MAT 225. Introduction to Electronic Materials. Fall 2003

Course info:

Instructor         Prof. Nicola Spaldin, Room 2007 MRL x7920, nicola@mrl.ucsb.edu
Office Hours    Monday and Wednesday 3.15 - 4

Class Time       Monday and Wednesday 2-3.15 pm
Place                 1445 Phelps

TA                     Katie Schaeffer
Office Hours     Tuesday 1-2 pm and Friday 9-10 am, trailer 942 room 1009

Books:

J.D. Livingston, Electronic properties of engineering materials,

Course outline:
 
Week  number Topics Reading (from Livingston's book) Homework (from Livingston's book) In-class problems (S=Sample Problem)
1 Introduction to quantum mechanics. Solution of the Schrodinger equation for simple cases. Chapter 8 8.1, 8.8, 8.14, additional exercise 1 8.2, 8.4, 8.6 (no time dependence), 8.7
2 Atomic orbitals. Molecular orbitals and chemical bonds.

 Chapters 9 and 10

 9.7, 9.12, 9.13, 10.9 and 10.10, additional exercise 2

9.5, 9.6, 10.7, 10.11
3 Classical picture of conductivity in metals. A little bit about the optical properties of metals.
 Chapters 1 and 2 (Summary)
 1.1, 1.5, 1.7 and 1.11
 S1.1, S1.2,  S1.3, derive RH for positively charged carriers
4 Electrical and optical properties of insulators within a classical picture.
 Chapters 3 and 4
 3.5, 3.11, 3.13 (extra credit), 4.2, 4.7, 4.10, look up cool applications of dielectrics.
 3.3, 3.6, S4.1, 4.5, 4.6, 4.11
5 An introduction to the concept of bands from a bonding picture. Quantum mechanical free electrons.
 Chapters 11 and 12
 11.4, 11.5, 12.3, 12.5, 12.6 and 12.11
11.2, 11.10, 12.5, 12.14
6  MID-TERM EXAM.
7 Elasticity in a classical atomic picture. Introduction to the concept of Brillouin Zones.
 Chapter 7 7.3, 7.4, 7.10, write a summary, in the form of a detailed course syllabus, of the material that we've covered so far.
 7.1, 7.2, 7.6
8 Nearly free electrons and band gaps. Metals and insulators within the band picture. Chapters 13 and 14 13.4, 13.5, 14.1, 14.4, 14.7, 14.8 and 14.12 13.2, 14.3, 14.4, 14.6, 14.11
9 Semiconductors and semiconductor devices. Chapters 15 and 16 15.1, 15.7, 15.13, 16.5, 16.6, 16.7 and 16.10 S15.2 (at 250K), 15.12, 16.1, 16.2
10  STUDENT PRESENTATIONS Complete take-home final exam.

Grading:

Your grade is based equally on your performance in four components of the course: homework sets, in-class mid-term exam., take home final exam. and final oral presentation.

Homework.
The assigned homework for the entire class is listed above. The homework for week N must be handed in before or during the Wednesday class of week N+1. The exception is the final exam. which is due on Monday December 1st. You are encouraged to work together on the homework problems, but the write-up that you turn in must be completed independently. Late homework will not be accepted but your lowest score will not be counted towards your grade.

Mid-term
The mid-term will be a closed book exam. during our regular class sessions on MONDAY OCTOBER 27th. You are allowed to bring in one 8.5 x 11" single-sided page of hand-written (or typed by yourself) notes. No photocopying allowed.

Here is last year's mid-term.

Presentations.
The last week of the quarter will be devoted to student presentations. Your presentation should explain your own thesis research at a level appropriate to a materials scientist who is not in your field, and should show how some aspect of the material that we have learned this quarter is relevant to your research.  You will be graded on your selection of an interesting topic, your knowledge of the topic, the relevance of your presentation to the course, and the quality of your oral presentation.

Final.
The final will be an open-book take home exam. and will be collected during our class session on Monday December 1st. You are not allowed to discuss the final with anyone else.
 
 

Additional Exercises:

1) Go to the following web-site:

http://www.quantum-physics.polytechnique.fr/en/index.html

a) Go to Wave mechanics, then Propagation of a free wavepacket. Watch the wave packet propagate (real part of the wavefunction and the probability density) for different initial widths. Comment on the rate of spreading in each case.

b) Go to Quantization in one dimension then Eigenstates in a step potential. Sketch and describe the form of the wavefunction when the energy is higher than the left hand side of the step, between the top and bottom of the step, and lower than the right hand side of the step.

c) Go to Quantization in one dimension then Eigenstates in a potential well. How many physically meaningful bound states do you find for the initial well size? Sketch the wavefunctions in order of increasing energy and comment on their symmetry. How does the number of bound states change when you increase first the depth of the well and second the width of the well?

d) Go to Quantum superposition in one dimension then Harmonic oscillator. Notice that states that are superpositions (linear combinations) of eigenstates are time-dependent (even though we haven't talked about this in class, you've got to agree it's very cool!) Build states that consists of just 1 eigenstate and look at the probability density (below the plot). Comment on the dependence of the probability distribution on the energy, and compare to a classical oscillator.

2) Go back to the following web-site:

http://www.quantum-physics.polytechnique.fr/en/index.html

Go to Quantization in three dimensions then Carbon 60.

Comment on the nature of the Huckel theory matrix for the C60 molecule. How would it differ for a linear chain of 60 C atoms?

Diagonalize the Huckel matrix.

What is the separation between the highest and lowest energy states?
What is the size of the energy gap between occupied (bonding) orbitals and unnocupied (antibonding) orbitals.
What is the energy spread of the bonding and antibonding orbitals.
Comment on the symmetry and degeneracies of the three lowest energy manifolds.

Lecture notes:

Here are pdf files of the overheads that I'm using in class:

Classical picture of conductivity in metals

Electrical properties of insulators

Elasticity:
page1  page2 page3  page4 page5  page6 page7  page8 page9  page10 page11
 

Quantum mechanics:
page1  page2 page3  page4 page5  page6 page7  page8 page9
 

Atomic and molecular orbitals
 
Bands from a bonding picture  

Nearly free electrons
 
Semiconductors 1st half and Semiconductors 2nd half
 

Scheduling foibles:

There will be NO CLASS or OFFICE HOURS on Wednesday October 22nd

There will be an EXTRA CLASS (in Snidecor 1649) on Friday October 31st at 10am. I'll do office hours straight after class.

Student presentations will be scheduled for Dec 1, 2, 3 and 4 from 2-3.30. You are required to show up to your own session and one other. On Dec. 2nd and 4th we will be in room Buchanan 1934.