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In Fig. 3 the calculated Young¡¯s moduli of SiNWs are plotted as a function of wire diameter. Similar to previous theoretical findings [20,21], the Young¡¯s modulus generally increases as the wire mean diameter increases. It can be inferred that the Young¡¯s modulus of nanowires would approach the bulk value at certain critical size, and afterwards it would not change much. Our calculations clearly show that nanowires of different directions have distinctly different Young¡¯s moduli. In the size range studied, the wires along [110] direction have the highest value, while [100] wires correspond to the lowest value. The values for [111] and [112] wires are intermediate in size. Previously, Lee et al. [11] studied the Young¡¯s modulus of Si [100] nanowires in detail and they also found that the Young¡¯s modulus increases slowly with wire size. The Young¡¯s modulus for micrometer-sized Si samples along the [100] direction was found to be 140 GPa [22]. For the [110] direction, the measured Young¡¯s modulus of micrometer-sized Si wires was 142¨C169 GPa [23]. For thinner samples, the Young¡¯s modulus was estimated to be 169 GPa [24]. These previous results showed that the Young¡¯s modulus is hardly influenced by the size reduction from millimeter to micrometer length scale [25]. |
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