## Physics of Nanoscale MOSFETs

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#### Abstract

Transistor scaling has pushed channel lengths to the nanometer regime where traditional approaches to MOSFET device physics are less and less suitable This short course describes a way of understanding MOSFETs that is much more suitable than traditional approaches when the channel lengths are of nanoscale dimensions. lecture 1 reviews traditional MOSFET theory, and Lecture 2 presents the new approach in its simplest form. Lectures 3A and 3B describe the mathematical treatment of ballistic MOSFETs and Lecture 4 discusses at a simple level the physics of scattering in quasi-ballistic MOSFETs. Lecture 5 illustrates how this approach us used to analyze and interpret experimental data. Lectures 1-5 are based on a semi-classical treatment; in Lecture 6, an introduction to the quantum transport in nano-MOSFETs is provided. Finally, Lecture 7 connects this sort course to the "bottom up" approach of Supriyo Datta.

#### Bio

Mark Lundstrom directs the National Science Foundations Network for Computational Nanotechnology (NCN) and is the Don and Carol Scifres Distinguished Professor of Electrical and Computer Engineering at Purdue University. He earned his bachelor's and master's degrees from the University of Minnesota in 1973 and 1974, respectively and joined the Purdue faculty upon completing his doctorate on the West Lafayette campus in 1980. Before attending Purdue, he worked at Hewlett-Packard Corporation on MOS process development and manufacturing. At Purdue, he has worked on solar cells, heterostructure devices, carrier transport physics, and his current research interests focus on the physics and technology of nanoscale transistors. He is the author of two books, Fundamentals of Carrier Transport (2nd Ed., Cambridge, 2000) and Nanoscale Transistors: Device Physics, Modeling, and Simulation (Springer, 2005). Lundstrom is a fellow of the Institute of Electrical and Electronic Engineers (IEEE), the American Physical Society, and the Association for the Advancement of Science. He is the recipient of several awards for his teaching and research, most recently Semiconductor Industry Association's 2005 University Researcher Award for his career contributions to the semiconductor industry and the 2006 Education Award from the IEEE Electron Devices Society.

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Lecture Number/Topic | Online Lecture | Video | Lecture Notes | Supplemental Material | Suggested Exercises |
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Introduction: Physics of Nanoscale MOSFETs | View Flash | View | Notes (pdf?1624958d7550cf89a321f2eed8ac6db6=1) | ||

Lecture 1: Review of MOSFET Fundamentals | View Flash | View | Notes (pdf?1624958d7550cf89a321f2eed8ac6db6=1) | Exercises | |

A quick review of the traditional theory of the MOSFET along with a review of key device performance metrics. A short discussion of the limits of the traditional (drift-diffusion) approach and... |
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Lecture 2: Elementary Theory of the Nanoscale MOSFET | View Flash | View | Notes (pdf?1624958d7550cf89a321f2eed8ac6db6=1) | Exercises | |

A very simple (actually overly simple) treatment of the nanoscale MOSFET. This lecture conveys the essence of the approach using only simple mathematics. It sets the stage for the subsequent... |
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Lecture 3A: The Ballistic MOSFET | View Flash | View | Notes (pdf?1624958d7550cf89a321f2eed8ac6db6=1) | Exercises | |

The IV characteristic of the ballistic MOSFET is formally derived. When Boltzmann statistics are assumed, the model developed here reduces to the one presented in Lecture 2. There is no new... |
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Lecture 3B: The Ballistic MOSFET | View Flash | View | Notes (pdf?1624958d7550cf89a321f2eed8ac6db6=1) | Exercises | |

This lecture is a continuation of part 3A. After discussion some bandstructure considerations, it describes how 2D and subthreshold electrostatics are included in the ballistic model. |
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Lecture 4: Scattering in Nanoscale MOSFETs | View Flash | View | Notes (pdf?1624958d7550cf89a321f2eed8ac6db6=1) | Exercises | |

No MOSFET is ever fully ballistic - there is always some carrier scattering. Scattering makes the problem complicated and requires detailed numerical simulations to treat properly. My objective... |
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Lecture 5: Application to State-of-the-Art FETs | View Flash | View | Notes (pdf?1624958d7550cf89a321f2eed8ac6db6=1) | Exercises | |

The previous lessons may seem a bit abstract and mathematical. To see how this all works, we examine measured data and show how the theory presented in the previous lessons help us understand the... |
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Lecture 6: Quantum Transport in Nanoscale FETs | View Flash | View | Notes (pdf?1624958d7550cf89a321f2eed8ac6db6=1) | ||

The previous lessons developed an analytical (or almost analytical) theory of the nanoscale FET, but to properly treat all the details, rigorous computer simulations are necessary. This lecture... |
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Lecture 7: Connection to the Bottom Up Approach | View Flash | View | Notes (pdf?1624958d7550cf89a321f2eed8ac6db6=1) | ||

While the previous lectures have been in the spirit of the bottom up approach, they did not follow the generic device model of Datta. In this lecture, the ballistic MOSFET theory will be formally... |
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Notes on Fermi-Dirac Integrals (3rd Edition) | notes_on_FD_integral3rdEd_revised_080411.pdf fd_integral_matlab.zip |
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Fermi-Dirac integrals appear frequently in semiconductor problems, so an understanding of their properties is essential. The purpose of these notes is to collect in one place, some basic... |