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nnp:optics:led_simulation
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nnp:optics:led_simulation [2017/02/02 14:44] stefan.birner [Input file structure] |
nnp:optics:led_simulation [2019/06/28 12:56] (current) stefan.birner [Input file structure] |
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| In the following example we are going to show how the spectra of a Light Emitting Diode (LED) can be calculated with the **nextnano++** software. | In the following example we are going to show how the spectra of a Light Emitting Diode (LED) can be calculated with the **nextnano++** software. | ||
| + | This example does not include the Schrödinger equation. | ||
| ==== Physics model ==== | ==== Physics model ==== | ||
| Line 7: | Line 8: | ||
| In an LED the photons are emitted in the radiative recombination process, | In an LED the photons are emitted in the radiative recombination process, | ||
| ;#; | ;#; | ||
| - | $$R_{\rm sp} = c_{\rm rad} (n p - n_i^2),$$ | + | $$R_{\rm sp} = c_{\rm rad} (n p - n_{\rm i}^2),$$ |
| ;#; | ;#; | ||
| where $R_{\rm sp}$ is the local spontaneous emission rate, | where $R_{\rm sp}$ is the local spontaneous emission rate, | ||
| - | $n$ and $p$ correspond to the density of the electrons and the holes in the volume element, and $n_i$ is the intrinsic density of the charge carriers. | + | $n$ and $p$ correspond to the density of the electrons and the holes in the volume element, and $n_{\rm i}$ is the intrinsic density of the charge carriers. |
| $R_{\rm sp}(x)$ depends on position $x$ because the densities depend on position. | $R_{\rm sp}(x)$ depends on position $x$ because the densities depend on position. | ||
| The bimolecular recombination coefficient $c_{\rm rad}$ is a material dependent constant and has units ${\rm cm}^3/{\rm s}$. | The bimolecular recombination coefficient $c_{\rm rad}$ is a material dependent constant and has units ${\rm cm}^3/{\rm s}$. | ||
| + | The order of magnitude is around $10^{-10}{\rm cm}^3/{\rm s}$. | ||
| This recombination rate is coupled into the drift-diffusion equation and the stationary solution of the problem, | This recombination rate is coupled into the drift-diffusion equation and the stationary solution of the problem, | ||
| Line 67: | Line 69: | ||
| output_carrier_densities{} | output_carrier_densities{} | ||
| output_intrinsic_density{} | output_intrinsic_density{} | ||
| - | energy_distribution{ # Calculation of carrier densities in function of energy | + | energy_distribution{ # Calculation of carrier densities as a function of energy |
| - | min = -5 # Integrate from | + | min = -5.0 # Integrate from |
| - | max = 5 # Integrate to | + | max = 5.0 # Integrate to |
| - | energy_resolution = 0.05 # Integration Resolution | + | energy_resolution = 0.05 # Integration resolution |
| + | emission_spectrum = yes # Output classical emission spectrum (both, photon count and intensity) | ||
| } | } | ||
| - | }<> | + | } |
| </Code> | </Code> | ||
| Line 78: | Line 81: | ||
| <Code> | <Code> | ||
| energy_distribution{ # Calculation of carrier densities as a function of energy | energy_distribution{ # Calculation of carrier densities as a function of energy | ||
| - | min = -5 # Integrate from | + | min = -5.0 # Integrate from |
| - | max = 5 # Integrate to | + | max = 5.0 # Integrate to |
| energy_resolution = 0.05 # Integration resolution | energy_resolution = 0.05 # Integration resolution | ||
| + | emission_spectrum = yes # | ||
| } | } | ||
| </Code> | </Code> | ||
| Line 91: | Line 95: | ||
| The simulated structure is a **p-i-n** diode. | The simulated structure is a **p-i-n** diode. | ||
| The layers of the heterostructure are //p//-GaAs - //p//-AlGaAs - InGaAs - //n//-AlGaAs - //n//-GaAs. | The layers of the heterostructure are //p//-GaAs - //p//-AlGaAs - InGaAs - //n//-AlGaAs - //n//-GaAs. | ||
| - | In the intrinsic InGaAs region in the center, the Fermi levels reach the band edges of the quantum well, which leads to a population in the well for both electrons, and holes. The applied bias in the drift-diffusion equation results in a splitting of the hole and electron quasi-Fermi levels. This can be seen in the plot of the band edge profile of figure {{ref>bandstructure}} | + | The applied bias in the drift-diffusion equation results in a splitting of the hole and electron quasi-Fermi levels. |
| + | This can be seen in the plot of the band edge profile of figure {{ref>bandstructure}}. | ||
| + | In the intrinsic InGaAs region in the center, the Fermi levels reach the band edges of the quantum well, which leads to a significant density of electrons and holes in the quantum well (//not shown//). | ||
| Line 98: | Line 103: | ||
| ;#; | ;#; | ||
| - | <dataplot center linepoints xrange=-50.0:50.0 yrange=-2.5:2.5 xlabel="x (nm)" ylabel="Energy (eV)" ylegends="Gamma LH HH SO Fermi_{electron} Fermi_{hole}" 600x400> | + | <dataplot center linepoints xrange=-50.0:50.0 yrange=-2.5:2.5 xlabel="Position (nm)" ylabel="Energy (eV)" ylegends="Gamma LH HH SO Fermi_{electron} Fermi_{hole}" title="Band edge profile of a pin diode" 600x400> |
| -85 -0.8 -0.8 -0.8 -0.8 -0.8 -0.8 | -85 -0.8 -0.8 -0.8 -0.8 -0.8 -0.8 | ||
| -84.801 -0.8 -0.8 -0.8 -0.8 -0.8 -0.8 | -84.801 -0.8 -0.8 -0.8 -0.8 -0.8 -0.8 | ||
| Line 1810: | Line 1815: | ||
| - | The carrier distribution with respect to energy can be seen in figure {{ref>carrierenergy}}. The density is summed up for the full device. | + | The carrier distribution with respect to energy ($n(E)$, $p(E)$) can be seen in figure {{ref>carrierenergy}}. The density is summed up (integrated) for the full device. |
| (This means that the position information of the carrier densities is "lost" in this view). | (This means that the position information of the carrier densities is "lost" in this view). | ||
| <figure carrierenergy> | <figure carrierenergy> | ||
| Line 2019: | Line 2024: | ||
| </dataplot> | </dataplot> | ||
| ;#; | ;#; | ||
| - | <caption>Energy distribution of carriers for the full device volume</caption> | + | <caption>Energy distribution $n(E)$ and $p(E)$ of the electrons and holes for the full device</caption> |
| </figure> | </figure> | ||
| Line 2232: | Line 2237: | ||
| </dataplot> | </dataplot> | ||
| ;#; | ;#; | ||
| - | <caption>Emission spectrum (Intensity) of the **p-i-n** diode structure in units of 1/eV.</caption> | + | <caption>Emission spectrum (intensity) of the **p-i-n** diode structure in units of 1/eV.</caption> |
| </figure> | </figure> | ||
| Line 2602: | Line 2607: | ||
| */ | */ | ||
| + | The input file can be downloaded from {{nnp:optics:ledsim_zb_-_p-i-n_device.zip?linkonly | here }} | ||
| + | |||
nnp/optics/led_simulation.1486046649.txt.gz · Last modified: 2017/02/02 14:44 by stefan.birner
