nextnano.NEGF - Software for
Quantum Transport

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====== Led Simulation ======

In the following example we are going to show you, how can be the spectra of a Light emitting diode calculated with the** nextano++** software.

==== Physics model ====

In a Led the photons are emitted in the radiate recombination process:
;#;
$$R_{rad} = c_r (n  p - n_i n_i)$$
;#;

Where the $n$, and $p$ correspond the density of the holes and the electrons in the volume element, and $n_i$ is the intrinsic density of the charge carriers. 
This recombination rate is coupled in the drift-diffusion solver of the **nextnano++**, and it calculates the stationary solution of the problem:
;#;
$$\frac{d}{dt}n = 0 $$ $$\frac{d}{dt}p = 0 $$
;#;

=== Spectrum of the emission ===

According to this simple model, where $c_r$ is just a material constant, the radiation recombination rate, which generates photons on energy $E_r$ could be written in the form:

;#;
$$R_{rad}(E_r) = c_r \int n(E_e)  \cdot p(E_h) \delta(E_e-E_h-E_r)  dE_e dE_h  $$
;#;

Where the density $n(E_e)$, and $p(E_h)$ the electron and hole densities on the energy niveu $E_e$, 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 model calculates with constant $c_r$, which is in **QW** structures not correct, and also 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>

In order to get physically valid results we have to calculate with radiative recombinations in the drift diffusion. 
<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 in 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 in function of energy
	min = -5                     # Integrate from
	max = 5                      # Integrate to
	energy_resolution = 0.05     # Integration Resolution
   }
</Code>


==== Results ====
The simulated test system was a **p-i-n** diode structure from //pGaAs-pAlGaAs-InGaAs-nAlGaAs-nGaAs// hetero-structure composition. In the center insulator part (//InGaAs//) the Fermi level reaches the band-edges of the Quantum well, which makes population in the well for both electrons, and holes. The applied bias in the drift diffusion equation results the splitting of the hole and electron Fermi levels. It can be seen on the band structure profile on figure {{ref>bandstructure}}


 
<figure bandstructure>
;#;
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;#;
<caption>Band Structure of the **p-i-n** diode under forward bias </caption>

</figure>



The carrier distribution in the energy can be seen on figure {{ref>carrierenergy}}. The density is summed for the full device, it results the loss of the position information for the carrier densities.
<figure carrierenergy>
;#;
{{http://mz-xience.com/dokuwiki/lib/plugins/dataplot/img.php?width=600&height=400&align=center&layout=2D&columns=3&plottype=boxes&smooth=&xlabel=E%28eV%29&ylabel=1%2Fm%5E3%2FeV&xrange=-2.0%3A2.0&yrange=&gnuplot=%23%20Input%20parameters%3A%0A%23%0A%23%20%20-%20width%20%3D%20600%0A%23%20%20-%20height%20%3D%20400%0A%23%20%20-%20align%20%3D%20center%0A%23%20%20-%20layout%20%3D%202D%0A%23%20%20-%20columns%20%3D%203%0A%23%20%20-%20plottype%20%3D%20boxes%0A%23%20%20-%20smooth%20%3D%20%0A%23%20%20-%20xlabel%20%3D%20E%28eV%29%0A%23%20%20-%20ylabel%20%3D%201%2Fm%5E3%2FeV%0A%23%20%20-%20xrange%20%3D%20-2.0%3A2.0%0A%23%20%20-%20yrange%20%3D%20%0A%23%20%20-%20debug%20%3D%20%0A%23%20%20-%20version%20%3D%202016-12-12%2009%3A40%3A07%0A%23%20%20-%20linestyle%20%3D%201%0A%23%20%20-%20hash%20%3D%20dataplot_584eb6c7afaa36.21470505%0A%23%0A%0Aset%20terminal%20pngcairo%20enhanced%20dashed%20font%20%22arial%2C14%22%20linewidth%202%20size%20600%2C400%0Aset%20xlabel%20%22E%28eV%29%22%0Aset%20ylabel%20%221%2Fm%5E3%2FeV%22%0Aset%20xrange%20%5B-2.0%3A2.0%5D%0Aset%20output%20%22%40gnu_output%40%22%0Aset%20style%20line%201%20linetype%20rgb%20%22red%22%20linewidth%201.2%20pointtype%201%0Aset%20style%20line%202%20linetype%20rgb%20%22medium-blue%22%20linewidth%201.2%20pointtype%202%0Aset%20style%20line%203%20linetype%20rgb%20%22orange-red%22%20linewidth%201.2%20pointtype%203%0Aset%20style%20line%204%20linetype%20rgb%20%22dark-violet%22%20linewidth%201.2%20pointtype%204%0Aset%20style%20line%205%20linetype%20rgb%20%22dark-turquoise%22%20linewidth%201.2%20pointtype%205%0Aset%20style%20line%206%20linetype%20rgb%20%22dark-chartreuse%22%20linewidth%201.2%20pointtype%206%0Aset%20style%20line%207%20linetype%20rgb%20%22grey40%22%20linewidth%201.2%20pointtype%207%0Aset%20style%20line%208%20linetype%20rgb%20%22black%22%20linewidth%201.2%20pointtype%208%0Aplot%20%22%40gnu_input%40%22%20using%201%3A2title%20%22electrons%22%20%20with%20boxes%20linestyle%201%20linecolor%201%2C%20%5C%0A%20%20%20%20%20%22%40gnu_input%40%22%20using%201%3A3title%20%22holes%22%20%20with%20boxes%20linestyle%201%20linecolor%202%0A&debug=&version=2016-12-12%2009%3A40%3A07&linestyle=1&hash=dataplot_584eb6c7afaa36.21470505&.png?}}
;#;
<caption>Energy distribution of carriers for the full device volume</caption>
</figure>



The emission spectrum of the Led is plotted on figure {{ref>emissionspectra}}. The dependence of the spectrum on the bias voltage can be calculated with voltage sweeps.
<figure emissionspectra>
;#;
{{http://mz-xience.com/dokuwiki/lib/plugins/dataplot/img.php?width=600&height=400&align=center&layout=2D&columns=2&plottype=boxes&smooth=&xlabel=E%28eV%29&ylabel=Intensity%281%2FeV%29&xrange=0.5%3A1.5&yrange=&gnuplot=%23%20Input%20parameters%3A%0A%23%0A%23%20%20-%20width%20%3D%20600%0A%23%20%20-%20height%20%3D%20400%0A%23%20%20-%20align%20%3D%20center%0A%23%20%20-%20layout%20%3D%202D%0A%23%20%20-%20columns%20%3D%202%0A%23%20%20-%20plottype%20%3D%20boxes%0A%23%20%20-%20smooth%20%3D%20%0A%23%20%20-%20xlabel%20%3D%20E%28eV%29%0A%23%20%20-%20ylabel%20%3D%20Intensity%281%2FeV%29%0A%23%20%20-%20xrange%20%3D%200.5%3A1.5%0A%23%20%20-%20yrange%20%3D%20%0A%23%20%20-%20debug%20%3D%20%0A%23%20%20-%20version%20%3D%202016-12-12%2009%3A57%3A49%0A%23%20%20-%20linestyle%20%3D%201%0A%23%20%20-%20hash%20%3D%20dataplot_584ebaedd53438.52952851%0A%23%0A%0Aset%20terminal%20pngcairo%20enhanced%20dashed%20font%20%22arial%2C14%22%20linewidth%202%20size%20600%2C400%0Aset%20xlabel%20%22E%28eV%29%22%0Aset%20ylabel%20%22Intensity%281%2FeV%29%22%0Aset%20xrange%20%5B0.5%3A1.5%5D%0Aset%20output%20%22%40gnu_output%40%22%0Aset%20style%20line%201%20linetype%20rgb%20%22red%22%20linewidth%201.2%20pointtype%201%0Aset%20style%20line%202%20linetype%20rgb%20%22medium-blue%22%20linewidth%201.2%20pointtype%202%0Aset%20style%20line%203%20linetype%20rgb%20%22orange-red%22%20linewidth%201.2%20pointtype%203%0Aset%20style%20line%204%20linetype%20rgb%20%22dark-violet%22%20linewidth%201.2%20pointtype%204%0Aset%20style%20line%205%20linetype%20rgb%20%22dark-turquoise%22%20linewidth%201.2%20pointtype%205%0Aset%20style%20line%206%20linetype%20rgb%20%22dark-chartreuse%22%20linewidth%201.2%20pointtype%206%0Aset%20style%20line%207%20linetype%20rgb%20%22grey40%22%20linewidth%201.2%20pointtype%207%0Aset%20style%20line%208%20linetype%20rgb%20%22black%22%20linewidth%201.2%20pointtype%208%0Aplot%20%22%40gnu_input%40%22%20using%201%3A2title%20%22Intensity%22%20%20with%20boxes%20linestyle%201%20linecolor%201%0A&debug=&version=2016-12-12%2009%3A57%3A49&linestyle=1&hash=dataplot_584ebaedd53438.52952851&.png?}}
;#;
<caption>Emission spectrum of the **p-i-n** diode structure in arbitrary units.</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{}
}<>

*/
nextnano.NEGF - Software for Quantum Transport

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nextnano.NEGF - Software for
Quantum Transport
