Multiple quantum wells and finite superlattices#

Last update: 2026-05-19

Files for the tutorial located in nextnano++\examples

Contents

Introduction#

This tutorial simulates a real layered structure with a finite number of quantum wells. The transition between a finite superlattice and a multiple quantum well system is also observed. This tutorial aims to reproduce the figures in Paul Harrison’s book “Quantum Wells, Wires and Dots” (Section 3.10, “Multiple Quantum Wells and Finite Superlattices”)

Structure#

The structure consists of N repeats of 4 nm GaAs wells and 4 nm Ga0.8Al0.2As quantum wells. This superlattice structure is sandwiched between 20 nm Ga0.8Al0.2As barriers.

We first define key variables, such as the well width, the right and left wall width, and the number of wells.

Following this, we are able to generate the structure of the GaAs/Ga0.8Al0.2As superlattice under structure{ }. The keywords array_x{} duplicate the structure in the x-direction to give us the number of wells required.

Ground state energies#

After generating the input file, we are able to run the simulation for a variable number of quantum wells using the variable sweep functionality in nextnanomat. One can go to “Template” on the tabs at the top, under “Sweep”, select the variable of interest and the range or list of values to iterate over. Click on “Create input file” at the bottom and run the simulations in the “Simulation” tab.

The reference potential energy used in Harrison’s book and nextnano++ is different. Thus, post-processing was done in Python to match the reference energy levels.

../_images/tutorials_1D_Superlattice_N_Wells-EnergyVsN.png

Figure 508 Ground state energies plotted as a function of N. Convergence at higher number of wells is observed.#

Wave function in a superlattice#

The wave functions can also be plotted. The first example in Harrison’s book has the following parameters:

  • 10 wells

  • 4 nm Ga0.8Al0.2As barrier

  • 4 nm Ga0.8Al0.2As quantum well width

  • 20 nm left and right Ga0.8Al0.2As walls

../_images/tutorials_1D_Superlattice_N_Wells-wf1.png

Figure 509 The wave function for a superlattice system#

This figure is in agreement with Harrison’s result. It is observed that the system functions as a superlattice as the wave function in each well overlaps with the wave function of the adjacent wells.

Wave function in a multiple quantum well system#

Harrison’s final figure uses the following parameters:

  • 4 wells

  • 10 nm Ga0.6Al0.4As barriers

  • 10 nm Ga0.6Al0.4As quantum wells

  • 10 nm Ga0.6Al0.4As left and right walls

../_images/tutorials_1D_Superlattice_N_Wells-wf2.png

Figure 510 The wave function for a multiple quantum well system#

This figure is also in good agreement with Harrison’s results. It is observed from the figure that this system functions as a multiple quantum well because the wave function reaches zero between the wells.