Heavily doped silicon: A potential replacement of conventional plasmonic metals

Md. Omar Faruque; Rabiul Al Mahmud; Rakibul Hasan Sagor

doi:10.1088/1674-4926/42/6/062302

J. Semicond. > 2021, Volume 42?>?Issue 6?> 062302

ARTICLES

Heavily doped silicon: A potential replacement of conventional plasmonic metals

Md. Omar Faruque, Rabiul Al Mahmud and Rakibul Hasan Sagor

+ Author Affiliations

Islamic University of Technology (IUT), Board Bazar Gazipur, Gazipur 1704, Bangladesh

Author Bio:

Md. Omar Faruque completed his B.Sc. in 2016 and M.Sc. in 2019 in Electrical and Electronic Engineering from the Islamic University of Technology (IUT), Gazipur, Bangladesh. He joined as a Lecturer in the Department of Electrical and Electronic Engineering of the Islamic University of Technology (IUT), Gazipur, Bangladesh, a subsidiary organ of OIC in Bangladesh, in 2017 and serving there to date. Plasmonic metamaterials, plasmonic devices and integrated optical systems are notable in his current research interests.

Rabiul Al Mahmud is currently Lecturer at the Department of Electrical and Electronic Engineering at the Islamic University of Technology (IUT), Gazipur, Bangladesh, a subsidiary organ of OIC in Bangladesh. He obtained the B.Sc. and M.Sc. degree in Electrical and Electronic Engineering from the Islamic University of Technology (IUT), Gazipur, Bangladesh, in 2016 and 2020 respectively. His areas of interests are plasmonics, plasmonic devices and materials. He has published four research papers in referred journals and conference proceedings like IEEE, Springer and Elsevier.

Rakibul Hasan Sagor received a B.Sc. degree in Electrical and Electronic Engineering from the Islamic University of Technology (IUT), Gazipur, Bangladesh, in 2007, a M.Sc. degree in electrical engineering from the King Fahd University of Petroleum and Minerals (KFUPM), Dhahran, Saudi Arabia, in 2011 and a Ph.D. degree in Electrical and Electronic Engineering from the Islamic University of Technology (IUT), Gazipur, Bangladesh, in 2018. Currently, he is serving as an Associate Professor of Electrical and Electronic Engineering at the Islamic University of Technology (IUT), Gazipur, Bangladesh, a subsidiary organ of OIC in Bangladesh. His current research interests include the generation and application of high-power microwaves, modeling and simulation of high-frequency active devices, optically controlled active devices, computational electromagnetics, plasmonics and nonlinear integrated optics.

Corresponding author: Md. Omar Faruque, omarfaruque@iut-dhaka.edu

DOI: 10.1088/1674-4926/42/6/062302

Abstract: The plasmonic property of heavily doped p-type silicon is studied here. Although most of the plasmonic devices use metal–insulator–metal (MIM) waveguide in order to support the propagation of surface plasmon polaritons (SPPs), metals that possess a number of challenges in loss management, polarization response, nanofabrication etc. On the other hand, heavily doped p-type silicon shows similar plasmonic properties like metals and also enables us to overcome the challenges possessed by metals. For numerical simulation, heavily doped p-silicon is mathematically modeled and the theoretically obtained relative permittivity is compared with the experimental value. A waveguide is formed with the p-silicon-air interface instead of the metal–air interface. Formation and propagation of SPPs similar to MIM waveguides are observed.

Key words: alternative plasmonic material, heavily doped p-silicon, surface plasmon polaritons

References

[1]	Barnes W L, Dereux A, Ebbesen T W. Surface plasmon subwavelength optics. Nature, 2003, 424, 824 doi: 10.1038/nature01937
[2]	Lu H, Liu X, Wang G, et al. Tunable high-channel-count bandpass plasmonic filters based on an analogue of electromagnetically induced transparency. Nanotechnology, 2012, 23, 444003 doi: 10.1088/0957-4484/23/44/444003
[3]	Wang H Q, Yang J B, Zhang J J, et al. Tunable band-stop plasmonic waveguide filter with symmetrical multiple-teeth-shaped structure. Opt Lett, 2016, 41, 1233 doi: 10.1364/OL.41.001233
[4]	Johnson P B, Christy R W. Optical constants of the noble metals. Phys Rev B, 1972, 6, 4370 doi: 10.1103/PhysRevB.6.4370
[5]	West P R, Ishii S, Naik G V, et al. Searching for better plasmonic materials. Laser Photonics Rev, 2010, 4, 795 doi: 10.1002/lpor.200900055
[6]	Cai W S, Chettiar U K, Kildishev A V, et al. Optical cloaking with metamaterials. Nat Photonics, 2007, 1, 224 doi: 10.1038/nphoton.2007.28
[7]	Abelès F, Borensztein Y, López Rios T. Optical properties of discontinuous thin films and rough surfaces of silver. In: Advances in Solid State Physics. Berlin, Heidelberg: Springer Berlin Heidelberg, 2007, 93
[8]	Berestetskii V B, Lifshitz E M, Pitaevskii L P. Quantum Electrodynamics. Volume 4. Butterworth-Heinemann, 1982
[9]	Shahzad M, Medhi G, Peale R E, et al. Infrared surface plasmons on heavily doped silicon. J Appl Phys, 2011, 110, 123105 doi: 10.1063/1.3672738
[10]	Linaschke D, Schilling N, Dani I, et al. Highly n-doped surfaces on n-type silicon wafers by laser-chemical processes. Energy Procedia, 2014, 55, 247 doi: 10.1016/j.egypro.2014.08.076
[11]	Mizushima I, Murakoshi A, Watanabe M, et al. Hole generation without annealing in high dose boron implanted silicon: Heavy doping by B12 icosahedron as a double acceptor. Jpn J Appl Phys, 1994, 33, 404 doi: 10.1143/JJAP.33.404
[12]	Vi?a L, Cardona M. Effect of heavy doping on the optical properties and the band structure of silicon. Phys Rev B, 1984, 29, 6739 doi: 10.1103/PhysRevB.29.6739
[13]	Ma Z, Liu Y, Deng L, et al. Heavily boron-doped silicon layer for the fabrication of nanoscale thermoelectric devices. Nanomaterials, 2018, 8, 77 doi: 10.3390/nano8020077
[14]	Miyao M, Motooka T, Natsuaki N, et al. Change of the electron effective mass in extremely heavily doped n-type Si obtained by ion implantation and laser annealing. Solid State Commun, 1981, 37, 605 doi: 10.1016/0038-1098(81)90144-7
[15]	Jellison G E, Modine F A, White C W, et al. Optical properties of heavily doped silicon between 1.5 and 4.1 eV. Phys Rev Lett, 1981, 46, 1414 doi: 10.1103/PhysRevLett.46.1414
[16]	Nobili, Solmi, Parisini, et al. Precipitation, aggregation, and diffusion in heavily arsenic-doped silicon. Phys Rev B, 1994, 49, 2477 doi: 10.1103/PhysRevB.49.2477
[17]	Maier S A. Spectroscopy and sensing. In: Plasmonics: Fundamentals and Applications. New York, NY: Springer US, 2007, 177
[18]	Saber M G, Abadía N, Plant D V. CMOS compatible all-silicon TM pass polarizer based on highly doped silicon waveguide. Opt Express, 2018, 26, 20878 doi: 10.1364/OE.26.020878
[19]	Qi Z P, Hu G H, Li L, et al. Design and analysis of a compact SOI-based aluminum/highly doped p-type silicon hybrid plasmonic modulator. IEEE Photonics J, 2016, 8, 1 doi: 10.1109/JPHOT.2016.2559439
[20]	Naik G V, Shalaev V M, Boltasseva A. Alternative plasmonic materials: Beyond gold and silver. Adv Mater, 2013, 25, 3264 doi: 10.1002/adma.201205076
[21]	Chen Y B, Zhang Z M. Heavily doped silicon complex gratings as wavelength-selective absorbing surfaces. J Phys D, 2008, 41, 095406 doi: 10.1088/0022-3727/41/9/095406
[22]	Schroder D K, Thomas R N, Swartz J C. Free carrier absorption in silicon. IEEE J Solid-State Circuits, 1978, 13, 180 doi: 10.1109/JSSC.1978.1051012
[23]	van Exter M, Grischkowsky D. Carrier dynamics of electrons and holes in moderately doped silicon. Phys Rev B, 1990, 41, 12140 doi: 10.1103/PhysRevB.41.12140
[24]	Raki? A D, Djuri?i? A B, Elazar J M, et al. Optical properties of metallic films for vertical-cavity optoelectronic devices. Appl Opt, 1998, 37, 5271 doi: 10.1364/AO.37.005271
[25]	Kildishev A V, Shalaev V M. Engineering space for light via transformation optics. Opt Lett, 2008, 33, 43 doi: 10.1364/OL.33.000043
[26]	Cai W S, Chettiar U K, Kildishev A V, et al. Designs for optical cloaking with high-order transformations. Opt Express, 2008, 16, 5444 doi: 10.1364/OE.16.005444

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.

DownLoad: Full-Size Img PowerPoint

Fig. 2. (Color online) Relative permittivity (a) real part and (b) imaginary part versus carrier concentration at different wavelength.

DownLoad: Full-Size Img PowerPoint

Fig. 3. (Color online) Real part of relative permittivity for silver, gold and, p-silicon for different values of carrier concentration of p-silicon.

DownLoad: Full-Size Img PowerPoint

Fig. 4. (Color online) Imaginary part of relative permittivity for silver and gold, and p-silicon for different values of carrier concentration.

DownLoad: Full-Size Img PowerPoint

Fig. 5. (Color online) Propagation of SPP along the silicon–air–silicon waveguide.

DownLoad: Full-Size Img PowerPoint

Fig. 6. (Color online) Comparison of the transmittance between (a) the silver and p-silicon waveguide and (b) the gold and p-silicon waveguide.

DownLoad: Full-Size Img PowerPoint

Fig. 7. (Color online) Notch type transmission response shown by ring resonators using gold, silver and psilicon.

DownLoad: Full-Size Img PowerPoint

Fig. 8. (Color online) Sensing characteristics shown by ring resonators formed with heavily doped silicon.

DownLoad: Full-Size Img PowerPoint

Table 1. Modelling parameters of heavily doped p-silicon by the Lorentz-Drude model.

Parameter	Value for carrier concentration of 6 × 10¹⁹ cm^–3	Value for carrier concentration of 1 × 10²⁰ cm^–3
${\varepsilon _0}$	11.7	11.7
$e$	1.60217662 × 10^–19	1.60217662 × 10^–19
$\mu $	50	50
${m_{\rm{eff}} }$	3.5526595884 × 10^–31	3.5526595884 × 10^–31
$\tau $	1.2417416061807 × 10^–10	1.241741606180 × 10^–10
$\sigma $	5.3833134432 × 10⁸	8.972189072 × 10⁸

DownLoad: CSV

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 (%)
Energy (eV)	Wavelength (μm)	Experimental (Shahzad et al.^[9])	Theoretical (Lorentz-Drude model)	Percentage of error (%)
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

DownLoad: CSV

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.

Energy (eV)	Wavelength (μm)	Values of relative permittivity (real part)		Percentage of error (%)
Energy (eV)	Wavelength (μm)	Experimental (Shahzad et al.^[9])	Theoretical (Lorentz-Drude model)	Percentage of error (%)
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

DownLoad: CSV

Table 4. Modelling parameters of gold and silver by the Drude and Lorentz-Drude model.

Parameter	Value for silver (eV)	Value for gold (eV)
Plasma frequency ($\hbar {\omega _{\rm p}}$)	9.01	9.03
Damping constant (${\Gamma _0}$)	0.048	0.053
Oscillator strength (${f_0}$)	0.845	0.760
Dominant frequency(${f_n}$)	[0.065; 0.011; 0.840; 5.646]	[0.024; 0.010; 0.071; 0.601; 4.384]
Damping frequency (${\Gamma _n}$)	[3.886; 0.452; 0.065; 0.916; 2.419]	[0.241; 0.345; 0.870; 2.494; 2.214]
Resonance frequency (${\omega _n}$)	[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

DownLoad: CSV

[1]	Barnes W L, Dereux A, Ebbesen T W. Surface plasmon subwavelength optics. Nature, 2003, 424, 824 doi: 10.1038/nature01937
[2]	Lu H, Liu X, Wang G, et al. Tunable high-channel-count bandpass plasmonic filters based on an analogue of electromagnetically induced transparency. Nanotechnology, 2012, 23, 444003 doi: 10.1088/0957-4484/23/44/444003
[3]	Wang H Q, Yang J B, Zhang J J, et al. Tunable band-stop plasmonic waveguide filter with symmetrical multiple-teeth-shaped structure. Opt Lett, 2016, 41, 1233 doi: 10.1364/OL.41.001233
[4]	Johnson P B, Christy R W. Optical constants of the noble metals. Phys Rev B, 1972, 6, 4370 doi: 10.1103/PhysRevB.6.4370
[5]	West P R, Ishii S, Naik G V, et al. Searching for better plasmonic materials. Laser Photonics Rev, 2010, 4, 795 doi: 10.1002/lpor.200900055
[6]	Cai W S, Chettiar U K, Kildishev A V, et al. Optical cloaking with metamaterials. Nat Photonics, 2007, 1, 224 doi: 10.1038/nphoton.2007.28
[7]	Abelès F, Borensztein Y, López Rios T. Optical properties of discontinuous thin films and rough surfaces of silver. In: Advances in Solid State Physics. Berlin, Heidelberg: Springer Berlin Heidelberg, 2007, 93
[8]	Berestetskii V B, Lifshitz E M, Pitaevskii L P. Quantum Electrodynamics. Volume 4. Butterworth-Heinemann, 1982
[9]	Shahzad M, Medhi G, Peale R E, et al. Infrared surface plasmons on heavily doped silicon. J Appl Phys, 2011, 110, 123105 doi: 10.1063/1.3672738
[10]	Linaschke D, Schilling N, Dani I, et al. Highly n-doped surfaces on n-type silicon wafers by laser-chemical processes. Energy Procedia, 2014, 55, 247 doi: 10.1016/j.egypro.2014.08.076
[11]	Mizushima I, Murakoshi A, Watanabe M, et al. Hole generation without annealing in high dose boron implanted silicon: Heavy doping by B12 icosahedron as a double acceptor. Jpn J Appl Phys, 1994, 33, 404 doi: 10.1143/JJAP.33.404
[12]	Vi?a L, Cardona M. Effect of heavy doping on the optical properties and the band structure of silicon. Phys Rev B, 1984, 29, 6739 doi: 10.1103/PhysRevB.29.6739
[13]	Ma Z, Liu Y, Deng L, et al. Heavily boron-doped silicon layer for the fabrication of nanoscale thermoelectric devices. Nanomaterials, 2018, 8, 77 doi: 10.3390/nano8020077
[14]	Miyao M, Motooka T, Natsuaki N, et al. Change of the electron effective mass in extremely heavily doped n-type Si obtained by ion implantation and laser annealing. Solid State Commun, 1981, 37, 605 doi: 10.1016/0038-1098(81)90144-7
[15]	Jellison G E, Modine F A, White C W, et al. Optical properties of heavily doped silicon between 1.5 and 4.1 eV. Phys Rev Lett, 1981, 46, 1414 doi: 10.1103/PhysRevLett.46.1414
[16]	Nobili, Solmi, Parisini, et al. Precipitation, aggregation, and diffusion in heavily arsenic-doped silicon. Phys Rev B, 1994, 49, 2477 doi: 10.1103/PhysRevB.49.2477
[17]	Maier S A. Spectroscopy and sensing. In: Plasmonics: Fundamentals and Applications. New York, NY: Springer US, 2007, 177
[18]	Saber M G, Abadía N, Plant D V. CMOS compatible all-silicon TM pass polarizer based on highly doped silicon waveguide. Opt Express, 2018, 26, 20878 doi: 10.1364/OE.26.020878
[19]	Qi Z P, Hu G H, Li L, et al. Design and analysis of a compact SOI-based aluminum/highly doped p-type silicon hybrid plasmonic modulator. IEEE Photonics J, 2016, 8, 1 doi: 10.1109/JPHOT.2016.2559439
[20]	Naik G V, Shalaev V M, Boltasseva A. Alternative plasmonic materials: Beyond gold and silver. Adv Mater, 2013, 25, 3264 doi: 10.1002/adma.201205076
[21]	Chen Y B, Zhang Z M. Heavily doped silicon complex gratings as wavelength-selective absorbing surfaces. J Phys D, 2008, 41, 095406 doi: 10.1088/0022-3727/41/9/095406
[22]	Schroder D K, Thomas R N, Swartz J C. Free carrier absorption in silicon. IEEE J Solid-State Circuits, 1978, 13, 180 doi: 10.1109/JSSC.1978.1051012
[23]	van Exter M, Grischkowsky D. Carrier dynamics of electrons and holes in moderately doped silicon. Phys Rev B, 1990, 41, 12140 doi: 10.1103/PhysRevB.41.12140
[24]	Raki? A D, Djuri?i? A B, Elazar J M, et al. Optical properties of metallic films for vertical-cavity optoelectronic devices. Appl Opt, 1998, 37, 5271 doi: 10.1364/AO.37.005271
[25]	Kildishev A V, Shalaev V M. Engineering space for light via transformation optics. Opt Lett, 2008, 33, 43 doi: 10.1364/OL.33.000043
[26]	Cai W S, Chettiar U K, Kildishev A V, et al. Designs for optical cloaking with high-order transformations. Opt Express, 2008, 16, 5444 doi: 10.1364/OE.16.005444

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Received: 26 September 2020 Revised: 05 January 2021 Online: Accepted Manuscript: 15 March 2021Uncorrected proof: 23 March 2021Published: 01 June 2021

The plasmonic property of heavily doped p-type silicon is studied here. Although most of the plasmonic devices use metal–insulator–metal (MIM) waveguide in order to support the propagation of surface plasmon polaritons (SPPs), metals that possess a number of challenges in loss management, polarization response, nanofabrication etc. On the other hand, heavily doped p-type silicon shows similar plasmonic properties like metals and also enables us to overcome the challenges possessed by metals. For numerical simulation, heavily doped p-silicon is mathematically modeled and the theoretically obtained relative permittivity is compared with the experimental value. A waveguide is formed with the p-silicon-air interface instead of the metal–air interface. Formation and propagation of SPPs similar to MIM waveguides are observed.

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Heavily doped silicon: A potential replacement of conventional plasmonic metals

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