Lecture 6, Feb 4

Assigned reading: Melissinos, pages 3-7; Bloomfield, Section 11.2 (Xerox copiers and laser printers).

Demos: photoconductivity (shine flashlight on SnO).

Reviewed band structure, valence and conduction band, energy gap. In insulators and semiconductors the conductivity is strongly affected by the concentration of carriers: both electrons added to the conduction band and holes left in the valence band act as carriers (of electrical current). Three mechanisms of creating carriers

1. Thermal excitation, dominated by Boltzmann factor where is the energy gap from the top of the valence band to the bottom of the conduction band. Orders of magnitude: eV is typical of a semiconductor; eV at room temperature,
2. Doping with impurities. Donor impurities supply extra electrons that go into the conduction band; acceptors create holes in the valence band, making the remaining valence electrons free to move.
3. Absorption of light (photoconductivity).

Electronic structure of Si and Ge, and of the elements that can be used in Si and Ge as donors (P, As, Sb) and acceptors (B, Al, Ga, In). Xerox copiers and laser printers (see Bloomfield; explained in addition how a rotating hexagonal mirror makes a simple scanner).

Problem session 3

Gone over the solution of problem set 1. Shown how to use SWP and Maple to plot equipotentials. Also plotted wavefunctions of harmonic oscillator.

Lecture 7, Feb 6

Assigned problem set 4

Handed out information on Scientific Workplace and Notebook, given hints on working with them.

Assigned reading: Melissinos, up to page 9, and Bloomfield, Sections 12.1 and 13.1.

Density of states and occupation probabilities for electrons and holes in solids. Intrinsic semiconductors. The basic formulas are given by Melissinos in eqs. (1.4), (1.5), and (1.7).

Melissinos does not derive the last formula or explain what is. See the class notes in the file carriers.tex.

References: assigned readings; class notes (carriers.tex); Kittel and Kroemer: Thermal Physics, pages 355 - 363

Lecture 8, Feb 11

Demo: laser printer, with optics needed for laser scanning.

Assigned reading: Bloomfield, Section 6.3 (incandescent light bulbs).

Carrier density in doped semiconductors. Conductivity, collision time, and mobility.

References: Melissinos, sections 1.2 and 1.3; Kittel and Kroemer: Thermal Physics, pages 363 - 372 and 379 - 381.

Problem session 4

Distributed and gone over the file carriers.tex. Shown and discussed incandescent light bulb. Shown how to use SWP to plot and made plots of interfering wave forms.

Lecture 9, Feb 13

Assigned problem set 5

Demo: photovoltaic cell

Assigned reading: Bloomfield, around pages 435 and 469; Melissinos, section 1.4

Reviewed mobility, conductivity and the relation of resistance to resistivity. Diffusion and the Nernst-Einstein relation .

Main topic: the p-n junction. Pointed out that the built-in voltage, given by Melissinos in eq. (1.18 ), can be rewritten using eq. (1.9 ) as

Typical values for Si are eV, eV (corresponds to 290 Kelvin, a cool room temperature), cm , cm then, in eV, : this shows how an overheated junction loses its and becomes useless.

References: assigned readings; PDR, page 311 (class handout); Kittel and Kroemer: Thermal Physics, pages 373 - 386; Ashcroft and Mermin: Solid State Physics, Chapter 29, especially eq. (29.6).

Lecture 10, Feb 18

Set up working groups for term paper. Outlines are due Feb 27.

Demo: LED's, vacuum tubes

Assigned reading: Bloomfield, Sections 13.1 1nd 13.2; Melissinos, rest of Chapter 1.

Use of p - n junctions in rectifiers, photovoltaic cells, and LED's. MOSFET's and their use in inverters and NAND gates.

For best photovoltaic response to sunlight, the choice element is Selenium; however, Se is very poisonous and expensive. Good performance (up to 13% conversion efficiency) can be achieved by using polycrystalline Silicon, which is cheap and easy to handle.

Light Emitting Diodes (LED's) are p - n junctions where the electron-hole recombination releases energy in the form of a single photon of visible light. The current flowing through the device (under forward bias) causes electrons from the n side and holes from the p side to drift into each other and recombine; some of the power supplied by the applied voltage goes into the emitted radiation. Most LED's in use today are made of III - V compounds such as GaAs; Silicon and Germanium are not suitable for LED's, because the energy released by e - h recombination goes mostly into local heating of the material, rather than light emission. The band gap of GaAs is 1.4 eV, barely enough to emit red light; a wider band gap, resulting in the emission of yellow and green light, is obtained by replacing some of the Gallium atoms with Aluminum, or some of the Arsenic with Phosphorus.. If a fraction x of Ga is replaced by Al, the resulting compound has chemical composition Ga Al As, but is called GaAlAs for short; similarly, GaAsP is short for GaAs P and so on.

Why is GaAs much better than Si in a LED? Mostly because GaAs is a direct gap semiconductor, while Si is an indirect gap semiconductor. Here is an explanation of what this means. In both materials the states near the top of the valence band have zero momentum, but, while in GaAs the quantum states at the bottom of the conduction band also have zero momentum, in Si they have a non-zero momentum, corresponding to wave functions that change sign in going from one Si atom to the next on the edge of the cubic cell (see the picture of the energy bands of Si in PDR, page 308). The momentum of an electron changes very little when it emits (or absorbs) a photon, and thus light emission can occur directly in GaAs, where the electron has nearly the same momentum in the initial state (near the bottom of the conduction band) as in the final state (near the top of the valence band). Conversely, in Si photon emission is an indirect process that cannot occur unless the conduction-band electron finds a way to get rid of its momentum. The words direct gap and indirect gap generally indicate whether the bottom of the valence band lines up directly above the top of the valence band in a plot vs momentum.

References: assigned readings; for the LED, Dalven: Introduction to Applied Solid State Physics (on reserve in the Physics Library), pages 159 and 199.

Problem session 5

Shown how to define constants and functions in SWP. Worked on problem 1.1 from Melissinos and shown lattice structure of semiconductors (diamond and zincblende structures).

Lecture 11, Feb 20

Demo: transistor and VLSI chip viewed under microscope

Assigned readings: Bloomfield, section 13.2; Serway, chapter 19 or equivalent (review)

Flip-flops, elements of digital electronics, binary arithmetic. Review of magnetostatics, emphasizing that the magnetic field is solenoidal (has no sources), in contrast to the electrostatic field, which is irrotational.

References: assigned readings; Melissinos, chapter 2, especially page 58 and 64.

Lecture 12, Feb 25

Assigned problem set 6 (pledged).

Demo: current generated in coils by moving magnet.

Assigned readings: Serway, chapter 20 or equivalent (review); Dorsey notes on Maxwell's equations (handed out), page 2.

Review of Faraday's law and electrical generators. The differential equations for the electromagnetic fields after Ampère and Faraday, before Maxwell. Magnetic moment of the electron and the nucleons.

References: assigned readings.

Problem session 6

Reviewed answers for problem set 4, especially how a full band accommodates an even number of electrons per atom. Bands in a ferromagnet. Viewed a periodic table with photos of the elements in their common state of aggregation: most are metallic. Showed how to convert numbers to binary and hexadecimal, manually and with convert(number, binary) in Maple. Also mentioned hexadecimal number basis.

Lecture 13, Feb 27

Demo: disassembled PC, showing power supply, motherboard, drives (hard disc, floppies, CD-ROM), cards and ports (video, printer, modem, ethernet)

Assigned readings: Bloomfield, sections 12.2 to 12.4; Serway, section 24.1 or equivalent (review); Dorsey notes on Maxwell's equations (handed out last time); Melissinos, pages 67 - 72 and 117 - 119.

Ferromagnets and their uses. Magnetic tape and magnetic discs. The full set of Maxwell's equations and the existence of plane wave solutions.

References: assigned readings.