Optical Properties of SiGe and Ge Virginia Semiconductor, Inc. 1501 Powhatan Street, Fredericksburg, VA 22401 (540) 373-2900, FAX (540) 371-0371 www.vriginiasemi.com, tech@virginiasemi.com A Introduction This article contains tables on the optical properties of SiGe and Ge. These tables contain information about the dielectric constant, index of refraction, and absorption coefficient of SiGe and Ge for different photon energies and wavelengths. It also contains information on the reflection, transmission, and absorption percentages at 600um. B Optical Properties These tables outline some basic optical properties of SiGe. For all calculations and data values given in this paper it is assumed that the wafers are double side polished and there are no reflective or absorptive phenomena associated with surface roughness, damage, or anomalies. Normal incident radiation is assumed for all reflection and transmission calculations. The following variables, and units are included in the table: E(eV)- energy, λ- wavelength (nm), E1- real part of the dielectric constant, E2- imaginary part of the dielectric constant, κ- imaginary part of index of refraction, n- real part of index of refraction, R1 –Percen reflection from an infinite, air-silicon interface. R600- percent reflected at 600um, α(cm-1)- absorption coefficient, A600- percent absorbed at 600 um, and T600- percent transmitted at 600 um. Table 1 shows the optical properties of SiGe at 20% Ge, Table 2 at 50% Ge, and Table 3 at 75% Ge. Table 4 shows the optical properties of Ge.

Table 1

Si1-xGex, x = 0.20

E(eV) Λ E1 E2 n κ α(cm-1) R1 R(600) T(600) A(601.00 1239.8 13.04 0.0001 3.61 0.00001 1.01 32.05% 46.36% 47.41%1.05 1180.8 13.18 0.0003 3.63 0.00005 4.97 32.27% 40.89% 36.00% 21.10 1127.1 13.26 0.0014 3.64 0.00019 2.17E+01 32.37% 33.48% 12.54% 51.15 1078.1 13.33 0.0039 3.65 0.00053 6.19E+01 32.48% 32.49% 1.11% 61.20 1033.2 13.48 0.0076 3.67 0.00104 1.27E+02 32.69% 32.69% 0.02% 61.25 991.9 13.55 0.0126 3.68 0.00171 2.17E+02 32.79% 32.79% 0.00% 61.30 953.7 13.70 0.0188 3.70 0.00253 3.34E+02 33.00% 33.00% 0.00% 61.35 918.4 13.84 0.0259 3.72 0.00348 4.76E+02 33.21% 33.21% 0.00% 61.40 885.6 13.99 0.0339 3.74 0.00453 6.43E+02 33.42% 33.42% 0.00% 6

2.0 619.9 16.78 0.08 4.10 0.01 2.03E+03 36.95% 36.95% 0.00% 62.1 590.4 17.43 0.08 4.18 0.01 2.13E+03 37.69% 37.69% 0.00% 62.2 563.6 18.26 0.09 4.27 0.01 2.23E+03 38.50% 38.50% 0.00% 62.3 539.1 19.11 0.17 4.37 0.02 4.47E+03 39.38% 39.38% 0.00% 62.4 516.6 20.15 0.75 4.49 0.08 2.03E+04 40.42% 40.42% 0.00% 52.5 495.9 21.39 1.20 4.63 0.13 3.30E+04 41.60% 41.60% 0.00% 52.6 476.9 22.93 2.04 4.79 0.21 5.60E+04 42.92% 42.92% 0.00% 5

2.7 459.2 24.81 2.95 4.99 0.30 8.08E+04 44.51% 44.51% 0.00% 52.8 442.8 27.12 4.31 5.22 0.41 1.17E+05 46.26% 46.26% 0.00% 52.9 427.5 30.16 6.85 5.53 0.62 1.82E+05 48.59% 48.59% 0.00% 53.0 413.3 33.47 11.66 5.87 0.99 3.02E+05 51.26% 51.26% 0.00% 43.1 400.0 34.27 19.65 6.07 1.62 5.08E+05 53.85% 53.85% 0.00% 43.2 387.5 29.85 26.79 5.91 2.26 7.34E+05 55.27% 55.27% 0.00% 43.3 375.7 23.76 30.16 5.57 2.71 9.05E+05 55.89% 55.89% 0.00% 43.4 364.7 18.44 30.72 5.21 2.95 1.02E+06 55.91% 55.91% 0.00% 43.5 354.2 15.10 29.64 4.92 3.01 1.07E+06 55.38% 55.38% 0.00% 43.6 344.4 13.38 29.27 4.77 3.07 1.12E+06 55.33% 55.33% 0.00% 43.8 326.3 10.23 30.36 4.60 3.30 1.27E+06 56.45% 56.45% 0.00% 44.0 310.0 6.41 33.09 4.48 3.69 1.50E+06 58.94% 58.94% 0.00% 44.2 295.2 -3.12 37.86 4.18 4.53 1.93E+06 64.69% 64.69% 0.00% 34.4 281.8 -17.03 26.63 2.70 4.93 2.20E+06 71.58% 71.58% 0.00% 24.6 269.5 -14.87 16.04 1.87 4.29 2.00E+06 71.92% 71.92% 0.00% 24.8 258.3 -11.53 12.01 1.60 3.75 1.83E+06 69.26% 69.26% 0.00% 35.0 248.0 -9.30 10.22 1.50 3.40 1.72E+06 66.31% 66.31% 0.00% 35.2 238.4 -7.97 9.48 1.49 3.19 1.68E+06 63.61% 63.61% 0.00% 35.4 229.6 -7.85 9.00 1.43 3.15 1.72E+06 63.86% 63.86% 0.00% 35.6 221.4 -7.78 7.83 1.28 3.07 1.74E+06 64.99% 64.99% 0.00% 3

6 206.6 -5.95 6.40 1.18 2.71 1.65E+06 60.98% 60.98% 0.00% 37 177.1 -4.16 3.36 0.77 2.18 1.55E+06 60.94% 60.94% 0.00% 38 155.0 -2.42 2.23 0.66 1.69 1.37E+06 52.96% 52.96% 0.00% 49 137.8 -1.60 1.68 0.60 1.40 1.28E+06 46.90% 46.90% 0.00% 5

10 124.0 -0.98 1.39 0.60 1.16 1.18E+06 38.55% 38.55% 0.00% 611 112.7 -0.57 1.22 0.62 0.98 1.09E+06 30.82% 30.82% 0.00% 612 103.3 -0.33 1.10 0.64 0.86 1.05E+06 25.35% 25.35% 0.00% 7

Table 2 Si1-xGex, x = 0.50

E(eV) Λ E1 E2 n κ α(cm-1) R1 R(600) T(600) A(60

0.95 1305.1 14.37 0.0003 3.79 0.00005 4.41 33.93% 43.24% 35.78% 21.00 1239.8 14.51 0.0018 3.81 0.00023 2.33E+01 34.13% 35.04% 10.80% 51.05 1180.8 14.67 0.0054 3.83 0.00071 7.51E+01 34.33% 34.33% 0.48% 61.10 1127.1 14.74 0.0111 3.84 0.00145 1.61E+02 34.43% 34.43% 0.00% 61.15 1078.1 14.90 0.0186 3.86 0.00241 2.81E+02 34.63% 34.63% 0.00% 61.20 1033.2 15.12 0.0279 3.89 0.00359 4.36E+02 34.93% 34.93% 0.00% 61.25 991.9 15.28 0.0386 3.91 0.00494 6.25E+02 35.13% 35.13% 0.00% 61.30 953.7 15.50 0.0507 3.94 0.00644 8.49E+02 35.42% 35.42% 0.00% 6

2.0 619.9 19.21 1.42 4.39 0.16 3.29E+04 39.61% 39.61% 0.00% 62.1 590.4 20.25 1.72 4.50 0.19 4.07E+04 40.57% 40.57% 0.00% 52.2 563.6 21.56 2.41 4.65 0.26 5.78E+04 41.86% 41.86% 0.00% 52.3 539.1 23.18 3.20 4.83 0.33 7.72E+04 43.34% 43.34% 0.00% 52.4 516.6 25.09 4.67 5.03 0.46 1.13E+05 44.99% 44.99% 0.00% 52.5 495.9 27.20 7.17 5.26 0.68 1.73E+05 46.94% 46.94% 0.00% 5

2.6 476.9 29.38 11.13 5.51 1.01 2.66E+05 49.22% 49.22% 0.00% 52.7 459.2 29.18 17.57 5.62 1.56 4.28E+05 51.40% 51.40% 0.00% 42.8 442.8 24.76 22.14 5.38 2.06 5.83E+05 52.12% 52.12% 0.00% 42.9 427.5 20.27 23.50 5.06 2.32 6.82E+05 51.93% 51.93% 0.00% 43.0 413.3 17.44 23.20 4.82 2.41 7.32E+05 51.41% 51.41% 0.00% 43.1 400.0 15.91 23.12 4.69 2.47 7.75E+05 51.24% 51.24% 0.00% 43.2 387.5 14.47 23.69 4.60 2.58 8.36E+05 51.60% 51.60% 0.00% 43.3 375.7 12.67 24.12 4.47 2.70 9.03E+05 51.95% 51.95% 0.00% 43.4 364.7 11.03 24.30 4.34 2.80 9.64E+05 52.25% 52.25% 0.00% 43.5 354.2 9.62 24.34 4.23 2.88 1.02E+06 52.53% 52.53% 0.00% 43.6 344.4 8.52 24.47 4.15 2.95 1.08E+06 52.87% 52.87% 0.00% 43.8 326.3 6.18 25.53 4.03 3.17 1.22E+06 54.40% 54.40% 0.00% 44.0 310.0 2.73 27.56 3.90 3.53 1.43E+06 57.23% 57.23% 0.00% 44.2 295.2 -4.68 29.65 3.56 4.17 1.77E+06 62.71% 62.71% 0.00% 34.4 281.8 -13.72 21.32 2.41 4.42 1.97E+06 69.07% 69.07% 0.00% 34.6 269.5 -12.01 13.81 1.77 3.89 1.81E+06 68.95% 68.95% 0.00% 34.8 258.3 -9.72 10.72 1.54 3.48 1.69E+06 66.81% 66.81% 0.00% 35.0 248.0 -8.03 9.09 1.43 3.17 1.61E+06 64.15% 64.15% 0.00% 35.2 238.4 -6.89 8.34 1.40 2.97 1.57E+06 61.59% 61.59% 0.00% 35.4 229.6 -6.45 8.05 1.39 2.89 1.58E+06 60.47% 60.47% 0.00% 35.6 221.4 -6.58 7.59 1.32 2.88 1.64E+06 61.39% 61.39% 0.00% 3

6 206.6 -5.68 6.58 1.23 2.68 1.63E+06 59.52% 59.52% 0.00% 47 177.1 -3.77 3.63 0.85 2.12 1.51E+06 57.05% 57.05% 0.00% 48 155.0 -2.07 2.52 0.77 1.63 1.32E+06 46.80% 46.80% 0.00% 59 137.8 -1.33 2.01 0.73 1.37 1.25E+06 40.04% 40.04% 0.00% 5

10 124.0 -0.80 1.64 0.72 1.15 1.16E+06 32.72% 32.72% 0.00% 611 112.7 -0.42 1.48 0.75 0.99 1.10E+06 25.79% 25.79% 0.00% 712 103.3 -0.19 1.35 0.77 0.88 1.07E+06 21.17% 21.17% 0.00% 7

Table 3 Si1-xGex, x = 0.75

E(eV) λ E1 E2 n κ α(cm-1) R1 R(600) T(600) A(60

0.90 1377.6 15.84 0.0003 3.98 0.00004 3.65 35.81% 46.12% 35.84% 10.95 1305.1 16.00 0.0023 4.00 0.00029 2.79E+01 36.00% 36.52% 7.71% 51.00 1239.8 16.16 0.0076 4.02 0.00094 9.53E+01 36.19% 36.19% 0.13% 61.05 1180.8 16.32 0.0156 4.04 0.00193 2.05E+02 36.38% 36.38% 0.00% 61.10 1127.1 16.48 0.0261 4.06 0.00322 3.59E+02 36.57% 36.57% 0.00% 61.15 1078.1 16.73 0.0391 4.09 0.00478 5.57E+02 36.85% 36.85% 0.00% 61.20 1033.2 16.89 0.0540 4.11 0.00657 7.99E+02 37.04% 37.04% 0.00% 6

2.0 619.9 24.22 2.86 4.93 0.29 5.88E+04 44.06% 44.06% 0.00% 52.1 590.4 25.93 4.39 5.11 0.43 9.15E+04 45.52% 45.52% 0.00% 52.2 563.6 28.00 6.82 5.33 0.64 1.43E+05 47.33% 47.33% 0.00% 52.3 539.1 30.40 10.98 5.60 0.98 2.28E+05 49.69% 49.69% 0.00% 52.4 516.6 30.25 17.96 5.72 1.57 3.82E+05 51.96% 51.96% 0.00% 42.5 495.9 25.25 23.00 5.45 2.11 5.35E+05 52.66% 52.66% 0.00% 42.6 476.9 19.99 24.23 5.07 2.39 6.30E+05 52.35% 52.35% 0.00% 42.7 459.2 16.28 23.13 4.72 2.45 6.70E+05 51.24% 51.24% 0.00% 42.8 442.8 14.39 21.78 4.50 2.42 6.87E+05 50.15% 50.15% 0.00% 4

2.9 427.5 13.65 21.03 4.40 2.39 7.02E+05 49.53% 49.53% 0.00% 53.0 413.3 13.35 20.75 4.36 2.38 7.24E+05 49.29% 49.29% 0.00% 53.1 400.0 13.01 21.36 4.36 2.45 7.70E+05 49.79% 49.79% 0.00% 53.2 387.5 12.23 22.31 4.34 2.57 8.33E+05 50.57% 50.57% 0.00% 43.3 375.7 10.94 23.06 4.27 2.70 9.03E+05 51.29% 51.29% 0.00% 43.4 364.7 9.63 23.41 4.18 2.80 9.65E+05 51.78% 51.78% 0.00% 43.5 354.2 8.38 23.64 4.09 2.89 1.03E+06 52.25% 52.25% 0.00% 43.6 344.4 7.63 24.02 4.03 2.98 1.09E+06 52.84% 52.84% 0.00% 43.8 326.3 5.00 25.24 3.92 3.22 1.24E+06 54.65% 54.65% 0.00% 44.0 310.0 1.62 27.21 3.80 3.58 1.45E+06 57.61% 57.61% 0.00% 44.2 295.2 -5.75 29.13 3.46 4.21 1.79E+06 63.21% 63.21% 0.00% 34.4 281.8 -14.60 20.52 2.30 4.46 1.99E+06 70.11% 70.11% 0.00% 24.6 269.5 -12.34 12.99 1.67 3.89 1.81E+06 69.99% 69.99% 0.00% 34.8 258.3 -9.94 10.06 1.45 3.47 1.69E+06 67.86% 67.86% 0.00% 35.0 248.0 -8.23 8.56 1.35 3.17 1.61E+06 65.32% 65.32% 0.00% 35.2 238.4 -6.99 7.87 1.33 2.96 1.56E+06 62.51% 62.51% 0.00% 35.4 229.6 -6.44 7.69 1.34 2.87 1.57E+06 60.91% 60.91% 0.00% 35.6 221.4 -6.71 7.40 1.28 2.89 1.64E+06 62.22% 62.22% 0.00% 3

6 206.6 -5.07 6.55 1.27 2.58 1.57E+06 56.98% 56.98% 0.00% 47 177.1 -3.29 4.26 1.02 2.08 1.48E+06 51.47% 51.47% 0.00% 48 155.0 -2.00 2.71 0.83 1.64 1.33E+06 45.02% 45.02% 0.00% 59 137.8 -1.21 2.17 0.80 1.36 1.24E+06 37.13% 37.13% 0.00% 6

10 124.0 -0.64 1.80 0.80 1.13 1.15E+06 29.15% 29.15% 0.00% 711 112.7 -0.28 1.66 0.84 0.99 1.10E+06 19.92% 19.92% 0.00% 812 103.3 -0.09 1.52 0.85 0.90 1.09E+06 0.66% 0.66% 0.00% 9

Table 4 Si1-xGex, x = 1.00

E(eV) λ E1 E2 n κ α(cm-1) R1 R(600) T(600) A(60

0.65 1907.5 16.81 0.0002 4.10 0.00002 1.32 36.95% 50.95% 41.01%0.70 1771.2 16.97 0.0032 4.12 0.00032 2.77E+01 37.13% 37.66% 7.54% 50.75 1653.1 17.06 0.0124 4.13 0.00150 1.14E+02 37.23% 37.23% 0.04% 60.80 1549.8 17.22 0.0270 4.15 0.00325 2.64E+02 37.41% 37.41% 0.00% 60.85 1458.6 17.47 0.0463 4.18 0.00554 4.77E+02 37.69% 37.69% 0.00% 60.90 1377.6 17.64 0.0694 4.20 0.00826 7.53E+02 37.87% 37.87% 0.00% 6

2.0 1305.1 30.48 11.80 5.62 1.05 2.13E+05 49.96% 49.96% 0.00% 52.1 1239.8 29.51 20.10 5.71 1.76 3.75E+05 52.54% 52.54% 0.00% 42.2 1180.8 22.93 23.19 5.27 2.20 4.91E+05 52.26% 52.26% 0.00% 42.3 1127.1 18.85 24.55 4.99 2.46 5.73E+05 52.40% 52.40% 0.00% 42.4 1078.1 13.90 23.52 4.54 2.59 6.30E+05 51.44% 51.44% 0.00% 42.5 1033.2 11.81 21.25 4.25 2.50 6.33E+05 49.72% 49.72% 0.00% 52.6 619.9 10.87 19.80 4.09 2.42 6.38E+05 48.50% 48.50% 0.00% 52.7 590.4 10.40 18.75 3.99 2.35 6.43E+05 47.54% 47.54% 0.00% 52.8 563.6 10.28 18.05 3.94 2.29 6.50E+05 46.84% 46.84% 0.00% 52.9 539.1 10.46 17.73 3.94 2.25 6.61E+05 46.51% 46.51% 0.00% 53.0 516.6 10.73 17.99 3.98 2.26 6.87E+05 46.77% 46.77% 0.00% 53.1 495.9 10.68 18.81 4.02 2.34 7.35E+05 47.58% 47.58% 0.00% 53.2 476.9 10.06 19.86 4.02 2.47 8.01E+05 48.63% 48.63% 0.00% 5

3.3 459.2 9.00 20.64 3.97 2.60 8.70E+05 49.52% 49.52% 0.00% 53.4 442.8 7.92 21.06 3.90 2.70 9.30E+05 50.16% 50.16% 0.00% 43.5 427.5 7.02 21.35 3.84 2.78 9.86E+05 50.70% 50.70% 0.00% 43.6 413.3 6.05 21.70 3.78 2.87 1.05E+06 51.36% 51.36% 0.00% 43.8 400.0 4.14 22.87 3.70 3.09 1.19E+06 53.22% 53.22% 0.00% 44.0 387.5 1.27 24.76 3.61 3.43 1.39E+06 56.26% 56.26% 0.00% 44.2 375.7 -5.17 26.99 3.34 4.04 1.72E+06 62.00% 62.00% 0.00% 34.4 364.7 -14.96 18.92 2.14 4.42 1.97E+06 70.88% 70.88% 0.00% 24.6 354.2 -11.53 11.31 1.52 3.72 1.73E+06 69.88% 69.88% 0.00% 34.8 344.4 -9.11 9.00 1.36 3.31 1.61E+06 67.08% 67.08% 0.00% 35.0 326.3 -7.46 7.79 1.29 3.02 1.53E+06 64.08% 64.08% 0.00% 35.2 310.0 -6.31 7.22 1.28 2.82 1.49E+06 61.07% 61.07% 0.00% 35.4 295.2 -5.76 7.10 1.30 2.73 1.49E+06 59.19% 59.19% 0.00% 45.6 281.8 -5.79 7.04 1.29 2.73 1.55E+06 59.36% 59.36% 0.00% 4

6 269.5 -5.04 7.21 1.37 2.63 1.60E+06 56.28% 56.28% 0.00% 47 258.3 -3.58 4.28 1.00 2.14 1.52E+06 53.38% 53.38% 0.00% 48 248.0 -2.30 2.87 0.83 1.73 1.40E+06 47.65% 47.65% 0.00% 59 238.4 -1.49 2.26 0.78 1.45 1.32E+06 40.81% 40.81% 0.00% 5

10 229.6 -1.00 1.88 0.75 1.25 1.27E+06 35.14% 35.14% 0.00% 611 221.4 -0.62 1.60 0.74 1.08 1.20E+06 29.42% 29.42% 0.00% 712 206.6 -0.37 1.42 0.74 0.96 1.17E+06 25.05% 25.05% 0.00% 7

The values for the percentage of light reflected were calculated using the following equation where R1 is the light reflected at an air-silicon interface with the air and silicon layers being infinitely thick:

R1 = ((n-1) 2+κ 2) / ((n+1) 2+κ2) (1)[8]

For absorption coefficient values greater than zero, the percentage of total light reflected can be determined using equation (2): R ≈ R1 + (1- R1 )R1e

- α2t - (1- R1 )R12e- α2t + (1- R1 )R1

3e- α4t - (1- R1 )R14e- α4t +…. (2)

Each term in the infinite series is associated with the successive reflections as the light bounces between the surfaces of the silicon wafer. Similarly, the percent transmission can be determined using equation (3):

T ≈ (1- R1 )e- αt - (1- R1 )R1e

- αt + (1- R1 )R12e- α3t - (1- R1 )R1

3e- α3t +…. (3) where the percent absorbed light is given by equation (4):

A≈ 1- (R + T). (4) When the absorption coefficient equals zero, equation (2) can be simplified to the following equation (5):

R ≈ 2R1 / (R1+1) (5) The geometric series has been factored from equation (2) for this condition. C Conclusion This article contains general information on the optical properties of SiGe and Ge and displays this information in several tables. The information was taken from references and derived from equations as described. D References [1] J. Humlicek [ in Properties of Strained and Relaxed Silicon Germanium

(INSPEC, IEE ,London, UK, 1988) ch.4.7 p.120-131.] [2] Tatiana Globus, Stephen H. Jones, Thomas Digges, Jr.,”Analysis of Refractive

Index and Absorption Coefficient of Silicon Membranes”, Proceedings of the 1997 International Semiconductor Device Research Symposium, Charlottesville, VA, ISBN1-880920-05-0

[3] J. Humlicek, F. Lukes, E. Schmidt [ in Handbook of Optical Constants of Solids II

Ed. E.D. Palik (Academic Press, New York, 1991) p.607] [4] J. Humlicek, A. Roeseler, T. Zettler, M.G. Kekoua, E. Khoutsishvili [Appl. Opt.

(USA) vol.31 (1992) p.90] [5] R. Braunstein, A.R Moore, F. Herman [ Phys. Rev. (USA) vol.109 (1958) p.695] [6] E. Schmidt [Phys. Status Solidi (Germany) vol.27 (1968) p.57] [7] J. Humlicek, M. Garriga, M.I. Alonso, M. Cardona [ J. Appl. Phys. (USA) vol.65

(1989) p.2827] [8] E. Hecht [ in Optics (Adison-Wesley, Reading Mass, 1987) p. 113]