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.
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.
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