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Intersubband absorption of strain-compensated valence-band quantum wells with
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Image of FIG. 1.
FIG. 1.

(Color online). Measured (symbols) and simulated (lines) specular reflectivity patterns of the samples LQW5–8. For clarity, the traces are vertically offset for the various samples. In the inset, the XRR pattern for sample LQW8 is shown on an extended scale in order to highlight the details of the experimental and simulated data.

Image of FIG. 2.
FIG. 2.

(Color online). Dependence of the XRR signal measured for LQW8 on the scattering wave vector in the , plane, where the direction is perpendicular to the sample surface. (a) XRR map. (b) The experimental data (symbols) were obtained by cross sections through the map shown in (a) at the coordinates indicated in (b). For clarity, the data corresponding to different are offset vertically. The full lines result from fitting the experimental data to the model described in Ref. 19.

Image of FIG. 3.
FIG. 3.

(Color online). Measured (bold lines) and calculated (lines with superimposed symbols) polarization-dependent intersubband absorption spectra for a temperature of . The spectra measured for TE (TM) polarization are shown by the full (broken) lines. The results calculated for radiation with electric field parallel to the plane ( direction) are shown by the lines with superimposed circles (triangles), where denotes the growth direction. The full symbols indicate the results obtained using the structural parameters listed in Table I, whereas the open symbols represent the results based on the nominal sample parameters. (Note that in the waveguide geometry employed in the experiment, the TM polarization contains both and polarizations.) For normalization, the absorption spectra calculated for polarization were multiplied by a factor of times larger than the spectra for polarization.

Image of FIG. 4.
FIG. 4.

(Color online). Band-structure parameters used in this work: (a) Energetic position of the HH, LH, and SO valence band edges for a layer grown on a substrate calculated according to Ref. 21 and references therein. The origin of the energy axis corresponds to the average of the HH, LH, and SO valence band edges in bulk Si. (b) Luttinger parameters as function of the Ge concentration obtained according to the interpolation scheme suggested in Ref. 23 and references therein.

Image of FIG. 5.
FIG. 5.

(a) Contour plot of the hole distribution probability density calculated for LQW5 at the point. (b) Contour plot of the hole distribution probability integrated over the in-plane and perpendicular wave vectors and weighted by the modulus of the transition matrix element for polarization from the HH1 ground state to the respective final state. In (a) and (b) the contour plot is gray-scale coded with black (white) indicating maximum (zero) probability. The spatial profiles of the HH, LH, and SO valence bands are shown by the full gray, dashed, and dashed-dotted black lines, respectively. The horizontal line labeled indicates the Fermi energy calculated for . The origin of the energy axis corresponds to the average of the HH, LH, and SO valence band edges in bulk Si.

Image of FIG. 6.
FIG. 6.

(Color online). Low-temperature measured (bold lines) and simulated (thin lines with superimposed symbols) waveguide absorption spectra for TE and TM polarizations. The simulation is based on the transfer-matrix method (Ref. 28). The lines with filled squares were obtained by assuming a bias-induced 10% modulation of the hole concentration in all ten QWs, whereas the lines with open circles result from assuming a complete hole depletion from the topmost QW only.


Generic image for table
Table I.

Nominal parameters of the samples LQW5–8. Since the structure of the samples is symmetric with respect to the middle of the QW, only half of the sample structure is listed.

Generic image for table
Table II.

Layer thicknesses as extracted by fitting the simulated to the measured XRR traces (see Fig. 1). The estimated error is in the range of . For the Si barriers, the two values given in the table correspond to the thicknesses of the upper and lower barriers. The Ge content of the QWs is extracted from the XRD measurements (Ref. 16). The estimated error is in the range of .


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Intersubband absorption of strain-compensated Si1−xGex valence-band quantum wells with 0.7⩽x⩽0.85