nnp:cbr_3d_nanowire
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nnp:cbr_3d_nanowire [2019/10/18 19:57] takuma.sato [Transmission through a 3D nanowire] |
nnp:cbr_3d_nanowire [2024/01/03 16:45] stefan.birner removed |
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| ===== Transmission through a 3D nanowire (CBR) ===== | ===== Transmission through a 3D nanowire (CBR) ===== | ||
| + | Author: Takuma Sato, nextnano GmbH | ||
| + | |||
| We apply the Contact Block Reduction (CBR) method to a simple GaAs nanowire of cuboidal shape. | We apply the Contact Block Reduction (CBR) method to a simple GaAs nanowire of cuboidal shape. | ||
| The corresponding tutorial for nextnano<sup>3</sup> is [[https://www.nextnano.com/nextnano3/tutorial/3Dtutorial_CBR_nanowire.htm|here]]. | The corresponding tutorial for nextnano<sup>3</sup> is [[https://www.nextnano.com/nextnano3/tutorial/3Dtutorial_CBR_nanowire.htm|here]]. | ||
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| ==== CBR efficiency assessment ==== | ==== CBR efficiency assessment ==== | ||
| - | The biggest advantage of the CBR method is that it can correctly predict the spectrum without calculating all eigenmodes of the 3D device. That means that, for low energies, one can significantly reduce the simulation load to calculate the transmission spectrum [Birner2009]. To demonstrate it we perform three different simulations, where the number of modes considered in the calculation is sweeped. | + | The biggest advantage of the CBR method is that it can correctly predict the spectrum without calculating all eigenmodes of the 3D device. That means that, for low energies, one can significantly reduce the simulation load for the calculation of transmission spectrum [Birner2009]. To demonstrate it we perform three different simulations, sweeping the number of modes considered in the calculation. In the input file, the variable ''$CBR_case'' switches the number of eigenmodes. |
| <code> | <code> | ||
| $CBR_case = 1 # (ListOfValues:1,2,3) | $CBR_case = 1 # (ListOfValues:1,2,3) | ||
| Line 56: | Line 58: | ||
| </code> | </code> | ||
| - | The following figure shows the calculated transmission coefficient as a function of energy. The result of nextnano<sup>3</sup> is shown for reference. | + | The following figure shows the calculated transmission coefficient as a function of energy. The result of nextnano<sup>3</sup> is shown for reference. Arrows indicate the cutoff energies, namely the eigenenergy of the highest device mode considered in each simulation. The transmission coefficient drops when the energy exceeds the cutoff value. In the low energy, however, it is sufficient to calculate only a part of all eigenfunctions of the device Hamiltonian. Lower cutoff energy means lower dimension of matrices and vectors in the simulation, e.g. Eq.(36) in [Birner2009], which reduces the calculation load. For example, a simulation performed at nextnano office took |
| + | * 42 sec for ''$CBR_case=1'' (black) | ||
| + | * 3 min 14 sec for ''$CBR_case=2'' (blue) | ||
| + | * 11min 17 sec for ''$CBR_case=3'' (red) | ||
| <figure transmission> | <figure transmission> | ||
| {{:nnp:transmission_cbrtutorial_3dnanowire2.png?direct&600}} | {{:nnp:transmission_cbrtutorial_3dnanowire2.png?direct&600}} | ||
| - | <caption>Transmission coefficient of a GaAs 3D nanowire. Arrows indicate the cut-off energies, namely the eigenenergy of the highest device eigenmode considered in each simulation.</caption> | + | <caption>Transmission coefficient of a GaAs 3D nanowire simulated with three different CBR parameters. nextnano<sup>3</sup> result is shown for reference. Arrows indicate the cutoff energies, namely the eigenenergy of the highest device eigenmode considered in each simulation.</caption> |
| </figure> | </figure> | ||
| + | ==== Lead modes ==== | ||
| + | The step-like increase of the transmission coefficient is attributed to the discrete energy levels of the lead modes. Let us have a close look at the first few steps (Figure {{ref>close}}). We can see that $T(E)$ increases by integers. | ||
| + | <figure close> | ||
| + | {{:nnp:transmission_cbrtutorial_3dnanowire4.png?direct&600}} | ||
| + | <caption>Zoom into the first few steps of $T(E)$. The transmission increases by integer at the eigenenergies of the lead.</caption> | ||
| + | </figure> | ||
| + | |||
| + | The lead mode probability distribution $|\psi(x,y)|^2$ and corresponding eigenvalues are exported to the following files: | ||
| + | * ~\Quantum\wf_probabilities_lead_1_Gamma_0000.fld | ||
| + | * ~\Quantum\wf_energy_spectrum_lead_1_Gamma_0000.dat | ||
| + | To see the energy eigenvalues, it is convenient to switch to ''Show Output File as Text'' (marked yellow). | ||
| + | |||
| + | {{:nnp:transmission_cbrtutorial_3dnanowire_nnm.png}} | ||
| + | Once the energy reaches 76 meV, the first lead mode energy is reached and then this mode transmits perfectly, giving a transmission of $1$. | ||
| + | |||
| + | As can be seen from ''\Quantum\wf_probabilities_lead_1_Gamma_0000.fld'', the second and third lead mode states are degenerate due to the symmetry of the lead cross-section. Thus they have the same energy 190 meV. Consequently, the spectrum increases by $2$ at the energy of 190 meV. In this fashon, the step-like behaviour of the transmission coefficient is explained by lead eigenmodes. | ||
| + | |||
| + | |||
| + | <figure lead mode> | ||
| + | {{:nnp:transmission_cbrtutorial_3dnanowire_leadmode.png?direct&600}} | ||
| + | <caption>The probability distribution $|\psi(x,y)|^2$ of the 2nd lead mode. </caption> | ||
| + | </figure> | ||
| + | |||
| + | |||
| + | * Please help us to improve our tutorial. Should you have any questions or comments, feel free to send to: support [at] nextnano.com | ||
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