Complex dielectric function of biaxial tensile strained silicon by spectroscopic ellipsometry

The complex dielectric function of biaxial tensile strained Si grown on a fully relaxed ${\mathrm{Si}}_{0.81}{\mathrm{Ge}}_{0.19}$ virtual substrate was obtained from spectroscopic ellipsometry measurement in the 2.5–5-eV energy range. Standard critical point (CP) line shapes were fit to numerically obtained second-derivative spectra to extract interband CP parameters. It is shown that the biaxial tensile strain increased the number of ellipsometrically observable CP’s from two to three in the $E_0^{\prime }∕E_1$ gap region, whereas the CP’s in the $E_2$ region were relatively unaffected. These results compare favorably to previous reports for uniaxially compressed stressed silicon. In particular, the experimentally observed splitting of the $E_1$ gap—$E_1\left(1\right)=3.310\mathrm{eV}$ and $E_1\left(2\right)=3.437\mathrm{eV}$—was in reasonable agreement with calculated expectations—$E_1\left(1\right)=3.304\mathrm{eV}$ and $E_1\left(2\right)=3.395\mathrm{eV}$—using previously reported Si deformation potentials.

Figure 1

Real $\left({\epsilon }_1\right)$ and imaginary $\left({\epsilon }_2\right)$ parts of the dielectric function extracted from experimentally measured SE data for bulk (unstrained) Si and strained Si (on a fully relaxed ${\mathrm{Si}}_{0.81}{\mathrm{Ge}}_{0.19}$ VS) at room temperature.

Figure 2

Second-derivative spectra in the $E_0^{\prime }∕E_1$ gap region for (a) unstrained (bulk) Si, along with best fits (solid lines) to real (squares) and imaginary (circles) parts of the spectra using two interband CP’s; (b) strained Si, with best fits using three CP’s; (c) strained Si extracted from a SiGe-free SSOI sample; and (d) strained Si imaginary spectrum only, fit with two CP’s. All second-derivative spectra were numerically obtained from dielectric function data in Fig. 1, except for (c) which was obtained from a SiGe-free SSOI wafer as noted. The spectral features seen around 3.4 eV in (b)–(d) are due to $E_1$ peak splitting, while the feature at 3.17 eV in (b) and (d) is an artifact from the underlying SiGe VS. Fit parameters for (a) and (b) are listed in Table .

Figure 3

Second-derivative spectra in the $E_2$ gap region numerically obtained from dielectric function data in Fig. 1, for (a) unstrained (bulk) Si, along with best fit (solid line) to imaginary (circles) part of the spectra using two 2D CP’s; (b) unstrained Si, real (squares) and imaginary parts fit using three 2D CP’s; and (c) strained Si, also fit with three 2D CP’s. It is seen that three CP’s are required to accurately fit the spectra in the $E_2$ region. Additionally, the strain is seen to have very little effect on the $E_2$ CP’s. Fit parameters for (b) and (c) are listed in Table .