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qcl:simulation_output [2021/08/18 13:22] takuma.sato [Simulation output for each voltage/temperature step] |
qcl:simulation_output [2022/09/20 17:10] (current) thomas.grange |
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| The folder ''Init_Electr_Modes\ReducedRealSpace\'' contains:\\ | The folder ''Init_Electr_Modes\ReducedRealSpace\'' contains:\\ | ||
| - | * ''ReducedRealSpaceModes.dat''\\ Conduction band edge and square of the wave functions (shifted in energy) vs. 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 is equal to 3 times the number of states per period, that is the number of selected minibands. | + | * ''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 |}} | {{ :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). | * ''ReducedRealSpaceModesOn.dat'' \\ Same as in ''ReducedRealSpaceModes.dat'' but the vanishing parts of the wavefunctions are not shown (plot not supported by nextnanomat). | ||
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| The Wannier-Stark states correspond to the eigenstates of the Schrödinger equation without accounting for Poisson equation (i.e. electrostatic mean-field).\\ | The Wannier-Stark states correspond to the eigenstates of the Schrödinger equation without accounting for Poisson equation (i.e. electrostatic mean-field).\\ | ||
| It contains: | 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_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 |}} | {{ :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. | * ''Wannier-Stark_levelsOn.dat''. Same as ''Wannier-Stark_States.dat'' except that the points with almost zero probability density are omitted. | ||
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| * ''Oscillator_Strength.mat'' gives the oscillator strengths. | * ''Oscillator_Strength.mat'' gives the oscillator strengths. | ||
| + | === Oscillator strength === | ||
| + | The oscillator strength is calculated from the formula | ||
| + | $$ | ||
| + | f_{\alpha \beta} = \frac{2 \vert p_{\alpha \beta}\vert^2}{m_0 (E_{\beta} - E_{\alpha})} | ||
| + | $$ | ||
| + | Note that the electron mass $m_0$ entering the above formula is the bare electron mass. | ||
| + | |||
| + | 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. | ||
| + | |||
| + | The advantage of this unnormalized definition is that it is general enough to be applied to the multiband case. | ||
| + | |||
| + | Note that in the parabolic single-band case, the usual sum-rule is retrieved by using the normalized definition | ||
| + | $$ | ||
| + | \sum_{\beta \neq \alpha} \frac{m^*}{m_0} f_{\alpha \beta} = 1 | ||
| + | $$ | ||
| === In-plane discretization === | === In-plane discretization === | ||
| Line 142: | Line 157: | ||
| * the wavefunction $\Psi_i(z)$ in the file ''Wavefunctions.dat'' | * the wavefunction $\Psi_i(z)$ in the file ''Wavefunctions.dat'' | ||
| * ''CarrierDistribution_Energy.dat'' shows the energy-resolved populations in each state. | * ''CarrierDistribution_Energy.dat'' shows the energy-resolved populations in each state. | ||
| - | * ''DensityMatrix.txt'' displays the density matrix in a text file. | + | * ''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_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. | * ''DensityMatrix_Imaginary.mat'' displays the imaginary part of the density matrix. | ||
| Line 148: | Line 163: | ||
| * ''EffectiveMasses.dat'' gives the position and energy-dependent effective mass | * ''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). | * ''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). | + | * ''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: | * ''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. | + | $$ \langle E_i \rangle = \frac{ \sum_{k} ~ p_{i,k} ~ E_{\parallel}(k)}{\sum_{k} ~ p_{i,k}}, $$ where $E_{\parallel}(k)$ is the in-plane kinetic energy. |
| * ''Subband_Temperature.txt'' gives the effective temperature of each level/subband $i$, according to | * ''Subband_Temperature.txt'' gives the effective temperature of each level/subband $i$, according to | ||
| $$ T^{\text{eff}}_i = \langle E_i \rangle / ~ k_b $$ | $$ T^{\text{eff}}_i = \langle E_i \rangle / ~ k_b $$ | ||
| Line 156: | Line 173: | ||
| ==== 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_energy_resolved.vtr'' / ''*.gnu'' / ''*.fld''\\ This file contains the energy-resolved local density of states ${\rm LDOS}(x,E)$ as a function of position and energy. The units are [eV<sup>-1</sup> nm<sup>-1</sup>]). | + | * ''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 $\mathbf{G}^<$. |
| - | The local density of states is related to the spectral function. It shows the available states for the electrons at $k_\parallel = 0$. | + | * ''CurrentDensity_energy_resolved.vtr'' / ''*.plt'' / ''*.fld''\\ Energy-resolved current density $j(z,E)$ [A cm<sup>-2</sup> eV<sup>-1</sup>]. |
| - | * ''CarrierDensity_energy_resolved.vtr'' / ''*.gnu'' / ''*.fld''\\ 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'' / ''*.gnu'' / ''*.fld''\\ 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 simulated. A 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>]. | + | 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'' | ||
| - | * ''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. | + | 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 ===== | ===== Combined temperature-voltage sweep ===== | ||
qcl/simulation_output.1629292938.txt.gz · Last modified: 2021/08/18 13:22 by takuma.sato
