In the following tutorial we demonstrate how can you simulate an ellipsoidal Quantum Wire in 2D. The material if the Quantum Wire is InAs, the surrounding material is GaAs. The growth direction points to the $001$ direction

#### Geometry

The geometry can be seen on the following Figure 1. The parameters of the ellipsoid are $a=10nm$, $b=5nm$, and the rectangle's edge lengths are $40nm$.

#### Physics Definitions

In order to simulate the Envelope functions with valid potential we need to Simulate with the Semiconductor Carrier Occupation interface. It has various sub items corresponding to the parameters of the simulations:

• Heat Flow Isotropic A Dirichlet boundary condition was applied to one boundary at $T = 100K$, which results a homogeneous 100IK temperature.
• Charge-distribution We are using the calculated mass from the band structure calculation, and not what is defined in the material parameters. Also for lower temperatures we are using Fermi distribution.
• Doping The simulation has no doping defined.
• Bandstructure Calculation We are calculating at $\Gamma$ point with strain included.
• ZincBlende Stress Calculation The strain is calculated with on side of the rectangle fixed, in order to make a Dirichlet boundary condition. The lattice mismatch deforms the crystal.
• Electrostatics Isotropic One boundary needs to be defined as Dirichlet condition. This potential on this boundary is being altered in order to find the Charge neutral potential distribution.
• Quantum mechanics The mass is used from the band structure calculation module. Every boundary is a Neumann condition.

#### Mesh

A simple triangular mesh was created which can be seen on Figure 2.

### Results

#### Envelope Functions

• physicswiki/semiconductors/qdot2d.txt