# Quantum Well¶

This tutorial is based on the following nextnano³ tutorial

and on the following paper: [KubisNEGF2005]

The following input files were used:

• QW_InGaAs_ballistic.in (input file for nextnano.MSB code)

• QW_InGaAs_scattering.xml.in (input file for nextnano.MSB code)

• Materials_QW_InGaAs.xml.xml (material database for nextnano.MSB code)

• 1DNEGF_InGaAs_QW_ballistic_CBR.in (input file for nextnano³ code, CBR method)

• 1DNEGF_InGaAs_QW_ballistic.in (input file for nextnano³ code, NEGF method)

• 1DNEGF_InGaAs_QW_scattering.in (input file for nextnano³ code, NEGF method)

• 1DNEGF_InGaAs_QW_scattering_bias.in (input file for nextnano³ code, NEGF method)

This example input file demonstrates how to calculate the current across a quantum well. It compares the results of a ballistic calculation to the results of a calculation including scattering. Here, input files for both the nextnano.MSB software and for the nextnano³ software are provided so that the MSB algorithm can be benchmarked against the full NEGF algorithm as implemented by T. Kubis. We use the database file called Materials_QW_InGaAs.xml where we adjusted the default material parameters so that they match the publication of [KubisNEGF2005].

Our structure consists of a 12 nm In0.14Ga0.86As QW in the center surrounded on each side by GaAs barriers (of width 19 nm each).

GaAs | InGaAs | GaAs

where the barrier material is indicated in bold.

Further comments regarding the MSB input file

• We used 1000 energy grid points. In contrast, the NEGF simulation used much less.

• In the database we have adjusted the material parameters, e.g. for InGaAs we used the effective mass of GaAs, the static and optical dielectric constant of GaAs and the GaAs LO phonon energy for simplicity. We use a conduction band offset of 0.150 eV.