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