Application Oriented Computational Nanotechnology Part 1

Learning Objective:

Understanding fundamentals of ballistic quantum transport simulation

Mastery in implementation and validation of nanodevice simulation setups

Knowledge of nanodevice models and their applications spaces 

Description:

The application oriented computational nanotechnology course sequence aims to train students in how to apply state-of-the-art quantum transport simulation tools. The emphasis lies here on acquiring the understanding which of the commonly available electronic models is appropriate for which situation, how to interpret typically available simulation results and how to reliably distinguish numerical artifacts from physically meaning device features. This class sequence trains students by guiding them to implement their own quantum transport simulation tool and connect it to Purdue's quantum code library. This way the students get hands-on experience in how to validate quantum transport tools, how to interpret simulation results and how to run state-of-the-art professional simulation engines. Part 1 of the class sequence covers basic concepts such as how to utilize transmission and density of states to validate simulation setups, how to ensure reliable convergence and numerical efficiency for nanodevices with few or many resonant states (such as nanosheets and nanowire transistors, FinFETs, quantum dots and quantum sensors). Part 1 also covers how to expand systems in 2D and 3D and how to apply low rank approximations to ease the numerical burden of quantum transport. 

Topics Covered:

• Discretizing electronic operators and quantum transport equations in single band real space
• Validating transmission and spectral function against analytical results
• Resolving and understanding the spectral function and resonant states
• Density, current and other observables
• Inhomogeneous real space discretization
• Steps to higher dimensions and atomic resolution
• Overview of electronic bandstructure models
• Nonanalytical lead methods
• Mode space method-physics behind low-rank approximations
• Atomistic tight binding and recent DFTB models

 Prerequisites:

• Basic coding knowledge (ideally in Python)
• Basic quantum mechanics
• Basic understanding of differential equations
• Basic understanding of transport (e.g. electrical current in semiconductor devices)

Applied / Theory:

50/50

Web Address:

https://purdue.brightspace.com

Homework:

Homework assignments will require students to step-by-step code their own quantum transport simulator. The correctness of the code will be tested on the code's results. Subsequent homework assignments will build on provided solutions (in Python) for assignments of previous weeks. 

Exams:

There will be 3 online quizzes.

Textbooks:

S. Datta, Electronic Transport in Mesoscopic Systems, Cambridge University Press, 1995, Online ISBN: 9780511805776

W.H. Press et al., Numerical Recipes

Computer Requirements:

Access to scholar.rcac.purdue.edu will be provided during the semester as needed

Python with NumPy (e.g. anaconda) or equivalent language with linear algebra library