Anisotropy and boundary scattering in the lattice thermal conductivity of silicon nanomembranes

Z. Aksamija and I. Knezevic

Phys. Rev. B 82, 045319 – Published 27 July 2010

Abstract

We present a calculation of the full thermal conductivity tensor for (001), (111), and (011) surface orientations of the silicon-on-insulator (SOI) nanomembrane, based on solving the Boltzmann transport equation in the relaxation-time approximation with the full phonon dispersions, a momentum-dependent model for boundary scattering, as well as three-phonon and isotope scattering. The interplay between strong boundary scattering and the anisotropy of the phonon dispersions results in thermal conduction that strongly depends on the surface orientation and exhibits marked in-plane vs out-of-plane anisotropy, as well as slight in-plane anisotropy for the low-symmetry (011) SOI. In-plane thermal conductivity is highest along [100] on Si(011) and lowest in Si(001) due to the strong scattering of the highly anisotropic TA modes with (001) surfaces. The room-temperature in-plane conductivities in (011) and (001) nanomembranes with thicknesses around 10 nm differ by a factor of 2, and the ratio can be much higher at lower temperatures or in rougher samples. We discuss surface facet orientation as a means of tailoring thermal conduction in low-dimensional nanostructrures and address the role of out-of-plane thermal conductivities in predicting vertical phonon transport in superlattices.

Received 11 May 2010

DOI:https://doi.org/10.1103/PhysRevB.82.045319

Authors & Affiliations

Z. Aksamija^* and I. Knezevic^†

Department of Electrical and Computer Engineering, University of Wisconsin–Madison, Madison, Wisconsin 53706, USA

^*aksamija@wisc.edu
^†knezevic@engr.wisc.edu

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Vol. 82, Iss. 4 — 15 July 2010

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Images

Figure 1
(Color online) Schematic of a silicon nanomembrane of thickness $L$ , showing a lattice wave scattering from the rough boundary. The phases of the waves reflected from different points on the boundary differ by amounts that depend on the local surface-roughness height $z (\vec{r})$ and the angle $Θ_{B}$ between the phonon momentum $\vec{q}$ and the boundary surface normal of the idealized smooth surface.Reuse & Permissions
Figure 2
(Color online) Average specularity parameter for LA (solid), TA1 (dashed), and TA2 (dashed-dotted) phonon branches. (a) Temperature variation in the average specularity parameter per phonon branch with surface-roughness rms heights of $Δ = 0.1$ , 0.5, and 1.5 nm. (b) Phonon dispersions and density of states for the acoustic branches. For completeness, optical-mode dispersions are also depicted. (c) Variation in the average specularity parameter with the rms roughness $Δ$ at 300 K (thick curves) and 50 K (thin curves).Reuse & Permissions
Figure 3
(Color online) Lattice thermal conductivity of 100 nm (filled circles), 30 nm (open circles), and 20 nm (squares) thick SOI, according to the measurements of Refs. 46, 47. The curves present our calculations with $Δ = 0.35 nm$ for 100 nm SOI, $Δ = 0.4 nm$ for 30, and $Δ = 0.45 nm$ for 20 nm SOI, in very good agreement with experiment. Thermal conductivity is lower by almost an order of magnitude than the room-temperature bulk value of $148 W / mK$ , owing primarily to boundary scattering at the rough $Si / {SiO}_{2}$ interfaces.Reuse & Permissions
Figure 4
(Color online) Lattice thermal conduction in thin SOI membranes. (a) Eigenvalues of the thermal conductivity tensor (1) for a 20-nm-thick SOI with rms surface roughness $Δ = 0.45 nm$ . Maximal in-plane thermal conductivity eigenvalue is along [100] on (011) SOI and it is minimal on (001) SOI due to the very strong scattering of TA modes from (001) boundaries, as described in the text. [(b) and (c)] Energy isosurfaces for (c) TA and (d) LA modes in silicon (dashed lines denote the Brillouin-zone shape). The TA constant-energy surfaces are boxlike with box faces perpendicular to $⟨ 001 ⟩$ directions. The LA mode energy isosurfaces have faces perpendicular to $⟨ 111 ⟩$ and $⟨ 001 ⟩$ directions. [(d) and (e)] Ratio of the highest to the lowest in-plane thermal conductivity, $κ_{[100] / (011)} / κ_{[100] / (001)}$ , for SOI with thicknesses in the 5–100 nm range, as a function of (d) temperature (surface-roughness rms height is 0.4 nm) and (e) rms roughness height (at room temperature).Reuse & Permissions

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