Transmission (CBR)
Header
- Input Files:
transmission-barrier_1D_nnp.in
transmission-step_1D_nnp.in
transmission-quantum-well_1D_nnp.in
transmission-double-barrier_Birner_JCEL_2009_1D_nnp.in
- Scope of the tutorial:
Transmission coefficient
- Relevant output files:
bias_00000\bandedge_Gamma.dat
bias_00000\CBR\transmission_cbr_Gamma.dat
bias_00000\Quantum\probabilities_shift_cbr_Gamma.dat
Introduction
In this tutorial, we calculate the transmission coefficient
Single potential barrier
Step potential
Quantum well
Double potential barrier [BirnerCBR2009]
To calculate transmission spectra with nextnano++, we use Contact Block Reduction (CBR) method. This tutorial is an analog of here.
Single potential barrier
We first consider transmission through a finite quantum barrier.
Figure 2.4.419 The conduction band edge profile (bandedge_Gamma.dat).
With nextnano++, one can calculate the transmission spectrum using the CBR method ([BirnerCBR2009]). The sample input file is generalized so that you can change the barrier width and alloy content (which determines the barrier height).
Here we look into the barrier width dependence.
In nextnanomat, go to ‘Template’ tab and select the input file.
Then, you can select how to sweep the value at the bottom (List of values
) and variable Barrier_Width
.
The list of values shows up automatically, as it is specified in the input file with the tag ListOfValues
.
Clicking the button Create input files generates multiple input files by sweeping variables.
Please go to ‘Simulation’ tab and run the simulation.

The result is written in transmission_cbr_Gammma.dat.
The barrier width
Figure 2.4.420 The transmission coefficient as a function of energy for different barrier width
Classical mechanics argues that the transmission is
Step potential
For a step potential structure (transmission-step_1D_nnp.in) as shown in Figure 2.4.421 (a), the transmission of electrons with energy below
Figure 2.4.421 The conduction band edge profile is shown in (a). The transmission spectrum for a step potential is shown in (b). Transmission is only allowed above the step.
Quantum well
Similarly, a quantum well structure can be simulated with transmission-quantum-well_1D_nnp.in.
The well width is
Figure 2.4.422 The conduction band edge profile is shown in (a). The transmission spectrum for a quantum well is shown in (b). The dashed line marks the top of the barrier.
Double potential barrier
Finally, we consider a double barrier structure with wall width
Figure 2.4.423 The conduction band edge profile is shown in (a). The probability distribution
This system has two resonant modes localized between the barriers. The band structure and wave functions are written in bandedge_Gamma.dat and Quantumprobabilities_shift_cbr_Gamma.dat, respectively. In the transmission spectrum, one can clearly see the sharp transmission at the energies of the resonant states in the quantum well. Note that the vertical axis is logarithmic scale.
A resonant tunneling diode (RTD) is an example of a device that exploits this
CBR efficiency assessment
Transmission_GaAs_AlAs_Birner_JCEL_2009_1D_Double_Barrier_nnp.in is used for this section.
Figure 4 in [BirnerCBR2009] compares the transmission coefficient of a double barrier structure for different number of eigenstates considered in the CBR method.
The following figure shows the result reproduced by nextnano++ and demonstrates that the first resonant peak is accurately reproduced using incomplete set of eigenstates.
The spectrum is not identical to the previous result because the barrier width here is
Figure 2.4.424 Transmission coefficient for three different CBR parameters. The blue curve is the result considering complete set of eigenstates, whereas violet and orange curves take into account only 40 % and 10 % of them, respectively.
See also for 3D case for another CBR efficiency assessment.
Last update: nn/nn/nnnn