This example performs the simulation of a InAs/GaAs Quantum Well (QW) structure by employing the new Empirical Tight Binding (ETB) Module

After defining an atomistic structure corresponding to the quantum cluster where we want to apply ETB calculations, we begin with continuous simulations on the whole device structure.

We first perform the drift-diffusion model to get the equilibrium solution for potentials and band profiles. Then quantum ETB calculations are performed to get the electron and hole states in the QW.

The device structure is defined in the geometry .geo file and is the following:
5 nm InAs QW
20 nm GaAs barriers
50 nm undoped GaAs buffer
(Note that in .geo file units are in Angstrom (A) )

In order to execute correctly this example you should have the following files in the same working directory:
InAs_qw.tib: input file for TiberCAD
InAs_qw.msh: mesh file produced by the GMSH script InAs_qw.geo

DEVICE STRUCTURE

In the following, some features of the input file will be described. For further details you can refer to the program reference manual.
In the Device section, the QW heterostructure is described: the InAs quantum well region, the GaAs barriers and the two GaAs buffer regions.
The crystal directions are defined as the default for zincblend (cubic):

x-growth-direction = (0, 0, 1)

y-growth-direction = (0, 1, 0)

z-growth-direction = (1, 0, 0)

The regions are defined in the usual way:

Region QW

{

 material = InAs

}

 
Region barrier_left
 
{
 
material = GaAs
 
}

 
Region barrier_right
 
{
 
material = GaAs
 
}

A cluster named Quantum is declared, to which the QW region and the two lateral barriers belong

Cluster Quantum

 {

 regions = (barrier_left, barrier_right, QW)
 
 }

ATOMISTIC STRUCTURE

An atomistic representation of the above defined Quantum cluster is generated by means of the Atomistic block

Atomistic tb
{
reference_region = barrier_left
regions = Quantum
passivation = yes
print = (xyb, xyz, gen, tgn)
}

The reference region is chosen to provide the lattice parameters with which the crystalline structure is built. In this case the lattice is that of GaAs, the material composing the barrier_left region.

reference_region = barrier_left

In the QW region, the InAs atoms are then substituted in the lattice basis.

By default 2D periodicity is applied in yz-plane orthogonal to the x growth direction of this 1D QW structure.
Passivation is finally performed at the ends of the heterostructure

passivation = yes

A print instruction gives in output the atomic structure for a visualization.

SIMULATION MODULES

1. Drift-diffusion

As for drift-diffusion, as usual we define a simulation

name = driftdiffusion

belonging to the model driftdiffusion and associated to the whole device (deafult choice)

We select a poisson calculation for an equilibrium solution:

coupling = poisson

The Boundary Regions for drift-diffusion are the two contact regions, defined by the two boundary surfaces anode and cathode

2. Quantum EFA

For the quantum calculations, we define an efaschroedinger simulation for kp 8x8 calculations:

Module efaschroedinger
{
name = kp
regions = (barrier_left, barrier_right, QW)
poisson_model_name = driftdiffusion
number_of_eigenstates = 4 
plot = (EigenFunctions, EigenEnergy)
Physics
{
   model = 8x8
}
}

The physical model is 8x8 for a k.p 4 bands calculations of electrons and holes

3. Empirical Tight-Binding

For the quantum calculations, we define a empirical_tb simulation, named tb:

Module empirical_tb
{
regions = Quantum
name = tb
atomistic_structure = tb
Harrison_scaling = false
potential_simulation = driftdiffusion 
plot = (tbstates)
Solver
{
guess_valence = -0.5
guess_conduction = 0.0
num_valence_eigenvalues = 4
num_conduction_eigenvalues = 4
}
}

In the Module empirical_tb we define the associated regions, given by

regions = Quantum

ETB Hamiltonian will be created and solved based on the atomistic structure named tb which has been previously built in the Atomistic section

atomistic_structure = tb

Information about potential profile to be applied (due to built-in, polarization fields, etc.) is given by

potential_simulation = driftdiffusion

In the Solver block, we define the number of eigenstates to be calculated in valence and conduction band:

num_valence_eigenvalues = 4
num_conduction_eigenvalues = 4

and we also may define a guess value for the eigensolver

guess_valence = -0.5
guess_conduction = 0.0

these keywords are optionals.
By default, reasonable guesses are generated internally to help the solver to get convergence. Usually these values are good enough to get a steady covergence of solutions. However, in this particular case of small energy gap material (InAs), it may be necessary to set manually a guess close to the expected value of the eigenstate.

In this way, we avoid erroneous states due to the folding of the Hamiltonian. The reference of the guess is the valence top band edge at 0.0 eV.

Run simulations

We may now run tiberCAD to calculate driftdiffusion ( dd simulation) for an equilibrium solution and ETB for calculation of eigenvalues of holes and electrons (tb)

solve = (driftdiffusion, tb)

tibercad InAs_qw.tib

ATTACHMENTS

• InAs_qw.geo
  
• InAs_qw.msh
  
• InAs_qw.tib