Strain and thermal conductivity in ultrathin suspended silicon nanowires

Daniel Fan, Hans Sigg, Ralph Spolenak, and Yasin Ekinci

Phys. Rev. B 96, 115307 – Published 15 September 2017

Abstract

We report on the uniaxial strain and thermal conductivity of well-ordered, suspended silicon nanowire arrays between 10 to 20 nm width and 22 nm half-pitch, fabricated by extreme-ultraviolet (UV) interference lithography. Laser-power-dependent Raman spectroscopy showed that nanowires connected monolithically to the bulk had a consistent strain of $\sim 0.1 %$ , whereas nanowires clamped by metal exhibited variability and high strain of up to 2.3%, having implications in strain engineering of nanowires. The thermal conductivity at room temperature was measured to be $\sim 1 W / m K$ for smooth nanowires and $\sim 0.1 W / m K$ for rougher ones, similar to results by other investigators. We found no modification of the bulk properties in terms of intrinsic scattering, and therefore, the decrease in thermal conductivity is mainly due to boundary scattering. Different types of surface roughness, such as constrictions and line-edge roughness, may play roles in the scattering of phonons of different wavelengths. Such low thermal conductivities would allow for very efficient thermal energy harvesting, approaching and passing values achieved by state-of-the-art thermoelectric materials.

Received 6 June 2017
Revised 27 July 2017

DOI:https://doi.org/10.1103/PhysRevB.96.115307

Physics Subject Headings (PhySH)

Strain Thermoelectric effects

Nanowires

Lithography Raman spectroscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Daniel Fan^1,2,*, Hans Sigg¹, Ralph Spolenak², and Yasin Ekinci¹

¹Laboratory for Micro and Nanotechnology, Paul Scherrer Institut, Villigen-PSI 5232, Switzerland
²Laboratory for Nanometallurgy, ETH Zurich, Zurich 8052, Switzerland

^*daniel.fan@psi.ch

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Issue

Vol. 96, Iss. 11 — 15 September 2017

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Images

Figure 1
(a) EUV-IL scheme, not to scale. Coherent EUV light is incident upon two gratings which diffract the beams such that they interfere. The interference pattern is then recorded. (b) Schematic of SiNWs clamped by Cr and released by VHF or BOE etching. (c) Schematic of SiNWs connected monolithically to Si pads. (d) SEM of SiNWs clamped by Cr where an air gap is apparent between SiNW and metal due to underetching. (e) SEM of SiNWs connected to Si pads and released by VHF, showing smooth surfaces but constrictions at both ends. (f) SEM of SiNWs connected to Si pads and released by BOE followed by width thinning in Piranha solution and then critical point drying. The resulting LER value is relatively high i.e. $\sim 4 nm$ .
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Figure 2
Top: example laser-power-dependent Raman spectra of suspended SiNWs with the dotted lines highlighting the SiNW Raman peak shift as laser power is varied. Bottom: measurement of temperature using Stokes/anti-Stokes peak intensities (solid) and Raman peak shift (hollow, dotted). The data points highlighted by arrows were ignored in the fitting due to hysteresis—as the laser power was cycled high and then low, the original low power spectra could not be recovered, possibly due to materials changes caused by high temperatures.
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Figure 3
Example laser-power-dependent Stokes peak shift for a variety of SiNWs processed using different methods. The SiNWs are either joined monolithically to bulk silicon pads or clamped by Cr metal and released by either VHF, wet BOE, or wet BOE combined with critical point drying. The data points highlighted by arrows were ignored in the fit due to hysteresis of the Raman spectra, indicating materials phase changes possibly due to the high temperatures.
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Figure 4
SiNW width vs extrapolated zero-laser-power Stokes shift. Estimate of the quantum confinement component (thick dotted line) and the uniaxial elastic strain (blue dotted lines) are plotted. Monolithically connected SiNWs (solid) have low strain. Metal clamped SiNWs (hollow) exhibit high and variable process-induced strain. Very rough SiNWs (solid triangle) have low but variable strain, possibly due to variable oxide formation.
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Figure 5
Thermal conductivity vs width for SiNWs connected monolithically to Si pads including data from various references. A model of the thermal conductivity due to purely diffusive scattering (Casimir limit) is shown (solid line). The SiNWs released by VHF and BOE had a LER of $\sim 2 nm$ , while SiNWs undergoing critical point drying had a LER of $\sim 4 nm$ . For e-beam defined SiNWs with rectangular cross-section, the effective diameter was calculated using Eq. (4) for better comparison.
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Figure 6
(a) Uniaxial elastic strain vs thermal conductivity for suspended SiNWs connected monolithically to bulk silicon pads. The strained SiNWs were fabricated from prestrained SOI substrates. Depending on the placement of metal pads for discharging during SEM inspection, the SiNWs exhibited either constrictions at the ends (metal pads, solid) or no constrictions (no metal pads, hollow). (b) Effective diameter [Eq. (4)] vs thermal conductivity for strained and nonstrained SiNWs. (c) Strained 17 nm width SiNWs without constrictions. (d) Strained 11 nm width SiNWs with constrictions. Scale bars equal 200 nm. Unstrained substrates indicated by SOI, strained substrates indicated by sSOI.
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