cm−2, which corresponds to cm−2 per QW). The effective mass is 0.14 me and the Dingle ratio is 4.4.
The mobility spectra at 300 K generally indicate two peaks, corresponding to transport within the QWs and within the doped SiGe layers. The QWs are represented by the peaks at higher mobility, in the region of 1500 cm2 V−1 s−1.
The magnetoresistance of a structure featuring a single QW; the magnetoresistance calculated from the mobility spectrum in Fig. 13 closely fits the data across the whole range of magnetic field. Positive magnetoresistance (increase of with B) is a clear sign of parallel conduction; the decrease in the slope of with increasing B is also visible.
The temperature measured by the SThAFM as a function of distance from the hot side thermometer on a Hall bar device of bulk p-Si0.2Ge0.8. As the SThAFM only has a 80 μm scan range, 7 scans have been stitched together using holes in the top Si3N4 layer as alignment markers. A simulation assuming a 40 Wm−1 K−1 thermal conductivity for the Hall bar material produces a best fit to the results.
The Seebeck coefficient versus QW width for design 1 (blue squares) and design 2 (red circles).
The thermal conductivity versus QW width for design 1 (blue squares) and design 2 (red circles).
The thermal conductivity plotted versus the electrical conductivity for each sample. Design 1 (blue squares), design 2 (red circles), and bulk p-Si0.2Ge0.8 reference samples (green diamonds).
The power factor as a function of the QW width for design 1 (blue squares) and design 2 (red circles).
The figure of merit ZT as a function of the QW width for design 1 (blue squares) and design 2 (red circles).
The figure of merit ZT as theoretically calculated 31 as a function of TDD. The two green solid symbols are data from design 1 samples.
A comparison of Si, Ge, Si/Ge, and SiGe thermoelectric parameters from the literature and the present work.
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