Page 119 - Science at the nanoscale

RPS: PSP0007 - Science-at-Nanoscale
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June 9, 2009
Chapter Six
Low-Dimensional Nanostructures
In this chapter, we will move from atoms and molecules to the
world of solids. Here, we are less concerned with large scale
extended solids, where “large scale” here refers to solids with all
dimensions larger than about 100 nm, where size-effects do not
play a significant role. Instead, we will concern ourselves with
“low dimensional” nanostructures, whereby at least one dimen-
sion of the solid is less than about 100 nm in length. In such
low dimensional systems and nanostructures, the physical prop-
erties differ dramatically from those of their corresponding bulk
materials because quantum effects become significant. As seen in
Chapter 3, confinement of quantum mechanical wave functions in
regions of nanoscale dimensions induces a discretisation of energy
levels, and in this chapter we will introduce the effects of low
dimensionality on the electron density of states and related elec-
tronic properties.
6.1 FROM 3D TO 0D NANOSTRUCTURES ch06
The band theory of solids described in undergraduate solid
state physics textbooks is a very successful model for explaining
the electronic properties of periodic three-dimensional extended
solids. Band theory is based on the assumption that electron prop-
erties can be derived by treating the system as a one-electron prob-
lem in an average potential determined primarily by the periodic
array of ionised atoms in an extended perfect crystal. We will
not describe band theory in any detail here, but a useful way
Science at the Nanoscale: An Introductory Textbook
by Chin Wee Shong, Sow Chorng Haur & Andrew T S Wee
Copyright c
2010 by Pan Stanford Publishing Pte Ltd
www.panstanford.com
978-981-4241-03-8