nnp:cbr_3d_nanowire
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nnp:cbr_3d_nanowire [2019/10/21 12:53] takuma.sato [CBR efficiency assessment] |
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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| </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. 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 required | + | 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 ''$CBR_case=1'' | + | * 42 sec for ''$CBR_case=1'' (black) |
| - | * 3 min 14 sec for ''$CBR_case=2'' | + | * 3 min 14 sec for ''$CBR_case=2'' (blue) |
| - | * 11min 17 sec for ''$CBR_case=3'' | + | * 11min 17 sec for ''$CBR_case=3'' (red) |
| <figure transmission> | <figure transmission> | ||
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| * ~\Quantum\wf_probabilities_lead_1_Gamma_0000.fld | * ~\Quantum\wf_probabilities_lead_1_Gamma_0000.fld | ||
| * ~\Quantum\wf_energy_spectrum_lead_1_Gamma_0000.dat | * ~\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). | ||
| - | <figure nnm> | + | {{:nnp:transmission_cbrtutorial_3dnanowire_nnm.png}} |
| - | {{:nnp:transmission_cbrtutorial_3dnanowire_nnm.png?direct&700}} | + | |
| - | <caption>'Output' tab of nextnanomat. For the energy eigenvalues, it is convenient to switch to 'Show Output File as Text' (marked yellow)</caption> | + | |
| - | </figure> | + | |
| Once the energy reaches 76 meV, the first lead mode energy is reached and then this mode transmits perfectly, giving a transmission of $1$. | 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. | + | 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> | <figure lead mode> | ||
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| </figure> | </figure> | ||
| - | The step-like behaviour of the transmission coefficient can be understood in this way. Above the cut-off energy, no lead modes | + | |
| + | * 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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