ABACUS - Assembly of Basic Applications for Coordinated Understanding of Semiconductors
Band Models / Band Structure
Piecewise Constant Potential Barriers Lab in ABACUS
This tool computes the transmission and the reflection coefficient of a five, seven, nine, eleven and 2n-segment piecewise constant potential energy profile. It enables the rapid visualization of the formation of band structures in a finite superlattice.
First time use of the tool is supported by: Piece-Wise Constant Potential Barriers Tool: First-Time User Guide
The materials below provide a detailed description of the physics required both to use this tool correctly and to interpret the results obtained:
Exercises that illustrate the importance of quantum-mechanical reflections in state-of-the-art devices and the resonance width dependence upon the geometry in the double-barrier structure that is integral part of resonant tunneling diodes are given below:
- Quantum-Mechanical Reflections
- Quantum-Mechanical Reflections in Nanodevices
- Double-Barrier Structure
The following assignments help to illustrate the formation of bands in periodic potentials and how the width and number of the energy bands changes by varying the geometry of the n-well potential:
- From one well, to two wells, to five wells, to periodic potentials
- Bands as a function of the geometry of the n-well potential
One can also use this tool to calculate the transmission coefficient through barriers that are approximated with Piece-Wise constant segments.
Piece-Wise Constant Potential Barriers Tool Learning Materials – Comprehensive set of learning materials for the Piece-Wise Constant Potential Barriers Tool.
Periodic Potential Lab
The Periodic Potential Lab in ABACUS solves the time independent Schrödinger Equation in a one-dimentional spatial potential variation. Rectangular, triangular, parabolic (harmonic), and Coulomb potential confinements can be considered. The user can determine energetic and spatial details of the potential profiles, compute the allowed and forbidden bands, plot the bands in a compact and an expanded zone, and compare the results against a simple effective-mass parabolic band. Transmission is also calculated through the well for the given energy range.
Exercises:
Periodic Potential Lab Learning Materials – Comprehensive set of learning materials for the Periodic Potential Lab.
Band Structure Lab in ABACUS
The Band Structure Lab in ABACUS enables the study of bulk dispersion relationships of silicon, gallium arsenide, and indium arsenide. The users can apply tensile and compressive strain and observe the variation in the band structure, bandgaps, and effective masses. Advanced users can study band structure effects in ultra-scaled (thin body) quantum wells, and nanowires of different cross sections. Band Structure Lab uses the sp3s*d5 tight-binding method to compute E(k) for bulk, planar, and nanowire semiconductors.
Exercises:
- Bulk Band Structure: a Simulation Exercise
- Computational Electronics HW - Simplified Band Structure Model
- Exercise: Density of States Function Calculation
- Can we define unique effective masses in Si nanowires?
Band Structure Lab Learning Materials – Comprehensive set of learning materials for the Band Structure Lab.
There is a dedicated group page for Faculty Only, where further assignments and solutions are shared. Access to that group is granted on an individual basis.