DOCUMENTATION
ATOMISTIC SIMULATION OF A RANDOM ALLOY InGaN/GaN QW 
TUTORIALS 
This example performs the simulation of a InGan/GaN Quantum Well (QW) structure by employing the new Empirical Tight Binding (ETB) Module on a relaxed atomic structure. 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 elasticity calculations to obtain the strain tensor in the heterostructure and to apply a strain deformation to the defined atomistic structure. We then perform the driftdiffusion model to get the equilibrium solution for potentials and band profiles. Quantum ETB calculations are finally performed on the VFFrelaxed structure, to get the electron and hole states in the QW.
The device structure is defined in the geometry .geo file and is the following:
In order to execute correctly this example you should have the following files in the same working directory: DEVICE STRUCTUREIn the following, some features of the input file will be described. For further details you can refer to the program reference manual. ygrowthdirection = (1,0,1,0) The regions are defined in the usual way: Region QW { material = InGaN 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 STRUCTUREAn atomistic representation of the above defined Quantum cluster is generated by means of the Atomistic block Atomistic tb { reference_region = barrier_left 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 GaN, the material composing the barrier_left region. reference_region = barrier_left
By default a 2D periodicity is applied in yzplane orthogonal to the x growth direction of this 1D QW structure. In this case, however, we define a custom supercell, with a 20x20 A size. supercell_size_y = 20 Therefore, the appropriate periodicity vectors will be applied to this defined supercell, not to the default minimal cell. random_alloy = true where the atoms of the components species are randomly distributed in the alloy region and their parameters are not averaged. 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. ElasticityNote that it is always highly advisable to solve first elasticity, before a VFF relaxation. This will provide a reasonable first guess for the VFF solver and also will apply the correct deformation to the mesh, assuring that all the atoms are still associated to the correct FEM elements. We solve elasticity for the latticemismatch induced strain Module elasticity { name = strain
Note that, in order to apply a strain deformation to the defined atomistic structure, it is convenient to define a mesh deformation with the default number of shape_iterations. mesh_deformation = true
strain_atomistic_structure = tb 2. VFFNow, based on the displacements obtained from the elasticity solution and projected onto the atomistic structure, we proceed to its relaxation with a valence force field (VFF) approach. We thus solve VFF on the atomic structure Module vff { atomistic_structure = tb with the b.c. boundary_conditions = all_around that is, all the outer atoms are fixed. Each atom which is not bonded to 4 atoms which belong to the same structure, or each atom bonded to a passivation hydrogen, is considered an outer atom. 3. DriftdiffusionAs for driftdiffusion, 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
4. Empirical TightBindingFor the quantum calculations, we define an empirical_tb simulation, named tb: Module empirical_tb { regions = Quantum
regions = Quantum
atomistic_structure = tb
potential_simulation = driftdiffusion
num_valence_eigenvalues = 4
Harrison_scaling = true In this way, the effect of strain relaxation in the heterostructure will be correctly talken into account in ETB calculations. RUN SIMULATIONSWe may now run tiberCAD to calculate and apply strain deformation first with a macroscopic elasticity model (strain) and then with a valence force field one (vff), we solve then driftdiffusion (dd) for an equilibrium solution and ETB for calculation of eigenvalues of holes and electrons (tb) solve = (strain ,vff, driftdiffusion, tb)
OUTPUTAfter the execution, the output directory contains, as usual, the results for the simulations performed. By using jmol, (an opensource Java viewer for chemical structures in 3D, see http://jmol.sourceforge.net) we can load the atomic structure generated by tiberCAD Atomistic Generator, contained in the file tb.xyz. It is made by a GaN/InGaN/GaN heterostucture grown along the xaxis direction. Note that a supercell with 20 Angstrom size in yz plane has been created. The supercell structure is then periodical in the yz plane. The InGaN QW has been bult with a random alloy approach and In atom are shown in red. View of the quantum well structure along x direction, together with the left and right GaN barrier regions. As for tightbinding simulation, the file tb.dat contains a table with the calculated eigenvalues for electrons and holes, together with their occupation index. The files .cube have been also generated, which contain the information on the electron and hole wavefunction (square module). The format of these data files is supported by the visualization software jmol. Thus we can visualize the isosurface of e.g. the electron ground state, with this command: Analogously, we can visualize the hole state. The figure above shows the confinement of the two states in the InGaN quantum well: in green the conduction state and in yellow the valence state. Note the spatial separation of the two states, induced by the strong polarization field occurring in this InGaN QW. View of the QW yz plane, which shows the random alloy configuration of InGaN structure (In atoms in red, Ga in grey and N in blue) We can now visualize the isosurface of the electron ground state on the previous view of the QW yz plane, to show the effect of particle localization due to the random alloy configuration: electron wavefunction is mostly localized close to In atoms. ATTACHMENTS
