Electrical Engineering
Non-equilibrium Processes in Modern Semiconductor Devices, Spring 2017.

A. F. J. Levi

EE 606
TTH 9.30am-10:50am KAP 138

First day of EE606 classes Tuesday, January 10, 2017

Last day of EE606 classes Thursday, April 27, 2017

Final exam: 8.00am-10.11am, Tuesday, May 9, 2017

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.


This course is divided into; (i) introductory material, (ii) specific examples of non-equilibrium effects determining the performance of devices, (iii) presentation of selected research papers. Participants should have a working knowledge of quantum mechanics and semiconductor physics on a level at least comparable to EE 539 and EE 506.


The prerequisite for this course is knowledge to the level of EE539 – “Applied Quantum Mechanics” by A.F.J. Levi, Cambridge University Press, Paperback: Call Cambridge University Press at (845) 353-7500 and ask for the "Print on demand version" ISBN: 978-0-521-18399-4

and knowledge to the level of EE506 that includes – "Essential Classical Mechanics for Device Physics" by A.F.J. Levi, 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.


Part (i):



Lecture 1: Introduction to the class. Discussion includes review of recent work on cavity opto-mechanics. See:

Vahala: Optics Express 15, 17172 (2007)

Kippenberg: Phys. Rev. Lett. 97, 243905 (2006)


Lecture 2: Discussion of disordered materials as example of non-equilibrium phenomena. Do cathedral glasses flow?

Zanotto: Am. J. Phys. 66, 392 (1998)

Pasachoff: Am. J. Phys. 66, 1021 (1998)

Zanotto: Am. J. Phys. 67, 260 (1999)


Lecture 3: Introduction to band structure:  Introduction to semiconductor crystal structure.  Hydrogenic orbitals.  Covalent bonding and LCAO.  Bloch states and band structure.  Survey of semiconductor properties including heterostructures and modern semiconductor devices.


Lecture 4: Semi-empirical tight-binding model of semiconductor band structure

Vogl: Phys. Chem. Solids 44, 365 (1983)


Lecture 5: Complex band structure

Chang: Phys. Rev. B 25, 605 (1982)

Stiles and Hamann: Phys. Rev. B 38, 2021 (1988)


Lecture 6: How to solve homework problems on band structure. This includes example MATLAB code.


Lecture 7: Simple dielectric functions part I. Plasma frequency. Optical susceptibility and the classical oscillator model of optical absorption.


Lecture 8: Simple dielectric functions part II. The Kramers-Kronig relations. Lattice dynamics and the contribution of longitudinal polar-optic phonons to the dielectric function.


Lecture 9: Introduction to electron transport. Doping in semiconductors and rs*. The Boltzmann transport equation including conductivity and diffusion in the relaxation-time approximation.


Lecture 10: Calculation of tunnel current in the absence of inelastic scattering. Limitations of semi-classical description of electron transport in semiconductors.


Lecture 11: Introduction to Coulomb scattering. Elastic scattering by non-randomly positioned ionized impurities in semiconductors. Estimating electron mobility in semiconductors.


Part (ii):


Lecture 12: Self-energy and scattering rates. Landau Fermi Liquid and quasi-particles

Landau "The theory of a Fermi Liquid" JETP 3, 920 (1957)

Landau "Oscillations in a Fermi Liquid"  JETP 5, 101 (1957)


Lecture 13: Lindhard dielectric function. Application to metals and semiconductors. Single particle excitations and coupled plasmon – phonon collective excitations.


Lecture 14: Analysis of semiconductor dielectric function. MATLAB example code.


Lecture 15: Calculation of electron lifetime and device design. Calculation of electron lifetime in unipolar transistors. Temperature dependence of non-equilibrium electron scattering rates. Non-equilibrium electron spectroscopy.

Phys. Rev. Lett. 55, 2071 (1985)

The non-equilibrium electron transistor.

Appl. Phys. Lett. 55, 1891 (1989)


Lecture 16: Numerical determination of non-equilibrium electron scattering rates. MATLAB code example. The truncated parabola of integration. Phase-space and its influence on scattering rate. Evaluation and interpretation of temperature dependence.


Lecture 17: Non-equilibrium electron transport in bipolar transistors. Theory. Minority carriers in conduction band interacting with majority carriers in valence band. Collective and single-particle excitation spectral function in three-band model. Calculation of scattering rates. Parabola of integration. Phase-space and device scaling.

Appl. Phys. Lett. 51, 42 (1987)

Electron. Lett. 24, 1273 (1988)

Reduction in elastic scattering rates by spatial correlation of impurity sites. Non-random doping and elastic scattering of carriers in semiconductors.

Appl. Phys. Lett. 54, 940 (1989)


Lecture 18: Non-equilibrium electron transport in bipolar transistors. Experiments. Proof that non-equilibrium electron transport dominates the static and dynamic performance of scaled HBTs.

Appl. Phys. Lett. 52, 2247 (1988)

Appl. Phys. Lett. 60, 460 (1992)

IEEE Trans. Elect. Device. 40, 1942 (1993)


Lecture 19: Limitations of perturbation theory and a path beyond perturbation theory. Non-local calculation of dielectric response in nano-scale particles.

Phys. Rev. Lett. 97, 036806 (2006)

Exact non-perturbative calculation of electron transmission in the presence of inelastic scattering.

Phys. Rev. Lett. 62, 1683 (1989)

Brandes: Phys. Stat. Sol. (b) 234, 378 (2002)


Lecture 20: The semiconductor laser. The weak coupling limit.  Phase transition analogy.  Mean field descriptions of static and dynamic behavior. Single mode, multimode, and traveling wave rate equations.  Cavity formation in laser diodes.  Fluctuations described by Langevin model.  The role of fluctuations and net optical gain in determining the temperature dependence of laser diodes.

Appl. Phys. Lett. 61, 889 (1992)

Appl. Phys. Lett. 62, 1454 (1993)

Appl. Phys. Lett. 60, 157 (1992)

Appl. Phys. Lett. 60, 1058 (1992)


Lecture 21: The semiconductor laser. Influence of electron and photon quantization on static and dynamic behavior of scaled laser diodes and photon statistics. The role of electron and photon correlations, fluctuations, and the failure of the non-equilibrium phase-transition description of laser light emission.


Lecture 22: Cavity QED. Introduction to coupled oscillators.  The two level atom coupled to a single optical mode.  Two level atom coupled to a continuum of optical modes.  Rabi oscillations semi-classical model and quantum model.  Jaynes-Cumming model and rotating wave approximation. 


Part (iii):


Lecture 23: How to prepare and present research papers.


Presentation of research papers:

Class discussion of selected research papers.




There is a part (i) examination which will contribute 20% to the final grade. Part (ii) contributes 20% and part (iii) 45%. The remaining 15% 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. Scampus, the Student Guidebook, contains the Student Conduct Code in Section 11.00, while the recommended sanctions are located in Appendix A:

http://www.usc.edu/dept/publications/SCAMPUS/gov/. 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. The Review process can be found at: