Effect of Germanium Concentration on the Dielectric Function of Strained Si1-xGex Films

Transistors fabricated using strained silicon-germanium alloy channels provide improved carrier mobility. While the electrical properties of Si_1-xGe_x for a variety of values of x and the optical properties of strain-free Si_1-xGe_x for x= 0 to 1 have been reported, reports of the optical properties of pseudomorphic Si_1-xGe_x were limited to x <; 0.3. For Ge concentrations of less than 30%, the optical properties follow the low shear elastic response [1, 2]. Here, we report an in-depth study of the optical properties of bi-axially strained pseudomorphic Si_1-xGe_x alloys for Ge concentrations ranging from 0.05 to 0.75. Optical properties (complex refractive index/dielectric function) of semiconductors are dominated by strong absorption at critical points (CP). Strain often shifts the E₁ and E₁+Δ CPs. The spin orbit splitting Δ increases with germanium concentration. Strained semiconductors are described by an elastic theory approach that predicts the shifts of the critical points. There are two approximations for the optical response depending on the magnitude of spin-orbit coupling versus the shift in CP energy for shear stress. The low shear approximation used previously for the calculation of elastic response of critical points (direct gap transitions) is no longer valid for psuedomorphic Si_1-xGe_x alloys having germanium concentrations greater than 40%. The optical properties of these alloys follow a high sheer approximation and high shear effects can be seen very prominently for concentrations above 50%, where two peaks are readily apparent for E₁ with an energy seperation greater than the spin orbit splitting. Undoped Si_1-xGe_x films, with Ge concentrations from 0.05 to 0.75 were grown on Si (001) substrates using ultra-high vacuum and reduced pressure chemical vapor deposition. Layer - hickness and composition was measured using high resolution X-ray diffraction. Figure 1 shows the Omega-2Theta 004 rocking curves for some of the wafers starting from 5% Ge concentration. Relaxation scans and reciprocal space maps confirmed the alloys as fully strained, low defect and high quality structural formations. The dielectric function of pseudomorphic alloys was evaluated using spectroscopic ellipsometry from 0.73 eV to 5.17 eV (245nm to 1700nm). Figure 2 shows two peaks near the E₁ and E₁+Δ critical points for higher germanium concentrations. Errors in ellipsometric based thickness measurements occur if the complex refractive index of relaxed SiGe alloys is used to measure pseudomorphic SiGe films.