## Introduction to the Theory of Microelectronics

(3-0-0-3)

**CMPE Degree:** This course is Not Applicable for the CMPE degree.

**EE Degree:** This course is Not Applicable for the EE degree.

**Lab Hours:** 0 supervised lab hours and 0 unsupervised lab hours.

**Technical Interest Group(s) / Course Type(s):** Nanotechnology

**Course Coordinator:**

**Prerequisites:** None.

**Corequisites:** None.

### Catalog Description

Basis of quantum mechanics, statistical mechanics, and the behavior ofsolids to serve as an introduction to the modern study of semiconductors

and semiconductor devices.

### Course Outcomes

Not Applicable

### Student Outcomes

In the parentheses for each Student Outcome:"P" for primary indicates the outcome is a major focus of the entire course.

“M” for moderate indicates the outcome is the focus of at least one component of the course, but not majority of course material.

“LN” for “little to none” indicates that the course does not contribute significantly to this outcome.

1. ( Not Applicable ) An ability to identify, formulate, and solve complex engineering problems by applying principles of engineering, science, and mathematics

2. ( Not Applicable ) An ability to apply engineering design to produce solutions that meet specified needs with consideration of public health, safety, and welfare, as well as global, cultural, social, environmental, and economic factors

3. ( Not Applicable ) An ability to communicate effectively with a range of audiences

4. ( Not Applicable ) An ability to recognize ethical and professional responsibilities in engineering situations and make informed judgments, which must consider the impact of engineering solutions in global, economic, environmental, and societal contexts

5. ( Not Applicable ) An ability to function effectively on a team whose members together provide leadership, create a collaborative and inclusive environment, establish goals, plan tasks, and meet objectives

6. ( Not Applicable ) An ability to develop and conduct appropriate experimentation, analyze and interpret data, and use engineering judgment to draw conclusions

7. ( Not Applicable ) An ability to acquire and apply new knowledge as needed, using appropriate learning strategies.

### Strategic Performance Indicators (SPIs)

Outcome 1 (Students will demonstrate expertise in a subfield of study chosen from the fields of electrical engineering or computer engineering):

1. Calculate eigenstates and eigenfunctions of electrons in infinite, periodic, or quantum confined structures

2. Calculate occupation probabilities or expectation values of physical observables for electrons with wave functions which are known

Outcome 2 (Students will demonstrate the ability to identify and formulate advanced problems and apply knowledge of mathematics and science to solve those problems):

1. Assess the influence of weak electrostatic and magnetostatic fields on the properties of electrons in sharp states of total energy

2. Assess the rate of transitions between sharp states of total energy for electrons subjected to weak electromagnetic fields.

Outcome 3 (Students will demonstrate the ability to utilize current knowledge, technology, or techniques within their chosen subfield):

1. Perform numerical calculations of electronic dispersion in 1D crystals

2. Perform perturbative numerical calculations of empirical electronic dispersion in zincblende crystals

### Course Objectives

### Topical Outline

I. Basic Concepts

A. Wave-particle duality and the two slit experiment

B. Dynamical variables and operators

C. Completeness theorem and the fundamental expansion postulate

D. The Uncertainty Principle

E. Dirac notation

F. Matrix formulation of quantum mechanics

II. One Dimensional Problems

A. Infinite square well

B. One dimensional barrier

C. Multiple barriers

D. Harmonic oscillator

1. Direct solution

2. Creation and annihilation operators

III. Three Dimensional Problems

A. Central force motion and angular momentum

B. Hydrogen atom

C. Periodic table of the elements

D. Spin

E. Stern-Gerlach experiment and spin-orbit interaction

IV. Approximation methods in quantum mechanics

A. Time independent perturbation theory

1. Nondegenerate theory

2. Degenerate theory

B. Time dependent theory

1. Transitions

2. Fermi's Golden Rule

V. Statistical Mechanics

A. Density of states

B. Condition of equilibrium and the laws of thermodynamics

C. Boltzmann distribution

D. Quantum distribution functions

E. Boltzmann equation and nonequilibrium

VI. Solid State Physics

A. Multiple electron atoms and systems

B. Crystalline symmetries and Bloch's theorem

C. Methods of band structure, tight binding, and Kronig-Penney

D. Reciprocal lattices and the Brillouin Zone

E. Nearly free electron model

F. Cellular methods