This course provides an in-depth discussion of the basic structure, electronic, and optical properties of semiconductor heterojunction interfaces and semiconductor heterostructures. It is intended primarily for graduate students in electrical engineering, applied physics, materials science and engineering, 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.

3/14/08: Problem Set 5 solutions are now available.

2/28/08: Problem Set 5 was handed out today and is due in class on 3/13/08.

2/28/08: Problem Set 4 solutions are now available.

2/20/08: Midterm Exam Solutions are now available.

2/19/08: The Final Research Paper Assignment was handed out today and is due Monday 3/17/08 at 12:00 noon.

2/19/08: Problem Set 4 was handed out today and is due in class on 2/28/08.

2/19/08: Problem Set 3 solutions are now available.

2/14/08: Results for the midterm exam are as follows: mean = 67.2, median = 67, standard deviation = 14.2, range = 45-85. The full distribution of midterm exam scores is also available.

2/7/08: Problem Set 3 was handed out today and is due in class on Tuesday 2/19/08.

2/7/08: Problem Set 2 solutions are now available.

2/4/08: To help you prepare for the midterm exam, the Winter 2007 ECE 236A Midterm Exam and Winter 2007 ECE 236A Midterm Exam Solutions are available.

1/31/08: The MIDTERM EXAM will be administered, as scheduled, on Tuesday 2/12/08, in class. For the exam you will be allowed to use your class notes, problem sets, problem set solutions (your own and the "official" solutions), and a calculator. Books, papers, etc. are not allowed. You should bring a blue book in which to write your exam.

1/31/08: There will be no lecture on Tuesday 2/5/08. There will be a MAKEUP LECTURE on Friday 2/8/08, 1:30-2:50PM in U413A Room 1.

1/26/08: As announced in class on Thursday, there will be no lecture on Tuesday 1/29/08. A MAKEUP LECTURE will be held on Wednesday 1/30/08, 9:00-10:20AM in U413A Room 1.

1/22/08: Problem Set 2 was handed out today and is due in class on Thursday 2/7/08.

1/22/08: Problem Set 1 solutions are now available.

1/18/08: There will be a MAKEUP LECTURE on Wednesday 1/23/08, 8:30-9:50AM in 3311 EBU1.

1/10/08: Problem Set 1 was handed out today and is due in class on Tuesday 1/22/08.

1/10/08: Due to my travel schedule, we will not have lecture on Tuesday 1/15/08 and I will not have office hours on Monday 1/14/08. A makeup lecture will be scheduled, and you should be able to reach me by email while I am away.

1/2/08: Please check this section of the Web site frequently for announcements pertaining to ECE 236A. The first lecture will be on Tuesday, 1/8/08 in Center 218.

Instructor

Teaching Assistants

Schedule

Texts

Grading

General Course Policy

Course Topics

Lecture Topics and Assigned Reading

Problem Sets (downloadable PostScript and .pdf files available) and Solutions

Other Course Handouts (downloadable PostScript and .pdf files available)

Instructor:

Professor Ed Yu

3809 EBU1

534-6619

ety@ece.ucsd.edu

Office Hours: M 1:00-2:00PM, Fr 9:00-10:00AM, or by appointment/drop-in

Teaching Assistant:

None

Schedule:

Lectures:

TuTh 9:30-10:50AM, Center 218

Discussion:

Due to the size and nature 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:

none - references will be cited during lectures

Recommended References:

M. Shur, Physics of Semiconductor Devices (Prentice Hall, 1990).

S. M. Sze, Physics of Semiconductor Devices, Second Edition (John Wiley & Sons, 1981).

S. Wang, Fundamentals of Semiconductor Theory and Device Physics (Prentice Hall, 1989).

C. Weisbuch and B. Vinter, Quantum Semiconductor Structures (Academic Press, 1991).

P. Y. Yu and M. Cardona, Fundamentals of Semiconductors, Third Edition (Springer-Verlag, 2001).
(Yu/Cardona also available online at 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 2/12/07 (tentative).

Paper: 50%

All students will be required to complete a final paper and presentation to the class on a topic related to the course material. The presentation dates/times will be announced later in the quarter.

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

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 236A. 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 236A 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:

Basic properties of semiconductor heterojunctions

Heterojunction formation and band alignments

Epitaxial growth

Lattice-mismatched heterojunctions

Basic heterojunction structures and electronic properties

Quantum wells and superlattices

Two-dimensional electron gas and modulation-doped structures

pn heterojunctions

Resonant tunneling diodes

Optical properties of heterojunction structures

Quantum wells, wires, and dots

Multiple quantum wells and superlattices

Electrical properties and transport in heterojunction structures

Lateral transport and mobility

Vertical transport and tunneling

Magneto-transport

Unusual material properties

III-nitride semiconductors

Semiconductor-dielectric interfaces

Other topics

Lecture Topics and Assigned Reading:

1/8/08: Introduction; basic definitions; types of band alignments; electron affinity rule; interface dipoles.
Handouts: Course syllabus, Policy on academic integrity.

1/10/08: Band offset values; "midgap" levels; first-principles determination of band offsets; experimental determination of band offsets; XPS; internal photoemission.
References: J. Tersoff, Phys. Rev. Lett. 52, 465 (1984);
C. G. Van de Walle and R. M. Martin, J. Vac. Sci. Technol. B 4, 1055 (1986); Phys. Rev. B 34, 5621 (1986);
R. G. Dandrea, C. B. Duke, and A. Zunger, J. Vac. Sci. Technol. B 10, 1744 (1992);
R. M. Martin, Electronic Structure (Cambridge, 2004).
Handouts: Problem Set 1

1/15/08: No lecture.

1/17/08: Capacitance-voltage profiling techniques; epitaxial growth - molecular beam epitaxy (MBE).
References: H. Kroemer, Appl. Phys. Lett. 36, 295 (1980).

1/22/08: Epitaxial growth - metalorganic chemical vapor deposition (MOCVD); lattice mismatch and strain effects; strain vs. dislocation formation; definitions of strain and stress; mathematical formulation of strain.
Handouts: Problem Set 2
References: E. H. C. Parker, ed., The Technology and Physics of Molecular Beam Epitaxy (Plenum Press, 1985).
J. Y. Tsao, Materials Fundamentals of Molecular Beam Epitaxy (Academic Press, 1993).
T. F. Kuech, Mat. Sci. Repts. 2, 1 (1987).

1/23/08: (Makeup lecture) Mathematical description of strain (continued); strain vs. rotation; strain tensor; stress and stress tensor; relationship between stress and strain; elastic stiffness and compliance tensors; elastic energy density.

1/24/08: Elastic energy density (continued); application to strained-layer heterojunctions; total strain energy; energy of dislocations.

1/29/08: No lecture.

1/30/08: (Makeup lecture) Dislocation types - edge and screw dislocations; Burgers circuits and vectors; dislocation line energy; total energy for lattice mismatch accommodation; critical thickness calculation; influence of strain on energy band structure.
Reading: C. G. Van de Walle, Phys. Rev. B 39, 1871 (1989).

1/31/08: Influence of strain on energy band structure; energy band shifts due to hydrostatic strain; band splittings due to uniaxial/biaxial stress and strain; deformation potentials for conduction and valence band shifts/splittings. Introduction to basic heterojunction structures; concept of envelope function.
Reading: C. Weisbuch and B. Vinter, Quantum Semiconductor Structures, Chapter II.

2/5/08: No lecture.

2/7/08: Envelope-function formalism for heterostructures; conduction-band (electron) quantum wells; infinite-barrier quantum well; finite-barrier quantum well.
Handout: Problem Set 3

2/8/08: (Makeup lecture) Quantum-well density of states; valence-band (hole) quantum wells; Luttinger Hamiltonian.

2/12/08: MIDTERM EXAM

2/14/08: Valence-band electronic structure; analysis of Luttinger Hamiltonian; formalism for analysis of valence-band quantum wells and heterostructures; multiple-quantum-well and superlattice states; analysis of electronic states in superlattice limit.
Reading: P. Yu and M. Cardona, Fundamentals of Semiconductors, 3rd ed. (Springer, 2001), Section 2.6.
C. Kittel, Quantum Theory of Solids (Wiley, 1963), Chapter 14.

2/19/08: Superlattice electronic states; miniband formation; introduction to modulation-doped heterostructures; two-dimensional electron gas formation.
Handout: Problem Set 4

2/21/08: Detailed analysis of modulation-doped heterostructures; energy levels in triangular quantum well; Airy functions; two-dimensional electron gas sheet carrier concentration; more complicated modulation-doped heterostructures.

2/26/08: Optical properties of semiconductors and heterostructures; incorporation of electromagnetic field into Hamiltonian; gauge invariance; electron-radiation Hamiltonian; Fermi's Golden Rule; computation of optical matrix element.
Reading: C. Weisbuch and B. Vinter, Quantum Semiconductor Structures, Chapter III.
P. Yu and M. Cardona, Fundamentals of Semiconductors, Section 6.2.

2/28/08: Calculation of optical transition rate in bulk semiconductors; joint density of states; Van Hove singularities; optical transitions in quantum wells; computation of quantum-well optical matrix element.
Handout: Problem Set 5

3/4/08: Selection rules for quantum-well optical transitions; intersubband transitions. Introduction to electron transport in semiconductor heterostructures.

3/6/08: Analysis of perpendicular transport in heterostructures; transfer matrix formalism; calculation of transmission and reflection coefficients.
Reading: P. Yu and M. Cardona, Fundamentals of Semiconductors, Sec. 9.5.
D. Ferry and S. Goodnick, Transport in Nanostructures (Cambridge, 1997), Secs. 3.1-3.3.

3/11/08: Calculation of current density in perpendicular transport; example - resonant tunneling diode; integration over parallel wave vector components. Introduction to laterally confined transport.
Reading: S. Datta, Electronic transport in mesoscopic systems (Cambridge, 1997), Secs. 1.6, 2.0-2.2.

3/13/08: Effects of lateral confinement on transport; 1D transport; Landauer formula and quantized conductance; quantum contact resistance; recovery of Ohmic resistance in presence of scattering.

Problem Sets:

Problem sets for ECE 236A may be viewed/downloaded as .pdf files using the links below. In addition, printed copies of the problem sets are generally available in the wall folders outside 3809 EBU1.

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 236A 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

Winter 2007 ECE 236A Midterm Exam

Winter 2007 ECE 236A Midterm Exam Solutions

Final Research Paper Assignment

ECE 236A Midterm Exam Solutions