nextnano.NEGF - Software for
Quantum Transport

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====== LED Simulation ======

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 ====

In an LED the photons are emitted in the radiative recombination process,
;#;
$$R_{\rm sp} = c_{\rm rad} (n  p - n_{\rm i}^2),$$
;#;
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 $n_{\rm i}$ is the intrinsic density of the charge carriers. 
$R_{\rm sp}(x)$ 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 ${\rm cm}^3/{\rm s}$.

This recombination rate is coupled into the drift-diffusion equation and the stationary solution of the problem,
;#;
$$\frac{\rm d}{{\rm d}t}n = 0,$$
$$\frac{\rm d}{{\rm d}t}p = 0,$$
;#;
is calculated.

=== Spectrum of the emission ===

According to this simple model, where $c_{\rm rad}$ is just a material constant, the radiative recombination rate, which generates photons of energy $E_{\rm rad}$ can be written in the form,

;#;
$$R_{\rm sp}(E_{\rm rad}) = c_{\rm rad} \int n(E_e) p(E_h) \delta(E_e-E_h-E_{\rm rad}) {\rm d}E_e {\rm d}E_h,$$
;#;

where $n(E_e)$ and $p(E_h)$ are the electron and hole densities of the energy level $E_e$ and $E_h$ in the volume element.

In order to get the spectra of the emission the integral should be calculated for each volume element, and integrated over volume. This simple model uses the bulk material constant $c_{\rm rad}$.
However, this approach is not correct for **QW** structures.
Additionally, the re-absorption of photons is not included.

==== Input file structure ====

=== Drift-Diffusion Calculation ===
<Code>
currents{
    mobility_model    = constant 
    recombination_model{
      SRH            = no        # Shockley-Read-Hall recombination
      Auger          = no        # Auger recombination
      radiative      = yes       # radiative recombination (direct recombination)
    }     
    output_fermi_levels{}
    output_currents{} 
}
</Code>

We have to include radiative recombination in the drift-diffusion equation in order to take into account the spontaneous emission rate.
<Code>
           radiative      = yes       # radiative recombination (direct recombination)
</Code>

=== Density Calculation ===
<Code>
classical{
   Gamma{}
   LH{}
   HH{}
   SO{}

   output_bandedges{ averaged = no }
   output_carrier_densities{}
   output_intrinsic_density{}
   energy_distribution{              # Calculation of carrier densities as a function of energy
	min = -5                     # Integrate from
	max =  5                     # Integrate to
	energy_resolution = 0.05     # Integration resolution
   }
}
</Code>

The density has to be calculated in the energy domain, which means we have to define the integration range
<Code>
   energy_distribution{              # Calculation of carrier densities as a function of energy
	min = -5                     # Integrate from
	max =  5                     # Integrate to
	energy_resolution = 0.05     # Integration resolution
   }
</Code>


===== Results =====

==== Band structure====

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 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//).

 
<figure bandstructure>
;#;

<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>
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5.999	0.39880524499089	-1.3181876982105	-1.3181876982105	-1.6469876982105	-0.045440509718243	-0.78405239639309
6.001	0.39880524499089	-1.3181876982105	-1.3181876982105	-1.6469876982105	-0.045440509718243	-0.78405239639309
6.199	0.39273757635124	-1.3242553668501	-1.3242553668501	-1.6530553668501	-0.041808322874311	-0.78006695522678
6.201	0.39273757635124	-1.3242553668501	-1.3242553668501	-1.6530553668501	-0.041808322874311	-0.78006695522678
6.399	0.38672848310797	-1.3302644600934	-1.3302644600934	-1.6590644600934	-0.038216722765569	-0.77607002903824
6.401	0.38672848310797	-1.3302644600934	-1.3302644600934	-1.6590644600934	-0.038216722765569	-0.77607002903824
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6.799	0.37488602271206	-1.3421069204893	-1.3421069204893	-1.6709069204893	-0.031224193298631	-0.76805528868972
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6.999	0.36905265548282	-1.3479402877186	-1.3479402877186	-1.6767402877186	-0.027870450925807	-0.76404167503374
7.001	0.36905265548282	-1.3479402877186	-1.3479402877186	-1.6767402877186	-0.027870450925807	-0.76404167503374
7.199	0.36327786348798	-1.3537150797134	-1.3537150797134	-1.6825150797134	-0.02465169801896	-0.76002561472242
7.201	0.36327786348798	-1.3537150797134	-1.3537150797134	-1.6825150797134	-0.02465169801896	-0.76002561472242
7.399	0.3575616466398	-1.3594312965616	-1.3594312965616	-1.6882312965616	-0.02160244185495	-0.75600788747272
7.401	0.3575616466398	-1.3594312965616	-1.3594312965616	-1.6882312965616	-0.02160244185495	-0.75600788747272
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7.601	0.35190400481778	-1.3650889383836	-1.3650889383836	-1.6938889383836	-0.018757314826209	-0.75198902250669
7.799	0.3463049378587	-1.3706880053427	-1.3706880053427	-1.6994880053427	-0.016146776733881	-0.74796937953916
7.801	0.3463049378587	-1.3706880053427	-1.3706880053427	-1.6994880053427	-0.016146776733881	-0.74796937953916
7.999	0.34076444554495	-1.3762284976564	-1.3762284976564	-1.7050284976564	-0.013792751932124	-0.74394920347932
8.001	0.34076444554495	-1.3762284976564	-1.3762284976564	-1.7050284976564	-0.013792751932124	-0.74394920347932
8.199	0.33528252759088	-1.3817104156105	-1.3817104156105	-1.7105104156105	-0.011705596450049	-0.73992866137883
8.201	0.33528252759088	-1.3817104156105	-1.3817104156105	-1.7105104156105	-0.011705596450049	-0.73992866137883
8.399	0.32985918362727	-1.3871337595741	-1.3871337595741	-1.7159337595741	-0.0098833612141296	-0.73590786740563
8.401	0.32985918362727	-1.3871337595741	-1.3871337595741	-1.7159337595741	-0.0098833612141296	-0.73590786740563
8.599	0.32449441318355	-1.3924985300178	-1.3924985300178	-1.7212985300178	-0.0083133518796833	-0.73188689974386
8.601	0.32449441318355	-1.3924985300178	-1.3924985300178	-1.7212985300178	-0.0083133518796833	-0.73188689974386
8.799	0.3191882156674	-1.397804727534	-1.397804727534	-1.726604727534	-0.0069751439448619	-0.72786581204682
8.801	0.3191882156674	-1.397804727534	-1.397804727534	-1.726604727534	-0.0069751439448619	-0.72786581204682
8.999	0.31394059034105	-1.4030523528603	-1.4030523528603	-1.7318523528603	-0.0058439604089363	-0.72384464121167
9.001	0.31394059034105	-1.4030523528603	-1.4030523528603	-1.7318523528603	-0.0058439604089363	-0.72384464121167
9.199	0.30875153629354	-1.4082414069078	-1.4082414069078	-1.7370414069078	-0.0048935958426182	-0.71982341266676
9.201	0.30875153629354	-1.4082414069078	-1.4082414069078	-1.7370414069078	-0.0048935958426182	-0.71982341266676
9.399	0.30362105240817	-1.4133718907932	-1.4133718907932	-1.7421718907932	-0.0040985242441488	-0.71580214397432
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9.599	0.29854913732416	-1.4184438058772	-1.4184438058772	-1.7472438058772	-0.0034351826742194	-0.71178084729007
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9.799	0.29353578939152	-1.4234571538099	-1.4234571538099	-1.7522571538099	-0.0028825985728702	-0.70775953104591
9.801	0.29353578939152	-1.4234571538099	-1.4234571538099	-1.7522571538099	-0.0028825985728702	-0.70775953104591
9.999	0.28858100661813	-1.4284119365832	-1.4284119365832	-1.7572119365832	-0.0024225680381109	-0.70373820110347
10.001	0.28858100661813	-1.4284119365832	-1.4284119365832	-1.7572119365832	-0.0024225680381109	-0.70373820110347
10.199	0.28368478660782	-1.4333081565936	-1.4333081565936	-1.7621081565936	-0.0020395631980489	-0.69971686154642
10.201	0.28368478660782	-1.4333081565936	-1.4333081565936	-1.7621081565936	-0.0020395631980489	-0.69971686154642
10.399	0.27884712648811	-1.4381458167133	-1.4381458167133	-1.7669458167133	-0.0017204976619847	-0.69569551522605
10.401	0.27884712648811	-1.4381458167133	-1.4381458167133	-1.7669458167133	-0.0017204976619847	-0.69569551522605
10.599	0.27406802282626	-1.4429249203751	-1.4429249203751	-1.7717249203751	-0.0014544336134648	-0.69167416413746
10.601	0.27406802282626	-1.4429249203751	-1.4429249203751	-1.7717249203751	-0.0014544336134648	-0.69167416413746
10.799	0.26934747153203	-1.4476454716693	-1.4476454716693	-1.7764454716693	-0.0012322799504458	-0.68765280967977
10.801	0.26934747153203	-1.4476454716693	-1.4476454716693	-1.7764454716693	-0.0012322799504458	-0.68765280967977
10.999	0.26468546774532	-1.4523074754561	-1.4523074754561	-1.7811074754561	-0.0010465079343308	-0.68363145283625
11.001	0.26468546774532	-1.4523074754561	-1.4523074754561	-1.7811074754561	-0.0010465079343308	-0.68363145283625
11.199	0.26008200570694	-1.4569109374944	-1.4569109374944	-1.7857109374944	-0.00089089654888547	-0.67961009429946
11.201	0.26008200570694	-1.4569109374944	-1.4569109374944	-1.7857109374944	-0.00089089654888547	-0.67961009429946
11.399	0.2555370786104	-1.461455864591	-1.461455864591	-1.790255864591	-0.0007603114705987	-0.67558873455825
11.401	0.2555370786104	-1.461455864591	-1.461455864591	-1.790255864591	-0.0007603114705987	-0.67558873455825
11.599	0.25105067843235	-1.465942264769	-1.465942264769	-1.794742264769	-0.00065051705595142	-0.67156737395844
11.601	0.25105067843235	-1.465942264769	-1.465942264769	-1.794742264769	-0.00065051705595142	-0.67156737395844
11.799	0.24662279573951	-1.4703701474619	-1.4703701474619	-1.7991701474619	-0.00055801855487831	-0.66754601274518
11.801	0.24662279573951	-1.4703701474619	-1.4703701474619	-1.7991701474619	-0.00055801855487831	-0.66754601274518
11.999	0.24225341946937	-1.474739523732	-1.474739523732	-1.803539523732	-0.00047993088957808	-0.66352465109268
12.001	0.24225341946937	-1.474739523732	-1.474739523732	-1.803539523732	-0.00047993088957808	-0.66352465109268
12.199	0.23794253668187	-1.4790504065195	-1.4790504065195	-1.8078504065195	-0.0004138701925756	-0.65950328912497
12.201	0.23794253668187	-1.4790504065195	-1.4790504065195	-1.8078504065195	-0.0004138701925756	-0.65950328912497
12.399	0.23369013227952	-1.4833028109219	-1.4833028109219	-1.8121028109219	-0.00035786452008318	-0.65548192693055
12.401	0.23369013227952	-1.4833028109219	-1.4833028109219	-1.8121028109219	-0.00035786452008318	-0.65548192693055
12.599	0.22949618869266	-1.4874967545087	-1.4874967545087	-1.8162967545087	-0.00031028054098358	-0.65146056457273
12.601	0.22949618869266	-1.4874967545087	-1.4874967545087	-1.8162967545087	-0.00031028054098358	-0.65146056457273
12.799	0.22536068552705	-1.4916322576743	-1.4916322576743	-1.8204322576743	-0.00026976343498026	-0.64743920209689
12.801	0.22536068552705	-1.4916322576743	-1.4916322576743	-1.8204322576743	-0.00026976343498026	-0.64743920209689
12.999	0.22128359917069	-1.4957093440307	-1.4957093440307	-1.8245093440307	-0.00023518765668608	-0.6434178395356
13.001	0.22128359917069	-1.4957093440307	-1.4957093440307	-1.8245093440307	-0.00023518765668608	-0.6434178395356
13.199	0.2172649023567	-1.4997280408447	-1.4997280408447	-1.8285280408447	-0.00020561660783591	-0.63939647691233
13.201	0.2172649023567	-1.4997280408447	-1.4997280408447	-1.8285280408447	-0.00020561660783591	-0.63939647691233
13.399	0.21330456367944	-1.5036883795219	-1.5036883795219	-1.8324883795219	-0.0001802695969126	-0.63537511424402
13.401	0.21330456367944	-1.5036883795219	-1.5036883795219	-1.8324883795219	-0.0001802695969126	-0.63537511424402
13.599	0.2094025470608	-1.5075903961406	-1.5075903961406	-1.8363903961406	-0.00015849475298332	-0.63135375154289
13.601	0.2094025470608	-1.5075903961406	-1.5075903961406	-1.8363903961406	-0.00015849475298332	-0.63135375154289
13.799	0.20555881116423	-1.5114341320371	-1.5114341320371	-1.8402341320371	-0.00013974680172641	-0.62733238881784
13.801	0.20555881116423	-1.5114341320371	-1.5114341320371	-1.8402341320371	-0.00013974680172641	-0.62733238881784
13.999	0.20177330875397	-1.5152196344474	-1.5152196344474	-1.8440196344474	-0.00012356881170006	-0.62331102607529
14.001	0.20177330875397	-1.5152196344474	-1.5152196344474	-1.8440196344474	-0.00012356881170006	-0.62331102607529
14.199	0.19804598599771	-1.5189469572037	-1.5189469572037	-1.8477469572037	-0.00010957718360437	-0.61928966331996
14.201	0.19804598599771	-1.5189469572037	-1.5189469572037	-1.8477469572037	-0.00010957718360437	-0.61928966331996
14.399	0.19437678171109	-1.5226161614903	-1.5226161614903	-1.8514161614903	-9.7449290158934e-05	-0.61526830055528
14.401	0.19437678171109	-1.5226161614903	-1.5226161614903	-1.8514161614903	-9.7449290158934e-05	-0.61526830055528
14.599	0.19076562654341	-1.526227316658	-1.526227316658	-1.855027316658	-8.6913284268655e-05	-0.61124693778375
14.601	0.19076562654341	-1.526227316658	-1.526227316658	-1.855027316658	-8.6913284268655e-05	-0.61124693778375
14.799	0.1872124421044	-1.529780501097	-1.529780501097	-1.858580501097	-7.7739682737886e-05	-0.60722557500723
14.801	0.1872124421044	-1.529780501097	-1.529780501097	-1.858580501097	-7.7739682737886e-05	-0.60722557500723
14.999	0.1837171400331	-1.5332758031683	-1.5332758031683	-1.8620758031683	-6.9734405617904e-05	-0.60320421222709
15.001	0.1837171400331	-1.5332758031683	-1.5332758031683	-1.8620758031683	-6.9734405617904e-05	-0.60320421222709
15.199	0.1802796210105	-1.5367133221909	-1.5367133221909	-1.8655133221909	-6.2733010425058e-05	-0.59918284944434
15.201	0.1802796210105	-1.5367133221909	-1.5367133221909	-1.8655133221909	-6.2733010425058e-05	-0.59918284944434
15.399	0.17689977371938	-1.540093169482	-1.540093169482	-1.868893169482	-5.6595908501808e-05	-0.59516148665974
15.401	0.17689977371938	-1.540093169482	-1.540093169482	-1.868893169482	-5.6595908501808e-05	-0.59516148665974
15.599	0.17357747375543	-1.5434154694459	-1.5434154694459	-1.8722154694459	-5.1204389804632e-05	-0.59114012387387
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15.799	0.17031258249566	-1.5466803607057	-1.5466803607057	-1.8754803607057	-4.6457314099973e-05	-0.58711876108715
15.801	0.17031258249566	-1.5466803607057	-1.5466803607057	-1.8754803607057	-4.6457314099973e-05	-0.58711876108715
15.999	0.16710494593125	-1.5498879972701	-1.5498879972701	-1.8786879972701	-4.2268352320741e-05	-0.58309739829994
16.001	0.16710494593125	-1.5498879972701	-1.5498879972701	-1.8786879972701	-4.2268352320741e-05	-0.58309739829994
16.199	0.16395439347393	-1.5530385497274	-1.5530385497274	-1.8818385497274	-3.8563682806819e-05	-0.57907603551251
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16.399	0.1608607367461	-1.5561322064553	-1.5561322064553	-1.8849322064553	-3.5280064234764e-05	-0.57505467272506
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16.799	0.15484326074858	-1.5621496824528	-1.5621496824528	-1.8909496824528	-2.976648795387e-05	-0.56701194715085
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17.001	0.15191896491566	-1.5650739782857	-1.5650739782857	-1.8938739782857	-2.7449671508273e-05	-0.56299058436439
17.199	0.14905060936738	-1.567942333834	-1.567942333834	-1.896742333834	-2.537809009998e-05	-0.55896922157854
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17.599	0.14348051408565	-1.5735124291157	-1.5735124291157	-1.9023124291157	-2.1854738179027e-05	-0.5509264960092
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17.799	0.1407781093962	-1.5762148338052	-1.5762148338052	-1.9050148338052	-2.0354491133847e-05	-0.54690513322597
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21.199	0.10278338267274	-1.6142095605286	-1.6142095605286	-1.9430095605286	-8.2121513754676e-06	-0.47854196623142
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21.799	0.097506009946693	-1.6194869332547	-1.6194869332547	-1.9482869332547	-7.3189301665953e-06	-0.46647787805172
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22.399	0.092605664710028	-1.6243872784913	-1.6243872784913	-1.9531872784913	-6.5842212952737e-06	-0.45441378992885
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22.799	0.08953734666427	-1.6274555965371	-1.6274555965371	-1.9562555965371	-6.1638310497565e-06	-0.44637106455091
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23.999	0.081213644911731	-1.6357792982896	-1.6357792982896	-1.9645792982896	-5.1493049365306e-06	-0.42224288863889
24.001	0.081213644911731	-1.6357792982896	-1.6357792982896	-1.9645792982896	-5.1493049365306e-06	-0.42224288863889
24.199	0.079946433790772	-1.6370465094106	-1.6370465094106	-1.9658465094106	-5.0085053767432e-06	-0.4182215260248
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75.599	-0	-0	-0	-0	0	0
75.601	-0	-0	-0	-0	0	0
75.799	-0	-0	-0	-0	0	0
75.801	-0	-0	-0	-0	0	0
75.999	-0	-0	-0	-0	0	0
76.001	-0	-0	-0	-0	0	0
76.199	-0	-0	-0	-0	0	0
76.201	-0	-0	-0	-0	0	0
76.399	-0	-0	-0	-0	0	0
76.401	-0	-0	-0	-0	0	0
76.599	-0	-0	-0	-0	0	0
76.601	-0	-0	-0	-0	0	0
76.799	-0	-0	-0	-0	0	0
76.801	-0	-0	-0	-0	0	0
76.999	-0	-0	-0	-0	0	0
77.001	-0	-0	-0	-0	0	0
77.199	-0	-0	-0	-0	0	0
77.201	-0	-0	-0	-0	0	0
77.399	-0	-0	-0	-0	0	0
77.401	-0	-0	-0	-0	0	0
77.599	-0	-0	-0	-0	0	0
77.601	-0	-0	-0	-0	0	0
77.799	-0	-0	-0	-0	0	0
77.801	-0	-0	-0	-0	0	0
77.999	-0	-0	-0	-0	0	0
78.001	-0	-0	-0	-0	0	0
78.199	-0	-0	-0	-0	0	0
78.201	-0	-0	-0	-0	0	0
78.399	-0	-0	-0	-0	0	0
78.401	-0	-0	-0	-0	0	0
78.599	-0	-0	-0	-0	0	0
78.601	-0	-0	-0	-0	0	0
78.799	-0	-0	-0	-0	0	0
78.801	-0	-0	-0	-0	0	0
78.999	-0	-0	-0	-0	0	0
79.001	-0	-0	-0	-0	0	0
79.199	-0	-0	-0	-0	0	0
79.201	-0	-0	-0	-0	0	0
79.399	-0	-0	-0	-0	0	0
79.401	-0	-0	-0	-0	0	0
79.599	-0	-0	-0	-0	0	0
79.601	-0	-0	-0	-0	0	0
79.799	-0	-0	-0	-0	0	0
79.801	-0	-0	-0	-0	0	0
79.999	-0	-0	-0	-0	0	0
80.001	-0	-0	-0	-0	0	0
80.199	-0	-0	-0	-0	0	0
80.201	-0	-0	-0	-0	0	0
80.399	-0	-0	-0	-0	0	0
80.401	-0	-0	-0	-0	0	0
80.599	-0	-0	-0	-0	0	0
80.601	-0	-0	-0	-0	0	0
80.799	-0	-0	-0	-0	0	0
80.801	-0	-0	-0	-0	0	0
80.999	-0	-0	-0	-0	0	0
81.001	-0	-0	-0	-0	0	0
81.199	-0	-0	-0	-0	0	0
81.201	-0	-0	-0	-0	0	0
81.399	-0	-0	-0	-0	0	0
81.401	-0	-0	-0	-0	0	0
81.599	-0	-0	-0	-0	0	0
81.601	-0	-0	-0	-0	0	0
81.799	-0	-0	-0	-0	0	0
81.801	-0	-0	-0	-0	0	0
81.999	-0	-0	-0	-0	0	0
82.001	-0	-0	-0	-0	0	0
82.199	-0	-0	-0	-0	0	0
82.201	-0	-0	-0	-0	0	0
82.399	-0	-0	-0	-0	0	0
82.401	-0	-0	-0	-0	0	0
82.599	-0	-0	-0	-0	0	0
82.601	-0	-0	-0	-0	0	0
82.799	-0	-0	-0	-0	0	0
82.801	-0	-0	-0	-0	0	0
82.999	-0	-0	-0	-0	0	0
83.001	-0	-0	-0	-0	0	0
83.199	-0	-0	-0	-0	0	0
83.201	-0	-0	-0	-0	0	0
83.399	-0	-0	-0	-0	0	0
83.401	-0	-0	-0	-0	0	0
83.599	-0	-0	-0	-0	0	0
83.601	-0	-0	-0	-0	0	0
83.799	-0	-0	-0	-0	0	0
83.801	-0	-0	-0	-0	0	0
83.999	-0	-0	-0	-0	0	0
84.001	-0	-0	-0	-0	0	0
84.199	-0	-0	-0	-0	0	0
84.201	-0	-0	-0	-0	0	0
84.399	-0	-0	-0	-0	0	0
84.401	-0	-0	-0	-0	0	0
84.599	-0	-0	-0	-0	0	0
84.601	-0	-0	-0	-0	0	0
84.799	-0	-0	-0	-0	0	0
84.801	-0	-0	-0	-0	0	0
85	-0	-0	-0	-0	0	0

</dataplot>

;#;
<caption>Band edges and quasi-Fermi levels of the **p-i-n** diode under forward bias</caption>

</figure>

==== Carrier distribution ====


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).
<figure carrierenergy>
;#;
<dataplot center boxes xrange=-2.0:2.0 xlabel="Energy (eV)" ylabel="1/m^3/eV" ylegends="electrons holes" 600x400>
-5	0	3.4251761815982e-71
-4.95	0	2.3546202365442e-70
-4.9	0	1.6185428115155e-69
-4.85	0	1.1124794043624e-68
-4.8	0	7.6458066098224e-68
-4.75	0	5.2543284191257e-67
-4.7	0	3.6105444240759e-66
-4.65	0	2.4807825535647e-65
-4.6	0	1.7043710350566e-64
-4.55	0	1.1708409332282e-63
-4.5	0	8.0424574859147e-63
-4.45	0	5.5237694261036e-62
-4.4	0	3.7934722770976e-61
-4.35	0	2.6049029502853e-60
-4.3	0	1.7885374418275e-59
-4.25	0	1.2278771322082e-58
-4.2	0	8.4287007469647e-58
-4.15	0	5.7851363190195e-57
-4.1	0	3.970197483459e-56
-4.05	0	2.7242966921115e-55
-4	0	1.8691261732342e-54
-3.95	0	1.2822207639953e-53
-3.9	0	8.794778592606e-53
-3.85	0	6.0314644866985e-52
-3.8	0	4.1357485341916e-51
-3.75	0	2.835414536703e-50
-3.7	0	1.9436029816851e-49
-3.65	0	1.3320619954519e-48
-3.6	0	9.1277635221156e-48
-3.55	0	6.2535178441644e-47
-3.5	0	4.2835250371881e-46
-3.45	0	2.9335383356197e-45
-3.4	0	2.0085941740898e-44
-3.35	0	1.374987676987e-43
-3.3	0	9.4103883796464e-43
-3.25	0	6.4389360884638e-42
-3.2	0	4.4046753522833e-41
-3.15	0	3.0123261782601e-40
-3.1	0	2.0595536972231e-39
-3.05	0	1.4077373081689e-38
-3	0	9.6192546780418e-38
-2.95	0	6.570917074443e-37
-2.9	0	4.4871258965268e-36
-2.85	0	3.0630959666541e-35
-2.8	0	2.0902333559879e-34
-2.75	0	1.4258104786401e-33
-2.7	0	9.7219175722809e-33
-2.65	0	6.6260473085575e-32
-2.6	0	4.5139626314556e-31
-2.55	0	3.0736149030284e-30
-2.5	0	2.0917750195537e-29
-2.45	0	1.4227841462266e-28
-2.4	0	9.6717356994722e-28
-2.35	0	6.5704042430974e-27
-2.3	0	4.4604709300326e-26
-2.25	0	3.0258429478364e-25
-2.2	0	2.0509834366597e-24
-2.15	0	1.3889847774375e-23
-2.1	0	9.3976130897135e-23
-2.05	0	6.3515891239447e-22
-2	0	4.287910595513e-21
-1.95	0	2.8910358010033e-20
-1.9	0	1.9464430088341e-19
-1.85	0	1.3083787160587e-18
-1.8	0	8.7787776963187e-18
-1.75	0	5.8779111464135e-17
-1.7	0	3.9259417602964e-16
-1.65	0	2.6146228781054e-15
-1.6	0	1.7363153766249e-14
-1.55	0	1.149247445921e-13
-1.5	0	7.5711949985325e-13
-1.45	0	4.9577670077506e-12
-1.4	0	3.2181510551346e-11
-1.35	0	2.064719296556e-10
-1.3	0	1.3088794140204e-09
-1.25	0	8.2103984198758e-09
-1.2	0	4.9899713213291e-08
-1.15	0	3.1181418871782e-07
-1.1	0	1.8932368155462e-06
-1.05	0	1.0817166121629e-05
-1	0	5.7541410028532e-05
-0.95	0	0.00027026010186588
-0.9	0	0.00084740379628309
-0.85	0	0
-0.8	0	0
-0.75	0	0
-0.7	0	0
-0.65	0	0
-0.6	0	0
-0.55	0	0
-0.5	0	0
-0.45	0	0
-0.4	0	0
-0.35	0	0
-0.3	0	0
-0.25	0	0
-0.2	9.3865224927421e-07	0
-0.15	7.5897111214008e-05	0
-0.1	0.0001946331256069	0
-0.05	0.00018404316687727	0
0	6.4677186388148e-05	0
0.05	0.00010536172863269	0
0.1	6.3469213804644e-05	0
0.15	1.4893295959395e-05	0
0.2	2.8787356674191e-06	0
0.25	5.1318559185331e-07	0
0.3	8.744144439374e-08	0
0.35	1.4426175393363e-08	0
0.4	2.3171732523833e-09	0
0.45	3.6479033789753e-10	0
0.5	5.6635115404347e-11	0
0.55	8.7100634436679e-12	0
0.6	1.3300808883881e-12	0
0.65	2.0199653698992e-13	0
0.7	3.0560781424047e-14	0
0.75	4.6053015131739e-15	0
0.8	6.9166237662488e-16	0
0.85	1.0358931527955e-16	0
0.9	1.5477388745087e-17	0
0.95	2.3076943780767e-18	0
1	3.4345189871232e-19	0
1.05	5.1032913672362e-20	0
1.1	7.5719305940986e-21	0
1.15	1.1220135772472e-21	0
1.2	1.6606533105665e-22	0
1.25	2.4552507407366e-23	0
1.3	3.6265127536143e-24	0
1.35	5.3517326505346e-25	0
1.4	7.8911906048638e-26	0
1.45	1.1626822731812e-26	0
1.5	1.7118841277517e-27	0
1.55	2.5188613001324e-28	0
1.6	3.7039936647857e-29	0
1.65	5.4436459458121e-30	0
1.7	7.9961148068738e-31	0
1.75	1.1739566404767e-31	0
1.8	1.7227491426892e-32	0
1.85	2.5269746757129e-33	0
1.9	3.7050962034852e-34	0
1.95	5.4303500304444e-35	0
2	7.9560054241605e-36	0
2.05	1.1652246919301e-36	0
2.1	1.7060016701882e-37	0
2.15	2.4969601264895e-38	0
2.2	3.653531325127e-39	0
2.25	5.3442817956966e-40	0
2.3	7.8153229941569e-41	0
2.35	1.142591444186e-41	0
2.4	1.6700385175087e-42	0
2.45	2.4403841371314e-43	0
2.5	3.5652540903285e-44	0
2.55	5.207478624873e-45	0
2.6	7.6045425900793e-46	0
2.65	1.1102759492607e-46	0
2.7	1.6207067204771e-47	0
2.75	2.3653577286529e-48	0
2.8	3.4515262213119e-49	0
2.85	5.0355898725032e-50	0
2.9	7.3454275333057e-51	0
2.95	1.0713069863264e-51	0
3	1.5622242335259e-52	0
3.05	2.2777586032119e-53	0
3.1	3.3205430312236e-54	0
3.15	4.8400484765663e-55	0
3.2	7.0539354226235e-56	0
3.25	1.027912881074e-56	0
3.3	1.4977040351226e-57	0
3.35	2.1819373247791e-58	0
3.4	3.178386897501e-59	0
3.45	4.6293608516819e-60	0
3.5	6.7419664147925e-61	0
3.55	9.817588851409e-62	0
3.6	1.4294769878479e-62	0
3.65	2.0811571562328e-63	0
3.7	3.029627390718e-64	0
3.75	4.409926944154e-65	0
3.8	6.4184853973852e-66	0
3.85	9.3410094507028e-67	0
3.9	1.3593028202573e-67	0
3.95	1.9778839043236e-68	0
4	2.877719939921e-69	0
4.05	4.186589206629e-70	0
4.1	6.0902787821257e-71	0
4.15	8.8589014175593e-72	0
4.2	1.2885144035304e-72	0
4.25	1.8739854250581e-73	0
4.3	2.7252819692048e-74	0
4.35	3.9630151482664e-75	0
4.4	5.7624849410706e-76	0
4.45	8.3784630165021e-77	0
4.5	1.2181199882669e-77	0
4.55	1.7708737289149e-78	0
4.6	2.5742905673103e-79	0
4.65	3.7419724944913e-80	0
4.7	5.4389775021008e-81	0
4.75	7.9051142555647e-82	0
4.8	1.1488777290383e-82	0
4.85	1.6696089957778e-83	0
4.9	2.4262277505093e-84	0
4.95	3.5255321734273e-85	0
5	0	0

</dataplot>
;#;
<caption>Energy distribution $n(E)$ and $p(E)$ of the electrons and holes for the full device</caption>
</figure>

==== Emission Spectrum ====

The emission spectrum of the LED is plotted in figure {{ref>emissionspectra}}. The dependence of the spectrum on the bias voltage can be calculated using a voltage sweep.
<figure emissionspectra>
;#;

<dataplot center boxes xrange=0.5:1.5 xlabel="Energy (eV)" ylabel="Intensity (1/eV)" ylegends="Intensity" 600x400>
0.05	0
0.1	0
0.15	0
0.2	0
0.25	0
0.3	0
0.35	0
0.4	0
0.45	0
0.5	0
0.55	0
0.6	0
0.65	0
0.7	0
0.75	0
0.8	0
0.85	0
0.9	2.6482294168259e-15
0.95	6.0453845954928e-15
1	3.1144534619013e-15
1.05	1.0341424291558e-15
1.1	2.732789585318e-16
1.15	6.2925176938864e-17
1.2	1.3260522241003e-17
1.25	2.6333604463522e-18
1.3	5.0181474206707e-19
1.35	9.2437256536515e-20
1.4	1.6309423294566e-20
1.45	2.4973934538272e-21
1.5	8.0147952608172e-23
1.55	8.388689748133e-25
1.6	1.48264064066e-25
1.65	2.5994371893835e-26
1.7	4.5123302317883e-27
1.75	9.2454674407998e-28
1.8	2.7827645225635e-28
1.85	7.7154122964728e-29
1.9	1.8806324489176e-29
1.95	4.1595280840403e-30
2	8.5793046479174e-31
2.05	1.6809730267727e-31
2.1	3.1783098072118e-32
2.15	5.8341300176299e-33
2.2	1.0319027536954e-33
2.25	1.6713064209254e-34
2.3	1.8506027512264e-35
2.35	0
2.4	0
2.45	0
2.5	0
2.55	0
2.6	0
2.65	0
2.7	0
2.75	0
2.8	0
2.85	0
2.9	0
2.95	0
3	0
3.05	0
3.1	0
3.15	0
3.2	0
3.25	0
3.3	0
3.35	0
3.4	0
3.45	0
3.5	0
3.55	0
3.6	0
3.65	0
3.7	0
3.75	0
3.8	0
3.85	0
3.9	0
3.95	0
4	0
4.05	0
4.1	0
4.15	0
4.2	0
4.25	0
4.3	0
4.35	0
4.4	0
4.45	0
4.5	0
4.55	0
4.6	0
4.65	0
4.7	0
4.75	0
4.8	0
4.85	0
4.9	0
4.95	0
5	0
5.05	0
5.1	0
5.15	0
5.2	0
5.25	0
5.3	0
5.35	0
5.4	0
5.45	0
5.5	0
5.55	0
5.6	0
5.65	0
5.7	0
5.75	0
5.8	0
5.85	0
5.9	0
5.95	0
6	0
6.05	0
6.1	0
6.15	0
6.2	0
6.25	0
6.3	0
6.35	0
6.4	0
6.45	0
6.5	0
6.55	0
6.6	0
6.65	0
6.7	0
6.75	0
6.8	0
6.85	0
6.9	0
6.95	0
7	0
7.05	0
7.1	0
7.15	0
7.2	0
7.25	0
7.3	0
7.35	0
7.4	0
7.45	0
7.5	0
7.55	0
7.6	0
7.65	0
7.7	0
7.75	0
7.8	0
7.85	0
7.9	0
7.95	0
8	0
8.05	0
8.1	0
8.15	0
8.2	0
8.25	0
8.3	0
8.35	0
8.4	0
8.45	0
8.5	0
8.55	0
8.6	0
8.65	0
8.7	0
8.75	0
8.8	0
8.85	0
8.9	0
8.95	0
9	0
9.05	0
9.1	0
9.15	0
9.2	0
9.25	0
9.3	0
9.35	0
9.4	0
9.45	0
9.5	0
9.55	0
9.6	0
9.65	0
9.7	0
9.75	0
9.8	0
9.85	0
9.9	0
9.95	0
10	0

</dataplot>
;#;
<caption>Emission spectrum (intensity) of the **p-i-n** diode structure in units of 1/eV.</caption>
</figure>

/*
#$FLAG     = 1               # 0 or 1   [Chim, Fig. 2a)]
 $FLAG     = 0               # 0 or 1   [Chim, Fig. 2b)]
 $ANTIFLAG = 1 - $FLAG       # 1 or 0   (DoNotShowInUserInterface)

 $OxideThickness = 1.0    # oxide thickness (DisplayUnit:nm) (RangeOfValues:From=1  ,To=3  ,Step=1) (ListOfValues:1.0,3.0) (HighLightInUserInterface) 
#$OxideThickness = 3.0    # oxide thickness (DisplayUnit:nm) (RangeOfValues:From=1  ,To=3  ,Step=1) (ListOfValues:1.0,3.0) (HighLightInUserInterface) 

# If the gate should be made of metal, choose $METALLICGATE = 1             (contact type is ohmic).
# For $METALLICGATE = 0 the gate is made of a doped semiconductor (poly-Si) (contact type is fermi).
 $METALLICGATE      = 0                   # 0 (n-poly-Si) or 1 (metallic gate)
#$METALLICGATE      = 1                   # 0 (n-poly-Si) or 1 (metallic gate)
 $SEMICONDUCTORGATE = 1 - $METALLICGATE   # 1 (n-poly-Si) or 0 (metallic gate) (DoNotShowInUserInterface)

# If Schroedinger equation (quantum mechanics) should not be solved, choose $QM = 0.
# In other case choose $QM = 1.
#$QM = 0              # 0 (classical calculation) or 1 (quantum mechanical calculation)
 $QM = 1              # 0 (classical calculation) or 1 (quantum mechanical calculation)
$contact_thickness = 20
$pGaN_thickness = 20
$pAlGaN_thickness = 40
$InGaN_thickness = 10
$nAlGaN_thickness = 40
$nGaN_thickness = 20

$leftcontact_l = 0- ($InGaN_thickness / 2 + $pAlGaN_thickness + $pGaN_thickness + $contact_thickness)
$leftcontact_r = 0- ($InGaN_thickness / 2 + $pAlGaN_thickness + $pGaN_thickness)

$pGaN_l = 0- ($InGaN_thickness / 2 + $pAlGaN_thickness + $pGaN_thickness)
$pGaN_r = 0- ($InGaN_thickness / 2 + $pAlGaN_thickness)

$pAlGaN_l = 0- ($InGaN_thickness / 2 + $pAlGaN_thickness)
$pAlGaN_r = 0- ($InGaN_thickness / 2)

$InGaN_l = 0- ($InGaN_thickness / 2)
$InGaN_r = ($InGaN_thickness / 2)

$nAlGaN_l = ($InGaN_thickness / 2)
$nAlGaN_r = ($InGaN_thickness / 2 + $nAlGaN_thickness)


$nGaN_l = ($InGaN_thickness / 2 + $nAlGaN_thickness)
$nGaN_r = ($InGaN_thickness / 2 + $nAlGaN_thickness + $nGaN_thickness)

$rightcontact_l =  ($InGaN_thickness / 2 + $nAlGaN_thickness + $nGaN_thickness)
$rightcontact_r =  ($InGaN_thickness / 2 + $nAlGaN_thickness + $nGaN_thickness + $contact_thickness)


global{ 
   simulate1D{}
    # Simulation coordinate system rotated from z to x
   #database = "../Syntax/zincblende.in"
   
   # WARNING: check conversion limitations:
   # - only one "simulation-dimension" subsection in $numeric-control allowed
   # - only one quantum cluster supported, which must be rectangular
   # - only one quantum model allowed
   # - only one current cluster supported, covering the whole simulation area
   
   crystal_zb{
      x_hkl = [1, 0, 0]
      y_hkl = [0, 1, 0]
   }

   substrate{
      name = "GaAs"
   }

   temperature = 300.0E0 # [Chim] ! Kelvin
   # WARNING: Varshni parameters are always used in nextnano++

}<>

grid{
   xgrid{ 
      line{ pos = $leftcontact_l spacing = 0.2 }
      line{ pos = $leftcontact_r spacing = 0.2 }
      line{ pos = $pGaN_l spacing = 0.2 }
      line{ pos = $pGaN_r spacing = 0.2 }
      line{ pos = $pAlGaN_l spacing = 0.2 }
      line{ pos = $pAlGaN_r spacing = 0.2 }
      line{ pos = $InGaN_l spacing = 0.2 }
      line{ pos = $InGaN_r spacing = 0.2 }
      line{ pos = $nAlGaN_l spacing = 0.2 }
      line{ pos = $nAlGaN_r spacing = 0.2 }
      line{ pos = $nGaN_l spacing = 0.2 }
      line{ pos = $nGaN_r spacing = 0.2 }
 	line{ pos = $rightcontact_l spacing = 0.2 }
      line{ pos = $rightcontact_r spacing = 0.2 }
   }

   periodic{
      x = no
   }
}<>

structure{
   output_region_index{ boxes = no }
   output_material_index{ boxes = no }
   output_alloy_composition{ boxes = no }
   output_impurities{ boxes = no }

   region{
      everywhere{ # (default region in nextnano3)
      }
      binary{
         name = "GaAs" # p-Si substrate
      }
   }
   region{
      line{ 
         x = [$leftcontact_l, $pGaN_r]
      }
      contact { name = LeftContact }
      binary{
         name = "GaAs" 
      }
   }
   region{
      line{ # p-Si substrate
         x = [$pAlGaN_l , $pAlGaN_r ]
      }
      ternary_constant{
         name = "Al(x)Ga(1-x)As"     
  	alloy_x = 0.2 
	}
   }
   region{
      line{ # p-Si substrate
         x = [$InGaN_l, $InGaN_r]
      }
      ternary_constant{
         name = "In(x)Ga(1-x)As" 
	alloy_x = 0.4
      }
   }
   region{
	line{ # p-Si substrate
         x = [$nAlGaN_l , $nAlGaN_r ]
      }
      ternary_constant{
         name = "Al(x)Ga(1-x)As"  
	alloy_x = 0.2
      }
   }
   region{
      line{ 
         x = [$nGaN_l, $rightcontact_r]
      }
      contact { name = RightContact }
      binary{
         name = "GaAs" 
      }
   }

   region{ # doping
      line{
         x = [$leftcontact_l, $pGaN_r]
      }
      doping{
         constant{
            name = "p-doping_contact" # properties of this impurity type have to be specified below
            conc = 1.0E18 
         }
      }
   }

  region{ # doping
      line{
         x = [$pAlGaN_l, $pAlGaN_r]
      }
      doping{
         constant{
            name = "p-doping_LED" # properties of this impurity type have to be specified below
            conc = 1.0E18 
         }
      }
   }

   region{ # doping
      line{
         x = [$nAlGaN_l, $nAlGaN_r]
      }
      doping{
         constant{
            name = "n-doping_LED" # properties of this impurity type have to be specified below
            conc = 1.0E18 
         }
      }
   }
region{ # doping
      line{
         x = [$nGaN_l, $rightcontact_r]
      }
      doping{
         constant{
            name = "n-doping_contact" # properties of this impurity type have to be specified below
            conc = 1.0E18 
         }
      }
   }
}<>

impurities{
   donor{ # n-type
      name = "n-doping_contact"
      energy = 0.054E0 # energy relative to 'nearest' band edge (n-type -> conduction band, p-type -> valence band)
      degeneracy = 2 # degeneracy of energy levels, 2 for n-type, 4 for p-type
   }

   donor{ # n-type
      name = "n-doping_LED"
      energy = 0.054E0 # energy relative to 'nearest' band edge (n-type -> conduction band, p-type -> valence band)
      degeneracy = 2 # degeneracy of energy levels, 2 for n-type, 4 for p-type
   }
   acceptor{ # p-type
      name = "p-doping_LED"
      energy = 0.045E0 # energy relative to 'nearest' band edge (n-type -> conduction band, p-type -> valence band)
      degeneracy = 2 # degeneracy of energy levels, 2 for n-type, 4 for p-type
   }
   acceptor{ # p-type
      name = "p-doping_contact"
      energy = 0.045E0 # energy relative to 'nearest' band edge (n-type -> conduction band, p-type -> valence band)
      degeneracy = 2 # degeneracy of energy levels, 2 for n-type, 4 for p-type
   }
}<>

contacts{

ohmic{
 name = LeftContact
 bias = 0.8
  
}

ohmic{
 name = RightContact
 bias = 0.0
}


}<>

currents{
 mobility_model    = constant
 recombination_model{
      SRH            = no        # Shockley-Read-Hall recombination
      Auger          = no        # Auger recombination
      radiative      = yes         # radiative recombination (direct recombination)
   }     
 output_fermi_levels{}
   output_currents{}
}

classical{
   Gamma{}
LH{}
	HH{}
	SO{}

   output_bandedges{ averaged = no }
   output_carrier_densities{}
   output_intrinsic_density{}
    energy_distribution{
	min = -5
	max = 5 
	energy_resolution = 0.05
   }
}<>

poisson{
   output_potential{}
	
}<>


quantum {
   region{
      name = "quantum_region"
      x = [($pAlGaN_l + $pAlGaN_r)/2 , ($nAlGaN_l + $nAlGaN_r)/2]
      boundary{
         x = neumann
      }
       kp_8band{ 
      	num_electrons =5 num_holes = 5
		k_integration{ 
					
					relative_size = 0.3
					num_subpoints = 10
					num_points = 10
				}
			lapack{}
#	kp_parameters{                       # advanced manipulation of k.p parameters from database
#         use_Luttinger_parameters = no     # use DKK (Dresselhaus-Kip-Kittel) parameters (L, M, N) (optional, default is: no)
#         approximate_kappa        = yes     # kappa for zinc blende crystal structure is taken from the database or input file (optional, default is: no)
#                  }
    	
      }	



	output_subband_densities{}      


      output_wavefunctions{
         max_num = 9999
         all_k_points = yes
         amplitudes = no
         probabilities = yes
      }
   }
}<>

optics{

		debuglevel = 2
	region{

		name = "quantum_region"



		interband = yes
		intraband = no		

            polarization{ name="ypiz" re = [0,1,0] im = [0,0,1] }
		
		output_transitions = yes
		occupation_threshold = 10E-10
		energy_threshold = 1E-8
		transition_threshold = 10E-10
		
		energy_min = 1.2
		energy_max = 1.8
		energy_resolution = 0.1
		
		k_integration{
		  num_points = 10
		  num_subpoints = 10
		  
			symmetry = 1			
			
			relative_size = 0.3
		}
	}
}

opticaldevice{
	name = "quantum_region"
	line_broadening = 1
#	photon_energy = 1
#	poynting_vector = 1
}

output{
   directory = "outputLED"
}<>

run{
           #solve_poisson{}
		solve_current_poisson{}
#solve_optical_device{}
	#solve_quantum{}
#		calculate_optics{}
}<>

*/
The input file can be downloaded from {{nnp:optics:ledsim_zb_-_p-i-n_device.zip?linkonly | here }}
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