Instructor: Azad Naeemi

Class: Instruction Center 215

Semester: Spring 2013

M-W 2-3 p.m.

In this course we will use carbon nanotubes to understand quantum transport as the foundation for all emerging nanoelectronic devices.

Carbon nanotubes and graphene, which were discovered in the past two decades, are considered potential candidates for a diverse set of electronic applications such as transistors, interconnects, sensors, nanoelectromechanical (NEMS) switches, optoelectronic devices, and electron guns. There are other emerging nanomaterials with potential electronic applications as well. The topics covered in this course are therefore vital for students interested in various electronic applications of nanomaterials.

In this course, carbon nanotubes and graphene nanoribbons will be used as a framework to understand electron transport in nano-scale structures in general. In virtually all nano-scale devices, whether they are silicon nanowires, ZnO nanowires and nanobelts, graphene nanoribbons, or carbon nanotubes, electrons are confined in one or two dimensions. Electron transport in low-dimensional devices is distinctly different from its classical form leading to unprecedented behaviors. We will explore novel electronic phenomena in low-dimensional systems and the limitations and opportunities that they pose to future devices and circuits.

We will also learn how to use first-principles calculations to obtain the electronic properties of carbon nanotubes. These techniques can be used to extract the electronic properties of other emerging nano-scale devices such as graphene nanoribbons. Finally, practical applications of carbon nanotubes and graphene such as transistors, interconnects and sensors will be discussed.

General understanding of electrical circuits, electronic devices, and linear algebra is required. No prior acquaintance with quantum mechanics is required. All necessary QM concepts will be covered in the course. Familiarity with MATLAB is needed for homework assignments.

*Quantum Transport: From Atoms to Transistors*, Supriyo Datta, Cambridge University Press, 2005 (available at GIT Bookstore).

*Quantum Mechanics for Scientists and Engineers*, David A. B. Miller, Cambridge University Press, 2008.

Helpful resources on this book such as solutions to selected problems, animations, and viewgraphs are available at: __http://www-ee.stanford.edu/~dabm/QMbook.html__

*Electronic Transport in Mesoscopic Systems*, Supriyo Datta, Cambridge Studies in Semiconductor Physics and Microelectronic Engineering (No. 3), Cambridge University Press, 2005.

The few sections from the above two books that will be used in the class will be distributed during the course.

The final grade will be calculated as follows:

- Homework 40%
- Exam 1 20%
- Exam 2 20%
- Term Paper 20%

The term paper in this course is in lieu of a final exam.

Homework assignments are an important component of this course. They are designed to make you master the material presented in class, prepare you for upcoming classes, and in some cases, complement what is taught in the class. A major part of assignments will be done with MATLAB. Your textbook has many MATLAB codes which can help you with writing such codes. You may discuss homework assignments with your classmates and also use the codes in your textbook as a guide. However, what you turn in must be your own work.

By March 29, you are expected to have chosen a specific application of carbon nanotubes, graphene nanoribbons, or another nanomaterial to write a term paper on it. You are required to submit a half page abstract on March 29. Original ideas for new applications of these materials or new operation mechanisms are strongly encouraged and will result in bonus credit. The goal of this project is to use the course material and your creativity to propose and/or model novel nanoelectronic devices, not writing term papers that are pure literature surveys.

Weeks 1 & 2: Course Overview and Introduction to Quantum Mechanics

Week 3 & 4: Free Electrons in Low Dimensional Systems

Week 5: Finite Difference Method and Self Consistent Solutions

Week 6: Basic Functions and Density Matrix

Week 7 & 8: Bandstructure Calculations, Graphene bandstructure

Week 9: Carbon Nanotubes and Graphene Nanoribbons

Week 10: Effective Mass Hamiltonian

Week 11: Self Consistent Solutions to Schrodinger’s and Poisson’s Equations

Week 12: Coherent Transport Modeling

Week 13: Non-coherent Transport

Weeks 14-15: Potential Applications of Carbon Nanomaterials

- Overview, From Microelectronics to Nanoelectronics

- Simple Rationalization of Schrödinger’s (time-independent) equation
- Simple Examples: Electrons in a Box
- Simple Rationalization of the Time-Dependent Schrödinger Equation
- Concept of Group Velocity

- Electrons in One Dimension, Fermi Distribution, Quantum Resistance, Number of Conduction channels (Exercise: 3D wires, density of states)
- Electron Scattering, Electron Mean Free Path, Ohm’s Law
- Coherent Transport, Optical Analogies, Voltage Probes
- Quantum capacitance and Kinetic Inductance

- Method of Finite Difference
- Matrix representation of Schrodinger Equation
- Eigenvalues and Eigenvectors
- Examples (particle in a box and the difference between analytical and matrix solutions)

- Method of Finite Difference (Continued)
- Boundary conditions
- Particles in a 3D box
- Spherical Coordinates

- Self consistent.
- Basic functions (Math)
- Basic functions (Conceptual significance)
- Density Matrix
- Bandstructure (1D)
- 1Bandstructure (Generalization, e.g. 2D)
- Subbands (Nanotubes, zone folding)
- Subbands (Graphene Nanoribbons)
- Density of States
- graphene nanoribbons
- Effective Mass Hamiltonian
- Density Matrix and Quantum Capacitance

- Level broadening and Local density of states
- Self Energy
- Life Time
- Coherent Transport
- Transmission
- NEGF Numerical Solutions
- Phonon Emission
- Non-coherent Transport

- Interconnects
- Transistors
- Sensors
- Other applications

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