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The thermal expansion effect of silicon nanowires (SiNW) in [100], [110] and[111] directions with different sizes is theoretically investigated. At lowtemperatures, all SiNW studied exhibit thermal contraction effect due to thelowest energy of the bending vibration mode which has negative effect on thecoefficient of thermal expansion (CTE). The CTE in [110] direction isdistinctly larger than the other two growth directions because of theanisotropy of the bending mode in SiNW. Our study reveals that CTE decreaseswith an increase of the structure ratio $\gamma=length/diameter$, and isnegative in whole temperature range with $\gamma=1.3$.

Thermal contraction in silicon nanowires at low temperatures