Gerhard Klimeck's course, in 59 executable notebooks
Nanoelectronic modeling,
from atoms to devices
Every lecture of Nanoelectronic Modeling — From Atoms to Devices (Purdue University, on nanoHUB), turned into a calculation you can read, play with and run. Where a lecture draws a transmission curve, the notebook computes it with open-nemo and checks it against the analytic formula; here you can also move the barriers yourself.
Read
The lecture's argument, its slides and the equations, with the numbers open-nemo computed for each claim.
Explore
Interactive figures recompute the physics in your browser as you move a slider: barrier heights, bias, strain, composition.
Run
Download the notebook and follow its local setup instructions to run the full open-nemo calculation behind every figure.
Course contents
Introduction
Why nanoelectronics is worth modelling, and what a model has to get right: the numbers behind the scaling of the transistor, a channel small enough that its atoms can be counted, the band structure a device engineer needs, a pn junction solved with drift-diffusion, the three small apps that stand in for the nanoHUB tools, and the open problems NEMO was written for.
- 1.1Why are nanoelectronic devices interesting?
- 1.2Basic device operation — raising 1,000 questions
- 1.3Band structure in nanoelectronics — a basic view
- 1.4Use of simulation to explain concepts — PN junction to device scaling
- 1.5nanoHUB access and tool demo
- 2Challenges at the frontier of quantum transport modeling (NEMO and nanoHUB)
Materials and quantum mechanics
The materials the rest of the course uses and the mechanics it needs: how many electrons a crystal holds and how few of them carry current, bonds and bond angles, the classical picture of particles and waves, the experiments that broke it, and the first analytic solutions for free and bound electrons.
- 606·2.1Typical semiconducting materials
- 606·2.2Applications of elemental and compound semiconductors
- 606·2.3Atomic positions and bond orientations
- 606·4.1Classical systems: particles, propagating waves and standing waves
- 606·4.2Strange experimental results: the advent of quantum mechanics
- 606·4.3Why do we need quantum mechanics?
- 5Analytical solutions for free and bound electrons
Tunneling and band structure
Tunneling as a scattering problem and bands as its periodic limit: transfer matrices and where they lose precision, one barrier, two barriers and a resonance, N barriers turning into a band, the Kronig-Penney model solved graphically and numerically, and the group velocity, effective mass and holes that follow from a band.
- 606·6.1Electron tunneling — the transfer matrix method
- 606·6.2Electron tunneling — tunneling through a single barrier
- 606·6.3Electron tunneling — tunneling through a double barrier
- 606·6.4Electron tunneling — N barriers and the formation of bands
- 606·6.5Analytical and numerical solution strategies
- 606·7.1Band structure in a periodic potential — problem formulation
- 606·7.2Band structure in a periodic potential — solutions
- 606·7.3Band properties: wave packets, effective mass, electrons and holes
Nanoscale electronic states
What confinement does to the states themselves: a well between barriers, bonding and antibonding pairs as two wells approach, and the particle in a box rebuilt as fifteen coupled wells whose sixty states carry the envelope of a band.
Introduction to transport
Current through a small device, built up one assumption at a time: scattering against non-equilibrium, a rate equation, coherent tunneling and Landauer, where the voltage actually drops, the transverse modes that turn a 1-D calculation into a 3-D current, and the Tsu-Esaki formula that collects them.
- 10.1Introduction to transport — scattering experiments versus non-equilibrium transport
- 10.2Introduction to transport — a simple rate-equation model of sequential tunneling
- 10.3Introduction to transport — coherent tunneling in a double barrier and the Landauer picture
- 10.4Introduction to transport — sequential versus coherent tunneling
- 10.5Introduction to transport — free charge interacting with the electrostatic potential: an NIN diode
- 10.6Introduction to transport — where is the voltage drop?
- 10.7Introduction to transport — from 1D to 3D: transverse degrees of freedom
- 10.8Introduction to transport — the Tsu–Esaki formula
Resonant tunneling diodes
The RTD from its simplest model to the one that matches experiment: a linear potential drop, realistic doping, relaxation in the reservoirs, Hartree self-consistency, asymmetry and charge accumulation, the recursive Green function that makes it affordable, and the incoherent scattering that fills the valley.
- 11.1Introduction to resonant tunneling diodes — RTDs with linear potential drops
- 11.2RTDs with realistic doping profiles
- 11.3Resonant tunneling diodes with relaxation in the reservoirs
- 11.4RTDs with quantum charge self-consistency (Hartree model)
- 11.5Asymmetric RTDs with charge accumulation and depletion
- 12The recursive Green function algorithm (RGF)
- 13Incoherent scattering concepts and impact in RTDs
Quantum dots and NEMO 3-D
Self-assembled quantum dots and the code written for them: multi-scale design, strain from balls and springs, the sp3d5s* basis, Lanczos for the eigenvalues that matter, the parallelism that makes million-atom dots possible, and the validation that decides whether it works.
- 20Introduction to quantum dots
- 21.1NEMO 3-D — multi-scale by design
- 21.2NEMO 3-D — strain: balls and springs
- 21.3NEMO 3-D — atomistic basis: nearest-neighbour sp3d5s* tight binding
- 21.4NEMO 3-D — eigenvalues: Lanczos
- 21.5NEMO 3-D — scaling to large problems: parallel computing
- 21.6NEMO 3-D — validation: does it work?
Optical matrix elements
What couples a state to light: the dipole matrix element computed from the states themselves, the selection rules that make transitions allowed or forbidden, and the analytic expression the numbers are checked against.
Stress and strain
The continuum theory the atomistic strain models answer to: deformation as strain, internal forces as stress, elastic constants as the response that links them, a thin layer forced onto a substrate, alloys with more than one bond length, and the band edges strain moves.
- 23.1Theory of stress and strain — introduction
- 23.2Theory of stress and strain — deformation: strain
- 23.3Theory of stress and strain — internal forces: stress
- 23.4Theory of stress and strain — material response: elastic constants
- 23.5Theory of stress and strain — a thin layer on a substrate
- 23.6Theory of stress and strain — alloys
- 23.7Theory of stress and strain — from strain to band edges
Long-range strain
How far strain reaches around a buried quantum dot, and what that costs: expanding the strain domain until the answer stops moving, shrinking the electronic domain until it starts to, and the boundary conditions and dot configurations the result depends on.
Source and credit
The slide images are details from Gerhard Klimeck's lecture decks, Copyright © Gerhard Klimeck, Purdue University / Network for Computational Nanotechnology, used with permission. Each is captioned with its slide number, and each page links the lecture's nanoHUB page, video and slides.
Gerhard Klimeck (2026), Nanoelectronic Modeling — From Atoms to Devices, https://nanohub.org/resources/45001.