1. CHAPTER 11 Semiconductor Theory and Devices
11.1 Band Theory of Solids
11.4 Nanotechnology

2. Categories of Solids
There are three categories of solids, based on their conducting properties:
conductors
semiconductors
insulators

3. Electrical Resistivity and Conductivity of Selected Materials at 293 K

4. Reviewing the previous table reveals that:
The electrical conductivity at room temperature is quite different for each of these three kinds of solids
Metals and alloys have the highest conductivities
followed by semiconductors
and then by insulators

5. Resistivity vs. Temperature
Figure 11.1: (a) Resistivity versus temperature for a typical conductor. Notice the linear rise in resistivity with increasing temperature at all but very low temperatures. (b) Resistivity versus temperature for a typical conductor at very low temperatures. Notice that the curve flattens and approaches a nonzero resistance as T → 0. (c) Resistivity versus temperature for a typical semiconductor. The resistivity increases dramatically as T → 0.

6. Band Theory of Solids
In order to account for decreasing resistivity with increasing temperature as well as other properties of semiconductors, a new theory known as the band theory is introduced.
The essential feature of the band theory is that the allowed energy states for electrons are nearly continuous over certain ranges, called energy bands, with forbidden energy gaps between the bands.

7. Band Theory of Solids
Consider initially the known wave functions of two hydrogen atoms far enough apart so that they do not interact.

8. Band Theory of Solids
Interaction of the wave functions occurs as the atoms get closer:
An atom in the symmetric state has a nonzero probability of being halfway between the two atoms, while an electron in the antisymmetric state has a zero probability of being at that location.
Symmetric
Antisymmetric

9. Band Theory of Solids
In the symmetric case the binding energy is slightly stronger resulting in a lower energy state.
Thus there is a splitting of all possible energy levels (1s, 2s, and so on)
When more atoms are added (as in a real solid), there is a further splitting of energy levels. With a large number of atoms, the levels are split into nearly continuous energy bands, with each band consisting of a number of closely spaced energy levels.

11. 11.4: Nanotechnology
Nanotechnology is generally defined as the scientific study and manufacture of materials on a submicron scale.
These scales range from single atoms (on the order of 0.1 nm up to 1 micron (1000 nm).
This technology has applications in engineering, chemistry, and the life sciences and, as such, is interdisciplinary.

12. Carbon Nanotubes
In 1991, following the discovery of C60 buckminsterfullerenes, or “buckyballs,” Japanese physicist Sumio Iijima discovered a new geometric arrangement of pure carbon into large molecules.
In this arrangement, known as a carbon nanotube, hexagonal arrays of carbon atoms lie along a cylindrical tube instead of a spherical ball.

13. Structure of a Carbon Nanotube
Figure 11.30: Model of a carbon nanotube, illustrating the hexagonal carbon pattern superimposed on a tubelike structure. There is virtually no limit to the length of the tube. From Chris Ewels/

14. Applications of Nanotubes
Because of their strength they are used as structural reinforcements in the manufacture of composite materials
(batteries in cell-phones use nanotubes in this way)
Nanotubes have very high electrical and thermal conductivities, and as such lead to high current densities in high-temperature superconductors.