Education

Teaching quantum mechanics!

Education

Schroedinger equation

The nextnano software can be used to study basic Quantum Mechanics text book examples. It can thus be used for teaching in classes.


Examples

  • Black body spectrum
  • 1D, 2D and 3D Schrödinger equation for arbitrary potential energy profiles
  • Infinite quantum well
  • Finite quantum well
  • Quantum harmonic oscillator
  • Triangular quantum well
  • Double quantum well
  • Matrix elements and selection rules
  • Expectation value
  • Perturbation theory
  • Tunneling: Transmission function of potential step, potential barrier, quantum well and double barrier
  • Periodic structures: Superlattice
  • Energy bands
  • Band structure (Tight-binding)
  • ... more examples will be added soon.

Handout

A preliminary handout containing some nextnano examples is available. (Version 2016-05-11)


Tight-binding (sp3s*)

Tight-binding band structure

Empirical tight-binding (sp3s*) band structure of GaAs, GaP, AlAs, InAs, C (diamond) and Si

What you can learn:
  • tight-binding band structure of bulk semiconductors

Dispersion in infinite superlattices: Minibands (Kronig-Penney model)

Minibands

Dispersion in infinite superlattices: Minibands (Kronig-Penney model)

What you can learn:
  • Schrödinger equation in 1D with periodic boundary conditions
  • superlattice dispersion
  • band structure of an artificial crystal (quantum well crystal)

Triangular quantum well

Triangular well

Triangular well

What you can learn:
  • Energy levels and wave functions of a triangular quantum well
  • Schrödinger equation

Double quantum well

Double quantum well

Double quantum well

What you can learn:
  • Energy levels and wave functions of a double quantum well as a function of quantum well separation (barrier width)
  • Schrödinger equation
  • Template feature of nextnanomat

Schottky barrier

Schottky barrier

Schottky Barrier

What you can learn:
  • Metal-semiconductor interface: Fermi-level pinning; Ohmic contact vs. Schottky contact vs. Surface charge density vs. Surface doping
  • Poisson equation

pn junction

pn junction

Example 1: GaAs pn junction (forward bias)

What you can learn:
  • doping
  • Poisson equation
  • apply a bias, drift-diffusion calculation, recombination
  • Current-Poisson equation

Quantum well (Interband transitions)

Quantum well

Optical interband transitions in a quantum well - Matrix elements and selection rules

What you can learn:
  • Energy levels and wave functions of an infinite and finite quantum well, interband transition matrix elements (spatial wave function overlap), selection rules
  • Schrödinger equation

Spherical Si Quantum Dot (Artificial Atom)

Spherical Si Quantum Dot (Artificial Atom)

Hole energy levels of an "artificial atom" - Spherical Si Quantum Dot (6-band k.p)

What you can learn:
  • 3D simulation, quantum dot, spin-orbit splitting, artificial atom
  • 6-band k.p Schrödinger equation in 3D