Md. Omar Faruque1, Rabiul Al Mahmud2, and Rakibul Hasan Sagor3
Author Affiliations
1Islamic University of Technology (IUT), Board Bazar Gazipur, Gazipur 1704, Bangladesh2Islamic University of Technology (IUT), Board Bazar Gazipur, Gazipur 1704, Bangladesh3Islamic University of Technology (IUT), Board Bazar Gazipur, Gazipur 1704, Bangladeshshow less
Fig. 1. (Color online) Comparison between theoretical value and experimental value for carrier concentration of (a) 6 × 1019 cm–3 and (b) 1 × 1020 cm–3.
Fig. 2. (Color online) Relative permittivity (a) real part and (b) imaginary part versus carrier concentration at different wavelength.
Fig. 3. (Color online) Real part of relative permittivity for silver, gold and, p-silicon for different values of carrier concentration of p-silicon.
Fig. 4. (Color online) Imaginary part of relative permittivity for silver and gold, and p-silicon for different values of carrier concentration.
Fig. 5. (Color online) Propagation of SPP along the silicon–air–silicon waveguide.
Fig. 6. (Color online) Comparison of the transmittance between (a) the silver and p-silicon waveguide and (b) the gold and p-silicon waveguide.
Fig. 7. (Color online) Notch type transmission response shown by ring resonators using gold, silver and psilicon.
Fig. 8. (Color online) Sensing characteristics shown by ring resonators formed with heavily doped silicon.
Parameter | Value for carrier concentration of
6 × 1019 cm–3 | Value for carrier concentration of
1 × 1020 cm–3 |
---|
| 11.7 | 11.7 | | 1.60217662 × 10–19 | 1.60217662 × 10–19 | | 50 | 50 | | 3.5526595884 × 10–31 | 3.5526595884 × 10–31 | | 1.2417416061807 × 10–10 | 1.241741606180 × 10–10 | | 5.3833134432 × 108 | 8.972189072 × 108 |
|
Table 1. Modelling parameters of heavily doped p-silicon by the Lorentz-Drude model.
Energy (eV) | Wavelength (µm)
| Values of relative permittivity (real part) | Percentage of error (%) |
---|
Experimental (Shahzad et al.[9])
| Theoretical (Lorentz-Drude model) |
---|
0.14 | 8.1 | 4.43 | 2.64 | 40 | 0.15 | 7.49 | 4.95 | 3.97 | 19.88 | 0.16 | 6.96 | 5.53 | 5.02 | 9.27 | 0.17 | 6.5 | 6.12 | 5.87 | 3.95 | 0.28 | 4.08 | 9.67 | 9.4 | 2.84 | 0.35 | 3.27 | 10.41 | 10.22 | 1.83 | 0.42 | 2.73 | 10.82 | 10.67 | 1.45 | 0.45 | 2.52 | 10.71 | 10.82 | 1.02 |
|
Table 2. Comparison of relative permittivity of p-silicon between the theoretical value and the experimental value for a carrier concentration of 6 × 1019 cm–3.
Energy (eV) | Wavelength (µm)
| Values of relative permittivity (real part) | Percentage of error (%) |
---|
Experimental (Shahzad et al.[9])
| Theoretical (Lorentz-Drude model) |
---|
0.064 | 17.69 | –44.85 | –60.24 | 34.33 | 0.067 | 16.72 | –39.97 | –52.62 | 31.66 | 0.11 | 10.23 | –17.14 | –12.40 | 27.60 | 0.29 | 3.86 | 6.88 | 8.29 | 20.35 | 0.30 | 3.71 | 7.56 | 8.53 | 12.86 | 0.34 | 3.34 | 8.53 | 9.14 | 7.12 | 0.43 | 2.63 | 10.81 | 10.11 | 6.43 | 0.46 | 2.49 | 10.81 | 10.27 | 4.98 |
|
Table 3. Comparison of relative permittivity of p-silicon between the theoretical value and the experimental value for a carrier concentration of 1 × 1020 cm–3.
Parameter | Value for silver (eV) | Value for gold (eV) |
---|
Plasma frequency (
)
| 9.01 | 9.03 | Damping constant (
)
| 0.048 | 0.053 | Oscillator strength (
)
| 0.845 | 0.760 | Dominant frequency(
)
| [0.065; 0.011; 0.840; 5.646] | [0.024; 0.010; 0.071; 0.601; 4.384] | Damping frequency (
)
| [3.886; 0.452; 0.065; 0.916; 2.419] | [0.241; 0.345; 0.870; 2.494; 2.214] | Resonance frequency (
)
| [0.816; 4.481; 8.185; 9.083; 20.29] | [0.415; 0.830; 2.969; 4.304; 13.32] | Number of resonance | 6 | 6 |
|
Table 4. Modelling parameters of gold and silver by the Drude and Lorentz-Drude model.