By completing the PCPBT Lab in ABACUS - Assembly of Basic Applications for Coordinated Understanding of Semiconductors, you will be able to:
a) understand the concept of quantum-mechanical transmissions and reflections,
b) understand double-barrier structure and the concept of quasi-bound states, and
c) understand the formation of energy bands due to the interation between the wells in a multi-well structure.
The specific objectives of the PCPBT Lab are:
Recommended Reading
If you have not had experience with analysis of open quantum systems, the concepts of transmission and reflection coefficient (needed for the calculation of the current in a quantum-mechanical system), the concept of resonant or quasi-bound states and operation of resonant tunneling diode, and the formation of energy bands in multiple-well structures, here is a list of resources that will help you have the required knowledge to get the most of these issues resolved:
1. D. K. Ferry, Quantum Mechanics: An Introduction for Device Physicists and Electrical Engineers, Second Edition (Institute of Physics Publishing, 2001).
2. Dragica Vasileska, Stephen M. Goodnick and G. Klimeck: Computational Electronics: Semiclassical and Quantum Device Modeling and Simulation, Chapter 2 (CRC Press, 2010).
Demo
Crystal Viewer Tool: First-Time User Guide
Theoretical descriptions
* Piece-Wise Constant Potential Barrier Tool MATLAB Code
Tool Verification
Comparison of PCPBT Lab and Periodic Potential Lab
Worked Examples
1. Comparison of PCPBT Lab and Periodic Potential Lab
Exercises and Homework Assignments
1. Quantum-Mechanical Reflections: an Exercise
2. Double-Barrier Case: An Exercise
3. Quantum-Mechanical Reflections in Nanodevices: an Exercise
4. From 1 well to 2 wells to 5 wells to periodic potentials: an Exercise
5. Energy Bands as a Function of the Geometry of the n-Well Potential: an Exercise
6. Tunneling Through Triangular Barrier: an Exercise for PCPBT
7. Stationary Perturbation Theory: an Exercise for PCPBT
8. Cosine Bands: an Exercise for PCPBT
10. PCPBT: Problem Assignment for Asymmetric Barriers
Solutions to Exercises
Solutions to exercises will be provided to Instructors ONLY!
Take a Test
This test will assess your conceptual understanding of the physical, mathematical and computational knowledge related to transmission coefficients calculation, resonant tunneling and formation of bandstructure in crystals.
Solve the Challenge
In this final challenge you will integrate all what you have learned about tunneling through piece-wise constant potential barriers such as the double barrier structure in resonant tunneling diodes.
Analytical and Numerical Solution of the Double Barrier Problem