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qcl:simulation_output [2021/08/18 13:00] takuma.sato [Initial electronic states] |
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 108: | Line 123: | ||
| For each voltage or temperature step, the following files are produced as a result of the NEGF calculation: | 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 [cm<sup>-3</sup>] as a function of position [nm]. | + | * ''CarrierDensity.dat''\\ Electron density in [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 $|\phi\rangle$ (which is in units of [V]), $E_{\rm c}^\prime = E_{\rm c} - e \phi$. | + | * ''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.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. | + | * 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 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 as close as possible to 0. |
| - | * number of iterations | + | * Number of iterations |
| - | * normalization of lesser Green's function $\mathbf{G}^<$. Should be the closest as possible from 1. | + | * Normalization of lesser Green's function $\mathbf{G}^<$ \\ Should be as close as possible to 1. |
| - | * sum normalised spectral function: should be the closest as possible from 1. If not, it usually means that the energy grid spacing is too large. | + | * 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. | * ''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]. | + | * ''CurrentDensity.dat''\\ Current density in [A/cm<sup>2</sup>] as a function of position [nm]. |
| - | * ''Current-miscellaneous.txt''\\ This file contains general information on the simulation. | + | * ''Current-miscellaneous.txt''\\ General information on the simulation. |
| - | * the current density in [A/cm<sup>2</sup>] | + | * Current density in [A/cm<sup>2</sup>] |
| - | * the average electron velocity in [nm/ps] | + | * Average electron velocity in [nm/ps] |
| - | * the time taken for one electron to travel through one period in [ps] | + | * Time for one electron to travel through one period in [ps] |
| - | * the electric field in [kV/cm] | + | * Electric field in [kV/cm] |
| - | * the doping sheet density per period in [cm<sup>-2</sup>] | + | * Doping sheet density per period in [cm<sup>-2</sup>] |
| - | * the 3D doping density averaged over one period in [cm<sup>-3</sup>] | + | * 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. This effective temperature is given by the following formula: | + | * 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: |
| $$ T_{\text{eff}} = \sum_{i} ~ p_{i} ~ E_{\parallel}(i) ~ / ~ k_b $$ | $$ T_{\text{eff}} = \sum_{i} ~ p_{i} ~ E_{\parallel}(i) ~ / ~ k_b $$ | ||
| 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. | 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. | ||
| - | * ''Electrostatic-Potential.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. | + | * ''Electrostatic-Potential.dat''\\ Mean field electrostatic potential $\phi$ [V] as a function of position. The electrostatic potential $\phi$ is the solution of the Poisson equation and has been calculated self-consistently. |
| ==== Output in basis sets (ReducedRealSpace, WannierStark, TightBinding) ==== | ==== Output in basis sets (ReducedRealSpace, WannierStark, TightBinding) ==== | ||
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| * 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. | ||
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| * ''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.1629291633.txt.gz · Last modified: 2021/08/18 13:00 by takuma.sato
