EE 506 - Semiconductor Physics

30530D

Tue, Thu: 12:30pm-1:50pm

KAP 140

TA is Aravind Krishnan, aravindk@usc.edu, meeting Fridays at 5.00pm in VHE309

Web sites:

http://alevi.usc.edu

http://classes.usc.edu/term-20163/classes/ee

First day of EE506 classes Tuesday, August 23, 2016

Last day of EE506 classes Thursday, December 1, 2016

Final Exam: Tuesday, December 13, 11.00am - 1.00pm, KAP140

Office Hours: TTH 8:00 a.m. - 9:15 a. m. or by appointment

 

Semiconductor devices in the form of Si integrated circuits have revolutionized our life by facilitating communications, computation and control of most aspects our daily living. The emergence of new semiconductor materials and devices are now enabling another revolution in energy, visual display, personal wireless communications and a myriad of other technologies. This course provides a unified understanding of the physical origins of semiconducting materials properties and device characteristics that enable these new applications. This is done by exploring the relationship between atomic properties and bonding in semiconductors, the crystalline structure and the energy band structure of materials more diverse than Si and the thermal, electronic transport and optical properties that are characteristic of these materials.  Finally, we will discuss interfaces between materials and the properties of heterojunctions made from them. Heterojunctions will lead us to discuss artificially structured materials and quantum structures. This journey will take us from atoms to crystals and back to artificial atoms. During this time we will constantly expand our understanding of the influence of the atoms that make up a semiconductor on the resulting crystals and develop a methodology for designing new device concepts.

Prerequisite: MS/EE 501 Solid State Physics; EE 539 Quantum Mechanics

Instructor: A.F.J. Levi

Text Book: Electronic and Optoelectronic Properties of Semiconductor Structures, Jasprit Singh. Cambridge University Press   ISBN-10: 0521035740 | ISBN-13: 978-0521035743; Kindle Version Available

Grading:              Homework         20%

                              Midterm Exam  30%

                              Final Exam        50%

Outline:

Week

Topic

1

Atomic Structure, Bonding and Crystalline structure

2

Crystalline Structures and Symmetry

3

Covalent Bonding  and Energy Bands

4

Energy Bands in Semiconductors

5

Tight Binding Approximation. Intrinsic and extrinsic carrier densities

6

kP Formalism for band structure calculations. The semiconductor heterostructure and tunneling

7

Lattice vibrations. Damping, Langevin equation, fluctuation-dissipation and diffusion.

8

Lorentz model of light-matter interaction

9

Review. Midterm

10

Drude model

11

Boltzmann transport equation; Impurity scattering

12

High field transport

13

Optical Properties- interband transitions in 2- and 3-D materials

14

Excitonic states and optical properties

15

Mesoscopic systems; nanostructures

16

Optional Material

 

Essential ideas:

Lecture 1: Atom "shape" determines crystal structure. The critical role of quantized electron orbitals. The hydrogen atom.

Lecture 2: The Pauli exclusion principle and the periodic table of elements. Hybridization.

Lecture 3: Bonds. The hydrogen molecule ion. The hydrogen molecule covalent bond using valence bond and molecular orbital description. The ionic bond.

Lecture 4: Crystal structure. Crystal systems in three-dimensions. The reciprocal lattice. Nonequilibrium materials and disordered materials. Isotropic materials with linear local response. Bloch's theorem. Localized Wannier functions.

Lecture 5: The generalized Kronig-Penney model of complex band structure. MATLAB code for Kronig-Penney with 1D rectangular potential.

Lecture 6: Introduction to the tight-binding method.  A single s-band in a one-dimensional lattice. A one-dimensional lattice with a two-atom basis, the example of trans-polyacetylene. MATLAB code for trans-polyacetylene band structure example.

Lecture 7: Graphene lattice. Carbon sp2 hyrbidization and bonding. Graphene band structure calculated using the tight-binding method.  Electron transport in graphene. MATLAB code for graphene band structure.

Lecture 8: Band structure: Tight-binding method in three dimensions based on the paper by Vogl et al., (1983).  The band structure of III-V and IV semiconductors. MATLAB code for tight binding band structure.

Lecture 9: Review

Lecture 10: Electrons and holes in semiconductors and doping

Lecture 11: Band structure: Kane's k.p method

Lecture 12: The semiconductor heterostructure. The gap state model. Current-voltage characteristic of a semiconductor heterostructure tunnel diode. MATLAB code for figures in handout:

TunnelCurrentSimple.m

TunnelCurrentFastB.m

CalculateChemicalPotential.m

PotentialProfileWithPoissonB.m

TunnelCurrentParameterInputB.txt

TunnelCurrentPotentialProfileInputB.txt

Lecture 13: Lattice vibrations. The damped driven oscillator.

Lecture 14: Noise, fluctuation-dissipation theorem, and diffusion. Einstein relation.

Lecture 15: Lorentz model of light-matter interaction. Kramers-Kronig relation

Lecture 16: Lorentz model of light-matter interaction. Propagation of electromagnetic waves in a dielectric medium

Lecture 17: Review

Lecture 18: Midterm

Lecture 19: The Drude model. DC and AC conductivity. Kinetic inductance.

Lecture 20: Permittivity of metal. The loss function of copper. Physical origin of plasma frequency. Local response in the Drude model. An electromagnetic field interacting with a metal. Drude dispersion of electromagnetic radiation. Changing the properties of a metal. Metal and electromagnetic fields in integrated circuits.

Lecture 21: Current. Charge transport in semiconductor devices. Electron transport in semiconductors. Crystal momentum and effective electron mass. Bloch oscillations. Material parameters contributing to current. Velocity field characteristics and electron transfer to subsidiary minima. The Gunn diode oscillator. Ballistic transport.

Lecture 22: The Boltzmann transport equation. Evolution of the distribution function with time. The scattering term. Relaxation time approximation. Conductivity. The diffusion term.

Lecture 23: Mean free path and scattering time from mobility. Mean free path and scattering time in 2DEG. Electron optics in the 2DEG. Diffusion in devices. Diffusion and recombination of minority carriers. The Schottky barrier. Depletion width. Thermionic emission. Capacitance as a function of voltage bias.

Lecture 24-25: Electron scattering in semiconductors. The electron-phonon interaction. The Frohlich interaction. The longitudinal polar-optic phonon scattering rate. The LO phonon scattering rate in the conduction band of GaAs. Energy and momentum conservation. Electron scattering rate from linear dielectric response. Scattering rates and fluctuation dissipation.

Lecture 26-27: Elastic scattering from ionized impurities. The screened coulomb potential. Elastic scattering of electron from ionized impurities in GaAs. Correlation effects due to spatial position of dopant atoms. estimating mean free path and mobility. Calculating the screened potetnial and dielectric function in wave vector space. Comparison between Thomas-Fermi screening and RPA.

Lecture 28: Review

Lecture 29: Final