Recursive Green's Function : Recursive Green's Function

Requires: Victory Atomistic
Minimum Versions: Victory Atomistic 1.0.0.R

This example demonstrates the use of a mode space basis based on G. Mil’nikov, N. Mori, and Y. Kamakura, “Equivalent transport models in atomistic quantum wires,” Phys. Rev. B, vol. 85, no. 3, p. 035317, Jan. 2012, to solve various self-consistent Born iterations and Poisson iterations with the Recursive Green's Function algorithm. It shows:

Solution of scattered RGF with a reduced mode space basis A form-factor application of mode space on self-energies

Transport calculations are solved for a silicon nanowire with a cross-section of 4-by-4 unit cells with a length of 38 unit cells (2.17 nm by 2.17 nm by 20.62 nm), with the an initial sp3d5s* tight-binding basis. The device is separated into three sections defined in the Geometry section of the input deck. This example is divided into three sections that make up a N-I-N type device, with a N-type material from 0 to 6 nm length-wise, I-type material from 6 nm to 14 nm, and N-type from 14 nm to 20.62 nm.

The simulation begins with the Test_MS solver (type ApplyModeSpace) reading in the basis file whose path is specified with the ApplyModeSpace solver option Unitary_matrix_filename. If this option is not set, a file named Unitary_matrix.dat must exist in the same directory as the input deck. If using the "-r" option for creating a results directory, the basis file must be specified with the Unitary_matrix_filename option as being one directory above, e.g, "../Unitary_matrix.dat".

The bands are then solved using Schroedinger solvers corresponding to source and drain.

After this, a semiclassical calculation is performed by the poisson_device_init solver, which results in an initial potential profile to be read in later by the density solver, rgf_test.

The rgf_test solver (solver type SelfconsistentBornModule) performs the scattered RGF calculations and solves for electron density, and must interact with the poisson_device solver (solver type NonlinearPoisson) in a self-consistent fashion. For this particular example, 15 scattering iterations and two self-consistent Poisson iterations are performed for a total of 30 RGF calculations. The rgf_test_solver obtains a reduced Hamiltonian from the lra_module solver (type LRAModule), and must also request from this solver reduced Green's functions and reduced self-energies. The type of scattering performed in this example is acoustic deformation potential. One important feature of this example is the ability to maintain real-space information while maintaining a reduced basis. This is performed integrating real space data into mode space with a method that can be activated by setting the LRAModule option LRA_method or LRA_scattering_method to form_factor.

The output for this example includes band-structure data, 3D potential data, I-V data, 3D electron density, and 3D hole density. The regression test validates the electron density (, energy- and slab-resolved current (rgf_test_RGF_device_backward_module_device_slab_resolved_energy_current_14_0.1V.dat), and I-V data (ramper_IV.dat).

To load and run this example, select the Load button in DeckBuild > Examples. This will copy the input file and any support files to your current working directory. Select the Run button in DeckBuild to execute the example.