**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://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
0521035740
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 |
k·P 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 sp^{2} 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:

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