Mechanical resonance of clamped silicon nanowires measured by optical interferometry

The mechanical resonance of laterally grown silicon nanowires measured by an optical interferometric technique is reported. The lengths and diameters of the nanowires ranged from L=2to20μm and D=39to400nm, respectively. The wires showed resonant frequencies in the f0=1–12MHz range and resonant quality factors Q at low pressure ranging from Q=5000 to Q=25000. The dependence of resonant frequency on the ratio of diameter to length squared, D∕L2, yielded a ratio of E∕ρ=9400±450m∕s. Assuming a density of ρ=2330kg∕m3, this experimental result yields an experimental Young modulus of E=205±10GPa, consistent with that of a bulk silicon. As the wires were cooled from T=270KtoT=77K, a 0.35% increase of resonant frequency was observed. This increase of resonant frequency with cooling resulted from a change in Young’s modulus and from the thermal contraction of silicon. The quality factor did not vary significantly from P=10−4to102Torr, suggesting that viscous damping does not dominate the dissipative processes in this pressure range. Although viscous damping became important above P=102Torr, relatively high quality factors of Q=7000 were still observed at atmospheric pressure.