# Silicon Nanowires: A Breakthrough for Thermoelectric Applications

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Thermoelectric Properties of Nanostructured Silicon

#### 2.1. Electrical Conductivity, Seebeck Coefficient and Power Factor

#### 2.2. Thermal Conductivity and Figure of Merit

## 3. Techniques for All-Silicon Thermoelectric Devices

#### 3.1. On-Chip Si Nanowires/Nanostructures for Energy Scavenging

#### 3.2. Si Nanowires/Nanostructures for Energy Macroharvesting

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Pourkiaei, S.M.; Ahmadi, M.H.; Sadeghzadeh, M.; Moosavi, S.; Pourfayaz, F.; Chen, L.; Pour Yazdi, M.A.; Kumar, R. Thermoelectric cooler and thermoelectric generator devices: A review of present and potential applications, modeling and materials. Energy
**2019**, 186, 115849. [Google Scholar] [CrossRef] - Caballero-Calero, O.; Ares, R.; Martin-Gonzalez, M. Environmentally Friendly Thermoelectric Materials: High Performance from Inorganic Components with Low Toxicity and Abundance in the Earth. Adv. Sustain. Syst.
**2021**, 2100095. [Google Scholar] [CrossRef] - Chen, L.; Meng, F.; Ge, Y.; Feng, H.; Xia, S. Performance optimization of a class of combined thermoelectric heating devices. Sci. China Technol. Sci.
**2020**, 63, 2640–2648. [Google Scholar] [CrossRef] - Pennelli, G. Review of nanostructured devices for thermoelectric applications. Beilstein J. Nanotechnol.
**2014**, 5, 1268. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Pennelli, G. Top-down fabrication of silicon nanowire devices for thermoelectric applications: Properties and perspectives. Eur. Phys. J. B
**2015**, 88, 121. [Google Scholar] [CrossRef] - Arora, N.D.; Hauser, R.J.; Roulston, J.D. Electron and Hole Mobilities in Silicon as a Function of Concentration and Temperature. IEEE Trans. Electron Devices
**1982**, ED-29, 292. [Google Scholar] [CrossRef] - Masetti, G.; Severi, M.; Solmi, S. Modeling of Carrier Mobility Against Carrier Concentration in Arsenic-, Phosphorus-, and Boron-doped Silicon. IEEE Trans. Electron Devices
**1983**, 30, 764. [Google Scholar] [CrossRef] - Reggiani, S.; Valdinoci, M.; Colalongo, L.; Rudan, M.; Baccarani, G.; Stricker, A.D.; Illien, F.; Felber, N.; Fichtner, W.; Zullino, L. Electron and Hole Mobility in Silicon at Large Operating Temperatures—Part I: Bulk Mobility. IEEE Trans. Electron Devices
**2002**, 49, 490. [Google Scholar] [CrossRef] - Geballe, T.H.; Hull, G.W. Seebeck Effect in Silicon. Phys. Rev.
**1955**, 98, 940. [Google Scholar] [CrossRef] - Brinson, M.E.; Dunstant, W. Thermal conductivity and thermoelectric power of heavily doped n-type silicon. J. Phys. C Solid State Phys.
**1970**, 3, 483. [Google Scholar] [CrossRef] - Stranz, A.; Kahler, J.; Waag, A.; Peiner, E. Thermoelectric Properties of High-Doped Silicon from Room Temperature to 900 K. J. Electron. Mater.
**2013**, 42, 2381. [Google Scholar] [CrossRef] - Ohishi, Y.; Xie, J.; Miyazaki, Y.; Aikebaier, Y.; Muta, H.; Kurosaki, K.; Yamanaka, S.; Uchida, N.; Tada, T. Thermoelectric properties of heavily boron- and phosphorus-doped silicon. Jpn. J. Appl. Phys.
**2015**, 54, 071301. [Google Scholar] [CrossRef] - Bennett, N.S. Thermoelectric performance in n-type bulk silicon: The influence of dopant concentration and dopant species. Phys. Status Solidi
**2017**, 214, 1700307. [Google Scholar] [CrossRef] - Dimaggio, E.; Pennelli, G. Potentialities of silicon nanowire forests for thermoelectric generation. Nanotechnology
**2018**, 29, 135401. [Google Scholar] [CrossRef] - Stranz, A.; Kahler, J.; Merzsch, A.; Peiner, E. Nanowire silicon as a material for thermoelectric energy conversion. Microsyst. Technol.
**2012**, 18, 857. [Google Scholar] [CrossRef] - Neophytou, N.; Foster, S.; Vargiamidis, V.; Pennelli, G.; Narducci, D. Nanostructured potential well/barrier engineering for realizing unprecedentedly large thermoelectric power factors. Mater. Today Phys.
**2019**, 11, 100159. [Google Scholar] [CrossRef] - Graziosi, P.; Kumarasinghe, C.; Neophytou, N. Impact of the scattering physics on the power factor of complex thermoelectric materials. J. Appl. Phys.
**2019**, 126, 155701. [Google Scholar] [CrossRef] - Neophytou, N.; Zianni, X.; Kosina, H.; Frabboni, S.; Lorenzi, B.; Narducci, D. Simultaneous increase in electrical conductivity and Seebeck coefficient in highly boron-doped nanocrystalline Si. Nanotechnology
**2013**, 24, 205402. [Google Scholar] [CrossRef] - Zulian, L.; Segrado, F.; Narducci, D. Annealing of heavily boron-doped silicon: Effect on electrical and thermoelectric properties. J. Nanosci. Nanotechnol.
**2017**, 17, 1657–1662. [Google Scholar] [CrossRef] - Bux, S.; Blair, R.; Gogna, P.; Lee, H.; Chen, G.; Dresselhaus, M.; Kaner, R.; Fleurial, J. Nanostructured Bulk Silicon as an Effective Thermoelectric Material. Adv. Funct. Mater.
**2009**, 19, 2445–2452. [Google Scholar] [CrossRef] - Li, D.; Wu, Y.; Kim, P.; Shi, L.; Yang, P.; Majumdar, A. Thermal conductivity of individual silicon nanowires. Appl. Phys. Lett.
**2003**, 83, 2934–2936. [Google Scholar] [CrossRef] - Boukay, A.; Bunimovich, Y.; Tahir-Kheli, J.; Yu, J.K.; Goddard, W.A., III; Heat, J.R. Silicon nanowires as efficient thermoelectric materials. Nat. Lett.
**2008**, 451, 168–171. [Google Scholar] [CrossRef] - Hochbaum, A.I.; Chen, R.; Delgrado, R.D.; Liang, W.; Garnett, C.E.; Najarian, M.; Majumdar, A.; Yang, P. Enhanced thermoelectric performance of rough silicon nanowires. Nat. Lett.
**2008**, 451, 163–167. [Google Scholar] [CrossRef] - Pennelli, G.; Nannini, A.; Macucci, M. Indirect measurement of thermal conductivity in silicon nanowires. J. Appl. Phys.
**2014**, 115, 084507. [Google Scholar] [CrossRef] - Park, Y.H.; Kim, J.; Kim, H.; Kim, I.; Lee, K.Y.; Seo, D.; Choi, H.J.; Kim, W. Thermal conductivity of VLS-grown rough Si nanowires with various surface roughnesses and diameters. Appl. Phys. A
**2011**, 104, 7–14. [Google Scholar] [CrossRef] - Feser, J.; Sadhu, J.; Azeredo, B.; Hsu, H.; Ma, J.; Kim, J.; Seong, M.; Fang, N.; Li, X.; Ferreira, P.; et al. Thermal conductivity of silicon nanowire arrays with controlled roughness. J. Appl. Phys.
**2012**, 112, 114306. [Google Scholar] [CrossRef] - Lim, J.; Hippalgaonkar, K.; Andrews, C.S.; Majumdar, A.; Yang, P. Quantifying surface roughness effects on phonon transport in silicon nanowires. Nano Lett.
**2012**, 12, 2475–2482. [Google Scholar] [CrossRef] [PubMed] - Karg, S.; Mensch, P.; Gotsmann, B.; Schmid, H.; DasKanungo, P.; Ghoneim, H.; Schmidt, V.; Bjork, M.; Troncale, V.; Riel, H. Measurement of thermoelectric properties of single semiconductor nanowires. J. Electron. Mater.
**2013**, 42, 2409. [Google Scholar] [CrossRef] - Zhang, T.; Wu, S.; Zheng, R.; Cheng, G. Significant reduction of thermal conductivity in silicon nanowire arrays. Nanotechnology
**2013**, 24, 505718. [Google Scholar] [CrossRef] [PubMed] - Sadhu, J.; Tian, H.; Ma, J.; Azeredo, B.; Kim, J.; Balasundaram, K.; Zhang, C.; Li, X.; Ferreia, P.; Sinha, S. Quenched Phonon Drag in Silicon Nanowires Reveals Significant Effect in the Bulk at Room Temperature. Nano Lett.
**2015**, 15, 3159. [Google Scholar] [CrossRef] - Raja, S.N.; Rhyner, R.; Vuttivorakulchai, K.; Luisier, M.; Poulikakos, D. Length Scale of Diffusive Phonon Transport in Suspended Thin Silicon Nanowires. Nano Lett.
**2017**, 17, 276–283. [Google Scholar] [CrossRef] [PubMed] - Glynn, C.; Jones, K.; Mogili, V.; McSweeney, W.; O’Dwyer, C. The Nature of Silicon Nanowire Roughness and Thermal Conductivity Suppression by Phonon Scattering Mechanisms. ECS J. Solid State Sci. Technol.
**2017**, 6, N3029. [Google Scholar] [CrossRef] [Green Version] - Fan, D.; Sigg, H.; Spolenak, R.; Ekinci, Y. Strain and thermal conductivity in ultrathin suspended silicon nanowires. Phys. Rev. B
**2017**, 96, 115307. [Google Scholar] [CrossRef] [Green Version] - Elyamny, S.; Dimaggio, E.; Magagna, S.; Narducci, D.; Pennelli, G. High Power Thermoelectric Generator Based on Vertical Silicon Nanowires. Nano Lett.
**2020**, 20, 4748–4753. [Google Scholar] [CrossRef] - Diez, G.; Gordillo, J.; Pujadó, M.; Salleras, M.; Fonseca, L.; Morata, A.; Rubio, A. Enhanced thermoelecric figure of merit of individual Si nanowires with ultralow contact resistance. Nano Energy
**2020**, 67, 104191. [Google Scholar] [CrossRef] - Melosh, N.; Boukay, A.; Diana, F.; Gerardot, B.; Badolato, A.; Petroff, P.; Heath, J. Ultrahigh-Density Nanowires Lattices and Circuits. Science
**2003**, 300, 112–115. [Google Scholar] [PubMed] [Green Version] - Pennelli, G.; Elyamny, S.; Dimaggio, E. Thermal conductivity of silicon nanowire forests. Nanotechnology
**2018**, 2018, 505402. [Google Scholar] [CrossRef] [PubMed] - Donadio, D.; Galli, G. Temperature dependence of the thermal conductivity of thin silicon nanowires. Nano Lett.
**2004**, 10, 847. [Google Scholar] [CrossRef] - Martin, P.; Aksamija, Z.; Pop, E.; Ravaioli, U. Impact of phonon-surface roughness scattering on thermal conductivity of thin Si nanowires. Phys. Rev. Lett.
**2009**, 102, 125503. [Google Scholar] [CrossRef] - Sojo Gordillo, J.; Gadea Diez, G.; Pacios Pujadó, M.; Salleras, M.; Estrada-Wiese, D.; Dolcet, M.; Fonseca, L.; Morata, A.; Tarancón, A. Thermal conductivity of individual Si and SiGe epitaxially integrated NWs by scanning thermal microscopy. Nanoscale
**2021**, 13, 7252–7265. [Google Scholar] [CrossRef] [PubMed] - Liu, W.; Asheghi, M. Thermal conduction in ultrathin pure and doped single-crystal silicon layers at high temperatures. J. Appl. Phys.
**2005**, 98, 123523. [Google Scholar] [CrossRef] - Dimaggio, E.; Pennelli, G.; Macucci, M. Thermal conductivity reduction in rough silicon nanomembranes. IEEE Trans. Nanotechnol.
**2018**, 17, 500. [Google Scholar] - Pennelli, G.; Dimaggio, E.; Macucci, M. Improvement of the 3ω thermal conductivity measurement technique for its application at the nanoscale. Rev. Scient. Instrum.
**2018**, 89, 016104. [Google Scholar] [CrossRef] [Green Version] - Hics, L.; Dresselhaus, M. Effect of quantum-well structures on the thermoelectric figure of merit. Phys. Rev. B
**1993**, 47, 12727–12731. [Google Scholar] [CrossRef] [PubMed] - Hics, L.; Dresselhaus, M. Thermoelectric figure of merit of a one-dimensional conductor. Phys. Rev. B
**1993**, 47, 16631–16634. [Google Scholar] [CrossRef] - Pennelli, G.; Macucci, M. Optimization of the thermoelectric properties of nanostructured silicon. J. Appl. Phys.
**2013**, 114, 214507. [Google Scholar] [CrossRef] - Lee, J.; Lee, W.; Lim, J.; Yu, Y.; Konq, Q.; Urban, J.; Yang, P. Thermal transport in silicon nanowires at high temperature up to 700 K. Nano Lett.
**2016**, 16, 4133. [Google Scholar] [CrossRef] - Pennelli, G.; Dimaggio, E.; Macucci, M. Fabrication Techniques for Thermoelecric Devices based on Nanostructured Silicon. J. Nanosci. Nanotechnol.
**2017**, 17, 1627. [Google Scholar] [CrossRef] - Gaeda, G.; Pacios, M.; Morata, A.; Tarancon, A. Silicon-based Nanostructures for Integrated Thermoelectric Generators. J. Phys. D Appl. Phys.
**2018**, 51, 423001. [Google Scholar] [CrossRef] - Li, Y.; Buddharaju, K.; Singh, N.; Lo, G.; Lee, S. Chip-level thermoelectric power generators based on high-density silicon nanowire array prepared with top-down CMOS technology. IEEE Electron Device Lett.
**2011**, 32, 674–676. [Google Scholar] [CrossRef] - Donmez Noyan, I.; Dolcet, M.; Salleras, M.; Stranz, A.; Calaza, C.; Gadea, G.; Pacios, M.; Morata, A.; Tarancon, A.; Fonseca, L. All-silicon thermoelectric micro/nanogenerator including a heat exchanger for harvesting applications. J. Power Sources
**2019**, 413, 125–133. [Google Scholar] [CrossRef] - Fonseca, L.; Donmez-Noyan, I.; Dolcet, M.; Estrada-Wiese, D.; Santander, J.; Salleras, M.; Gadea, G.; Pacios, M.; Sojo, J.M.; Morata, A.; et al. Transitioning from Si to sige nanowires as thermoelectric material in silicon-based microgenerators. Nanomaterials
**2021**, 11, 517. [Google Scholar] [CrossRef] - Domnez Noyan, I.; Gadea, G.; Salleras, M.; Pacios, M.; Calaza, C.; Stranz, A.; Dolcet, M.; Morata, A.; Tarancon, A.; Fonseca, L. SiGe nanowire arrays based thermoelectric microgenerator. Nano Energy
**2019**, 57, 492–499. [Google Scholar] [CrossRef] - Tomita, M.; Oba, S.; Himeda, Y.; Yamato, R.; Shima, K.; Kumada, T.; Xu, M.; Takezawa, H.; Mesaki, K.; Tsuda, K.; et al. Modeling, simulation, fabrication, and characterization of a 10-μW/cm
^{2}class si-nanowire thermoelectric generator for IoT applications. IEEE Trans. Electron Devices**2018**, 65, 5180–5188. [Google Scholar] [CrossRef] - Davila, D.; Tarancon, A.; Calaza, C.; Salleras, M.; Fernandez-Regulez, M.; SanPaulo, A.; Fonseca, L. Monolithically integrated thermoelectric energy harvester based on silicon nanowire arrays for powering micro/nanodevices. Nano Energy
**2012**, 1, 812. [Google Scholar] [CrossRef] - Davila, D.; Tarancon, A.; Fernandez-regulez, M.; Calaza, C.; Salleras, M.; SanPaulo, A.; Fonseca, L. Silicon nanowire arrays as thermoelectric material for a power microgenerator. J. Micromechan. Microeng.
**2011**, 21, 104007. [Google Scholar] [CrossRef] - Gadea, G.; Morata, A.; Tarancon, A. Semiconductor Nanowires for Thermoelectric Generation. Semicond. Semimetals
**2018**, 98, 321–407. [Google Scholar] [CrossRef] - Fonseca, L.; Santos, J.D.; Roncaglia, A.; Narducci, D.; Calaza, C.; Salleras, M.; Donmez, I.; Tarancon, A.; Morata, A.; Gadea, G.; et al. Smart integration of silicon nanowire arrays in all-silicon thermoelectric micro-nanogenerators. Semicond. Sci. Technol.
**2016**, 31, 084001. [Google Scholar] [CrossRef] [Green Version] - Calaza, C.; Fonseca, L.; Salleras, M.; Donmez, I.; Tarancón, A.; Morata, A.; Santos, J.; Gadea, G. Thermal Test of an Improved Platform for Silicon Nanowire-Based Thermoelectric Micro-generators. J. Electron. Mater.
**2016**, 45, 1689–1694. [Google Scholar] [CrossRef] [Green Version] - Gadea Díez, G.; Sojo Gordillo, J.; Pacios Pujadó, M.; Salleras, M.; Fonseca, L.; Morata, A.; Tarancón Rubio, A. Enhanced thermoelectric figure of merit of individual Si nanowires with ultralow contact resistances. Nano Energy
**2020**, 67, 104191. [Google Scholar] [CrossRef] - Yuan, Z.; Ziouche, K.; Bougrioua, Z.; Lejeune, P.; Lasri, T.; Leclercq, D. A planar micro thermoelectric generator with high thermal resistance. Sens. Actuators A Phys.
**2015**, 221, 67–76. [Google Scholar] [CrossRef] - Ziouche, K.; Yuan, Z.; Lejeune, P.; Lasri, T.; Leclercq, D.; Bougrioua, Z. Silicon-Based Monolithic Planar Micro Thermoelectric Generator Using Bonding Technology. J. Microelectromechan. Syst.
**2017**, 26, 45–47. [Google Scholar] [CrossRef] - Ziouche, K.; Bel-Hadj, I.; Bougrioua, Z. Thermoelectric properties of nanostructured porous-polysilicon thin films. Nano Energy
**2021**, 80, 105553. [Google Scholar] [CrossRef] - Pennelli, G.; Totaro, M.; Piotto, M.; Bruschi, P. Seebeck coefficient of nanowires interconnected into large area networks. Nano Lett.
**2013**, 13, 2592. [Google Scholar] [CrossRef] - Totaro, M.; Bruschi, P.; Pennelli, G. Top down fabricated silicon nanowire networks for thermoelectric applications. Microelectron. Eng.
**2012**, 97, 157. [Google Scholar] [CrossRef] - Pennelli, G.; Macucci, M. High-power thermoelectric generators based on nanostructured silicon. Semicond. Sci. Technol.
**2016**, 31, 054001. [Google Scholar] [CrossRef] - Pournia, M.; Firoozabadi, S.; Fathipour, M.; Kolahdouz, M. Fabrication of ultra-high-aspect-ratio nano-walls and nano-structures on silicon substrates. J. Micromechan. Microeng.
**2020**, 30, 125008. [Google Scholar] [CrossRef] - Nguyen, V.; Shkondin, E.; Jensen, F.; Hübner, J.; Leussink, P.; Jansen, H. Ultrahigh aspect ratio etching of silicon in SF6-O2plasma: The clear-oxidize-remove-etch (CORE) sequence and chromium mask. J. Vac. Sci. Technol. A Vac. Surfaces Film.
**2020**, 38, 053002. [Google Scholar] [CrossRef] - Bagolini, A.; Scauso, P.; Sanguinetti, S.; Bellutti, P. Silicon Deep Reactive Ion Etching with aluminum hard mask. Mater. Res. Express
**2019**, 6, 085913. [Google Scholar] [CrossRef] - Parasuraman, J.; Summanwar, A.; Marty, F.; Basset, F.; Angelescu, D.; Bourouina, T. Deep reactive ion etching of sub-micrometer trenches with ultra high aspect ratio. Microelectron. Eng.
**2014**, 113, 35. [Google Scholar] [CrossRef] - Stranz, A.; Waag, A.; Peiner, E. High-temperature performance of stacked silicon nanowires for thermoelectric power generation. J. Electron. Mat.
**2013**, 42, 2233. [Google Scholar] [CrossRef] - Huang, Z.; Geyer, N.; Werner, P.; de Boor, J.; Gosele, U. Metal-assisted chemical etching of silicon: A review. Adv. Mater.
**2011**, 23, 285–308. [Google Scholar] [CrossRef] - Kim, J.; Han, H.; Kim, Y.; Choi, S.H.; Kim, J.C.; Lee, W. Au/Ag bilayered metal mesh as a Si etching catalyst for controlled fabrication of Si nanowires. ACS Nano
**2011**, 5, 3222. [Google Scholar] [CrossRef] - Magagna, S.; Narducci, D.; Alfonso, C.; Dimaggio, E.; Pennelli, G.; Charaï, A. On the mechanism ruling the morphology of silicon nanowires obtained by one-pot metal-assisted chemical etching. Nanotechnology
**2020**, 31, 404002. [Google Scholar] [CrossRef] - To, W.; Tsang, C.; Li, H.; Huang, Z. Fabrication of n-Type Mesoporous Silicon Nanowires by One-Step Etching. Nano Lett.
**2011**, 11, 5252–5258. [Google Scholar] [CrossRef] - Bollani, M.; Osmond, J.; Nicotra, G.; Spinella, C.; Narducci, D. Strain-induced generation of silicon nanopillars. Nanotechnology
**2013**, 24, 335302. [Google Scholar] [CrossRef] - Mallavarapu, A.; Ajay, P.; Barrera, C.; Sreenivasan, S. Ruthenium-Assisted Chemical Etching of Silicon: Enabling CMOS-Compatible 3D Semiconductor Device Nanofabrication. ACS Appl. Mater. Interfaces
**2021**, 13, 1169–1177. [Google Scholar] [CrossRef] - Peng, K.; Yan, Y.; Gao, S.; Zhu, J. Dendride-assisted growth of silicon nanowires in electroless metal deposition. Adv. Funct. Mater.
**2003**, 13, 127. [Google Scholar] [CrossRef] - Peng, K.; Hu, J.; Yan, Y.; Wu, Y.; Fang, H.; Xu, Y.; Lee, S.; Zhu, J. Fabrication of single-crystalline silicon nanowires by scratching a silicon surface with catalytic metal particles. Adv. Funct. Mater.
**2006**, 16, 387–394. [Google Scholar] [CrossRef] - Qi, Y.; Wang, Z.; Zhang, M.; Yang, F.; Wang, Z. A Processing Window for Fabricating Heavily Doped Silicon Nanowires by Metal-Assisted Chemical Etching. J. Phys. Chem. C
**2013**, 117, 25090. [Google Scholar] [CrossRef] - Dimaggio, E.; Narducci, D.; Pennelli, G. Fabrication of Silicon Nanowire Forests for Thermoelectric Applications by Metal-Assisted Chemical Etching. J. Mater. Eng. Perform.
**2018**, 27, 6279–6285. [Google Scholar] [CrossRef] - Elyamny, S.; Dimaggio, E.; Pennelli, G. Seebeck coefficient of silicon nanowire forests doped by thermal diffusion. Beilstein J. Nanotechnol.
**2020**, 11, 1707–1713. [Google Scholar] [CrossRef] [PubMed] - Sadhu, J.S.; Tian, H.; Spila, T.; Kim, J.; Azeredo, B.; Ferreira, P.; Sinha, S. Controllable doping and wrap-around contacts to electrolessly etched silicon nanowire arrays. Nanotechnology
**2014**, 25, 375701. [Google Scholar] [CrossRef] [PubMed] - Xu, B.; Fobelets, K. Spin-on-doping for output power improvement of silicon nanowire array based thermoelectric power generators. J. Appl. Phys.
**2014**, 115, 214306. [Google Scholar] [CrossRef] - Dimaggio, E.; Pennelli, G. Reliable Fabrication of Metal Contacts on Silicon Nanowire Forests. Nano Lett.
**2016**, 7, 4348. [Google Scholar] [CrossRef]

**Figure 1.**Available experimental data of the Seebeck coefficient are reported both for n-doping (Panel (

**a**)) and for p-doping (Panel (

**b**)). The logarithmic fit (see text) is also shown. The red lines show the Seebeck coefficient calculated with the Stratton formula (both for n and for p doping): experimental measurement give higher values of the Seebeck coefficient. Panel (

**a**) is a modification of the figure published on [14].

**Figure 2.**The room temperature power factor ${S}^{2}\sigma $ is reported as a function of the doping concentration, both for n (Panel (

**a**)) and for p type silicon (Panel (

**b**)). An optimal doping for the maximum power factor is established both for n ($n=5.5\times {10}^{25}$ m${}^{-3}$) and for p ($p=1.2\times {10}^{26}$ m${}^{-3}$) type silicon. Panel (

**a**) has been reprinted from [14] with permission.

**Figure 3.**The power factor of n (Panel (

**a**)) and p (Panel (

**b**)) doped silicon is reported as a function of temperature. The blue curves concern the doping concentration, which maximizes the power factor at room temperature, the red curves have been calculated considering $S=S\left(T\right)$ experimentally determined by Ohishi [12] for doping concentrations different from that for the maximum power factor.

**Figure 4.**The electrical conductivity for $n=5.5\times {10}^{25}$ m${}^{-3}$, normalized with respect to the bulk value, is reported as a function of the nanowire width (continuous curve). Furthermore, the experimental measurements of the thermal conductivity (scatters) are reported. For diameters between 30 nm and 100 nm (roughly), the electrical conductivity is comparable with that in the bulk, the thermal conductivity results were instead strongly reduced for sufficiently rough nanowires.

**Figure 5.**The factor Z (Panel (

**a**)) and the figure of merit $ZT$ (Panel (

**b**)) are reported as a function of temperature, for the optimum thermoelectric doping of n type silicon. Different curves consider different values of the thermal conductivity ${k}_{t}$. The highest values of Z are related to ${k}_{t}=2$ W/(m K), achievable in rough silicon nanowires.

**Figure 6.**Original SEM micrographs of fabricated prototypes, together with a sketch of these planar thermoelectric devices. These prototypes confirm the feasibility of an all-silicon thermoelectric device, based on large arrays of silicon nanostructures.

**Figure 7.**Sketches and SEM micrographs of thermoelectric devices based on silicon nanowires fabricated perpendicular to the substrate.

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Pennelli, G.; Dimaggio, E.; Masci, A.
Silicon Nanowires: A Breakthrough for Thermoelectric Applications. *Materials* **2021**, *14*, 5305.
https://doi.org/10.3390/ma14185305

**AMA Style**

Pennelli G, Dimaggio E, Masci A.
Silicon Nanowires: A Breakthrough for Thermoelectric Applications. *Materials*. 2021; 14(18):5305.
https://doi.org/10.3390/ma14185305

**Chicago/Turabian Style**

Pennelli, Giovanni, Elisabetta Dimaggio, and Antonella Masci.
2021. "Silicon Nanowires: A Breakthrough for Thermoelectric Applications" *Materials* 14, no. 18: 5305.
https://doi.org/10.3390/ma14185305