## Nanoelectronic Modeling: From Quantum Mechanics and Atoms to Realistic Devices

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#### Abstract

The goal of this series of lectures is to explain the critical concepts in the understanding of the state-of-the-art modeling of nanoelectronic devices such as resonant tunneling diodes, quantum wells, quantum dots, nanowires, and ultra-scaled transistors. Three fundamental concepts critical to the understanding of nanoelectronic devices will be explored: 1) open systems vs. closed systems, 2) non-equilibrium systems vs. close-to-equilibrium systems, and 3) atomistic material representation vs. continuum matter representation.

Device engineers are interested in the management of information through electronic device state representations. Transistors regulate the voltage and current states in electrical circuits and the current flow in these transistors needs to be designed and understood well. Current flow implies that the electronic systems have a finite extent and they are open with finite contact regions which inject and extract carriers. The systems are open. However most quantum mechanical calculations are performed for closed systems. Students need to understand the critical difference betweeen open and closed systems.

Current flow under finite biases implies that the central device region is out-of-equilibrium and cannot be treated with traditional quasi-equilibrium or even equilibrium methods at the nanometer scale. Relaxation or carriers is critical in contact regions and students need to understand the critical difference between equilibrium and non-equilibrium systems.

At the nanometer scale the concepts of device and material meet and a new device is a new material and vice versa. While atomistic device representations are novel to device physicists, the semiconductor materials modeling community usually treats infinitely periodic structures. The importance of the appropriate basis set representation which needs to be selected to cover the important physics of semiconductor devices will become evident.

The lectures do not focus on the underlying theories, but focus on the application of the theories using the nanoelectronic modeling tools NEMO 1- D, NEMO 3-D, and OMEN to realistically extended devices. Basic device operations and advanced simulations will be explored through interactive online simulations on nanoHUB.org using the tools 1) Piece-wise Constant Potential Barrier Tool (pcpbt), 2) Periodic Potential Lab, and 3) Resonant Tunneling Diode Lab with NEGF (RTDnegf).

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#### Location

Università di Pisa, Pisa, Italy