At T = 0, a pure semimetal behaves as good conductor, as there are some partialy filled electrons and holes band.
At T = 0, a pure semiconductor behaves as insulator, as the carriers are either due to thermal excitation or presence of impurities.
Key concepts include:
The many-body Schrodinger equation
Hartree approximation and the self-consistent field
Hartree-Fock approximation and the exchange interaction
Fermi liquid theory
This is a nice little collection of info on the de Haas van Alphen effect I found (might be where Ross pinched some pictures from).
For an example of how you can actually apply the effect to construct the Fermi surface, have a look through this paper:
If you don't want to get into the gritty details at least check out fig. 2 to look at the relations between measurement and theory.
Now just as fast as silicon plus much cheaper, this inexpensive organic conductor could be used in areas where silicon struggles to compete, eventually slashing the cost of transistors, PDA’s, flat panel screens and bringing electronic paper into common use.
Metals, Superconductors and Semiconductors. Lecture 2A. Introduction and Synthesis of Important. Conjugated Polymers. Lecture 2B. Solid State Polymerization
Lecture 3. Fullerene Chemistry. Lecture 3B. Molecular Engineering. www.lios.at/VirtualAcademy/.../Organic_Conductors_Intro_Lecture.pdf - Similar
Has anyone had success with question 2 iv) of the practice mid-semester? I know that:
h^2/2m* = d^2E/dk^2
and have tried a few other methods, but I can't quite seem to get the answer. Any suggestions? I'm figuring I'm probably not taking the approximation near the boundary correctly.
One of the main advantages of organic electronics is the possibility of manufacturing components and circuits over large areas, while silicon chips are restricted to the area of circular pads of limited sizes.
Most of these advantages, however, is certainly the fact that organic electronics can be fabricated on plastic substrates, thin and flexible.
Only the flash memory transistor, the silicon component found in the pen-drives in digital cameras and MP3 players, continued to resist the benefits of plastic.
Now, Physicists built the first organic transistor Flash memory plastic.
For the open orbit case we discussed in the lecture the form of the current:
j = sigma(0)n(n.E) + sigma(1).E
Where n unit vector in the direction of the open orbit. It was argued that the component sigma(1) vanishes in the high-field limit, whereas the sigma(0) contribution does not. This means that unlike the closed-orbit case the magneto-resistance will not approach a constant.
To see this last assertion it is useful to examine a simple case where in the high-field limit the current flow is directed in a direction =/ n, say n'. From our statement above this means that the projection of the electric field, E.n = 0.
Following the working in Ashcroft and Mermin, this gives a particular form for the electric field which I will not write here. Suffice to say, defining the magneto-resistance rho as;
rho = E.j/|j|
One can arrive at the expression:
rho = (n'.j)^2/(n'.sigma(1).n')
Now as we have previously argued that sigma(1) vanishes in the high-field limit we clearly see that the magneto-resistance must diverge, i.e. it grows with increasing magnetic field.
The semi-classical model looks at the effect on the electron dynamics of external electric or magnetic fields that are approximately uniform over the scale of one such wave-packet. The periodic potential considered in the Bloch model is responsible for the important distinction between the classical and semi-classical models (because the free electron approximation is no longer valid). This potential changes on a scale far smaller than that of the wave-packet, requiring a quantum mechanical treatment.
Ross McKenzie lectures on transport in the Bloch model
Ross gives tutorial looking at old mid-semester exam questions
Paul Shaw lectures on the relationship between tight-binding and the Huckel model in chemistry.
quasiperiodic in two dimensions (polygonal or dihedral quasicrystals)
There is one periodic direction perpendicular to the quasiperodic layers.
- octagonal quasicrystals with local 8-fold symmetry [primitive & body-centered lattices]
- decagonal quasicrystals with local 10-fold symmetry [primitive lattice]
- dodecagonal quasicrystals with local 12-fold symmetry [primitive lattice]
quasiperiodic in three dimensions, no periodic direction
- icosahedral quasicrystals (axes:12x5-fold, 20x3-fold, 30x2-fold) [primitive, body-centered & face-centered lattices]
new type (reported in Nature, Nov.2000)
- "icosahedral" quasicrystal with broken symmetry (stable binary Cd5.7Yb)
* octagonal quasicrystals with local 8-fold symmetry [primitive & body-centered lattices]
* decagonal quasicrystals with local 10-fold symmetry [primitive lattice]
* dodecagonal quasicrystals with local 12-fold symmetry [primitive lattice]
- In three dimensions (no periodic direction), there is only one type:
* icosahedral quasicrystals (axes:12x5-fold, 20x3-fold, 30x2-fold) [primitive, body-centered & face-centered lattices]
- Interestingly, there is a New type that was reported in Nature, Nov.2000). it is "icosahedral" quasicrystal with broken symmetry (stable binary Cd5.7Yb).
The symmetry and other properties are completely equivalent between the three styles, and is an example of of substitution. This is where one can break the original shapes into smaller variations, and use these to reconstruct the the tiling.
Due to this possible substitution the tiling shares some features with fractals, in that it may be inflated or deflated, yet present the same image and symmetry.
A list of other forms of aperiodic tiling in various geometries can be found here:
Self study material in Solid State Electronics using Multimedia: A great website that shows lots of plots for the Crystal structure, Brillouin zones, energy bands and energy surface...
For anyone interested this collection of slides is a useful discussion of the basics of tight-binding theory. It goes through the same mathematical derivation of the energy eigenvalues, but also gives a good graphical example in k-space.
- A laptop with the software installed
- A copy of the "Bloch" chapter from "Simulations for Solid State Physics". You can download it here if you haven't already done so.
Cleavage is an important mechanism in examining the structure of solids and also in some industries. Some crystals have the probability to split along certain crystal planes. And because of the repeated structure these distinct and week planes repeat and become visible even to the naked eye.
Pic. ref.: ( http://www.doitpoms.ac.uk/tlplib/atomic-scale-structure/single2.php?printable=1)