2.14.5. cbr{ }

Calling sequence

quantum{ cbr{ } }

Properties

usage: \(\mathrm{\textcolor{ForestGreen}{optional}}\)
items: maximum 1

Dependencies

if global{ simulate1D{} } is called then quantum{ cbr{ lead } } cannot be used
quantum{ cbr{ min_energy } } and quantum{ cbr{ rel_min_energy} } cannot be used simultaneously
quantum{ cbr{ max_energy } } and quantum{ cbr{ rel_max_energy } } cannot be used simultaneously

Functionality

Specifications that define CBR (Contact Block Reduction method) calculation, i.e. ballistic current calculations. This method is based on the following publications: [BirnerCBR2009], [MamaluyCBR2003]

CBR current calculation at a glance:

full 1D, 2D and 3D calculation of quantum mechanical ballistic transmission probabilities for open systems with scattering boundary conditions
Contact Block Reduction method:
- only incomplete set of quantum states needed (~ 100)
- reduction of matrix sizes from \(O(N^3)\) to \(O(N^2)\)
ballistic current according to Landauer–Büttiker formalism

The CBR method is an efficient method that uses a limited set of eigenstates of the decoupled device and a few propagating lead modes to calculate the retarded Green’s function of the device coupled to external contacts. From this Green’s function, the density and the current is obtained in the ballistic limit using Landauer’s formula with fixed Fermi levels for the leads. It is important to note that the efficiency of the calculation and also the convergence of the results are strongly dependent on the cutoff energies for the eigenstates and modes. Thus it is important to check during the calculation if the specified number of states and modes is sufficient for the applied voltages. To summarize, the code may do its job very efficiently but is far away from being a black box tool.

cbr{
    name = "qr" # quantum region to which cbr method will be
    lead{
        name = "lead_1"             # name of the lead
        x = 12.0                    # position of the lead in  1D simulation
        kinetic_coupling = 1.5
        rel_kinetic_coupling = 0.2
    }

    min_energy =  2.5        # lower boundary (absolute)
    max_energy =  2.6        # upper boundary (absolute)

    rel_min_energy = -0.01       # lower boundary (relative)
    rel_max_energy =  0.3        # upper boundary (relative)

    energy_resolution   =  1e-6       # energy grid resolution
    transmission_threshold  = 0.01

    ildos          =  yes        # outputs integrated LDOS
    ldos           =  yes        # outputs LDOS

    output_ldos_single_file = yes
}

Figure 2.14.5.1 shows the calculated transmission from lead 1 to lead 3 as a function of energy \(T_{13}(E)\). Full line: All eigenfunctions of the decoupled device are taken into account. Dashed line: Only the lowest 7% of the eigenfunctions are included. Here, Neumann boundary conditions are used for the propagation direction. The vertical line indicates the cutoff energy, i.e. the highest eigenvalue that is taken into account.

Transmission using the CBR method — Figure 2.14.5.1 The transmission calculated with the CBR method using all eigenstates and only 7% of the eigenstates. In the latter case, the transmission is still very accurate for the lower energies.

Special boundary conditions are applied for the Schrödinger equation while using the CBR method:

Neumann boundary conditions along the propagation direction.
Dirichlet boundary conditions perpendicular to the propagation direction.

Note

The quantum region must be a surface in a 3D simulation, a line in a 2D simulation, and a point in a 1D simulation.

Nested keywords

name
lead{ }
lead{ name }
lead{ x }
lead{ kinetic_coupling }
lead{ rel_kinetic_coupling }

min_energy
max_energy
rel_min_energy
rel_max_energy
energy_resolution

transmission_threshold
ildos
ldos
output_ldos_single_file
two_particle_options

name

Calling sequence

quantum{ cbr{ name = ... } }

Properties

usage: \(\mathrm{\textcolor{WildStrawberry}{required}}\)
type: character string

Functionality

refers to quantum region to which CBR method will be applied (\(d\)-dimensional)

lead{ }

Calling sequence

quantum{ cbr{ lead{ } } }

Properties

usage: \(\mathrm{\textcolor{WildStrawberry}{required}}\)
items: minimum 2

Functionality

Defining a lead. The lead region has dimension \(d-1\).

lead{ name }

Calling sequence

quantum{ cbr{ lead{ name = ... } } }

Properties

usage: \(\mathrm{\textcolor{WildStrawberry}{required}}\)
type: character string

Functionality

Provides the name of the quantum region of the lead. It must be corresponding to a defined quantum{ region{} } unless the global simulation is held in 1D.

lead{ x }

Calling sequence

quantum{ cbr{ lead{ x = ... } } }

Properties

usage: \(\mathrm{\textcolor{ForestGreen}{optional}}\)
type: real number
values: no constraints
default: \(r=0.0\)
unit: \(\mathrm{nm}\)

Functionality

—

Note

Only needed for 1D.

lead{ kinetic_coupling }

Calling sequence

quantum{ cbr{ lead{ kinetic_coupling = ... } } }

Properties

usage: \(\mathrm{\textcolor{Dandelion}{conditional}}\)
type: real number
values: (0.0, ...)
unit: \(\mathrm{eV}\)

Dependencies

rel_kinetic_coupling is not defined

Functionality

—

lead{ rel_kinetic_coupling }

Calling sequence

quantum{ cbr{ lead{ rel_kinetic_coupling = ... } } }

Properties

usage: \(\mathrm{\textcolor{Dandelion}{conditional}}\)
type: real number
values: (0.0, ...)
default: \(r=1.0\)
unit: \(\mathrm{-}\)

Dependencies

kinetic_coupling is not defined

Functionality

—

min_energy

Calling sequence

quantum{ cbr{ min_energy = ... } }

Properties

usage: \(\mathrm{\textcolor{ForestGreen}{optional}}\)
type: real number
values: no constraints
default: \(r=-1e100\)
unit: \(\mathrm{eV}\)

Dependencies

rel_min_energy is not defined

Functionality

Lower boundary for transmission energy interval on an absolute energy scale

max_energy

Calling sequence

quantum{ cbr{ max_energy = ... } }

Properties

usage: \(\mathrm{\textcolor{ForestGreen}{optional}}\)
type: real number
values: no constraints
default: \(r=1e100\)
unit: \(\mathrm{eV}\)

Dependencies

rel_max_energy is not defined

Functionality

Upper boundary for transmission energy interval on an absolute energy scale

rel_min_energy

Calling sequence

quantum{ cbr{ rel_min_energy = ... } }

Properties

usage: \(\mathrm{\textcolor{ForestGreen}{optional}}\)
type: real number
values: no constraints
default: \(r=-1e100\)
unit: \(\mathrm{-}\)

Dependencies

min_energy is not defined

Functionality

Lower boundary for transmission energy interval relative to the lowest eigenvalue

rel_max_energy

Calling sequence

quantum{ cbr{ rel_max_energy = ... } }

Properties

usage: \(\mathrm{\textcolor{ForestGreen}{optional}}\)
type: real number
values: no constraints
default: \(r=1e100\)
unit: \(\mathrm{-}\)

Dependencies

max_energy is not defined

Functionality

Upper boundary for transmission energy interval relative to the highest eigenvalue

energy_resolution

Calling sequence

quantum{ cbr{ energy_resolution = ... } }

Properties

usage: \(\mathrm{\textcolor{ForestGreen}{optional}}\)
type: real number
values: (0.0, ...)
default: \(r=1e-4\)
unit: \(\mathrm{eV}\)

Functionality

This value determines the resolution of the transmission curve \(T(E)\).

transmission_threshold

Calling sequence

quantum{ cbr{ transmission_threshold = ... } }

Properties

usage: \(\mathrm{\textcolor{ForestGreen}{optional}}\)
type: real number
values: [0.0, ...)
default: \(r=0.0\)
unit: \(\mathrm{-}\)

Functionality

This value determines the resolution of the transmission curve \(T(E)\).

ildos

Calling sequence

quantum{ cbr{ ildos = ... } }

Properties

usage: \(\mathrm{\textcolor{ForestGreen}{optional}}\)
type: choice
values: yes or no
default: no

Functionality

If set to yes then outputs integrated local density of states.

ldos

Calling sequence

quantum{ cbr{ ldos = ... } }

Properties

usage: \(\mathrm{\textcolor{ForestGreen}{optional}}\)
type: choice
values: yes or no
default: no

Functionality

If set to yes then outputs local density of states.

output_ldos_single_file

Calling sequence

quantum{ cbr{ output_ldos_single_file = ... } }

Properties

usage: \(\mathrm{\textcolor{ForestGreen}{optional}}\)
type: choice
values: yes or no
default: yes

Functionality

Outputs all LDOS data into a single large file.

Warning

Enabling ILDOS or LDOS can massively increase runtime and RAM usage in 2D and 3D simulations. Moreover, enabling LDOS also will rewrite huge amounts of data to disk in 2D and 3D simulations.

If your system environment cannot handle a huge number of files (e.g. you are using a slow hard disk instead of a SSD), outputting all LDOS data into a single large file (as set per default) is strongly recommended.

Please note that writing all LDOS data in one file is not possible in 3D simulations or when output{ only_sections = yes } is set (the respective flag is ignored then). See output{ } for reference.

two_particle_options

Calling sequence

quantum{ cbr{ two_particle_options = [ ..., ..., ..., ..., ..., ..., ..., ..., ..., ..., ... ] } }

Properties

usage: \(\mathrm{\textcolor{ForestGreen}{optional}}\)
type: vector of 11 real numbers: \((r_1, r_2, \ldots, r_{11})\)
—

Functionality

Contains 11 values for two-particle model [number of states, relative permittivity, x1, y1, z1, x2, y2, z2, splitting, tunneling] with units [ –, –, nm, nm, nm, nm, nm, nm, eV, eV ]. Constraint: number of states = 2

Last update: 2025-05-27