Network for Computational Nanotechnology

2008 NCN@Purdue Summer School Structure and Agenda

Day 1: What and where is the resistance?
1a. The quantum of conductance
1b. Two kinds of “voltage”

Objective: To introduce a simple quantitative model that highlights the essential parameters that determine electrical conduction: the density of states in the channel, D and the rates γ1,2 at which electrons hop in and out of the two contacts, labeled source and drain. This model is used to explain diverse phenomena such as (1) why a small conductor has a maximum conductance that it cannot exceed even with the best of contacts, (2) how this conductance quantum evolves into Ohm’s law for large conductors, (3) how even a hydrogen atom can exhibit hermoelectric effects, (4) how even symmetric devices can be rectifying due to asymmetric electrostatics, and (5) how the “voltage” varies spatially inside a nanoscale device.

Day 2: Microscopic model for electrical resistance
2a. Wavefunctions and Green functions
2b. The Non-Equilibrium Green Function (NEGF) method

Objective: To extend the simple model from Day 1 into the full-fledged Non-equilibrium Green’s Function (NEGF) model by introducing a spatial grid of N points and turning numbers like γ1,2 into (NxN) matrices like Σ1,2, with incoherent scattering introduced through Σs. This model will be used to provide a quantitative description of key experiments such as the conductance of point contacts and the quantum Hall effect and also to introduce key concepts like transverse modes, spectral functions and density matrices.

Day 3: Spins and magnets
3a. Injection, detection and manipulation of electron spins.
3b. Spin current and spin torque: using spins to manipulate magnets

Objective: To extend the model from Days 1 and 2 to include electron spin. Every electron is an elementary “magnet” with two states having opposite magnetic moments. Usually this has no major effect on device operation except to increase the conductance by a factor of two.

But it is now possible to inject, detect and manipulate spins in a controlled way and even use them to manipulate nanometer-sized magnets. The extended model will be used to describe such phenomena including spin-Hall effect, tunneling magnetoresistance (TMR) and spin-torque devices.

Day 4: Energy conversion
4a. Energy, entropy and the second law
4b. From reversible dynamics to irreversible devices

Objective: To incorporate energy exchange processes into the previous models from days 1 through 3 which are based on a “Landauer-like picture” where the Joule heating associated with current flow occurs entirely in the two contacts. Although there is experimental evidence that this idealization is not too far from the truth in many nanodevices of today, dissipation generally occurs throughout the channel. Moreover there is great interest energy conversion devices that convert heat into electricity or use electrical energy to pump heat. Our purpose here is (1) to describe the basic principles that must be obeyed by any model for energy conversion processes in order to comply with the laws of thermodynamics and (2) to convey the insights that nanodevices provide into the subtle issues of irreversibility that Boltzmann struggled with over a century ago when he constructed the first transport theory.

Day 5: Beyond the one-electron picture
5a. Coulomb blockade and Fock space
5b. Correlations and entanglement

Objective: To relate the one-electron picture used throughout these lectures to the more general but less tractable many-particle picture that underlies it. We introduce this new viewpoint using the example of Coulomb blockaded electronic devices that are difficult to model within the picture developed so far, but can be understood fairly simply in terms of a many-electron picture. I will then use this picture to discuss what I view as some of the unanswered questions in our understanding of electronic transport.

Week 2: July 21-25, 2008

Title: Nanoscale Transistors
Instructor: Mark Lundstrom

Present day MOSFETs have channel lengths of less than 50 nm and are not well-described by traditional, textbook MOSFET theories. When traditional approaches are extended, they can become overly complex – hiding the simple physics of the nanoscale MOSFET. This short course will introduce a new approach to the nanoscale MOSFET and discuss the limits of MOSFETs and how this new approach connects to the traditional treatment of MOSFETs.

Lecture 1: Review of MOSFET Fundamentals
A brief review of conventional MOSFET theory, basic MOSFET IV characteristics, and a quick introduction to the ballistic MOSFET
Exercises: basic MOSFET characteristics with nano-CMOS

Lecture 2: Elementary Theory of the Nanoscale MOSFET

Lecture 3: Theory of Ballistic MOSFETs: Part 1
Derivation of the I-V characteristics of a ballistic MOSFET and an examination of the results
Exercises with FETToy

Lecture 4: Theory of Ballistic MOSFETs: Part 2
Derivation of the I-V characteristics of a ballistic MOSFET and an examination of the results
Exercises with FETToy

Lecture 5: Scattering in Nanoscale MOSFETs
The essential physics of carrier scattering in nanoscale MOSFETs
Exercises: comparing FETToy to experiments

Lecture 6: Application to State-of-the-Art MOSFETs

Lecture 7: Quantum Transport in MOSFETs

Lecture 8: Connection to the Bottom Up Approach

Title: Percloative Transport in Electronic Devices
Instructor: Muhammad A. Alam

The electronic devices these days have become so small that the number of dopant atoms in the channel of a MOFET transistor, the number of oxide atoms in its gate dielectric, the number silicon- or metal crystals in nanocrystal Flash memory, the number of Nanowires in a flexible nanoNET transistor, the number of crystal in an poly-crystalline transistors, etc. are all finite, and countable. What is the average current through such systems and what is the distribution of the current that a system designer must be aware of? The traditional approaches based on effective media theory or Monte Carlo simulation are generally not very effective in describing such transport well. This short course will introduce percolation theory as a powerful technique to handle such stochastically random transport problems of electronic devices.

Lecture 1: Percolative Transport in Electronic Devices

Lecture 2: Basic Concepts: Thresholds, Islands, and Fractal Dimensions