Physics 322a – 2007 Walter F. Smith Final Exam Coverage

Equation sheet: You will be allowed 75 equations.

You are also responsible for the Exam 1 and Exam 2 topics. This exam will be cumulative, and will include questions from the first part of the course (e.g. about the Tight-binding model.)

Material covered since exam 2:

Chapters covered: Livingston Chapters 13-16

Classes covered: Class 30 (Friday 11-16-07) through the end of the semester

Assignments covered: 10-11

Most important topics covered since exam 2:

Fermi surface

Definition

Know what the free-electron Fermi surface looks like in 1D, 2D, and 3D, be able to calculate its radius, given the number of electrons per unit cell

Volume inside Fermi surface is conserved when interactions are turned on

Nearly Free Electron Model

Be able to explain why gaps are formed at the BZ boundaries (using the standing wave argument)

Know that gap is “evenly split” around the free electron result

With interactions, Fermi surface gets “sucked” toward BZ boundary; be able to explain why

Each band occupies a “volume” equal to the 1BZ => One can make a one-to-one association between bands and BZs (i.e. second band corresponds to second BZ, etc.)

Each band can “hold” 2 electrons/unit cell

Understand how multiple bands are represented in the reduced zone scheme (i.e. that each k in the 1BZ can be associated either with a state in band 1, or with a state in band 2, etc.)

How to sketch the Fermi surface, qualitatively including the effects of lattice interactions, from a knowledge of the crystal structure and the number of electrons per unit cell

Be able to make the above sketch in extended, reduced, or repeated zone schemes

Be able to calculate the minimum gaps needed to form a semiconductor, given information about the gap at the furthest point on the 1BZ boundary

Metals and Semiconductors

Why band overlap is needed to create a divalent metal

Why this means that 1D divalent systems can’t be metallic (in NFE model)

How band overlap arises in 2D or 3D for free electron or NFE models

Topics continue on the next page

Semiclassical model of electron dynamics

(in one dimension: )

Why this, combined with the standing wave argument means that at a BZ boundary

; understand this equation, and be able to derive it from the equation for v_electron

meaning of negative m^*

Filled bands are inert

Be able, given all of the above, to reproduce the argument of why we can treat a mostly full band as a hole band

Why (qualitatively) narrow bands have high m^*

Semiconductor statistics

Be able to use equations 15.9 through 15.12 to calculate carrier densities.

Law of mass action.

Be ready to explain qualitatively the direction that e_F moves when the doping is changed.

Understand figure 15.2

Semiconductors: general

Energy near a band edge: be able to reproduce the argument that leads to

Know the definitions of m_e* and m_h*

Intrinsic (undoped) vs. Extrinsic (doped)

Hydrogenic model for dopants:

Binding energy of electron associated with n-type dopant

Bohr radius of electron associated with n-type dopant

Topics continue on the next page

pn junctions

Be able to explain how/why the band structure develops.

Understand distribution of mobile charge.

Understand distribution of excess charge.

Know how the electric field varies within the junction (including equation).

Dependence of depletion region width on dopant density (including equation).

Understanding of equilibrium current flows.

How this leads to diode behavior.

Equation for current density as a function of bias voltage and temperature.

Know how the degree of band bending depends on doping concentrations (including equation).

No homework problems were assigned on the topics below. This will be taken into account when designing any exam problems relating to these topics.

Devices

LEDs: qualitative argument for how they work (based on band structure diagram), how materials are chosen based on bandgap and direct vs. indirect band structure

Solar Cells: qualitative argument for how they work (based on band structure diagram)

MOSFETs: qualitative argument for how they work (based on band structure diagram)

Schottky diodes: qualitative argument for how they work (based on band structure diagram)