ECE 230c: Solid State Electronics

Spring 2008, Professor Ed Yu


This course provides an in-depth, quantum-mechanical treatment of electronic structure, transport properties, and other phenomena in semiconductors, and is intended primarily for beginning graduate students in electrical engineering, applied physics, and related fields.

Course information, announcements, problem sets, exams, etc. will be made available as the quarter progresses.

This site will be updated throughout the quarter.



Announcements

6/20/08: Final exam solutions are now available. They will be available for only a few weeks before being removed.
6/20/08: Results for the final exam are as follows: mean = 66.1, median = 64.5, standard deviation = 16.7, range = 38-96. The full distribution of scores is also available.
6/5/08: Problem Set 5 solutions are now available.
6/3/08: For this week I will have office hours Thursday 6/5/08 2-3PM rather than Friday 6/6/08 9-10AM. Also, I will have office hours next week on Monday 6/9/08, 1-2PM.
6/2/08: The FINAL EXAM for ECE 230C will be held Tuesday 6/10/08, 8:00-11:00AM in CENTER 207.
5/27/08: Problem Set 5 was handed out today and is due Thursday 6/5/08.
5/27/08: Problem Set 4 solutions are now available.
5/27/08: To help you prepare for the final exam, a copy of the Spring 2007 ECE 230C Final Exam is available.
5/27/08: The FINAL EXAM will be on Tuesday 6/10/08, 8:00-11:00AM in a location to be announced (by the registrar). The final exam will cover material from the entire quarter. The rules for the final exam will be the same as those for the midterm. You are allowed to use class notes, problem sets and solutions, and a calculator. Other materials are not allowed. You should bring a blue book in which to write your exam.
5/19/08: Since there are two lectures on Tuesday 5/27/08, Problem Set 4 will be due at the morning lecture.
5/19/08: Due to my travel schedule I will not be available for office hours Friday 5/23/08. However, I should be reachable by email over the weekend if you have questions.
5/19/08: There will be no lecture on Thursday 5/22/08. A makeup lecture has been scheduled for Tuesday 5/27/08, 5:00-6:20PM in Center 224A.
5/13/08: Problem Set 4 was handed out today and is due Tuesday 5/27/08.
5/13/08: Problem Set 3 solutions are now available.
5/9/08: Midterm exam solutions are now available.
5/7/08: Results for the midterm exam are as follows: mean = 59.9, median = 60, standard deviation = 9.4, range = 44-78. The full distribution of scores is also available.
5/1/08: Problem Set 3 was handed out today and is due Tuesday 5/13/08.
5/1/08: Problem Set 2 solutions are now available.
4/30/08: The midterm exam will cover material through the end of the discussion of band structure calculations (pseudopotentials), but not including any of the discussion of electron-electron interaction effects. Thus the midterm will include material through part of this Thursday's lecture (5/1/08).
4/24/08: The MIDTERM EXAM will be administered as scheduled on TUESDAY 5/6/08, in class. The rules for the midterm exam will be as follows. You are allowed to use your class notes, problem sets and solutions (your own and those posted on the web site), and a calculator. You should bring a blue book in which to write your exam. Books, papers, and other materials are not allowed. To help you prepare for the midterm exam, copies of last year's midterm exam and solutions have been posted.
4/15/08: Problem Set 2 was handed out today and is due Thursday 5/1/08.
4/15/08: Problem Set 1 solutions are now available.
4/10/08: The makeup lecture on Friday 4/11/08 will be extended until 6:00PM to make up for the lecture missed on Thursday 4/10/08.
4/9/08: Due to the MD-80 flight cancellations by American Airlines I am stuck in Washington, DC until Thursday 4/10/08. Therefore we will not have our regularly scheduled lecture on Thursday 4/10/08. I am checking to see if our makeup lecture scheduled for Friday 4/11/08 can be extended until ~5:30-6PM.
4/7/08: There will be no lecture on Tuesday 4/22/08. A makeup lecture has been scheduled for Friday 4/18/08, 3:30-4:50PM in York 3050B.
4/7/08: A makeup lecture has been scheduled for Friday 4/11/08, 3:30-4:50PM in York 3050B.
4/3/08: There will be no lecture on Tuesday 4/8/08. A makeup lecture will be scheduled, most likely for Friday 4/11/08.
4/3/08: Problem Set 1 was handed out today and is due Tuesday 4/15/08.
3/20/08: IMPORTANT - we have moved to a larger classroom to allow wait-listed students to enroll. Lectures will be held in YORK 3050B, not in our originally assigned lecture room in McGill.
3/19/08: Please check this section of the Web site frequently for announcements pertaining to ECE 230C.



Table of Contents

Instructor
Teaching Assistants
Schedule
Texts
Grading
General Course Policy
Course Topics
Lecture Topics and Assigned Reading
Problem Sets (downloadable .pdf files available) and Solutions
Other Course Handouts (downloadable .pdf files available)



Instructor:

Professor Ed Yu
3809 EBU1
534-6619
ety@ece.ucsd.edu
Office Hours: Mo 1:00-2:00PM, Fr 9:00-10:00AM or by appointment/drop-in



Teaching Assistant:

None



Schedule:

Lectures:
TuTh 9:30-10:50AM, York 3050B
Discussion:
Due to the size of the class, no discussion sections have been scheduled. Students are encouraged to come to the instructor's office hours with any questions about the course material.



Texts:

Required Text:
J. M. Ziman, Principles of the Theory of Solids, Second Edition (Cambridge University Press, 1972).

Recommended References:
J. Callaway, Quantum Theory of the Solid State, (Academic Press, 1974).
C. Kittel, Introduction to Solid State Physics, Eighth Edition (John Wiley & Sons, 2005).
P. Y. Yu and M. Cardona, Fundamentals of Semiconductors, Third Edition (Springer-Verlag, 2001).
[Yu/Cardona is also available online http://www.knovel.com/knovel2/Toc.jsp?BookID=1111]



Grading:

Problem Sets: 20%
Midterm: 30%
The midterm will be 9:30 - 10:50AM, in class, Tuesday May 6, 2008 (tentative).
Final Exam: 50%
The final exam will be 11:30AM-2:30PM, Tuesday June 10, 2008.

The above percentages are not carved in stone. If it appears that you have merely had a "bad day" during one of the exams, I am willing to be flexible. However, the degree of flexibility exhibited will be highly dependent on your performance on the other exam and especially on the problem sets!



General Course Policy:

See section on Grading for course policies on grading.
Discussion of course material and homework problems is permitted and indeed encouraged. However, each student should work through the homework problems and write up his or her solutions independently. See the class handout or the section of this web site on academic integrity for a more explicit statement of this policy.

Homework assignments are to be handed in in class. Solutions for the problem sets will generally be available after class on the due date. Since solutions are generally distributed on the homework due date, credit generally will not be given for assignments turned in late.
Requests for exam rescheduling should be made well in advance of the anticipated exam date. Such requests will generally be honored only for extremely compelling and thoroughly documented reasons. If a rescheduled exam is truly needed, however, I will do my best to make the necessary arrangements.

POLICY ON ACADEMIC INTEGRITY:

Ethics and integrity in both academic and professional affairs should be part of your education at UCSD. Academic integrity is a serious matter and will be treated as such in ECE 230C. My hope is that this will be beneficial to your education both technically and in a much broader sense.

While I am confident that the large majority of students will naturally perform in accordance with the university's guidelines and regulations regarding academic integrity, I provide below an explicit statement of course policy in this regard.

Problem Sets: ECE 230C course policy is that discussion of course material, including homework problems, is allowed and indeed encouraged. However, each student should work through assigned homework problems and write up his or her solutions independently. Problem-solving is an extremely useful skill in itself, and in addition is the only really effective way to learn the material!

Specifically, each student is responsible for working out and writing up his or her own solutions to each problem set. Discussion of the course material and problems is encouraged, but practices such allowing a classmate to copy your homework solutions, or a group working out a problem solution together which everyone then copies down and turns in, are forbidden. In addition, students are not allowed to consult problem set solutions from prior years in completing their own solutions. It is usually extremely obvious when this has occurred. Students caught violating course policy on problem sets will receive a warning possibly followed by a grading penalty and further disciplinary action, in accordance with university policy.

Examinations: In general you will be allowed to use your class notes, problem sets and problem set solutions, a calculator, writing implements and erasers, and blue books during exams. No other materials will be allowed. Students who are caught using unauthorized materials during an exam, copying from a classmate on exams, continuing to work on an exam after time has been called, or violating exam or course rules in some other manner are likely, at a minimum, to receive a score of zero on that exam and may be subject to further disciplinary action, again in accordance with university policy.

For further information: Students with questions about course policy should consult the course instructor. UCSD's policy on academic integrity is posted at http://ugr8.ucsd.edu/judicial/ad-guide.html.




Course Topics:

Electron states in periodic potentials:
Bloch's theorem
Kronig-Penney potential
Calculation of band structure:
Tight-binding approach
Review of perturbation theory
k.p theory
Other techniques
Electron-electron interaction effects
Electron dynamics and transport properties:
Equations of motion
Motion in electric and magnetic fields
Boltzmann equation and transport phenomena
Optical properties of solids:
Dielectric function
Kramers-Kronig relations
Optical transitions



Lecture Topics and Assigned Reading:

4/1/08: Introduction; electrons in periodic potentials; Bloch's theorem.
Reading: Kittel, Chapter 7.
Handouts: Course syllabus, Policy on academic integrity.
4/3/08: Proof of Bloch's theorem (continued); formation of energy band gaps.
Handout:Problem Set 1

4/8/08: NO LECTURE
4/10/08: NO LECTURE
4/11/08: (DOUBLE MAKEUP LECTURE) Formation of energy band gaps (continued); Kronig-Penney potentials; analysis of one-dimensional Kronig-Penney model; illustration of band gap formation and complex band structure in band gap; extended and reduced zone schemes; number of states per energy band and implications. Calculation of electronic band structure; tight-binding approximation; tight-binding with simple cubic lattice and nearest-neighbor interactions.
Reading: Ziman, Chapter 3.

4/15/08: Example of tight-binding band structure calculation (continued); k.p theory for band structure calculation; introduction to quantum-mechanical perturbation theory.
Reading: E. Merzbacher, Quantum Mechanics, Chapter 17, or any other text on quantum mechanics.
Handout: Problem Set 2
4/17/08: Basic approach to perturbation theory; nondegenerate perturbation theory; first-order terms in perturbation expansion; second-order term in perturbation expansion for energy; degenerate perturbation theory.
4/18/08: (MAKEUP LECTURE) Degenerate perturbation theory; application of perturbation theory formalism to k.p theory; zone-center (unperturbed) Hamiltonian and k.p perturbation term; calculation of inverse effective mass tensor; two-band model for conduction and light-hole bands in direct band gap semiconductor; calculation of effective masses in two-band model.

4/22/08: NO LECTURE
4/24/08: Effective masses in two-band model - comparison with experimental values for cubic zincblende direct bandgap semiconductors; nonperturbative analysis of k.p Hamiltonian; nonperturbative analysis of two-band model; complex band structure in the two-band model.

4/29/08: Other methods for calculating band structure; plane-wave-based basis elements; orthogonalized plane wave method and OPW basis elements; pseudopotentials.
5/1/08: Pseudopotentials (continued); cancellation "theorem"; nonlocality of pseudopotential operator. Electron-electron interaction effects; screening; linear response functions and electron gas dielectric function.
Reading: Ziman, Chapter 5. Kittel, Chapter 14.
W. A. Harrison, Solid State Theory (Dover, 1979), Chapter III.4.
Handout: Problem Set 3

5/6/08: MIDTERM EXAM
5/8/08: Electrostatic screening; linearized Thomas-Fermi approximation; Thomas-Fermi screening length; plasmon excitations.

5/13/08: Dynamics of electrons; Wannier functions; envelope function.
Reading: Ziman, Chapter 6; Kittel, Chapter 8.
5/15/08: Schrodinger's equation for envelope function; analysis of impurity levels; impurity ionization energies; impurity concentration effects; Mott transition, impurity band formation, band gap narrowing.

5/20/08: Quasi-classical dynamics; correspondence principle; recovery of semi-classical equations of motion; inverse effective mass tensor; excitons; exciton binding energy and radius; Mott-Wannier excitons.
5/22/08: No lecture.

5/27/08: (Lecture 1) Frenkel excitons; many-particle vs. single-particle wave functions; Frenkel exciton dispersion relation; exciton features in absorption.
Handout: Problem Set 5
5/27/08: (Lecture 2 - MAKEUP LECTURE) Surface states. Analysis of transport properties of carrier populations; distribution functions; Boltzmann equation; equilibrium and non-equilibrium distribution functions; linearized Boltzmann equation.
Reading: Ziman, Section 6.9; Chapter 7.
5/29/08: Calculation of scattering term in Boltzmann equation; analysis of electrical conductivity; relaxation time; calculation of electrical current density; recovery of conductivity expression for free-electron gas.

6/3/08: Calculation of scattering/relaxation time; transport in electric and magnetic fields; analysis of Hall Effect; Hall coefficient and mobility, and Hall factor.
6/5/08: Introduction to optical properties of solids; wave equation; complex refractive index; Kramers-Kronig relations.
Reading: Ziman, Chapter 8, Section 8.1.



Problem Sets:

Problem sets and solutions for ECE 230c may be viewed/downloaded as .pdf files using the links below.

Problem Set 1
Problem Set 1 solutions

Problem Set 2
Problem Set 2 solutions

Problem Set 3
Problem Set 3 solutions

Problem Set 4
Problem Set 4 solutions

Problem Set 5
Problem Set 5 solutions




Other Course Handouts

Handouts and other supplementary materials for ECE 230c are available using the links below. In addition, printed copies of the handouts are generally available in the wall folders outside 3809 EBU1.

Course Syllabus: .pdf file
Course Policy on Academic Integrity: .pdf file

Spring 2007 Midterm Exam
Spring 2007 Midterm Exam solutions

Spring 2007 Final Exam



Last updated: 6/20/2008
Ed Yu
ety@ece.ucsd.edu