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qcl:tutorials:thz_qcl_-_fathololoumi_2012 [2017/02/17 17:41]
stefan.birner [Current-voltage characteristics] 		qcl:tutorials:thz_qcl_-_fathololoumi_2012 [2018/03/20 11:14] (current)
thomas.grange [Device definition]
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 This ''​*-FAST.xml''​ file is only intended to show the user how to run a "​quick"​ simulation. This ''​*-FAST.xml''​ file is only intended to show the user how to run a "​quick"​ simulation.
 The results shown here correspond to the ''​*-MEDIUM.xml''​ file. The results shown here correspond to the ''​*-MEDIUM.xml''​ file.
 +''​​[Fathololoumi2012]''​​ designed the laser to operate at an electric field of -12.2 kV/cm.
  
-''​[Fathololoumi2012]''​ designed the laser to operate at an electric field of 12.2 kV/cm with a transition energy of 15.1 meV (or 11.5 meV?). 
 ===== Simulation details ===== ===== Simulation details =====
  
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 ==== Device definition ==== ==== Device definition ====
  
-First, the well (GaAs) and barrier materials (AlGaAs) have to be defined.+First, the materials used in the structure ​(GaAs and AlGaAs) have to be defined. Each material is referred by an alias, which is here '​well'​ for GaAs and '​barrier'​ and AlGaAs.
  
 <​code>​ <​code>​
-  <Material_Well>​ +  <Materials>
-   <​name>​ GaAs </​name>​ +
-  </​Material_Well>+
  
-  ​<Material_Barrier> +    ​<Material> 
-   ​<name> Al(x)Ga(1-x)As </name> +      <Name>​GaAs</​Name>​ 
-   ​<​Alloy_Composition>​ 0.15 </​Alloy_Composition>​ <​!-- ​x=0.15 (Al0.15Ga0.85As) ​--> +      <​Alias>​well</​Alias>​ 
-  </Material_Barrier>+      <​Effective_mass_from_kp_parameters>​yes</​Effective_mass_from_kp_parameters>​ 
 +    </​Material>​ 
 + 
 +    <​Material>​ 
 +      <Name>​Al(x)Ga(1-x)As</​Name> 
 +      <​Alloy_Composition>​0.15</​Alloy_Composition>​ 
 +      <​Alias>​barrier</​Alias>​ 
 +      <​Effective_mass_from_kp_parameters>​yes</​Effective_mass_from_kp_parameters>​ 
 +    </​Material>​ 
 +     
 +    ​<​!-- ​Model nonparabolicity ​--> 
 +    <​NonParabolicity>​yes</​NonParabolicity>​ 
 + 
 +    <​UseConductionBandOffset>​yes</​UseConductionBandOffset>​ 
 + 
 +  </Materials>
 </​code>​ </​code>​
 +In addition, it is specified that the effective mass is calculated from the k.p parameters. Also, non
 +
  
 Then, alternating layers consisting of barrier and well have to be specified, i.e. **4.1** / __16.0__ / **4.3** / 8.9 / **2.46** / 8.15, where AlGaAs is in bold fonts and the doping region is underlined, i.e. the wide GaAs quantum well is doped. Then, alternating layers consisting of barrier and well have to be specified, i.e. **4.1** / __16.0__ / **4.3** / 8.9 / **2.46** / 8.15, where AlGaAs is in bold fonts and the doping region is underlined, i.e. the wide GaAs quantum well is doped.
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 </​code>​ </​code>​
  
-The resulting conduction band edge profile can be found in the file called ''​Band-Edge_vs_position.dat''​.+The resulting conduction band edge profile can be found in the file called ''​BandEdge_conduction.dat''​.
 This file includes the (small) band bending due to the electrostatic potential. This file includes the (small) band bending due to the electrostatic potential.
 At a bias voltage of 54 mV per period, it looks as follows. At a bias voltage of 54 mV per period, it looks as follows.
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 <​figure>​ <​figure>​
 ;#; ;#;
-<​dataplot xlabel="​Position (nm)" ylabel="​Energy (eV)" ylegends="​E_c">​+<​dataplot xlabel="​Position (nm)" ylabel="​Energy (eV)" ylegends="​E_c" title="​Conduction band edge">
 -1.9959090909E-001  ​  ​7.4383341270E-002 ​   -1.9959090909E-001  ​  ​7.4383341270E-002 ​  
 0.0000000000E+000  ​  ​1.4844107543E-001 ​   0.0000000000E+000  ​  ​1.4844107543E-001 ​  
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 ;#; ;#;
-<​caption>​Conduction band edge at a bias of 54 mV/period which corresponds to an electric field of 12.3 kV/​cm</​caption>​+<​caption>​Conduction band edge at a bias of 54 mV/period which corresponds to an electric field of -12.3 kV/​cm</​caption>​
  
 </​figure>​ </​figure>​
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 </​code>​ </​code>​
 ==== Material parameters ==== ==== Material parameters ====
-We set the conduction band offset between GaAs and Al<​sub>​0.15</​sub>​Ga<​sub>​0.85</​sub>​As to 0.120 eV, i.e. we overwrite the default material parameters that are contained in the [[qcl:​material_database|material database]].+We set the conduction band offset ​(CBO) between GaAs and Al<​sub>​0.15</​sub>​Ga<​sub>​0.85</​sub>​As to 0.120 eV, i.e. we overwrite the default material parameters that are contained in the [[qcl:​material_database|material database]].
 <​code>​ <​code>​
  <​Material_Parameters>​  <​Material_Parameters>​
-  <Band_Offset ​           unit="​meV">​ 120 </Band_Offset>+  <Overwrite_ConductionBandOffset>​true</​Overwrite_ConductionBandOffset>​ 
 +  <​ConductionBandOffset ​unit="​meV">​ 120 </ConductionBandOffset>
  </​Material_Parameters>​  </​Material_Parameters>​
 </​code>​ </​code>​
 +(In fact, the figures shown in the tutorial were generated using a different CBO of 0.149 eV.)
 ==== Electric field ==== ==== Electric field ====
 The total length of one period is L = 43.91 nm. The total length of one period is L = 43.91 nm.
-A bias of V = 54 mV per period then corresponds to an electric field of F = V/L = 12.3 kV/cm.+A bias of V = 54 mV per period then corresponds to an electric field of F = V/L = -12.3 kV/cm.
  
 ==== Wannier-Stark states ==== ==== Wannier-Stark states ====
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 ;#; ;#;
-<​caption>​Conduction band edge at a bias of 54 mV/period which corresponds to an electric field of 12.3 kV/cm and corresponding probability densities ($\left|\psi_i(x)\right|^2$) of the Wannier-Stark states.</​caption>​+<​caption>​Conduction band edge at a bias of 54 mV/period which corresponds to an electric field of -12.3 kV/cm and corresponding probability densities ($\left|\psi_i(x)\right|^2$) of the Wannier-Stark states.</​caption>​
  
 </​figure>​ </​figure>​
  
-The following two figures show the Wannier-Stark states at an applied bias of 56 mV/period (12.8 kV/cm).+The following two figures show the Wannier-Stark states at an applied bias of 56 mV/period (-12.8 kV/cm).
 They compare Fig. 1 of the publication of T. Grange, PRB 92, 241306(R) (2015) with the results of this input file. They compare Fig. 1 of the publication of T. Grange, PRB 92, 241306(R) (2015) with the results of this input file.
  
 {{ :​qcl:​tutorials:​fathololoumi:​fig1_grangeprb2015.jpg |}} {{ :​qcl:​tutorials:​fathololoumi:​fig1_grangeprb2015.jpg |}}
 <​figure>​ <​figure>​
-<​caption>​Wannier-Stark states at a bias of 56 mV/period (12.8 kV/cm) (Fig. 1 of T. Grange, PRB 92, 241306(R) (2015)).+<​caption>​Wannier-Stark states at a bias of 56 mV/period (-12.8 kV/cm) (Fig. 1 of T. Grange, PRB 92, 241306(R) (2015)).
 The three-well design consists of one large well and two small wells. The three-well design consists of one large well and two small wells.
 The optical photon transition is a diagonal transition (i.e. from the left thin well to the right thin well) and occurs between the states 2 (blue) and 3 (red). The optical photon transition is a diagonal transition (i.e. from the left thin well to the right thin well) and occurs between the states 2 (blue) and 3 (red).
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 {{ :​qcl:​tutorials:​fathololoumi:​fig1_grangeprb2015_nextnano.jpg |}} {{ :​qcl:​tutorials:​fathololoumi:​fig1_grangeprb2015_nextnano.jpg |}}
 <​figure>​ <​figure>​
-<​caption>​Wannier-Stark states at a bias of 56 mV/period (12.8 kV/cm) (Results of this input file)</​caption>​+<​caption>​Wannier-Stark states at a bias of 56 mV/period (-12.8 kV/cm) (Results of this input file)</​caption>​
 </​figure>​ </​figure>​
 ==== Local density of states ==== ==== Local density of states ====
-The following figure shows the local density of states (LDOS) at a bias of 54 mV / period corresponding to 12.3 kV/cm).+The following figure shows the local density of states (LDOS) at a bias of 54 mV / period corresponding to -12.3 kV/cm).
 The LDOS tells us where and at which energy electronic states are available that the charge carriers can occupy. The LDOS tells us where and at which energy electronic states are available that the charge carriers can occupy.
 The LDOS is shown for $k_\parallel=0$,​ i.e. there are also electronic states available for $k_\parallel \ne 0$. The LDOS is shown for $k_\parallel=0$,​ i.e. there are also electronic states available for $k_\parallel \ne 0$.
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 </​figure>​ </​figure>​
 ==== Electron density ==== ==== Electron density ====
-The following figure shows the energy resolved electron density $n(x,E)$ at a bias of 54 mV / period corresponding to 12.3 kV/cm).+The following figure shows the energy resolved electron density $n(x,E)$ at a bias of 54 mV / period corresponding to -12.3 kV/cm).
 The electron density is obtained from occupying the LDOS (for both $k_\parallel=0$ and $k_\parallel \ne 0$) with charge carriers. The electron density is obtained from occupying the LDOS (for both $k_\parallel=0$ and $k_\parallel \ne 0$) with charge carriers.
 The occupation is not described by a Fermi distribution (equilibrium). The occupation is not described by a Fermi distribution (equilibrium).
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 <​figure>​ <​figure>​
-<​caption>​Energy resolved electron density $n(x,E)$ and conduction band edge $E_{\rm c}$ at a bias of 54 mV / period (12.3 kV/​cm)</​caption>​+<​caption>​Energy resolved electron density $n(x,E)$ and conduction band edge $E_{\rm c}$ at a bias of 54 mV / period (-12.3 kV/​cm)</​caption>​
 </​figure>​ </​figure>​
  
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 <​figure>​ <​figure>​
-<​caption>​Electron density $n(x)$ at a bias of 54 mV/period which corresponds to an electric field of 12.3 kV/​cm</​caption>​+<​caption>​Electron density $n(x)$ at a bias of 54 mV/period which corresponds to an electric field of -12.3 kV/​cm</​caption>​
 </​figure>​ </​figure>​
  
-The following two figures show the energy resolved electron density at an applied bias of 58 mV/period (13.2 kV/cm). They compare Fig. 3 (a) of the publication of T. Grange, PRB 92, 241306(R) (2015) with the results of this input file.+The following two figures show the energy resolved electron density at an applied bias of 58 mV/period (-13.2 kV/cm). They compare Fig. 3 (a) of the publication of T. Grange, PRB 92, 241306(R) (2015) with the results of this input file.
  
 {{ :​qcl:​tutorials:​fathololoumi:​fig3_grangeprb2015.jpg |}} {{ :​qcl:​tutorials:​fathololoumi:​fig3_grangeprb2015.jpg |}}
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 <​figure>​ <​figure>​
 <​caption>​ <​caption>​
-Energy resolved electron density $n(x,E)$ at a bias of 58 mV/period (13.2 kV/cm) (Fig. 3(a) of T. Grange, PRB 92, 241306(R) (2015))+Energy resolved electron density $n(x,E)$ at a bias of 58 mV/period (-13.2 kV/cm) (Fig. 3(a) of T. Grange, PRB 92, 241306(R) (2015))
 </​caption>​ </​caption>​
 </​figure>​ </​figure>​
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 <​figure>​ <​figure>​
 <​caption>​ <​caption>​
-Energy resolved electron density $n(x,E)$ at a bias of 58 mV/period (13.2 kV/cm) (Results of this input file)+Energy resolved electron density $n(x,E)$ at a bias of 58 mV/period (-13.2 kV/cm) (Results of this input file)
 </​caption>​ </​caption>​
 </​figure>​ </​figure>​
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 ==== Current density ==== ==== Current density ====
  
-The following figure shows the energy resolved current density $j(x,E)$ at a bias of 54 mV / period corresponding to 12.3 kV/cm).+The following figure shows the energy resolved current density $j(x,E)$ at a bias of 54 mV / period corresponding to -12.3 kV/cm).
  
 {{ :​qcl:​tutorials:​fathololoumi:​current_density_image.png |}} {{ :​qcl:​tutorials:​fathololoumi:​current_density_image.png |}}
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 </​code>​ </​code>​
 ==== Gain ==== ==== Gain ====
-The following figure shows the energy resolved gain $g(x,E_{\rm ph})$ at a bias of 54 mV / period corresponding to 12.3 kV/​cm). ​+The following figure shows the energy resolved gain $g(x,E_{\rm ph})$ at a bias of 54 mV / period corresponding to -12.3 kV/​cm). ​
 Note that the energy axis corresponds to the photon energy $E_{\rm ph}$. Note that the energy axis corresponds to the photon energy $E_{\rm ph}$.
 The thin white lines indicate the barrier/​well interfaces and are only a guide to the eye. The thin white lines indicate the barrier/​well interfaces and are only a guide to the eye.
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 Time for electron to travel through one period = 8.90375389605566 ps Time for electron to travel through one period = 8.90375389605566 ps
  
-Electric Field = 12.2978820314279 kV/cm+Electric Field = -12.2978820314279 kV/cm
 Doping sheet density per period 30000000000 cm^-2 Doping sheet density per period 30000000000 cm^-2
 Average 3D doping density ​ 6.83215668412662E+15 cm^-3 Average 3D doping density ​ 6.83215668412662E+15 cm^-3
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       <​Amplitude_in_Z unit="​nm">​ 0.1 </​Amplitude_in_Z>​       <​Amplitude_in_Z unit="​nm">​ 0.1 </​Amplitude_in_Z>​
       <​InterfaceAutoCorrelationType>​ 0 </​InterfaceAutoCorrelationType>​       <​InterfaceAutoCorrelationType>​ 0 </​InterfaceAutoCorrelationType>​
-          ​<!-- Correlation type: 0=Exponential,​ 1=Gaussian -->+               <!-- Correlation type: 0=Exponential,​ 1=Gaussian -->
       <​Correlation_Length_in_XY unit="​nm">​ 8 </​Correlation_Length_in_XY>​       <​Correlation_Length_in_XY unit="​nm">​ 8 </​Correlation_Length_in_XY>​
       <​Asymmetric_Interfaces>​ false </​Asymmetric_Interfaces>​       <​Asymmetric_Interfaces>​ false </​Asymmetric_Interfaces>​
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   </​Roughness>​   </​Roughness>​
 </​code>​ </​code>​
 +
 +==== Computational resources ====
 +
 +The CPU time was about 5-6 hours and used about 9 GB RAM.
  
 ==== Feedback ==== ==== Feedback ====
qcl/tutorials/thz_qcl_-_fathololoumi_2012.1487353302.txt.gz · Last modified: 2017/02/17 17:41 (external edit)

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