Page 33 - Science at the nanoscale

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June 9, 2009
2.1. Mechanical Frequency
shown (left as an exercise for the reader) that for a thin rod made
of a material with atomic spacing a and atomic mass m:
2
(2.11)
v =
m
ρ
If the silicon cantilever is further reduced to 1 µm in length, the
resonant frequency will be about 14 MHz. Carr et al. have mea-
sured the resonant frequencies of silicon nanowires and found it
to be 400 MHz for a 2 µm long nanowire.
had lengths in the nanometre range, they will have resonant
frequencies in the GHz range, which would have novel device
applications.
The upper limit to oscillation frequencies will be those of molec-
ular bonds. For molecular bond vibrations with bond lengths of
13
about 1-2 A, the frequencies are of the order of 10
Hz. This is rou-
tinely measured by chemists using Infrared (IR) Spectroscopy, a
typical spectrum of which is shown in Fig. 2.2. Note that chemists
100
80
% Transm ittance
60
40
1092
1049
3349
C-H
C-O
20 O-H 2974 Y = ka 2 1 If such nanowires 23 ch02
stretch
stretch stretches
0
4000 3500 3000 2500 2000 1500 1000 500
Wavenumber(cm )
-1
Figure 2.2. FT-IR spectrum of ethanol molecules in liquid state (note:
Wavenumber cm −1 = Hz/c) (from author’s lab).
1 D. W. Carr, Appl. Phys. Lett. 75, 920 (1999).