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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 folder Input/
contains all information that is input to the simulation such as material parameters.
AlloyContent.dat
Al(x)Ga(1-x)As
BandEdge_conduction.dat
BandEdges.dat
BandGap.dat
DeformationPotential_ConductionBand.dat
EffectiveMass.dat
ElasticConstants.dat
EpsOptic.dat
EpsStatic.dat
LatticeConstants.dat
MaterialDensity.dat
PhononEnergy_LO.dat
PiezoConstants.dat
PyroConstants.dat
VelocityOfSound.dat
If the strain option is activated, a folder Strain/
is created containing the strain tensor components $\epsilon_{ij}$ which are dimensionless.
Strain_CrystalSystem.dat
Strain_Simulation.dat
If the crystal has not been rotated, both files contain identical values.
The folder Polarization/
contains the piezoelectric and pyroelectric polarization if these options are activated.
PiezoChargeDensity.dat
PyroChargeDensity.dat
The folder Init_Electr_Modes/
contains 3 different folders corresponding to 3 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>/2. This voltage at which the states are visualized can be modified by the input file command:
<Simulation_Parameter> ... <Bias_for_initial_Electronic_Modes unit="meV">54</Bias_for_initial_Electronic_Modes> ... </Simulation_Parameter>
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.
The folder Init_Electr_Modes/ReducedRealSpace/
contains:
ReducedRealSpaceModes.dat
ReducedRealSpaceModesOn.dat
ReducedRealSpaceModes.dat
but the vanishing parts of the wavefunctions are not shown.H0ReducedRealSpace_nobias.mat
gives the expression of the Hamiltonian in this basis when no external bias voltage is applied.H0ReducedRealSpace_nobias.mat
gives the expression of the Hamiltonian in this basis with an applied external voltage.
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 Wannier-Stark states. Schrödinger equation. Wannier-Stark_levelsOn.dat
. Same than Wannier-Stark_States.dat
except that points where the probability density is almost zero are omitted.WannierStark_H0.mat
gives the Hamiltonian in the Wannier-Stark basis.Dipoles.mat
gives the dipoles elements (i.e. matrix elements of the position operator).Oscillator_Strength.mat
gives the oscillator strengths.
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 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 or temperature step, the following files are produced as a result of the NEGF calculation:
CarrierDensity.dat
Conduction_BandEdge.dat
Convergence.txt
NO-CONVERGENCE.txt
CurrentDensity.dat
Current-miscellaneous.txt
Electrostatic-Potential.dat
3 folders are created to output physical quantities in the 3 different basis sets (Reduced Real Space
, Wannier-Stark
, and Tight-Binding
).
For each basis set, the folder contains:
DensityMatrix_Real.mat
displays the real part of the density matrix. The labelling 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. The diagonal elements (i,i) corresponds to the populations of the level $\Psi_i$. DensityMatrix_Real.mat
displays the imaginary part of the density matrix.SpectralFunctions.dat
shows the diagonal part of the spectral function, i.e. the energy-resolved density of states (DOS).CarrierDistribution_Energy.dat
shows the energy-resolved populations in each state.
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_energy_resolved.vtr
/ *.gnu
/ *.fld
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
Current_Density.fld
/ *.coord
/ *.dat
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
Gain_Simple-Approximation.dat
Gain_SelfConsistent.dat
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>
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
GreenLesser_Z.dat
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
<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
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
DensityMatrix_RealPart_AbsoluteValue.mat
DensityMatrix_ImaginaryPart_AbsoluteValue.mat
For each simulation, the following files are produced.
Energy_WannierStarkStates.dat
Gain_vs_Voltage.dat
and Gain_vs_EField.dat
Current_vs_Voltage.dat
and Current_vs_EField.dat
Current-Density.dat
.