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qcl:simulation_output [2018/06/06 12:34]
thomas.grange [Initial electronic states]
qcl:simulation_output [2022/09/20 17:10] (current)
thomas.grange
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 ====== Simulation output ====== ====== Simulation output ======
  
-For each simulation run, a new output folder is created in the simulation output folder. The created folder has the name of the input file. In addition date-time ​is added to the folder name if the option is selected in Options->​Expert settings ​of nextnanomat ​(this option is recommended in order to avoid overwritten ​existing output data).+For each simulation run, a new output folder is created in the simulation output folder. The created folder has the name of the input file. 
 + 
 +In additiondate-time ​can be added to the folder name by the nextnanomat setting (Tools -> Options -> Expert settings ​before Aug 2021, Tools -> Options -> View/Output since Aug 2021). For nextnanomat ​before Aug 2021, this option is recommended in order to avoid overwriting ​existing output data. For nextnanomat after Aug 2021, simulation output is per default not overwritten and instead enumerated unless you manually check the option "​Overwrite existing simulation..."​. 
 The created output folder contains: The created output folder contains:
   * the **input file** (.xml) and the **material database** (.xml).   * the **input file** (.xml) and the **material database** (.xml).
-  * a folder '​**Input**'​ which gives material parameters used in the calculation.+  * a folder '​**Input**'​ which contains ​material parameters used in the calculation.
   *  a folder **Strain** (only if the strain option is activated).   *  a folder **Strain** (only if the strain option is activated).
   * a folder **Polarization** if pyroelectric and/or piezoelectric effects are considered.   * a folder **Polarization** if pyroelectric and/or piezoelectric effects are considered.
-  * a folder '​**Init_Electron_Modes**' ​where the results of the initial Schrödinger solution ​is reported.+  * a folder '​**Init_Electron_Modes**' ​for the results of the initial Schrödinger solution.
   * a **folder for each parameter step**. In particular, in case of voltage sweep, the name of the folder is the potential drop per period.   * a **folder for each parameter step**. In particular, in case of voltage sweep, the name of the folder is the potential drop per period.
   * Several files related to the sweep made. For a voltage sweep, it contains plots of physical quantities (current, gain,...) as a function of the applied voltage.   * Several files related to the sweep made. For a voltage sweep, it contains plots of physical quantities (current, gain,...) as a function of the applied voltage.
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 ===== '​Input'​ folder ===== ===== '​Input'​ folder =====
-The folder ''​Input/''​ contains all information that is input to the simulation such as material parameters.+The folder ''​Input/''​ contains all the simulation ​input such as material parameters ​as a function of position.
   * ''​AlloyContent.dat''​\\ alloy concentration $x$ vs. position for ternary materials such as ''​Al(x)Ga(1-x)As''​   * ''​AlloyContent.dat''​\\ alloy concentration $x$ vs. position for ternary materials such as ''​Al(x)Ga(1-x)As''​
-  * ''​BandEdge_conduction.dat''​\\ ​conduction band edge $E_{\rm c}including shift due to strain ​vs. position ​in units of [eV]+  * ''​AlloyScatteringTerm.dat''​\\ ​alloy scattering term (in unit of [eV$^2$]) vs. position ​for ternary materials
   * ''​BandEdges.dat''​\\ conduction band edge $E_{\rm c}$ and valence band edge $E_{\rm v}$ vs. position in units of [eV]   * ''​BandEdges.dat''​\\ conduction band edge $E_{\rm c}$ and valence band edge $E_{\rm v}$ vs. position in units of [eV]
   * ''​BandGap.dat''​\\ energy band gap $E_{\rm gap}$ vs. position in units of [eV]   * ''​BandGap.dat''​\\ energy band gap $E_{\rm gap}$ vs. position in units of [eV]
 +  * ''​Conduction_BandEdge.dat''​\\ conduction band edge $E_{\rm c}$ including shift due to strain vs. position in units of [eV]
   * ''​DeformationPotential_ConductionBand.dat''​\\ conduction band deformation potential vs. position   * ''​DeformationPotential_ConductionBand.dat''​\\ conduction band deformation potential vs. position
-  * ''​EffectiveMass.dat''​\\ effective conduction band mass $m_{\rm c}$ vs. position in units of [m0]+  ​* ''​DeformationPotential_ValenceBand.dat''​\\ valence band deformation potential vs. position 
 +  * ''​DeformationPotential_ValenceBand_Uniaxial.dat''​\\ valence band uniaxial deformation potential vs. position 
 +  * ''​DopingDensity.dat''​\\ Doping density [cm$^{-3}$] vs. position 
 +  * ''​E_p(Kane energy).dat''​\\ Kane energy [eV] (material-dependent k.p parameter) vs. position 
 +  ​* ''​EffectiveMass.dat''​\\ effective conduction band mass $m_{\rm c}$ vs. position in units of [m0]. This input is not used for a k.p calculation.
   * ''​ElasticConstants.dat''​\\ elastic constants $c_{ij}$ vs. position in units of [GPa]   * ''​ElasticConstants.dat''​\\ elastic constants $c_{ij}$ vs. position in units of [GPa]
   * ''​EpsOptic.dat''​\\ optical dielectric constant $\epsilon(\infty)$ vs. position   * ''​EpsOptic.dat''​\\ optical dielectric constant $\epsilon(\infty)$ vs. position
   * ''​EpsStatic.dat''​\\ static dielectric constants $\epsilon(0)$ vs. position   * ''​EpsStatic.dat''​\\ static dielectric constants $\epsilon(0)$ vs. position
 +  * ''​L (Dresselhaus parameter L).dat''​\\ Dresselhaus parameter (material-dependent k.p parameter) vs. position. Default is $-1$.
   * ''​LatticeConstants.dat''​\\ lattice constants $a$ vs. position in units of [nm]   * ''​LatticeConstants.dat''​\\ lattice constants $a$ vs. position in units of [nm]
   * ''​MaterialDensity.dat''​\\ material density vs. position in units of [kg/​m<​sup>​3</​sup>​]   * ''​MaterialDensity.dat''​\\ material density vs. position in units of [kg/​m<​sup>​3</​sup>​]
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   * ''​PiezoConstants.dat''​\\ piezoelectric constants $e_{ij}$ in units of [C/​m<​sup>​2</​sup>​]   * ''​PiezoConstants.dat''​\\ piezoelectric constants $e_{ij}$ in units of [C/​m<​sup>​2</​sup>​]
   * ''​PyroConstants.dat''​\\ pyroelectric polarization $P_z$ (spontaneous polarization) in units of [C/​m<​sup>​2</​sup>​] (wurtzite only)   * ''​PyroConstants.dat''​\\ pyroelectric polarization $P_z$ (spontaneous polarization) in units of [C/​m<​sup>​2</​sup>​] (wurtzite only)
 +  * ''​S (remote band parameter).dat''​\\ remote band parameter (material-dependent k.p parameter) vs. position
   * ''​VelocityOfSound.dat''​\\ sound velocity in units of [m/s]   * ''​VelocityOfSound.dat''​\\ sound velocity in units of [m/s]
  
 ===== Strain ===== ===== Strain =====
-If the strain option is activated, a folder ''​Strain/''​ is created ​containing the strain tensor components $\epsilon_{ij}$ which are dimensionless+If the strain option is activated, a folder ''​Strain/''​ is created. 
-  * ''​Strain_CrystalSystem.dat''​\\ ​This file contains the strain tensor components with respect to the crystal coordinate system. +  * ''​Strain_CrystalSystem.dat''​\\ ​(dimensionless) ​strain tensor components with respect to the crystal coordinate system. 
-  * ''​Strain_Simulation.dat''​\\ ​This file contains the strain tensor components with respect to the simulation coordinate system. +  * ''​Strain_Simulation.dat''​\\ ​(dimensionless) ​strain tensor components with respect to the simulation coordinate system. 
-If the crystal has not been rotated, ​both files contain identical values.+If the crystal has not been rotated, ​above files contain identical values. 
 +  * ''​Strain_trace.dat''​\\ trace of the strain tensor
  
 ===== Piezo and pyroelectric polarization ===== ===== Piezo and pyroelectric polarization =====
 The folder ''​Polarization/''​ contains the piezoelectric and pyroelectric polarization if these options are activated. The folder ''​Polarization/''​ contains the piezoelectric and pyroelectric polarization if these options are activated.
-  * ''​PiezoChargeDensity.dat''​\\ ​This file contains the piezoelectric charge density due to strain. If the strain is zero, the piezoelectric charge density is zero. +  * ''​InterfaceCharges\PiezoCharges.dat''​\\ piezoelectric charge density due to strain. If the strain is zero, the piezoelectric charge density is zero. 
-  * ''​PyroChargeDensity.dat''​\\ ​This file contains the pyroelectric charge density due to spontaneous polarization. Pyroelectric charge density only exists for wurtzite ​but not for zinc blende materials.+  * ''​InterfaceCharges\PyroCharges.dat''​\\ pyroelectric charge density due to spontaneous polarization ​in wurtzite ​crystals. 
 +  * ''​PiezoPolarization.dat''​\\ $z$-component of the piezoelectric polarization vector 
 +  * ''​PyroPolarization.dat''​\\ $z$-component of the pyroelectric polarization vector
  
 ===== Initial electronic states ===== ===== Initial electronic states =====
-The folder ''​Init_Electr_Modes/''​ contains 3 different folders corresponding to the different sets of basis states. They correspond to the initial solution ​of the Schrödinger equation without accounting ​for Poisson equation (i.eelectrostatic mean-field) nor scattering self-energies.\\+The folder ''​Init_Electr_Modes\''​ contains 3 different folders corresponding to different sets of basis states. They are calculated at the first step of the calculation,​ before the NEGF calculation. These 3 sets of states are basis of the reduced Hilbert space obtained after applying the energy cut-off <​Energy_Range_Axial>​. 
 + 
 +These states are displayed ​for a default voltage of <​Energy_Range_Axial>/​2This voltage at which the states are visualized can be modified by the input file command: 
 +<​code>​ 
 +<​Simulation_Parameter>​ 
 +  ​..
 +  <​Bias_for_initial_Electronic_Modes unit="​meV">​54</​Bias_for_initial_Electronic_Modes>​ 
 +  ... 
 +</​Simulation_Parameter>​ 
 +</​code>​
  
 === '​Reduced Real Space' modes === === '​Reduced Real Space' modes ===
-The folder ''​Init_Electr_Modes/ReducedRealSpace/''​ contains:​\\ +The '​reduced real space' modes are eigenstates of the position operator in the reduced Hilbert space (i.e. after the energy cut-off). Because of the energy cut-off, these states are spatially extended instead of being $\delta$ functions. This basis set is the one which is used in the NEGF calculation. It does not depend on the applied voltage. However, this basis has generally little use in terms of physical interpretation. 
-  * ''​ReducedRealSpaceModes.dat''​\\ ​This file contains the conduction ​band edge and the square of the wave functions ​with respect to the heterostructure coordinate position.\\ 3 periods are displayed. ​(p0) means period ​(left period), (p1) means period 1 (central period), and p2 period 2 (right period). The numbers of states displayed ​in equal to 3 times the number of states per period, that is the number of selected minibands. + 
-  * ''​RealSpaceModesOn.dat''​ +The folder ''​Init_Electr_Modes\ReducedRealSpace\''​ contains:​\\ 
-  * ''​H0RealSpace.txt''​+  * ''​ReducedRealSpaceModes.dat''​\\ ​Conduction ​band edge and square of the wave functions ​(shifted in energy) vs. the heterostructure coordinate position.\\ 3 periods are displayed. ​'per.0' '​per.1'​ '​per.2'​ in the wavefunction names refer to the left, middle ​and right period ​shown. The numbers of states displayed ​is equal to 3 times the number of states per period, that is the number of selected minibands. 
 +{{ :​qcl:​ReducedRealSpace.png?​direct&​500 |}} 
 +  * ''​ReducedRealSpaceModesOn.dat'' ​\\ Same as in ''​ReducedRealSpaceModes.dat''​ but the vanishing parts of the wavefunctions are not shown (plot not supported by nextnanomat). 
 +  * ''​H0ReducedRealSpace_nobias.mat'' ​\\ Expression of the Hamiltonian in this basis when no external bias voltage is applied. 
 +  *  ''​H0ReducedRealSpace_nobias.mat''​ \\ Expression of the Hamiltonian in this basis with an applied external voltage. 
 +  *  Single-band case: ''​Wavefunction.dat''​ \\ Envelope function of the wavefunction $\Psi_i(z)$ 
 +  *  Multiband-case:​ ''​Wavefunction_ConductionBand.dat'',​ ''​Wavefunction_LHBand.dat'',​ and ''​Wavefunction_SOBand.dat''​ \\ Different component of the envelope wavefuntions 
 +$$\Psi_i(z) = f^{\text{c}}_i(z)u_{\text{c}}(z) +  f^{\text{LH}}_i(z)u_{\text{LH}}(z) +  f^{\text{SO}}_i(z)u_{\text{SO}}(z)$$ 
  
-=== Wannier-Stark states === 
-The folder ''​Init_Electr_Modes/​Wannier-Stark_States/''​ shows the eigenstates of the Schrödinger equation. In this folder, a default potential drop per period is taken as 1/2 of the <​Energy_Range_Axial>​ specified in the input file. Otherwise it can be specified in the input file using the command ''<​Bias_for_initial_Electronic_Modes>''​ in the ''<​Simulation_Parameter>''​ section. 
- It contains: 
-  * ''​Effective_masses.dat''​\\ ''​Miniband #'' ​   ''​Effective mass in the well [m0]'' ​    ''​Effective mass in the barrier [m0]''​ 
-  * ''​Wannier-Stark_Energy_Separation.dat''​ 
-  * ''​Wannier-Stark_levels.dat''​ This file contains the conduction band edge and the probability densities. 
-{{ :​qcl:​wannierstarkstates.jpg?​direct&​300 |}} 
-  * ''​Wannier-Stark_levelsOn.dat''​ This file contains the conduction band edge and the probability densities. Points where the probability density is almost zero are omitted. 
-{{ :​qcl:​wannier-stark.png?​direct&​600 |}} 
  
 === '​Tight-binding'​ states === === '​Tight-binding'​ states ===
-The Tight-binding folder contains data only if one or several ''<​Analysis_Separator>''​ are defined in the input file. The tight-binding basis corresponds to piecewise solution of the Schrödinger equation between these separators.+The ''​Tight-binding\'' ​folder contains data only if one or several ''<​Analysis_Separator>''​ are defined in the input file. The tight-binding basis corresponds to piecewise solution of the Schrödinger equation between these separators. 
 +{{ :​qcl:​tight-binding.png?​direct&​500 |}}
  
-=== In-plane discretization === 
-The file ''​Lateral_spectrum.dat''​ gives the energy discretization for the states used to describe the 2-Dimensional (2D) motion in the directions (x,y) perpendicular to the heterostructure. The lateral motion is discretized ​ using cylindrical boundary conditions, and the corresponding eigenstates are Bessel funcitons. \\ $x$ axis: ''​Lateral state index''​\\ $y$ axis: ''​order of Bessel'' ​  ''​(zero index)-1 of Bessel'' ​    ''​Relative Energy (meV)''​. 
-===== For each voltage/​temperature step ===== 
-For each voltage or temperature step, the following files are produced as a result of the NEGF calculation:​ 
  
-  * ''​CarrierDensity.dat''​\\ This file contains the electron density in [10<​sup>​18</​sup>​ cm<​sup>​-3</​sup>​] as a function of position [nm]. 
  
-  ​* ''​Conduction_BandEdge.dat''​\\ This file contains ​the calculated heterostructure ​conduction band edge profile $E_{\rm c}^\prime$ ​as a function ​of position in units of [eV]. It includes ​the mean field electrostatic potential ​$\phi$ (which is in units of [V])$E_{\rm c}^\prime = E_{\rm c- e \phi$.+=== Wannier-Stark states === 
 +The Wannier-Stark states correspond to the eigenstates of the Schrödinger equation without accounting for Poisson equation (i.e. electrostatic mean-field).\\ 
 +It contains: 
 +  ​* ''​Wannier-Stark_States.dat'' ​shows the conduction band edge and the probability densities of the eigenstates of the Schrödinger equation (the Wannier-Stark states).  
 +{{ :​qcl:​wannier-stark.png?​direct&​500 |}
 +  * ''​Wannier-Stark_levelsOn.dat''​. Same as ''​Wannier-Stark_States.dat''​ except that the points with almost zero probability density are omitted. 
 +{{ :​qcl:​wannier-starkOn.png?​direct&​500 |}} 
 +  * ''​Dipoles.mat''​ gives the dipole matrix elements (i.e. matrix elements ​of the position ​operator)  
 +The expression ​in the single-band case is: $$ d_{ij} = \int dz f_i(z) ~ z ~ f_j(z) $$  
 +In the multiband case: $$ d_{ij} = \sum_{\mu} \int dz f^{(\mu)}_i(z) ~ z ~ f^{(\mu)}_j(z) ​$
 +  * ''​EffectiveMasses.dat''​ gives the position and energy-dependent effective mass 
 +  * ''​H0_WannierStark.mat''​ gives the Hamiltonian in the Wannier-Stark basis. 
 +  * ''​Oscillator_Strength.mat''​ gives the oscillator strengths.
  
-  * ''​Convergence.txt''​\\ This file contains values for +=== Oscillator strength === 
-    * convergence factor: convergence factor for the lesser Green'​s function ​$\mathbf{G}^<$, which corresponds to the relative variation between the last two consecutive Green'​s functions. Should be the closest as possible from 0. +The oscillator strength is calculated from the formula 
-    * current convergence factor: convergence factor for the current density, which corresponds to the relative variation of the last two consecutive current density values. Should be the closest as possible from 0. +$$  
-    * number of iterations +f_{\alpha \beta} = \frac{2 \vert p_{\alpha \beta}\vert^2}{m_0 (E_{\beta} - E_{\alpha})} 
-    * normalization of lesser Green'​s function $\mathbf{G}^<+$
-    * sum normalised spectral function: should be the closest as possible from 1. +Note that the electron mass $m_0$ entering the above formula ​is the bare electron mass.
-  * ''​NO-CONVERGENCE.txt''​\\ This file is generated instead if the calculation did not converge.+
  
-  ​''​CurrentDensity.dat''​\\ This file contains ​the current density in [A/​cm<​sup>​2</​sup>​] as a function of position [nm].+This oscillator strength (which is sometimes referred as the unnormalized one), differs from the usual definition in the single band case by the ratio $m^*/m_0$, i.e. $\frac{m^*}{m_0} f_{\alpha \beta}$ is called ​the normalized oscillator strength.
  
-  * ''​Current-miscellaneous.txt''​\\ This file contains ​general ​information on the simulation. +The advantage of this unnormalized definition is that it is general ​enough to be applied ​to the multiband case.
-    * the current density in [A/​cm<​sup>​2</​sup>​] +
-    * the average electron velocity in [nm/ps] +
-    * the time taken for one electron ​to travel through one period in [ps] +
-    * the electric field in [kV/cm] +
-    * the doping sheet density per period in [cm<​sup>​-2</​sup>​] +
-    * the 3D doping density averaged over one period in [cm<​sup>​-3</​sup>​] +
-    * the effective electronic temperature in [Kelvin]. This is only an effective temperature as electrons are not in thermal equilibrium,​ which is obtained by averaging the kinetic energy for the in-plane motion+
  
 +Note that in the parabolic single-band case, the usual sum-rule is retrieved by using the normalized definition ​
 +$$ 
 +\sum_{\beta \neq \alpha} \frac{m^*}{m_0} f_{\alpha \beta} = 1
 +$$
  
-  * ''​Electrostatic-Potential.dat''​\\ This file contains ​the mean field electrostatic potential $\phi$ ​(in [V]as a function of position. The electrostatic potential ​$\phiis the solution ​of the Poisson equation and has been calculated self-consistently.+=== In-plane discretization === 
 +The file ''​Lateral_spectrum.dat'' ​gives the energy discretization for the states used to describe the 2-Dimensional ​(2D) motion ​in the directions (x,yperpendicular to the heterostructure. The lateral motion is discretized ​ using cylindrical boundary conditions, and the corresponding eigenstates are Bessel funcitons. \\ $x$ axis: ''​Lateral state index''​\\ $y$ axis: ''​order ​of Bessel'' ​  ''​(zero index)-1 of Bessel'' ​    ''​Relative Energy (meV)''​.
  
-=== Output in basis sets (ReducedRealSpace,​ WannierStark,​ TightBinding) ​=== +===== Simulation output for each voltage/​temperature step ===== 
-3 folders ​are created to output physical quantities ​in 3 different basis set (reduced real space, Wannier-Starkand Tight-binding).+For each voltage or temperature step, the following files are produced as a result of the NEGF calculation:​ 
 + 
 +  * ''​CarrierDensity.dat''​\\ Electron density ​in [cm<​sup>​-3</​sup>​] as a function of position [nm]. 
 + 
 +  * ''​Conduction_BandEdge.dat''​\\ Calculated heterostructure conduction band edge profile $E_{\rm c}^\prime$ as a function of position in units of [eV]. It includes the mean field electrostatic potential $\phi$ [V] as $E_{\rm c}^\prime = E_{\rm c} e \phi$. 
 + 
 +  * ''​Convergence.txt''​\\ This file contains values for 
 +    * Convergence factor \\ convergence factor for the lesser Green'​s function $\mathbf{G}^<​$which corresponds to the relative variation between the last two consecutive Green'​s functions. Should be as close as possible to 0. 
 +    * Current convergence factor \\ convergence factor for the current density, which corresponds to the relative variation of the last two consecutive current density values. Should be as close as possible to 0. 
 +    * Number of iterations 
 +    * Normalization of lesser Green'​s function $\mathbf{G}^<​$ \\ Should be as close as possible to 1. 
 +    * Sum normalised spectral function \\ Should be as close as possible to 1. If not, it usually means that the energy grid spacing is too large. 
 +  * ''​NO-CONVERGENCE.txt''​\\ This file is generated instead if the calculation did not converge.
  
 +  * ''​CurrentDensity.dat''​\\ Current density in [A/​cm<​sup>​2</​sup>​] as a function of position [nm].
  
 +  * ''​Current-miscellaneous.txt''​\\ General information on the simulation.
 +    * Current density in [A/​cm<​sup>​2</​sup>​]
 +    * Average electron velocity in [nm/ps]
 +    * Time for one electron to travel through one period in [ps]
 +    * Electric field in [kV/cm]
 +    * Doping sheet density per period in [cm<​sup>​-2</​sup>​]
 +    * 3D doping density averaged over one period in [cm<​sup>​-3</​sup>​]
 +    * Effective electronic temperature in [Kelvin]. This is only an effective temperature as electrons are not in thermal equilibrium,​ which is obtained by averaging the kinetic energy for the in-plane motion. This effective temperature is given by the following formula: ​
 +$$ T_{\text{eff}} = \sum_{i} ~ p_{i} ~ E_{\parallel}(i) ~  / ~ k_b $$
 +where $p_{i}$ is the fraction (i.e. population normalized to 1) of occupation in the in-plane state $i$, $E_{\parallel}(i)$ is the in-plane energy for the in-plane state $i$, and k_b the Boltzmann constant.
  
-  * ''​WannierStark_Energy_Separation.dat''​\\ ​This file contains the same as ''​EnergySpacing.dat''​ for a particular voltage.+  * ''​Electrostatic-Potential.dat''​\\ ​Mean field electrostatic potential $\phi$ [V] as a function of positionThe electrostatic potential $\phi$ is the solution of the Poisson equation and has been calculated self-consistently.
  
-  * ''​Wannier-Stark_levels.dat''​\\ This file contains the calculated conduction band edge $E_{\rm c}$ and the probability densities of the eigenstates $\left|\psi_i(x)\right|^2$. "​(p0)",​ "​(p1)"​ refer to period 0, period 1, ...) (? CHECK: Does this statement makes sense?: This file contains the same as ''​EnergyLevel_Absolute.dat'' ​for a particular voltage.) +==== Output in basis sets (ReducedRealSpace,​ WannierStark,​ TightBinding) ==== 
-{{ :​qcl:​wannierstarkstates.jpg?​direct&​300 |}}+3 folders are created to output physical quantities in the 3 different basis sets (''​Reduced Real Space'', ​''​Wannier-Stark''​and ''​Tight-Binding''​).
  
-  ​* ''​Wannier-Stark_levelsOn.dat''​\\ ​Same information but but points ​where the probability density $\left|\psi_i\right|^2$ is almost zero are omitted+For each basis set, the folder contains: 
-{{ :​qcl:​wannierstarkstates_nice.jpg?​direct&​300 |}}+  ​the probability density $\vert \Psi_i(z) \vert^2$ for the each state $\Psi_i$. Each level is shifted accordingly to its energy. 
 +  * the wavefunction $\Psi_i(z)$ in the file ''​Wavefunctions.dat''​ 
 +  *  ''​CarrierDistribution_Energy.dat''​ shows the energy-resolved populations in each state.  
 +  * ''​DensityMatrix.txt''​ and ''​DensityMatrix_elements.txt''​ display the density matrix in a text file. 
 +  * ''​DensityMatrix_Real.mat''​ displays the real part of the density matrix. The labeling is made accordingly to the one of the wavefunctions $\Psi_i(z)$, so that the matrix element (i,j) corresponds to the real part of $\langle \Psi_i \vert \rho \vert \Psi_j \rangle$, ​where $\rho$ is the density matrix. Note that the diagonal element (i,i) is equal to the population of the level $\Psi_i$.  
 +  * ''​DensityMatrix_Imaginary.mat''​ displays the imaginary part of the density matrix. 
 +  * ''​Dipoles.mat''​ gives the dipole matrix elements (see above for definition) 
 +  * ''​EffectiveMasses.dat''​ gives the position and energy-dependent effective mass 
 +  * ''​Populations.text''​ indicates the population (i.e. the probability ​of occupation) in each level $\Psi_i$ (normalized to 1 for one period of the structure). 
 +  * ''​SpectralFunctions.dat''​ shows the diagonal part of the spectral function, i.e. the energy-resolved ​density ​of states (DOS) 
 +  * ''​SpontaneousemissionRate.txt''​ gives for each pair of initial and final state the scattering rate (s^-1) of spontaneous photon emission. 
 +  * ''​SpontaneousemissionRate.mat''​ gives the same information but in matrix form: the element ($i$,$j$) gives the scattering rate (s^-1) of spontaneous photon emission between the initial state $i$ and final state $j$.  
 +  * ''​Subband_KineticEnergy.txt''​ contains the averaged kinetic energy for each level/​subband $i$. Its calculation is given by: 
 +$$ \langle E_i \rangle = \frac{ \sum_{k} ~ p_{i,k} ~ E_{\parallel}(k)}{\sum_{k} ~ p_{i,k}}, $$ where $E_{\parallel}(k)$ is the in-plane kinetic energy
 +  * ''​Subband_Temperature.txt''​ gives the effective temperature of each level/​subband $i$, according to  
 +$$ T^{\text{eff}}_i = \langle E_i \rangle / ~ k_b $$
  
  
 ==== 2D plots ==== ==== 2D plots ====
-The folder ''​2D_Plots_Position-nm_Energy-eV/​''​ contains ​files where the $x$ axis is position ​in [nm] and the $y$ axis is energy ​in units of [eV]. +The folder ''​2D_plots\''​ contains ​2D color maps as a function of **position [nm]** (horizontal ​axis) and **energy [eV]** (vertical axis). Note that these 2D plots show 2 QCL periods although only 1 period is simulated. 
-Note that these 2D plots show 2 QCL periods although only 1 period is simulated. +  * ''​DOS_energy_resolved.vtr''​ / ''​*.plt''​ / ''​*.fld''​\\ ​Energy-resolved local density of states ​(LDOS) in units of [eV<​sup>​-1</​sup>​ nm<​sup>​-1</​sup>​]. The LDOS is related to the spectral function. It shows the available states for the electrons at $k_\parallel = 0$. 
-  * ''​DOS.fld''​ / ''​*.coord''​ / ''​*.dat''​\\ ​This file contains the energy-resolved local density of states ​${\rm LDOS}(x,E)$ as a function of position and energy. The units are [cm<​sup>​-3</​sup>​ eV<​sup>​-1</​sup>​]. (Note that the units of the nextnano.MSB code are [eV<​sup>​-1</​sup>​ nm<​sup>​-1</​sup>​]). The local density of states ​is related to the spectral function.\\ It shows the available states for the electrons at $k_\parallel = 0$. +  * ''​CarrierDensity_energy_resolved.vtr''​ / ''​*.plt''​ / ''​*.fld''​\\ ​Energy-resolved electron density $n(z,E)$ [cm<​sup>​-3</​sup>​ eV<​sup>​-1</​sup>​]. ​It is related to the lesser ​Green'​s function $\mathbf{G}^<​$. 
-  * ''​Carrier_Density.fld''​ / ''​*.coord''​ / ''​*.dat''​\\ ​This file contains the energy-resolved electron density $n(x,E)$ as a function of position and energy. The units are [cm<​sup>​-3</​sup>​ eV<​sup>​-1</​sup>​]. ​The energy-resolved electron density ​is related to the Green'​s function $\mathbf{G}^<​$ ​("G lesser"​)+  * ''​CurrentDensity_energy_resolved.vtr''​ / ''​*.plt''​ / ''​*.fld''​\\ ​Energy-resolved current density $j(z,E)$ [A cm<​sup>​-2</​sup>​ eV<​sup>​-1</​sup>​].
-  * ''​Current_Density.fld''​ / ''​*.coord''​ / ''​*.dat''​\\ ​This file contains the energy-resolved current density $j(x,E)$ as a function of position and energy. The units are [A cm<​sup>​-2</​sup>​ eV<​sup>​-1</​sup>​].+
  
 +For different extensions of 2D outputs, please also see [[qcl:​advanced_settings#​output_format_for_2d_plots|advanced settings in the input file]].
 ==== Gain ==== ==== Gain ====
-The folder ''​Gain/''​ contains ​files where the $x$ axis is position in [nm] and the $y$ axis is photon energy $E_{\rm ph}$ in units of [eV]. +The folder ''​Gain\''​ contains ​one- and two-dimensional plots of the intensity gain simulatedA negative value of gain corresponds to absorption.
-Note that these 2D plots show 2 QCL periods although only 1 period is simulated. +
-  * ''​Energy-Resolved_Gain_Simple-Approximation.fld''​ / ''​*.coord''​ / ''​*.dat''​\\ This file contains ​the energy-resolved ​intensity gain $G(x,E_{\rm ph})$ as a function of position and photon energy $E_{\rm ph}$The units are [cm<​sup>​-1</​sup>​ nm<​sup>​-1</​sup>​]. (Note that the units of the nextnano.MSB code are [eV<​sup>​-1</​sup>​ cm<​sup>​-1</​sup>​].+
  
-  * ''​Gain_Simple-Approximation.dat''​\\ This file contains ​the gain obtained without the self-consistent calculation.\\ The $x$ axis is energy in units of [meV].\\ The $y$ axis is the gain in units of [1/​cm]. ​A negative value of gain corresponds to absorption.+2D color maps show the gain $G(z,E_{\rm ph})[cm<​sup>​-1</​sup>​ nm<​sup>​-1</​sup>​],​ where the horizontal axis is **position** ​$z$ [nm] and the vertical ​axis is photon ​energy ​$E_\rm{ph}$ ​in units of either **energy** ​[meV] or **frequency** [THz]. Note that the units of gain in the nextnano.MSB code are [eV<​sup>​-1</sup> ​cm<​sup>​-1</​sup>​]. 
 +Also note that these 2D plots show 2 QCL periods although only 1 period is simulated. 
 +  * ''​Energy-Resolved_Gain_Simple-Approximation.fld''​ / ''​*.coord''​ / ''​*.dat''​\\  
 +  * ''​Gain_vs_Position_and_Energy_SelfConsistent.vtr''​ 
 +  * ''​Gain_vs_Position_and_Frequency_SelfConsistent.vtr''​ 
 + 
 +1D plots show the gain $G(E_\rm{ph})$ [cm<​sup>​-1</​sup>​] against photon **energy** [meV], **frequency** [THz], and **wavelength** [micron]. 
 +  * ''​Gain_Simple-Approximation.dat''​ Intensity gain obtained without the self-consistent calculation.  
 +  * ''​GainSemiClassical_vs_Energy.dat''​ 
 +  * ''​GainSemiClassical_vs_Frequency.dat''​ 
 +  * ''​GainSemiClassical_vs_Wavelength.dat''​ 
 +  * ''​Gain_SelfConsistent_vs_Energy.dat''​ 
 +  * ''​Gain_SelfConsistent_vs_Frequency.dat''​ 
 +  * ''​Gain_SelfConsistent_vs_Wavelength.dat''​
  
-  * ''​Gain_SelfConsistent.dat''​\\ This file contains the intensity gain obtained with the self-consistent calculation.\\ The $x$ axis is energy in units of [meV].\\ The $y$ axis is the gain in units of [1/cm]. 
-A negative value of gain corresponds to absorption. 
  
 Note that the gain output is only done for the voltages specified in the input file. Note that the gain output is only done for the voltages specified in the input file.
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 ===== Output files for voltage sweep ===== ===== Output files for voltage sweep =====
-For each simulation, the following files are produced+If you sweep voltage, the following files are generated
-  * ''​Energy_WannierStarkStates.dat''​\\ ​This file contains the energy ​levels of the Wannier-Stark states ("E_1 = Energy of level 1", "E_2 = Energy of level 2",​...) as a function of voltage, i.e. potential drop per period in units of [mV]. +  * ''​Energy_WannierStarkStates.dat''​\\ ​Energy ​levels of the Wannier-Stark states ("$E_1= Energy of level 1", "$E_2= Energy of level 2",​...) as a function of voltage, i.e. potential drop per period in units of [mV]
-  * ''​Gain_vs_Voltage.dat''​ and ''​Gain_vs_EField.dat''​\\ ​These files contain the intensity ​gain as a function of voltage or electric field respectively.\\ The $x$ axis is the potential drop per period ​[mV] (or electric field [kV/cm]).\\ The $y$ axis contains the maximum gain in [1/cm] and the photon energy ​for maximum gain [meV] (or photon frequency in [THz]).0 +  * ''​Energy_TightBinding.dat''​\\ Energy levels of the tight-binding states
-  * ''​Current_vs_Voltage.dat''​ and  ''​Current_vs_EField.dat''​ \\ These files contain current-voltage characteristics,​ i.e. the current density in units of [A/​cm<​sup>​2</​sup>​] as a function of voltage (i.e. potential drop per period ​in units of [mV]) or electrif ​field in [kV/cm]. The current is the average of the file ''​Current-Density.dat''​.+  * ''​Gain_vs_Voltage.dat''​ and ''​Gain_vs_EField.dat''​\\ ​Intensity ​gain [cm<​sup>​-1</sup>] and the photon energy ​at maximum gain [meV] (or photon frequency in [THz]) ​as a function of **voltage** (potential drop per period [mV]) or **electric field** [kV/cm]
 +  * ''​Current_vs_Voltage.dat''​ and  ''​Current_vs_EField.dat''​ \\ Current-voltage characteristics,​ i.e. the current density in units of [A/​cm<​sup>​2</​sup>​] as a function of **voltage** (potential drop per period [mV]) or **electric ​field** [kV/cm]. The current is the average of the file ''​Current-Density.dat''​. 
 + 
 +===== Combined temperature-voltage sweep ===== 
 + a combined temperature-voltage sweep can be done using the keyword ''​Temperature-Voltage''​ in the field ''<​SweepType>''​ of ''<​SweepParameters>''​ (see the example of code below). In this case, the simulation can be parallelized. ''<​Threads>''​ defines the number of parallel threads. Its optimal value should be the number of CPU cores available (if the available memory is sufficient). Within each parallel temperature sweep, a serial voltage sweep is performed. 
 + 
 +<​code>​ 
 +<​SweepParameters> ​   
 +    <​SweepType>​Temperature-Voltage</​SweepType>​ 
 +    <​MinV>​ 50</​MinV>​  
 +    <​MaxV>​ 60</​MaxV>​  
 +    <​DeltaV>​ 2</​DeltaV>​  
 + 
 +    <​MinT>​ 25</​MinT>​  
 +    <​MaxT>​ 300</​MaxT>​  
 +    <​DeltaT>​ 25</​DeltaT>​  
 + 
 +    <​Threads>​12</​Threads>​ <!-- Parallelization for Temperature-Voltage sweep --> 
 +</​SweepParameters>​ 
 +</​code>​ 
 +Note that for such voltage-temperature sweep, ''<​Maximum_Number_of_Threads>''​ in ''<​Simulation_Parameter>''​ should be set to ''​1''​. (A combined parallelization will result in lower performances.) 
 +<​code>​ 
 +<​Simulation_Parameter>​ 
 +  ... 
 +  <​Maximum_Number_of_Threads>​1</​Maximum_Number_of_Threads>​ 
 +</​Simulation_Parameter>​ 
 +</​code>​ 
 + 
 + 
 +At the end of the simulation, current and gain maps can be displayed. 
 +''​Gain_map.fld''​ gives the maximum gain at each (voltage,​temperature) point. 
 +''​Max_Gain_frequency.fld''​ gives the map of the corresponding photon energy for which the gain is maximum. 
 + 
 +Folder view: 
 +{{ :​qcl:​gainmap1.png?​direct |}}
  
 +Gain map (V,T):
 +{{ :​qcl:​gainmap2.png?​direct |}}
  
qcl/simulation_output.1528288481.txt.gz · Last modified: 2018/06/06 12:34 by thomas.grange