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qcl:simulation_output

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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). The created output folder contains:

  • the input file (.xml) and the material database (.xml).
  • a folder 'Input' which gives material parameters used in the calculation.
  • a folder Strain (only if the strain option is activated).
  • 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 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.
  • a log file is created at the end of the simulation, containing all the information displayed during the simulation.

'Input' folder

The folder Input/ contains all information that is input to the simulation such as material parameters.

  • 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]
  • 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]
  • DeformationPotential_ConductionBand.dat
    conduction band deformation potential vs. position
  • EffectiveMass.dat
    effective conduction band mass $m_{\rm c}$ vs. position in units of [m0]
  • ElasticConstants.dat
    elastic constants $c_{ij}$ vs. position in units of [GPa]
  • EpsOptic.dat
    optical dielectric constant $\epsilon(\infty)$ vs. position
  • EpsStatic.dat
    static dielectric constants $\epsilon(0)$ vs. position
  • LatticeConstants.dat
    lattice constants $a$ vs. position in units of [nm]
  • MaterialDensity.dat
    material density vs. position in units of [kg/m3]
  • PhononEnergy_LO.dat
    longitudinal optical (LO) phonon energy in units of [eV]
  • PiezoConstants.dat
    piezoelectric constants $e_{ij}$ in units of [C/m2]
  • PyroConstants.dat
    pyroelectric polarization $P_z$ (spontaneous polarization) in units of [C/m2] (wurtzite only)
  • VelocityOfSound.dat
    sound velocity in units of [m/s]

Strain

If the strain option is activated, a folder Strain/ is created containing the strain tensor components $\epsilon_{ij}$ which are dimensionless.

  • Strain_CrystalSystem.dat
    This file contains the 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.

If the crystal has not been rotated, both files contain identical values.

Piezo and pyroelectric polarization

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.
  • 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.

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.e. electrostatic mean-field) nor scattering self-energies.

'Reduced Real Space' modes

The folder Init_Electr_Modes/ReducedRealSpace/ contains:

  • 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 0 (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
  • H0RealSpace.txt

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.

  • 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.

'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 file Lateral_spectrum.dat gives the energy discretization for the states used to describe the 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 step

For each voltage, the following files are produced.

  • BandEdge_conduction.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]), $E_{\rm c}^\prime = E_{\rm c} - e \phi$.
  • Electrostatic-Potential_vs_position.dat
    This file contains the mean field electrostatic potential $\phi$ (in [V]) as a function of position. The electrostatic potential $\phi$ is the solution of the Poisson equation and has been calculated self-consistently.
  • CarrierDensity.dat
    This file contains the electron density in [1018 cm-3] as a function of position [nm].
  • Current-Density.dat
    This file contains the current density in [A/cm2] as a function of position [nm].
  • Current-miscellaneous.txt
    This file contains general information on the simulation.
    • the current density (mode space) in [A/cm2]
    • the current density (real space average) in [A/cm2]
    • 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-2]
    • the 3D doping density averaged over the all periods in [cm-3]
    • the effective electronic temperature obtained by averaging $1/(k_{\rm B}T)$ in [Kelvin]
    • the effective electronic temperature obtained by averaging the lateral energy in [Kelvin]
  • WannierStark_Energy_Separation.dat
    This file contains the same as EnergySpacing.dat for a particular voltage.
  • 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.)

  • Wannier-Stark_levelsOn.dat
    Same information but but points where the probability density $\left|\psi_i\right|^2$ is almost zero are omitted.

  • 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 the closest as possible from 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 the closest as possible from 0.
    • number of iterations
    • normalization of lesser Green's function $\mathbf{G}^<$
    • sum normalised spectral function: should be the closest as possible from 1.
  • NO-CONVERGENCE.txt
    This file is generated if the calculation did not converge.

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]. Note that these 2D plots show 2 QCL periods although only 1 period is simulated.

  • 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-3 eV-1]. (Note that the units of the nextnano.MSB code are [eV-1 nm-1]). The local density of states is related to the spectral function.
    It shows the available states for the electrons at $k_\parallel = 0$.
  • 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-3 eV-1]. The energy-resolved electron density is related to the Green's function $\mathbf{G}^<$ (“G lesser”).
  • 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-2 eV-1].

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]. 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-1 nm-1]. (Note that the units of the nextnano.MSB code are [eV-1 cm-1].
  • 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.
  • 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.

<!-- Calculate gain only between the following values of
     potential drop per period in order to save CPU time -->
     <Vmin unit="mV"> 160 </Vmin>
     <Vmax unit="mV"> 400 </Vmax>

Green's functions

The folder GreenFunctions/ contains information on the Green's functions.

The electron density $n(x,E_x)$ is related to the lesser Green's function $\mathbf{G}^<$ (“G lesser”): $$n(x,E_x) = - \frac{{\rm i}}{2\pi} \mathbf{G}(x,x^\prime=x,E_x)$$

  • GreenLesser_All.dat
    lesser Green's function $\mathbf{G}^<$
    This file contains the sum over all the diagonal (i.e. $x=x^\prime$) lesser Green's functions (sum over one period) as a function of energy $E_x$.
  • GreenLesser_Z.dat
    lesser Green's function $\mathbf{G}^<$
    This file contains the lesser Green's function $\mathbf{G}^<$ (i.e. density $n(E)$) for each mode space used in the calculation.

The local density of states $\rho(x,E_x)$ is related to the spectral function $\mathbf{A}$: $$\rho(x,E_x) = \frac{1}{2\pi} \mathbf{A}(x,x^\prime=x,E_x)$$ $\mathbf{A}$ is defined as $\mathbf{A} = {\rm i} (\mathbf{G}^{\rm R} - \mathbf{G}^{{\rm R}\dagger}) = - 2 {\rm Im}(\mathbf{G}^{\rm R})$. $\mathbf{G}^{\rm R}$ is the retarded Green's function.

  • GreenSpectral_All.dat
    This file contains the sum over all the spectral functions (sum over one period) as a function of energy $E_x$.
    Example: In the figure below, for instance, one can see that <Emin_shift unit="meV"> can be increased (by 200 meV) to reduce the calculation time. Essentially, the energy range of the Green's functions is altered by adjusting <Emin_shift unit=meV> and <Emax_shift unit=meV>.
  • GreenSpectral_Z.dat
    This file contains the spectral function for each mode space used in the calculation.

Density matrix

The folder DensityMatrix/ contains the density matrix $\rho$ which is a complex quantity and it is dimensionless. The trace of the density matrix equals 1. In our case, the trace is 1 if we sum over one period. The state labels (state $i$, period $j$) are specified in the complex density matrix. $$\rho(i,j) = \rho({\rm state},{\rm period})$$

  • DensityMatrix_complex.mat
    This file contains the density matrix.
    The $x$ axis contains real and imaginary value.
    The $y$ axis is number of periods.
  • DensityMatrix_RealPart_AbsoluteValue.mat
    This file contains the absolute value of the real part of the density matrix.
    The $x$ axis contains absolute value of the imaginary part.
    The $y$ axis is number of periods.
  • DensityMatrix_ImaginaryPart_AbsoluteValue.mat
    This file contains the absolute value of the imaginary part of the density matrix.
    The $x$ axis contains absolute value of the real part.
    The $y$ axis is number of periods.

Output files for voltage sweep

For each simulation, the following files are produced.

  • 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].
  • 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
  • Current_vs_Voltage.dat and Current_vs_EField.dat
    These files contain current-voltage characteristics, i.e. the current density in units of [A/cm2] 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.
qcl/simulation_output.1524039546.txt.gz · Last modified: 2018/04/18 08:19 by thomas.grange