nnp:cbr_1d_potential
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nnp:cbr_1d_potential [2019/10/21 15:26] takuma.sato [CBR efficiency assessment] |
nnp:cbr_1d_potential [2024/01/03 16:50] stefan.birner removed |
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| ===== 1D Transmission (CBR) ===== | ===== 1D Transmission (CBR) ===== | ||
| + | Author: Takuma Sato, nextnano GmbH | ||
| + | |||
| In this tutorial we calculate the transmission coefficient $T(E)$ as a function of energy $E$. We consider the following pedagogical examples we learn in undergraduate quantum mechanics courses. | In this tutorial we calculate the transmission coefficient $T(E)$ as a function of energy $E$. We consider the following pedagogical examples we learn in undergraduate quantum mechanics courses. | ||
| * Single potential barrier | * Single potential barrier | ||
| Line 18: | Line 20: | ||
| * Transmission_CBRpaper_1Ddoublebarrier_nnp.in | * Transmission_CBRpaper_1Ddoublebarrier_nnp.in | ||
| ==== Single Potential Barrier ==== | ==== Single Potential Barrier ==== | ||
| - | We first consider transmission through a finite quantum barrier. 10 nm Al<sub>0.3</sub>Ga<sub>0.7</sub>As barrier is located in a 50 nm GaAs sample. For this compound the top of the barrier is at $E_{\mathrm{barrier}}=3.243$ eV. | + | We first consider transmission through a finite quantum barrier. 10 nm barrier is located in a 50 nm sample. After running the input file, we obtain the following bandedge profile. The barrier height is set to $E_{\mathrm{barrier}}=0.3$ eV. |
| - | <figure single barrier gamma> | + | <figure single_barrier_gamma> |
| - | {{:nnp::transmission_1dsinglebarrier_gamma.png?direct&600}} | + | {{:nnp::transmission_1dsinglebarrier_gamma.png}} |
| - | <caption>The conduction bandedge profile.</caption> | + | <caption>The conduction bandedge profile (''bandedge_Gamma.dat'').</caption> |
| </figure> | </figure> | ||
| With nextnano++, one can calculate the transmission spectrum using the CBR method (cf. [[https://www.nextnano.com/nextnanoplus/software_documentation/input_file/cbr.htm|here]] for details). The sample input file is generalised so that you can change the barrier width and alloy content (which determines the barrier height). | With nextnano++, one can calculate the transmission spectrum using the CBR method (cf. [[https://www.nextnano.com/nextnanoplus/software_documentation/input_file/cbr.htm|here]] for details). The sample input file is generalised 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 in the bottom you can select how to sweep the value ''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 start the simulation. | + | Here we look into the barrier width dependence. In nextnanomat, go to **'Template'** tab and select the input file. Then at the bottom you can select how to sweep the value (here ''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. |
| {{:nnp::transmission_1dsinglebarrier_nnm.png}} | {{:nnp::transmission_1dsinglebarrier_nnm.png}} | ||
| - | The result is written in ''~\bias_000_000\transmission_cbr_Gamma1.dat''. The barrier width $w$ affects the transmission coefficient as shown in Figure {{ref>single_barrier}}. | + | The result is written in ''transmission_cbr_Gamma1.dat''. The barrier width $w$ affects the transmission coefficient as shown in Figure {{ref>single_barrier}}. |
| <figure single_barrier> | <figure single_barrier> | ||
| - | {{:nnp::transmission_1dsinglebarrier.png?direct&600}} | + | {{:nnp::transmission_1dsinglebarrier.png}} |
| <caption>Transmission coefficient as a function of energy for different barrier width $w$ [nm]. The dashed line marks $E_{\mathrm{barrier}}$.</caption> | <caption>Transmission coefficient as a function of energy for different barrier width $w$ [nm]. The dashed line marks $E_{\mathrm{barrier}}$.</caption> | ||
| </figure> | </figure> | ||
| Line 43: | Line 45: | ||
| <figure step_gamma> | <figure step_gamma> | ||
| - | {{:nnp::transmission_1dstep_gamma.png?direct&600}} | + | {{:nnp::transmission_1dstep_gamma.png}} |
| </figure> | </figure> | ||
| <figure step> | <figure step> | ||
| - | {{:nnp::transmission_1dstep.png?direct&600}} | + | {{:nnp::transmission_1dstep.png}} |
| + | <caption>Transmission spectrum for a step potential. Transmission is only allowed above the step.</caption> | ||
| </figure> | </figure> | ||
| ==== Quantum Well ==== | ==== Quantum Well ==== | ||
| - | Similarly a quantum well structure can be simulated. | + | Similarly a quantum well structure can be simulated. The well width is w=10nm here. |
| <figure well gamma> | <figure well gamma> | ||
| - | {{:nnp::transmission_1dwell_gamma.png?direct&600}} | + | {{:nnp::transmission_1dwell_gamma.png}} |
| </figure> | </figure> | ||
| - | Again the transmission of electron with energy lower than $E_{\mathrm{barrier}}$ is impossible because the barrier is infinitely thick. | + | Again the transmission of electron within the barriers is impossible because the barrier is infinitely thick. Above 0eV, the spectrum shows an oscillatory behaviour. |
| <figure well> | <figure well> | ||
| - | {{:nnp::transmission_1dwell.png?direct&600}} | + | {{:nnp::transmission_1dwell.png}} |
| + | <caption>Transmission spectrum for the quantum well structure. The dashed line marks the top of the barrier.</caption> | ||
| </figure> | </figure> | ||
| ==== Double Potential Barrier ==== | ==== Double Potential Barrier ==== | ||
| - | Finally we consider a double barrier structure with wall width 10 nm. The distance between the barriers is 10 nm. | + | Finally we consider a double barrier structure with wall width 10 nm. The barrier interval is 10 nm. |
| <figure double barrier gamma> | <figure double barrier gamma> | ||
| - | {{:nnp::transmission_1ddoublebarrier_gamma.png?direct&600}} | + | {{:nnp::transmission_1ddoublebarrier_gamma.png}} |
| </figure> | </figure> | ||
| - | This system has two resonant modes localized between the barriers. The bandstructure and wavefunctions are written in ''~\bias_000_000\bandedge_Gamma.dat'' and ''~\Quantum\wf_probabilities_shift_cbr_Gamma_0000.dat'', respectively. | + | This system has two resonant modes localized between the barriers. The bandstructure and wavefunctions are written in ''bandedge_Gamma.dat'' and ''\Quantum\wf_probabilities_shift_cbr_Gamma_0000.dat'', respectively. |
| <figure resonant> | <figure resonant> | ||
| - | {{:nnp::transmission_1ddoublebarrier_resonant.png?direct&600}} | + | {{:nnp::transmission_1ddoublebarrier_resonant.png}} |
| - | <caption>Probability distribution $|\psi(x)|^2$ of the resonant modes.</caption> | + | <caption>Probability distribution $|\psi(x)|^2$ of the two resonant modes.</caption> |
| </figure> | </figure> | ||
| - | In the transmission spectrum, one can clearly see the 100% transmission at the energies of the resonant states in the quantum well. Please note that the vertical axis is logarithmic scale. | + | In the transmission spectrum, one can clearly see the sharp transmission at the energies of the resonant states in the quantum well. Please note that the vertical axis is logarithmic scale. |
| <figure double_barrier> | <figure double_barrier> | ||
| - | {{:nnp::transmission_1ddoublebarrier.png?direct&600}} | + | {{:nnp::transmission_1ddoublebarrier.png}} |
| <caption>Transmission coefficient of the double barrier structure. The spectrum has two sharp peaks below the barrier height 3.084 eV, which corresponds to the resonant mode within the barriers.</caption> | <caption>Transmission coefficient of the double barrier structure. The spectrum has two sharp peaks below the barrier height 3.084 eV, which corresponds to the resonant mode within the barriers.</caption> | ||
| </figure> | </figure> | ||
| - | A [[https://www.nextnano.de/nextnano3/tutorial/1Dtutorial_RTD_green.htm|resonant tunneling diode (RTD)]] is an example of a device that exploits this particular feature of transmission coefficient $T(E)$. | + | A [[https://www.nextnano.de/nextnano3/tutorial/1Dtutorial_RTD_green.htm|resonant tunneling diode (RTD)]] is an example of a device that exploits this $\delta$-function-like behaviour of transmission coefficient $T(E)$. |
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