nnp:cbr_1d_potential
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nnp:cbr_1d_potential [2019/10/22 13:13] takuma.sato [Single Potential Barrier] |
nnp:cbr_1d_potential [2024/01/03 16:50] stefan.birner removed |
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| * 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. After running the input file, we obtain the following bandedge profile. 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 (''bandedges.dat'').</caption> | + | <caption>The conduction bandedge profile (''bandedge_Gamma.dat'').</caption> |
| </figure> | </figure> | ||
| Line 36: | Line 36: | ||
| <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 45: | 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. Above $E_{\mathrm{barrier}}$ the spectrum shows an oscillatory behaviour. | + | 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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