Energy-Gap-Refractive Index Relations in Semiconductors—Using Wemple–DiDomenico Model to Unify Moss, Ravindra, and Herve–Vandamme Relationships
Abstract
:1. Introduction
2. Mathematical Formulation
3. , , and
4. Results
4.1. Moss Relation
4.2. Ravindra Relation
4.3. Herve–Vandamme Relation
5. Discussion
5.1. Empirical Fitting Constants
5.2. Convergence Criterion
5.3. Exceptional Materials
6. Conclusions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Ravindra Constants: ; | H-V Constants: A; B | Moss Constant | |||||
---|---|---|---|---|---|---|---|
C | 5.4 | 10.9 | 49.7 | 3.32; 0.30 | 23.27; 5.5 | 166.91 | 2.35 |
1.1 | 4.0 | 44.4 | 4.08; 0.70 | 13.32; 2.9 | 161.06 | 3.46 | |
0.67 | 2.7 | 41.0 | 4.64; 1.14 | 10.52; 2.03 | 175.51 | 4.0 | |
1.43 | 3.55 | 33.5 | 4.18; 0.98 | 10.90; 2.12 | 155.76 | 3.3 | |
2.24 | 4.46 | 36.0 | 4.27; 0.96 | 12.67; 2.22 | 184.34 | 2.9 | |
0.18 | 2.3 | 35.0 | 4.19; 0.99 | 8.97; 2.12 | 47.34 | 3.95 | |
2.45 | 5.6 | 34.9 | 3.58; 0.57 | 13.98; 3.15 | 128.14 | 2.75 | |
2.18 | 4.7 | 33.7 | 3.90; 0.77 | 12.58; 2.52 | 145.52 | 3.0 | |
12.50 | 17.1 | 14.9 | 2.63; 0.28 | 15.96; 4.6 | 43.77 | 1.39 | |
10.5 | 15 | 11.3 | 2.42; 0.27 | 13.01; 4.5 | 32.28 | 1.33 | |
10.3 | 14.8 | 12.3 | 2.45; 0.27 | 13.50; 4.5 | 34.53 | 1.36 | |
8.9 | 10.3 | 13.6 | 4.13; 1.47 | 11.83; 1.40 | 47.92 | 1.54 | |
8.5 | 10.5 | 12.3 | 3.38; 0.84 | 11.96; 2 | 40.08 | 1.49 | |
8.3 | 10.4 | 12.2 | 3.28; 0.78 | 11.26; 2.1 | 39.19 | 1.49 | |
8 | 10.6 | 14 | 3.97; 0.59 | 12.18; 2.60 | 43.09 | 1.61 | |
7.6 | 9.2 | 12.4 | 3.67; 1.15 | 10.68; 1.60 | 41.90 | 1.55 | |
7.2 | 9.1 | 12.1 | 3.34; 0.88 | 10.54; 1.90 | 39.08 | 1.55 | |
6.17 | 7.7 | 12.8 | 3.66; 1.19 | 9.92; 1.53 | 43.73 | 1.67 | |
5.8 | 7.7 | 12.1 | 3.23; 0.85 | 9.65; 1.90 | 38.35 | 1.64 | |
8.0 | 10.6 | 17.1 | 3.26; 0.63 | 13.46; 2.6 | 54.63 | 1.61 | |
7.0 | 9.4 | 17 | 3.32; 0.69 | 12.64; 2.40 | 55.21 | 1.67 | |
6.3 | 7.5 | 15.2 | 4.35; 1.81 | 10.67; 1.20 | 57.71 | 1.82 | |
2.11 | 5.8 | 20.6 | 2.67; 0.36 | 10.93; 3.69 | 43.71 | 2.08 | |
2.68 | 5.3 | 21.7 | 3.21; 0.61 | 10.72; 2.62 | 69.55 | 2.25 | |
11.8 | 15.7 | 15.9 | 2.84; 0.36 | 15.80; 3.90 | 47.80 | 1.43 | |
10.5 | 13.8 | 15.9 | 3.0; 0.45 | 14.81; 3.3 | 48.63 | 1.47 | |
5.13 | 7.4 | 22 | 3.6; 0.80 | 12.76; 2.27 | 80.97 | 1.9 | |
3.31 | 7.3 | 18.1 | 2.52; 0.31 | 11.49; 3.99 | 40.07 | 2.19 | |
3.7 | 6.4 | 17.1 | 2.95; 0.55 | 10.46; 2.70 | 49.88 | 1.92 | |
2.4 | 4.9 | 20.4 | 3.18; 0.64 | 9.99; 2.5 | 63.98 | 2.38 | |
1.74 | 4.0 | 20.6 | 3.29; 0.73 | 9.08; 2.26 | 65.81 | 2.49 | |
3.54 | 6.15 | 25.2 | 3.46; 0.66 | 12.45; 2.61 | 91.98 | 2.27 | |
7.8 | 11.3 | 22.0 | 3.08; 0.44 | 15.77; 3.5 | 67.74 | 1.62 | |
6.26 | 9.9 | 22.6 | 2.98; 0.41 | 14.96; 3.64 | 67.46 | 1.39 | |
6.96 | 13.4 | 27.5 | 2.52; 0.195 | 19.19; 6.44 | 64.84 | 1.63 | |
6.5 | 11.1 | 25.4 | 2.82; 0.31 | 16.80; 4.60 | 70.28 | 1.71 | |
3.7 | 6.24 | 23.2 | 3.40; 0.67 | 12.03; 2.54 | 82.36 | 2.2 | |
4.10 | 5.68 | 23.7 | 4.31; 1.36 | 11.60; 1.58 | 109.70 | 2.38 | |
4.12 | 5.57 | 23.3 | 4.46; 1.54 | 11.40; 1.45 | 110.68 | 2.4 | |
3.70 | 6.50 | 23.7 | 3.28; 0.58 | 12.41; 2.8 | 79.87 | 2.2 | |
4.7 | 7.49 | 26.1 | 3.47; 0.62 | 13.98; 2.80 | 94.53 | 2.18 | |
4.0 | 6.65 | 25.9 | 3.50; 0.66 | 13.12; 2.65 | 95.83 | 2.34 | |
3.2 | 5.24 | 25.7 | 3.89; 0.95 | 11.60; 2.04 | 111.56 | 2.72 | |
7.80 | 12.1 | 23.3 | 2.87; 0.33 | 16.80; 4.3 | 66.76 | 1.52 | |
4.20 | 9.15 | 23.3 | 2.56; 0.25 | 14.60; 4.95 | 52.82 | 1.81 | |
3.56 | 7.46 | 26.0 | 2.93; 0.37 | 13.93; 3.9 | 71.62 | 2.1 | |
4.50 | 8.26 | 23.0 | 2.88; 0.38 | 13.78; 3.76 | 64.45 | 1.90 | |
3.2 | 5.40 | 22.60 | 3.56; 0.81 | 11.04; 2.2 | 86.03 | 2.2 | |
4.16 | 8.60 | 21.30 | 2.60; 0.29 | 13.53; 4.44 | 50.28 | 1.85 | |
9.3 | 13.6 | 18.3 | 2.72; 0.32 | 15.77; 4.30 | 51.16 | 1.46 | |
3.54 | 6.36 | 26.1 | 3.39; 0.60 | 12.88; 2.82 | 92.21 | 2.27 | |
2.58 | 5.54 | 27.0 | 3.31; 0.56 | 12.23; 2.96 | 89.0 | 2.43 | |
2.26 | 4.34 | 27.0 | 3.88; 0.93 | 10.82; 2.08 | 117.85 | 2.70 | |
1.58 | 4.13 | 25.7 | 3.42; 0.67 | 10.30; 2.55 | 82.42 | 2.7 | |
0.286 | 3.5 | 55.33 | 4.28; 0.66 | 13.91; 3.21 | 80.55 | 4.1 | |
0.165 | 3.0 | 66.12 | 4.94; 0.87 | 14.08; 2.83 | 87.58 | 4.8 | |
0.190 | 2.2 | 66.80 | 5.86; 1.46 | 12.12; 2.01 | 186.90 | 5.6 |
Moss (n) | Ravindra (n) | H-V (n) | Equation (33) (n) | |||
---|---|---|---|---|---|---|
0.67 | 3.45 | 3.66 | 3.48 | 4.02 | 4.0 | |
0.18 | 4.79 | 3.97 | 3.93 | 4.02 | 3.95 | |
0.286 | 4.27 | 3.90 | 3.94 | 4.09 | 4.1 | |
0.165 | 4.89 | 3.98 | 3.94 | 4.79 | 4.8 | |
0.190 | 4.73 | 3.96 | 3.92 | 5.51 | 5.6 |
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Lamichhane, A. Energy-Gap-Refractive Index Relations in Semiconductors—Using Wemple–DiDomenico Model to Unify Moss, Ravindra, and Herve–Vandamme Relationships. Solids 2023, 4, 316-326. https://doi.org/10.3390/solids4040020
Lamichhane A. Energy-Gap-Refractive Index Relations in Semiconductors—Using Wemple–DiDomenico Model to Unify Moss, Ravindra, and Herve–Vandamme Relationships. Solids. 2023; 4(4):316-326. https://doi.org/10.3390/solids4040020
Chicago/Turabian StyleLamichhane, Aneer. 2023. "Energy-Gap-Refractive Index Relations in Semiconductors—Using Wemple–DiDomenico Model to Unify Moss, Ravindra, and Herve–Vandamme Relationships" Solids 4, no. 4: 316-326. https://doi.org/10.3390/solids4040020