Non-equilibrium Processes in Modern Semiconductor Devices

EE 606, 4-units

A. F. J. Levi

TTH 9.30am-10:50am KAP 138

First day of EE606 classes Tuesday, January 8, 2019

Last day of EE606 classes Thursday, April 25, 2019

Final exam: 8.00am-10.11am, Tuesday, May 7, 2019

Course outline in pdf form


Outline and course content

Practical sub-micron and nano-scale devices usually operate in a regime dominated by non-equilibrium effects. However, most conventional semiconductor device courses still use equilibrium or near equilibrium concepts to describe device operation. The purpose of this course is to introduce a more realistic approach to understanding device operation in modern sub-micron and nano-scale devices. Much of what will be introduced relies on the concept that many important non-equilibrium effects can be described in terms of a family of elementary excitations which usually only interact weakly with each other. The course will emphasize the actual calculation of useful parameters relevant to the design and operation of practical and research devices such as scaled transistors and scaled lasers.


Participants should have a working knowledge of quantum mechanics and semiconductor physics on a level at least comparable to EE 539.


The prerequisite for this course is knowledge to the level of EE539 – “Applied Quantum Mechanics”  Cambridge University Press. ISBN: 978-0-521-18399-4


Also, free to download for USC students - "Essential Classical Mechanics for Device Physics" IoP, Morgan & Claypool Publishers, 2016. Print ISBN: 978-1-6817-4412-4


Books worth using for reference and background reading include "Semiconductors" by D. K. Ferry, ISBN 0-02-337130-7, “Quantum Theory of the Optical and Electronic Properties of Semiconductors” by H. Haug and S. W. Koch, ISBN 981-02-0024-2, “Semiconductor-laser fundamentals” by W. W. Chow and S. W. Koch, ISBN 3-540-64166-1, “Physics of Optoelectronic Devices” by S. L. Chuang, ISBN 0-471-10939-8.


Some material covered by this course does not appear in any textbook.


1. Lattice vibration and electron states

Fermion anti-commutation relations

Quantum field theory

Periodic crystal structure

Bloch theorem

Crystal momentum and effective electron mass

Tight binding dispersion relation and band structures

Graphene band structure

Particle statistics

         Few electron Fermi-particle statistics

         Fermi-Dirac distribution

Density of states

Quantized electron conductance and the Landauer formula  

2. Electron transmission through a semiconductor heterostructure

The propagation matrix method

Electron transmission in the presence of rectangular potential barriers

         The single potential barrier

         Resonant tunneling through a double potential barrier

         Resonant tunneling through a triple potential barrier

Electron motion in the presence of inelastic scattering using first-order theory

         Inelastic electron tunneling spectroscopy

Electron motion in the presence of coherent inelastic scattering

         Electron interacting with a localized phonon at a potential step

         Electron interacting with localized phonons in an arbitrary potential

         Electron transmission in the presence of a localized phonon

         Electron tunneling through a delta-function barrier in the presence of coherent inelastic scattering

         Electron wave functions in presence of coherent inelastic scattering

         Transient coherent inelastic scattering effects


3. Optimal heterostructure device design

Current-voltage characteristic of a semiconductor heterostructure tunnel diode

         Potential profile in the deletion approximation

         Calculation of tunnel current

         Self-consistent potential profile

Optimal device design

         The adjoint method


4. Current

Charge transport in semiconductor devices

         Electron transport in semiconductors

         Bloch oscillations

         Material parameters contributing to current

         Velocity-field characteristics

         The Gunn diode

         Ballistic transport

The Boltzmann transport equation

         Evolution of the distribution function with time

         Relaxation-time approximation


         The diffusion term

Mean free path and scattering time from mobility

         Mean free path and scattering time in high mobility 2DEG

         Electron optics in the 2DEG

Diffusion in devices

         Diffusion and recombination of minority carriers

The Schottky barrier

         Depletion width

         Thermionic emission


5. Electron scattering in semiconductors

Electron phonon interaction

         Linear response

         The Frohlich interaction

         The longitudinal polar-optic phonon scattering rate

         The LO phonon scattering rate in the conduction band of GaAs

         Electron mean-free-path due to LO phonon scattering in GaAs

         Energy and momentum conservation

Electron scattering rate from linear dielectric response

         Dielectric response and longitudinal polar-optic phonon scattering

6. Inelastic scattering of electrons


7. Elastic scattering from ionized impurities




There is a midterm and final that each contribute 40% to the final grade. The remaining 20% is for homework problems.


Statement for Students with Disabilities


Any student requesting academic accommodations based on a disability is required to register with Disability Services and Programs (DSP) each semester. A letter of verification for approved accommodations can be obtained from DSP. Please be sure the letter is delivered to me (or to TA) as early in the semester as possible. DSP is located in STU 301 and is open 8:30 a.m.–5:00 p.m., Monday through Friday. The phone number for DSP is (213) 740-0776.


Statement on Academic Integrity


USC seeks to maintain an optimal learning environment. General principles of academic honesty include the concept of respect for the intellectual property of others, the expectation that individual work will be submitted unless otherwise allowed by an instructor, and the obligations both to protect one’s own academic work from misuse by others as well as to avoid using another’s work as one’s own. All students are expected to understand and abide by these principles.


Students will be referred to the Office of Student Judicial Affairs and Community Standards for further review, should there be any suspicion of academic dishonesty.