DOCUMENTATION
TIGHTBINDING SIMULATION OF A GaN QUANTUM DOT 
TUTORIALS 
In this Tutorial we will see how to perform the simulation of a GaN/AlN Quantum Dot (QD) structure by employing the Empirical Tight Binding (ETB) Module.
We first define an atomistic structure corresponding to the quantum cluster where we want to apply ETB calculations, than we apply continuous simulations on the whole device structure, in order to calculate strain map and equilibrium solution for potentials in device.
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: In the following, some features of the input file will be described. For further details you can refer to the program reference manual. DEVICE STRUCTURE
In the Device section, the QD heterostructure is described: the GaN quantum dot region (ball), the AlN qbox, an intrinsic buffer AlN region and two n and pdoped AlN regions. xgrowthdirection = (1,2,1,0) The regions are defined in the usual way: Region ball A Cluster named atomistic is declared, including the ball QD region and the qbox AlN barrier region Cluster atomistic ATOMISTIC STRUCTUREAn atomistic representation of the above defined atomistic cluster is generated by means of the Atomistic block Atomistic tb1
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 AlN, the material composing the nside region. reference_region = nside
In the QD region, the GaN atoms are then substituted in the lattice basis. Finally, passivation is performed at the boundaries of the heterostructure passivation = yes A print instruction gives in output the atomic structure for a visualization. SIMULATION MODULES1. Elasticity
Elasticity is used here to calculate lattice mismatch induced strain tensor in the whole structure. Moreover, in this case a nonlinear calculation is performed, to feed back obtained displacements to the mesh elements. The mesh is thus deformed and a new strain calculation is performed with the new mesh. mesh_deformation = true
the strain is computed iteratively until the convergence on the structure deformation is reached. 2. DriftdiffusionAs for driftdiffusion, as usual we define a simulation name = dd
belonging to the model driftdiffusion and associated to the whole device (default choice). polarization (piezo, pyro) {} The Boundary Regions for driftdiffusion are the two contact regions, defined by the two boundary surfaces anode and cathode. 3. Empirical TightBindingFor the atomistic quantum calculations, we define two empirical_tb simulations, named tb1 and tb2. In the first we will calculate the ground states, in the second one these calculate states will be loaded from output file, to complete the calculation of tb states. Module empirical_tb In both cases the associated region is the Cluster atomistic and the associated potential simulation is the driftdiffusion dd simulation. Note that with this link the potential profile including builtin and polarization fields are correctly included into the TB Hamiltonian, through a correction on the onsite elements.
Another critical point is that Harrison scaling of ETB parameters is here applied In tb1, only one state is calculated for holes and electrons: num_valence_eigenvalues = 1 In tb2: Module empirical_tb calculated states are loaded from output file by defining in the Solver block: load_path = output_tb1 and the calculation of 4 states is completed, starting from those alreay available. num_valence_eigenvalues = 4 # 2 This option may be useful to continue a long calculation of many eigenstates after that it has been stopped by the user for any reason. 4. TB OpticsWith the Module opticstb it is possible to perform the calculation of the optical matrix from the TB Hamiltonian. Module opticstb Note that, differently from the analogous Optics Module for EFA, here the initial state and the final state source models must be the same. In this case, we choose tb2 simulation, which compute four eigenstates. compute_strengths = true to calculate optical strength output. Run simulations
We may now run tiberCAD to calculate strain with Elasticity (str) and driftdiffusion (dd) for an equilibrium solution. solve = (str, dd, tb1) then we run tb2 with load_states = true to load existing ground state solution and calculate further states and then finally the optical properties (opt) solve = (str, dd, tb2, opt) Now we can execute tiberCAD: tibercad quantum_dot_GaN_TB.tib Output
After the execution, the output directory contains, as usual, the results for the simulations performed. As for tightbinding simulation, the file tb2.dat contains a table with the calculated eigenvalues for electrons and holes, together with their occupation index.
isosurface mo1 color green cutoff 0.00005 "mo_cb_01.cube" Analogously, we can visualize the hole state. The figure below shows the confinement of the two states inside the spherical GaN quantum dot: in green the conduction state and in yellow the valence state. ATTACHMENTS
