2.1.1. Size Dependence of Properties

Many properties of solids depend on the size range over which they are measured. Microscopic details become averaged when investigating bulk materials. At the macro- or large-scale range ordinarily studied in traditional fields of physics such as mechanics, electricity and magnetism, and optics, the sizes of the objects under study range from millimeters to kilometers. The properties that we associate with these materials are averaged properties, such as the density and elastic moduli in

Introduction to Nanotechnology, by Charles P. Poole Jr. and Frank J. Owens. ISBN 0-471-07935-9. Copyright © 2003 John Wiley & Sons, Inc.

mechanics, the resistivity and magnetization in electricity and magnetism, and the dielectric constant in optics. When measurements are made in the micrometer or nanometer range, many properties of materials change, such as mechanical, ferroelectric, and ferromagnetic properties. The aim of the present book is to examine characteristics of solids at the next lower level of size, namely, the nanoscale level, perhaps from 1 to lOOnm. Below this there is the atomic scale near 0.1 nm, followed by the nuclear scale near a femtometer (10-15 m). In order to understand properties at the nanoscale level it is necessary to know something about the corresponding properties at the macroscopic and mesoscopic levels, and the present chapter aims to provide some of this background.

Many important nanostructures are composed of the group IV elements Si or Ge, type m-V semiconducting compounds such as GaAs, or type II-VI semiconducting materials such as CdS, so these semiconductor materials will be used to illustrate some of the bulk properties that become modified with incorporation into nanostructures. The Roman numerals IV, III, V, and so on, refer to columns of the periodic table. Appendix B provides tabulations of various properties of these semiconductors.

2.1.2. Crystal Structures

Most solids are crystalline with their atoms arranged in a regular manner. They have what is called long-range order because the regularity can extend throughout the crystal. In contrast to this, amorphous materials such as glass and wax lack long-range order, but they have what is called short-range order so the local environment of each atom is similar to that of other equivalent atoms, but this regularity does not persist over appreciable distances. Liquids also have short-range order, but lack long-range order. Gases lack both long-range and short-range order.

Figure 2.1 shows the five regular arrangements of lattice points that can occur in two dimensions: the square (a), primitive rectangular (b), centered rectangular (c), hexagonal (d), and oblique (e) types. These arrangements are called Bravais lattices. The general or oblique Bravais lattice has two unequal lattice constants a ^ b and an arbitrary angle 0 between them. For the perpendicular case when 6 = 90°, the lattice becomes the rectangular type. For the special case a = b and 6 = 60°, the lattice is the hexagonal type formed from equilateral triangles. Each lattice has a unit cell, indicated in the figures, which can replicate throughout the plane and generate the lattice.

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