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Introduction to Nanotechnology

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58 METHODS OF MEASURING PROPERTIES<br />

Figure 3.22. AFM image of nanostructure array formed when the laser focused Cr deposition is<br />

carried Out in twu standim waves oriented at 90 relative <strong>to</strong> each other. [From R. Gupta,<br />

J. J. McClelland, 2. J. Jabbour, and R. L. CelotEa, Ami. Fhys. Left 67. 1378 (1995),]<br />

3.4. SPECTROSCOPY<br />

3.4.1. Infrared and Raman Spectroscopy<br />

Vibrational spectroscopy involves pho<strong>to</strong>ns that inducc transitions bctween vibra-<br />

tional states in molecules and solids, typically in thc infrared (IR) frequency range<br />

from 2 <strong>to</strong> 12 x IO'> Hz. Secrion 2.1.5 discusses the normal modes of' vibration of<br />

molecules and solids. The energy gaps of many wrniconductm are in !his same<br />

frequency region, nnd can be studied by infmred 'techniques.<br />

In infrmd spectroscopy an IR pho<strong>to</strong>n hi, is absorhed directly <strong>to</strong> induce a<br />

transition between two vibrational lcvcls E,, and E,,,. where<br />

E,, = (11 f f)ho (3.8)<br />

The vibrational quantum nuniber IF = 0. 1,2, ". . is a positive integer, and vo is the<br />

chamcteristic freqiiency for a particular normal mode. In accordance with theselection<br />

rule An = +l, infrared transitions are observed only between adjacent<br />

vibrational energy Imels, and hence have the frequency v,. In Raman spectroscopy B<br />

vibrational tnrisrtion is induccd when an incident optical pho<strong>to</strong>n of frequency hint<br />

is absorbed and another optical pho<strong>to</strong>n hvtm,L<br />

if emjtted:

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