Introduction to Nanotechnology (B)

Credits: 3

Instructors: Dr. Song, Ker-Jar 宋克嘉, Dr. Yu, Tsyr-Yan 余慈顏

Class hour: Tuesday 10:10-11:00, Thursday 13:40-15:20 

Classroom: R209, IAMS, AS

Introduction:

We will go through the following chapters: Chap. 2 Structure, Chap. 3 Length Scales, Review of Linear Algebra, Chap.6 Quantum Mechanics Review, Chap. 7 & 8 Model Quantum Mechanics Problem, Chap. 9 Density of states, Chap. 10 Bands, Chap. 11 Time-Dependent Perturbation Theory and Chap. 12 lnterband Transitions. We will adjust the pace of the course and materials covered according to the average level of the students. In general, we expect the students to put in significant effort to grasp the basics.

Syllabus:

Outline

Chap. 2  Structure p. 9~29 (20)- 2.1 Introduction  2.2 Basic properties  2.3 Examples of crystal structures  2.4 Miller indices  2.5 Surface-to volume ratio

Chap. 3 Length Scales p. 29~61 (32)-  3.1 Introduction  3.2 de Broglie wavelength  3.3 The Bohr radius  3.4 Excitons  3.5 Confinement regimes  3.6 Metals  3.7 The Fermi energy, Fermi velocity, and Kubo gap  3.8 The mean free path in metals  3.9 Charging energy

Review of Linear Algebra

Chap. 6 A Quantum Mechanics Review p. 101~137  (36)-  6.1 Introduction  6.2 Wavefunctions  6.3 Observables and the correspondence principle  6.4 Eigenvalues and eigenfunctions

6.5 Wave packets  6.6 Expectation values  6.7 Dirac bra-ket notation  6.8 Operator math  6.9 More on operators

6.10 Commutators  6.11 More commutator relationships  6.12 The uncertainty principle  6.13 The Schrodinger equation

6.14 The postulates of quantum mechanics  6.15 Time-independent, nondegenerate perturbation theory

Chap. 7 Model Quantum Mechanics Problem p.137~179 (42)-  7.1 Introduction  7.2 Standard model problems  7.3 Model problems for wells, wires, and dots

Chap. 8 Additional Model Problems p.179~203 (24)-  8.1 Introduction  8.2 Particle in a finite one-dimensional box  8.3 Particle in an infinite circular box  8.4 Harmonic oscillator (This chapter can be omitted if there is not enough time. It is more important that the students do some calculation.)

Chap. 11 Time-Dependent Perturbation Theory p.275~294(19)-  11.1 Introduction  11 .2 Time-dependent perturbation theory  11.3 Example: A two-level system  11.4 Rates (This Chap. can be mentioned before  Ch.9 without derivation, just making use of the formulas and practice doing the calculations. ) Chap. 9 Density of states p.203~239 (36)  9.1 Introduction  9.2 Density of states for bulk materials, wells, wires, and dots  9.3 Population of the conduction and valence bands  9.4 Quasi-Fermi levels  9.5 Joint density of states

Chap. 10 Bands p. 239~275 (36)  (This chapter involves many concepts and need some supplemental material.)- 10.1 Introduction  10.2 The Kronig-Penney model  10.3 Kronig-Penney model with delta-function barriers

10.4 Other band models  10.5 Metals, semiconductors, and insulators

Surface state, localized impurity state, band bending, pn junction

Chap. 11 revisited

Chap. 12 lnterband Transitions p.295~344 (49)-  12.1 Introduction   12.2 Preliminaries: -u· E versus -(q/m0)A · p     12.3 Back to transition probabilities   12.4 Bulk semiconductor   12.5 Equivalence of H(1) ＝-(q/m0)A · P and H(1) ＝-u·E      12.6 Multiple states   12.7 Fermi's golden rule and the associated transition rate    12.8 Absorption coefficient α   12.9 Transitions in low-dimensional semiconductors

Reference:

1. Introductory NanoScience, Physical and Chemical Concepts, Masaru Kuno