Theoretical surface image

There are a number of concepts concerning the structure of small particles which have a bearing upon geometrical catalytic effects (e.g. 41-43). These follow both from the surface imaging results, and a detailed experimental (13-15) and theoretical (44-47) study of particle morphologies. 

Using the expressions of the tunneling matrix elements derived in Chapter 3, theoretical STM images can be calculated. In this section, we discuss the theoretical STM images of the simple metal surface we presented in the previous subsection. 

Ohnishi, M. Suzuki, K. Saigo, Y. Saotome, and H. Gokan, Postirradiation polymerization of e beam negative resists Theoretical analysis and method of inhibition, Proc. SPIE 539, 62 (1985). " R.R. Kunz, M.W. Horn, R.B. Goodman, P.A. Bianconi, D.A. Smith, J.R. Eshelman, G.M. Wallraff, R.D. Miller, and E.J. Ginsberg, Surface imaged silicon polymers for 193 nm excimer laser lithogra phy, Proc. SPIE 1672, 385 (1992). 

Related to the spectroscopy of crystals is the spectroscopy of surfaces and, particularly, the spectroscopy of species adsorbed on crystal surfaces. For perfectly conducting metals, there is an important selection rule in that such surfaces image any electric dipole within an adsorbed molecule. When such dipoles are perpendicular to the surface the dipoles reinforce when they are parallel to the surface they cancel. This gives rise to the so-called surface selection rule , that it is only possible to observe by electric dipole spectroscopy those modes which involve dipole moment changes perpendicular to the surface. This requirement can be expressed group theoretically by use of the so-called diperiodic groups in two dimensions. 

The theoretical lateral spatial resolution achievable with Raman imaging using the optical arrangements of our system (50 x objective with NA = 0.75, 633 nm HeNe laser) should be about 1 pm. In this investigation the resolution is worse than predicted. In practice, sample drift during long acquisition times, uneven surface structures and penetration of laser light into the material worsen the lateral spatial resolution to a value of about 2 pm (estimated). 

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