Thermal conductivity in porous silicon nanowire arrays
© Weisse et al.; licensee Springer. 2012
Received: 16 August 2012
Accepted: 24 September 2012
Published: 6 October 2012
The nanoscale features in silicon nanowires (SiNWs) can suppress phonon propagation and strongly reduce their thermal conductivities compared to the bulk value. This work measures the thermal conductivity along the axial direction of SiNW arrays with varying nanowire diameters, doping concentrations, surface roughness, and internal porosities using nanosecond transient thermoreflectance. For SiNWs with diameters larger than the phonon mean free path, porosity substantially reduces the thermal conductivity, yielding thermal conductivities as low as 1 W/m/K in highly porous SiNWs. However, when the SiNW diameter is below the phonon mean free path, both the internal porosity and the diameter significantly contribute to phonon scattering and lead to reduced thermal conductivity of the SiNWs.
KeywordsThermal conductivity Silicon nanowires Porous silicon Thermoreflectance
Silicon with a high density of nanoscale features such as interfaces, porosity, and impurities can have thermal conductivities (κ) up to three orders of magnitude lower than that of bulk Si through enhanced phonon scattering [1–17]. For example, the thermal conductivity of nanoporous bulk Si generally decreases with increasing porosity and decreasing pore size [1–9] and, with high porosity, approaches the amorphous limit (0.2 to 0.5 W/m/K) [1–3]. Similarly, silicon nanowires (SiNWs) with diameters significantly smaller than the bulk phonon mean free path (Λ ≈ 100 to 300 nm at 300 K) were reported to have thermal conductivity values as low as 0.76 W/m/K due to strong phonon scattering at the SiNW boundary [10, 11]. Introducing surface roughness to the SiNWs leads to additional phonon scattering at length scales even smaller than the NW diameter [12–16]. However, there have been few investigations on the combined effects of external dimensions and internal porosity on the thermal conductivity values of SiNWs. In this work, we report the effects of internal porosity on the thermal conductivity of SiNWs of two different diameters that allow the phonon propagation to span the range from ballistic to diffusive thermal transport (davg ≈ 350 and 130 nm) by measuring the thermal conductivity of vertically aligned SiNW arrays using nanosecond transient thermoreflectance (TTR). As opposed to measurements of individual SiNWs, measurements of arrays of SiNWs offer the advantage of averaging out the inherent thermal conductivity variations that are caused by differences in SiNW diameter, surface roughness, and defects within the arrays.
Summary of SiNW arrays with varied diameters and porosities
Etching method and doping concentration
davg≈ 300 to 350 nm
VFDRIE = 21% to 23%
Low porosity: Ag/Au MACE
VFMACE = 45% to 60%
Moderate porosity: Ag MACE, lightly doped
High porosity: Ag MACE, heavily doped
MACE etchant solution
davg≈ 130 nm
Low porosity, 0.15 M H2O2
VF = 26% to 35%
High porosity, 1.2 M H2O2
Following the formation of the SiNW arrays, the gaps between SiNWs are completely filled with parylene N (poly-para-xylylene; Figure 1b,f), which has a thermal conductivity significantly lower than the SiNWs (Kparylene = 0.125 W/m/K) and a high melting temperature (Tm ≈ 410°C). The parylene filling quality is inspected by examining multiple freshly cut cross sections under a scanning electron microscope (SEM), and no parylene voids are observed. The SiNW tips are subsequently exposed via chemical mechanical polishing to remove the parylene covering the SiNWs (Figure 1c,g) that facilitates the SiNWs to form a good thermal contact with the top metal film. Finally, a 15-nm Cr layer (for adhesion) and a 500-nm Cu layer are deposited by electron beam evaporation on top of the SiNW tips to form a flat, reflective transducer layer for the thermoreflectance measurements (Figure 1d,h).
where Δkparylene is the thermal conductivity variation from the literature. Δkfilm and ΔVF are the measured spot-spot variation in the same type of samples. Detailed error analysis data for all the data reported here can be found in Additional file 1.
Results and discussion
In summary, we measured the thermal conductivity of SiNW arrays with various nanowire diameters, doping concentrations, surface roughness and internal porosities using a nanosecond transient thermoreflectance method. When the SiNW diameter (davg ≈ 350 nm) is larger than the phonon mean free path in the bulk silicon, the thermal conductivity shows little dependence on the doping concentration and surface roughness but decreases significantly with increasing porosity due to phonon scattering at the pore interfaces. In contrast, when the SiNW diameter (davg ≈ 130 nm) is smaller than the phonon mean free path, the thermal conductivity strongly depends on both the external boundary-phonon scattering and the internal pore interface-phonon scattering, leading to a significant reduction in the thermal conductivity for small-diameter SiNWs.
The authors gratefully acknowledge the support of the PECASE program, the Link Foundation Energy Fellowship program, the National Science Foundation Graduation Research Fellowship program, and the Stanford Graduate Fellowship program.
- Gesele G, Linsmeier J, Drach V, Fricke J, Arens-Fischer R: Temperature-dependent thermal conductivity of porous silicon. J Phys D: Appl Phys 1997, 30: 2911–2916. 10.1088/0022-3727/30/21/001View Article
- Yang CC, Li S: Basic principles for rational design of high-performance nanostructured silicon-based thermoelectric materials. ChemPhysChem 2011, 12: 3614–3618. 10.1002/cphc.201100514View Article
- Miyazaki K, Tanaka S, Nagai D: Heat conduction of a porous material. J Heat Transfer 2012, 134: 051018. 10.1115/1.4005709View Article
- Alvarez FX, Jou D, Sellitto A: Pore-size dependence of the thermal conductivity of porous silicon: a phonon hydrodynamic approach. Appl Phys Lett 2010, 97: 033103. 10.1063/1.3462936View Article
- de Boor J, Kim DS, Ao X, Hagen D, Cojocaru A, Foell H, Schmidt V: Temperature and structure size dependence of the thermal conductivity of porous silicon. Europhys Lett 2011, 96: 16001. 10.1209/0295-5075/96/16001View Article
- Gomes S, David L, Lysenko V, Descamps A, Nychyporuk T, Raynaud M: Application of scanning thermal microscopy for thermal conductivity measurements on meso-porous silicon thin films. J Phys D: Appl Phys 2007, 40: 6677–6683. 10.1088/0022-3727/40/21/029View Article
- He Y, Donadio D, Lee J-H, Grossman JC, Galli G: Thermal transport in nanoporous silicon: interplay between disorder at mesoscopic and atomic scales. ACS Nano 2011, 5: 1839–1844. 10.1021/nn2003184View Article
- Lee J-H, Galli GA, Grossman JC: Nanoporous Si as an efficient thermoelectric material. Nano Lett 2008, 8: 3750–3754. 10.1021/nl802045fView Article
- Romano G, Di Carlo A, Grossman JC: Mesoscale modeling of phononic thermal conductivity of porous Si: interplay between porosity, morphology and surface roughness. J Comput Electron 2012, 11: 8–13. 10.1007/s10825-012-0390-2View Article
- Boukai AI, Bunimovich Y, Tahir-Kheli J, Yu JK, Goddard WA, Heath JR: Silicon nanowires as efficient thermoelectric materials. Nature 2008, 451: 168–171. 10.1038/nature06458View Article
- Li DY, Wu YY, Kim P, Shi L, Yang PD, Majumdar A: Thermal conductivity of individual silicon nanowires. Appl Phys Lett 2003, 83: 2934–2936. 10.1063/1.1616981View Article
- Hochbaum AI, Chen RK, Delgado RD, Liang WJ, Garnett EC, Najarian M, Majumdar A, Yang PD: Enhanced thermoelectric performance of rough silicon nanowires. Nature 2008, 451: 163–167. 10.1038/nature06381View Article
- Lim J, Hippalgaonkar K, Andrews SC, Majumdar A, Yang P: Quantifying surface roughness effects on phonon transport in silicon nanowires. Nano Lett 2012, 12: 2475–2482. 10.1021/nl3005868View Article
- Liu L, Chen X: Effect of surface roughness on thermal conductivity of silicon nanowires. J Appl Phys 2010, 107: 033501. 10.1063/1.3298457View Article
- Luisier M: Investigation of thermal transport degradation in rough Si nanowires. J Appl Phys 2011, 110: 074510. 10.1063/1.3644993View Article
- 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.View Article
- Abramson AR, Kim WC, Huxtable ST, Yan HQ, Wu YY, Majumdar A, Tien CL, Yang PD: Fabrication and characterization of a nanowire/polymer-based nanocomposite for a prototype thermoelectric device. J Microelectromech Syst 2004, 13: 505–513. 10.1109/JMEMS.2004.828742View Article
- Haynes CL, Van Duyne RP: Nanosphere lithography: a versatile nanofabrication tool for studies of size-dependent nanoparticle optics. J Phys Chem B 2001, 105: 5599–5611. 10.1021/jp010657mView Article
- Zhong X, Qu YQ, Lin YC, Liao L, Duan XF: Unveiling the formation pathway of single crystalline porous silicon nanowires. ACS Appl Mater Interfaces 2011, 3: 261–270. 10.1021/am1009056View Article
- Qu Y, Zhou H, Duan X: Porous silicon nanowires. Nanoscale 2011, 3: 4060–4068. 10.1039/c1nr10668fView Article
- Weisse JM, Lee CH, Kim DR, Zheng X: Fabrication of flexible and vertical silicon nanowire electronics. Nano Lett 2012, 12: 3339–3343. 10.1021/nl301659mView Article
- Garnett E, Yang PD: Light trapping in silicon nanowire solar cells. Nano Lett 2010, 10: 1082–1087. 10.1021/nl100161zView Article
- Qu YQ, Liao L, Li YJ, Zhang H, Huang Y, Duan XF: Electrically conductive and optically active porous silicon nanowires. Nano Lett 2009, 9: 4539–4543. 10.1021/nl903030hView Article
- Weisse JM, Kim DR, Lee CH, Zheng X: Vertical transfer of uniform silicon nanowire arrays via crack formation. Nano Lett 2011, 11: 1300–1305. 10.1021/nl104362eView Article
- Kim J, Han H, Kim YH, 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: 3222–3229. 10.1021/nn2003458View Article
- Zhang ML, Peng KQ, Fan X, Jie JS, Zhang RQ, Lee ST, Wong NB: Preparation of large-area uniform silicon nanowires arrays through metal-assisted chemical etching. J Phys Chem C 2008, 112: 4444–4450.View Article
- Chiappini C, Liu X, Fakhoury JR, Ferrari M: Biodegradable porous silicon barcode nanowires with defined geometry. Adv Funct Mater 2010, 20: 2231–2239. 10.1002/adfm.201000360View Article
- Panzer MA, Zhang G, Mann D, Hu X, Pop E, Dai H, Goodson KE: Thermal properties of metal-coated vertically aligned single-wall nanotube arrays. J Heat Transfer 2008, 130: 052401. 10.1115/1.2885159View Article
- Asheghi M, Kurabayashi K, Kasnavi R, Goodson KE: Thermal conduction in doped single-crystal silicon films. J Appl Phys 2002, 91: 5079–5088. 10.1063/1.1458057View Article
- Slack GA: Thermal conductivity of pure and impure silicon, silicon carbide, and diamond. J Appl Phys 1964, 35: 3460–3465. 10.1063/1.1713251View Article
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