Extraction of large valence-band energy offsets and comparison to theoretical values for strained-Si/strained-Ge type-II heterostructures on relaxed SiGe substrates

Metal-oxide-semiconductor capacitors were fabricated on type-II staggered gap strained-Si/strained-Ge heterostructures epitaxially grown on relaxed SiGe substrates of various Ge fractions. Quasistatic quantum-mechanical capacitance-voltage (CV) simulations were fit to experimental CV measurements to extract the band alignment of the strained layers. The valence-band offset of the strained-Si/strained-Ge heterostructure was found to be 770, 760, and 670 meV for 35, 42, and 52$\%$ Ge in the relaxed SiGe substrate, respectively. These values are approximately 100 meV larger than the usually recommended band offsets for modeling Si/Ge structures. It is shown that the larger valence-band offsets found here are consistent with an 800-meV average valence-band offset between Si and Ge, which also explains the type-II band alignment observed in strained-Si${}_{1-x}$Ge${}_x$ on unstrained-Si heterostructures.

Figure 1

(a) Schematic energy band diagram illustrating the type-II band alignment between tensile strained-Si and compressively strained-Ge. The heavy-hole (HH) band is the topmost s-Ge valence band, and the $\Delta$2 band is the bottom most s-Si conduction band. (b) MOS capacitor structure with a 35$\%$ SiGe relaxed buffer fabricated for valence-band offset extraction.

Figure 2

Experimental and simulated QSCV curves for s-Si/s-Ge on a relaxed 35$\%$ SiGe substrate. The following parameters were used to produce the simulated CV curve: 38 Å EOT, 49 Å s-Si cap thickness, $\Delta E_v$ $=$ 770 meV, and $E_{G,\mathrm{eff}}$ $=$ 190 meV. The CV analysis does not provide significant sensitivity to other parameters. Voltage regions of distinct carrier distributions are identified by Roman numerals and described in the text and shown schematically in Fig. 3.

Figure 3

Depiction of the heterostructure band diagrams and carrier populations (not drawn to scale) under the different regimes labeled in Fig. 2.

Figure 4

Valence-band diagram of the s-Si/s-Ge/relaxed SiGe heterostructure. The heavy hole (hh) and light hole (lh) valence bands in s-Si and s-Ge split due to tensile and compressive strain, respectively. The valence-band offset quoted in this paper is the difference between the top valence-band edges of s-Ge and s-Si. The simulation models quantization effects, but only the band-edge difference is quoted in order to provide information about the band lineup that is independent of the quantum well thicknesses.

Figure 5

Simulated QSCV for different s-Si cap thicknesses. The simulated CV displays a high sensitivity to small changes in the s-Si cap thickness, which allows the physical thickness to be extracted with low uncertainty ($\pm 2$ Å).

Figure 6

Measured and simulated CV curves illustrating the high sensitivity of the simulation to $\Delta E_v$. A 25-meV change in $\Delta E_v$ produces about a 90-mV change in the plateau width. A change in $\Delta E_v$ only impacts the portion of the CV curve shown here.

Figure 7

(a) Calculations by People and Bean[7] of the band gap of s-Si for different Ge fractions of the relaxed Si${}_{1-x}$Ge${}_x$ substrate compared to values extracted from CV analysis in this work. The experimental data from Welser[24] is also included for comparison. (b) Valence-band offset, $\Delta E_v$, as a function of Ge fraction in the substrate. People and Bean[7] calculate a linear relation from theoretical work by Van de Walle and Martin in 1985 (Ref. 8). The dotted line is a linear relationship derived from updated calculations in Van de Walle and Martin's 1986 paper.[6] The valence-band offsets extracted in this work are about 100 meV larger than the linear relationship derived from theoretical values of Ref. 6.

Figure 8

Illustration of the changes in the band edges with increased Ge fraction in the substrate ($xs$).

Figure 9

Valence-band offset for s-Si/s-Si${}_{1-x}$Ge${}_x$ grown on a relaxed SiGe substrate with ∼40$\%$ Ge, as a function of Ge fraction in the s-Si${}_{1-x}$Ge${}_x$ layer. The inset shows a depiction of the heterostructure band diagram highlighting the valence-band offset. Ni Chleirigh[36] extracted the valence-band offset using a CV technique similar to this work. Both calculations shown in the plot are linear relations derived from theory by Van de Walle and Martin. People and Bean[7] calculate a linear relation from Van de Walle and Martin's 1985 paper,[8] while the purple (dark gray) data point is calculated using updated values from Van de Walle and Martin's 1986 paper.[6]

Figure 10

Calculated band lineups of the (a) s-Si/s-Ge heterostructure pseudomorphic to 42$\%$ SiGe and (b) s-Si${}_{0.70}$Ge${}_{0.30}$/Si heterostructure pseudomorphic to Si using standard deformation potential theory. The calculations assume that the average valence-band offset between Si and Ge is $\Delta E_{v,av}$ $=$ 800 meV.

Figure 11

Experimental $\Delta$-like absorption edges of strained Si${}_{1-x}$Ge${}_x$ alloys on relaxed Si substrates from Lang et al. (circles; Ref. 57), and our calculation of these edges (lines) using the experimental compositional dependence of the band gap in relaxed Si${}_{1-x}$Ge${}_x$ alloys from Ref. 58 and the deformation potentials in Table .