epdf.pub_nanotechnology-and-nanoelectronics-materials-devic

8 2 Quantum Mechanical Aspects
Fig. 2.3
Development of the diamond band gap
est neighbors which are cut out of the diamond. For the purpose of electronic saturation
12 hydrogen atoms are hung on this complex. The difference to a neopentane
molecule lies in the binding lengths and angles.
In the examples concerning carbon and silicon, the development of the band
structure is clearly visible. In another approach the band gap of silicon is determined
as a function of a typical length coordinate, say the cluster radius or the
length of a wire or a disc. In Fig. 2.5, the band gap versus the reciprocal of the
length is shown [8]. For a solid state, the band gap converges to its well known
value of 1.12 eV.
It is worthwhile comparing the above-mentioned predictions with subsequent
experimental results [9]. The band gap of Si n clusters is investigated by photoelectron
spectroscopy. Contrary to expectations, it is shown that almost all clusters
from n = 4 to 35 have band gaps smaller than that of crystalline silicon (see Fig.
2.6). These observations are due to pair formation and surface reconstruction.
Scientists are in fact interested in obtaining details which are even more
specific. For example, optical properties are not only determined through the band
gap but through the specific dependency of the energy bands on the wave vectors.
It is a much harder theoretical and computational assignment to determine this
dependency. An earlier result [10] for SiC cluster is reproduced in Fig. 2.7.
2.4 Preliminary Considerations for Lithography
An obvious effect of the quantum mechanics on the nanostructuring can be found in
lithography. For readers with little experience, the lithographic method will be
briefly explained with the help of Fig. 2.8.