This is an old revision of the document!
We apply the Contact Block Reduction (CBR) method to a simple GaAs nanowire of cuboidal shape. The corresponding tutorial for nextnano3 is here.
We consider a GaAs cuboidal tube of dimensions 10 nm$\times$10 nm$\times$20 nm. Two leads of 10 nm$\times$10 nm each are attached to the edge of the device. The grid spacing is 1 nm in all directions. The effective electron mass is assumed to be constant throughout the device and equal to $0.067m_0$.
To simulate 3D (or 2D) system with CBR method in nextnano++ correctly, The quantum regions have to be appropriately specified in the input file.
quantum{ region{ name = "lead_1" x = [-6,6] y = [-6,6] z = [-0.1,0.1] boundary{ x=dirichlet y=dirichlet z=cbr } Gamma{ num_ev = $num_eigenstates_device } } }
The perpendicular directions, i.e. x- and y-directions, of the system are elongated by one grid due to the treatment of edge points in nextano++. Since the simulation is three dimensional, the lead region specified here has to be two dimensional. The number $\pm0.1$ is chosen to be smaller than the grid spacing, so that the region “lead_1” becomes a 2D sheet (Note: this is slightly different in nextnano3 input). CBR boundary condition has to be imposed in the propagation direction, i.e. z-direction, whereas Dirichlet boundary condition is set for perpendicular directions.
cbr{ name = "device" lead{ name = "lead_1" } lead{ name = "lead_2" } delta_energy = $delta_energy abs_min_energy = $E_min abs_max_energy = $E_max options = [1, 0, 0] }
Here we specify the device region and leads attached to the device. The program calculates transmission through the region “device”, from “lead_1” to “lead_2”. The resolution, minimum and maximum of the energy axis can be also tuned here.
The following figure shows the calculated transmission coefficient as a function of energy. nextnano++ reproduces consistent results with nextnano3. The biggest advantage of the CBR method is that it can correctly predict the spectrum without calculating all eigenmodes of the 3D device.