In this tutorial, we will see how to perform 3D calculations of strain and transport properties of an AlGaN nanocolumn heterostructure diode with a GaN quantum disk. Since the nitride materials present a wurtzite crystal structure, strain generated piezoelectric properties are found and taken in account in the calculation of current.
Here we  consider  only  classical  calculations;  for  a  quantum  treatment  of  this  kind  of  structure  you  can refer  to  Tutorial 12.

In order to execute correctly this example you should have the following files in the same working directory:
nanocolumn.tib : input file for TiberCAD
nanocolumn.msh : mesh file produced by the GMSH script nanocolumn.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 structure of the nanocolumn is described: the GaN quantum disk region , the AlGaN barriers and
two high doped AlGaN contact regions .
For example, here is the GaN well region:

Note that crystal structure is defined as wurtzite (structure = wz) and the crystal orientation is defined by the 3 vectors x-growth-direction, y-growth-direction and z-growth-direction.

When in the modeling script file nanocolumn.geo we have defined

we have created in the mesh a physical region with the name GaN_qdisc; we can refer to this GMSH physical region (which is a volume, in this 3D example), by writing Region GaN_qdisc
In the same way we can refer to the AlGaN volume regions, for example for the one defined with :

we write

in the TiberCAD region p_algan :

In this high doped contact region, note that the AlGaN alloy composition is defined by x = 0.2 . Energy level of the dopant is defined by doping_level = 0.17 (it determines incomplete dopant ionization at room temperature).

Simulation models

1. Strain

We want strain calculation, so we define a simulation (simulation_name = strain) belonging to the model macrostrain, to be associated to the whole device (physical_regions = all); a substrate type boundary condition is defined, related to the BC_Region   ncontact and to AlGaN material :

2. Drift-diffusion

As for drift-diffusion, as usual we define a simulation (simulation_name = dd) belonging to the model driftdiffusion and associated to the whole device (physical_regions = all).

• A srh recombination model is implemented and also one for radiative (direct) recombination, in this way:

Field dependent mobility model is chosen for both holes and electrons.

The BC Regions for drift-diffusion are the the two contact regions, defined by the two boundary surfaces BC_Region ncontact and BC_Region p_contact

In Physics section, note that for (all the simulations of the kind) driftdiffusion model , we choose the strained implementation :

Thus, with strain_simulation = strain, we specify that strain effects will be taken in account correctly in the calculation of current.
In particular, the piezoelectric polarization arising from strain in the wurtzite nitrides materials of this nanocolumn will enter in Poisson equation and heavily modify the band profiles.

• Note that if strain_simulation = strain is not defined, strain results, even if calculated, will NOT be used in drift-diffusion model.

Run simulations

Let's now run TiberCAD to calculate strain (strain simulation ) and driftdiffusion (sweep for dd simulation)

tibercad nanocolumn.tib

Output

TiberCAD supports 3 packages for 2D and 3D data visualization and post-processing:

Free:
1) GMV, http://www-xdiv.lanl.gov/XCM/gmv/GMVHome.html
output_format = gmv
2) Paraview, http://www.paraview.org/New/index.html
output_format = vtk

Commercial:
3) Tecplot-ise, http://www.amtec.com/
output_format = ise

After a successful execution, the following output files are present in the working directory:

• strain_elemental.plt : strain tensor and polarization vector components;

here are, for example, the in-plane components eps_11 and eps_22 of the strain tensor: they are are negative in GaN, since GaN is subjected to compressive strain.

These are the Polarization components Pz and Px: piezoelectric polarization arises in correspondance to the AlGaN/GaN interfaces, where the strain is large. Both pyro and piezo polarizations are included in the drift-diffusion calculations.

• dd_nodal_bias_biasvalue.plt: drift-diffusion nodal quantities for each sweep step, given by biasvalue

Here are the electron and hole density distribution for a bias Vd = 5V, which show a peak in the quantum disk region.

Since we have contacted the two extremes of the nanocolumn, we have calculated the diode IV characteristic.
By defining ContactCurrents output variable in plot, TiberCAD generates the output file sweep_dd_bias.dat, where dd is the name of the drift-diffusion simulation and bias is the variable used in the sweep calculation. In this file, the currents integrated on the two contacts are reported, for each value of the cathode voltage (bias).