ECE 230c: Solid State Electronics

Spring 2009, 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

6/10/09: The results for the final exam are as follows: mean=62.1, median=68.5, standard deviation=14.2, range=38-80. The full distribution of scores is also available.

6/5/09: Problem Set 5 has been graded, and you can pick up your graded problem sets on the small bookcase outside 3809 EBU1.

6/4/09: Problem Set 5 solutions are now available.

6/3/09: To help you prepare for the final exam, copies of the Spring 2008 Final Exam and Spring 2008 Final Exam solutions are available. Note that the topics covered this year differed somewhat from those covered last year, particularly for the second half of the course.

6/3/09: The final exam will be held as scheduled on Tuesday 6/9/09, 8-11AM in our regular lecture location, HSS 1315. The exam will cover material from the entire quarter. For the exam, you will be allowed to use your class notes, problem sets, problem set solutions (your own and those distributed on the web site), and a calculator. Books, papers, etc. are not allowed. You should bring a blue book in which to write your exam.

6/3/09: As a reminder, my office hours this Friday will be 2-3PM instead of 9-10AM.

5/27/09: Problem Set 5 was handed out in class on 5/26/09 and is due in class on 6/4/09.

5/27/09: Problem Set 4 solutions are now available.

5/17/09: Problem Set 4 was handed out in class on 5/12/09 and is due in class on 5/26/09.

5/17/09: Problem Set 3 solutions are now available.

5/11/09: For this week, I will have office hours Thursday 5/14/09 4-5PM instead of Friday 5/15/09 9-10AM.

5/11/09: Midterm Exam solutions are now available.

5/11/09: The results for the midterm exam are as follows: mean = 56.8, median = 55.5, standard deviation = 15.2, range = 27-85. The full distribution of scores is also available.

4/28/09: There will be no lecture on Thursday 5/7/09. A makeup lecture will be scheduled for later in the month.

4/28/09: Problem Set 3 was handed out in class today and is due in class on 5/12/09.

4/28/09: Problem Set 2 solutions are now available.

4/24/09: To help you prepare for the midterm exam, copies of the following are available: Spring 2008 ECE 230C Midterm Exam and Spring 2008 ECE 230C Midterm Exam Solutions. Note that we have covered slightly different content this year, so some topics included in last year's exam, e.g., Kronig-Penney model, have not been discussed this year, and you are not responsible for such topics.

4/24/09: The MIDTERM EXAM for ECE 230C will be given as scheduled, in class 9:30-10:50AM on Tuesday 5/5/09. During the exam you will be allowed to use your class notes, problem sets and problem set solutions (your own and those distributed on the web site), and a calculator. Books, papers, and other materials are not allowed. You should bring a blue book in which to write your exam.

4/14/09: Problem Set 2 was handed out in class today and is due in class on 4/28/09.

4/14/09: Problem Set 1 solutions are now available.

4/6/09: Makeup lectures have been scheduled as follows: Friday 4/17/09, 5:00-6:20PM, HSS 1305, and Friday 4/24/09, 4:00-6:50PM, HSS 2152.

4/6/09: As announced in class, there are a few changes to the lecture schedule for the next few weeks. We will have no lecture on Thursday 4/9/09, Thursday 4/16/09, and Tuesday 4/21/09. I will be off campus during my scheduled office hours on Friday 4/10/09, Monday 4/13/09, and Monday 4/20/09. However, I should be reachable by email during most or all of my various trips.

4/6/09: Problem Set 1 was distributed in class on Thursday 4/2/09 and is due in class on Tuesday 4/14/09.

3/27/09: To accommodate wait-listed students, ECE 230C has been MOVED TO HSS 1315.

3/24/09: Please check this section of the Web site frequently for announcements pertaining to ECE 230C.

Instructor

Teaching Assistants

Schedule

Texts

Grading

General Course Policy 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, HSS 1315
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 5, 2009 (tentative).
Final Exam: 50%: The final exam will be 8:00-11:00AM, Tuesday June 9, 2009.

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:

Electronic structure in semiconductors and solid-state materials:: Bloch's theorem (review); Tight-binding approach; Review of perturbation theory; k.p theory; Other techniques; Electron-electron interaction effects; Electron dynamics and the envelope function approximation
Structural and electronic properties of heterojunctions:: Heterojunction formation and band alignments; Strain and critical thickness; Strain and electronic band structure
Optical properties of solids:: Dielectric function; Kramers-Kronig relations; Optical transitions
Other topics

Lecture Topics and Assigned Reading:

3/31/09: Introduction; electron-ion vs. electron-electron interactions; properties of electronic states in periodic structures; proof of Bloch's theorem.
Reading: Kittel, Chapter 7.
4/2/09: Techniques for calculating electronic band structure; tight-binding approximation; example of tight-binding band structure for one orbital model.
Reading: Ziman, Chapter 3.
Handout: Problem Set 1
4/7/09: k.p theory for band structure calculations; k.p Hamiltonian; introduction to quantum-mechanical perturbation theory; nondegenerate perturbation theory; first-order perturbation theory.
Reading: E. Merzbacher, Quantum Mechanics, Chapter 17, or any other text on quantum mechanics.
4/9/09: No lecture.
4/14/09: Second-order perturbation theory; degenerate perturbation theory; application to k.p Hamiltonian.
Handout: Problem Set 2
4/16/09: No lecture.
4/17/09: (Makeup lecture) Perturbation approach to k.p theory (continued); inverse effective mass tensor; two-band scalar model for direct-band gap semiconductors; comparison to data for III-V compound semiconductors; nonperturbative approach to two-band k.p model.
4/23/09: Two-band k.p model - nonperturbative solution; complex band structure (imaginary wave vector) in band gap; introduction to orthogonalized plane wave (OPW) method for band structure calculation.
4/24/09: (Makeup, double lecture) OPW method (continued); construction of orthogonalized plane wave states; pseudopotential; cancellation theorem. Introduction to electron-electron interaction effects; screening; formulation in terms of dielectric function.
Reading: R. M. Martin, Electronic Structure: Basic Theory and Practical Methods (Cambridge, 2004).
Ziman, Chapter 5.
Kittel, Chapter 14.
W. A. Harrison, Solid State Theory (Dover, 1979), Chapter III.4.
4/28/09: Electrostatic screening; Thomas-Fermi and linearized Thomas-Fermi approximations; screening by free-electron gas; screening of spatially uniform electric field; plasmon excitations.
Handout: Problem Set 3
4/30/09: Dynamics of electrons; Wannier functions; envelope function; equation for envelope function.
Reading: Ziman, Chapter 6; Kittel, Chapter 8.
5/5/09: MIDTERM EXAM
5/7/09: No lecture
5/12/09: Envelope function approximation; analysis of impurity levels; quasi-classical dynamics.
Handout: Problem Set 4
5/14/09: Introduction to semiconductor heterostructures and lattice mismatch effects; basic definitions; determination of heterojunction band offsets - theories and "rules".
5/19/09: Heterojunction band offsets (continued); lattice mismatch and strain effects; strain in lattice-mismatched heterojunctions; quantitative description of strain, stress and energetics.
Reading: C. G. Van de Walle and R. M. Martin, J. Vac. Sci. Technol. B 4, 1055 (1986); Phys. Rev. B 34, 5621 (1986); C. G. Van de Walle, Phys. Rev. B 39, 1871 (1989).
R. G. Dandrea, C. B. Duke, and A. Zunger, J. Vac. Sci. Technol. B 10, 1744 (1992).
R. M. Martin, Electronic Structure (Cambridge, 2004) - general methods.
J. Y. Tsao, Materials Fundamentals of Molecular Beam Epitaxy (Academic Press, 1993).
J. F. Nye, Physical Properties of Crystals (Oxford University Press, 1985).
5/21/09: Quantitative analysis of strain, stress, and energetics (continued); stress and strain tensors.
5/26/09: Elastic energy density; elastic stiffness tensor for cubic and hexagonal crystals; strain tensor and energy in strained-layer heterojunctions.
Handout: Problem Set 5
5/28/09: Dislocations - basic phenomenology and description; Burgers vector; edge vs. screw dislocations; dislocation energy; computation of critical thickness for strain relaxation; influence of strain on electronic band structure.
Reading: C. G. Van de Walle, Phys. Rev. B 39, 1871 (1989).
6/2/09: Influence of strain on electronic band structure (continued); deformation potentials; valence- and conduction-band-edge shifts and splittings. Introduction to optical properties of solids.
Reading: Ziman, Section 8.1.
6/4/09: Formulation of optical properties of solids; dielectric function and complex refractive index; Kramers-Kronig relations; determination of optical constants from reflection and transmission.