# 5. Simulation output¶

Output files of the simulation

Note

The output of a simulation can easily exceed 1 GB. Please make sure you have enough disk space available.

All files that have the file extension

`.dat`

can be plotted with next**nano**mat or any other visualization software like e.g. Origin.`.gnu.plt`

can be plotted with Gnuplot.`.fld`

can be plotted with next**nano**mat or AVS/Express.`.vtr`

can be plotted with next**nano**mat, Paraview or VisIt.

Note

Recommendation: Please install Gnuplot.
It is then very convenient to plot the results of the next**nano**.MSB calculations.
Within next**nano**mat, one can plot the band profile together with other data using *Keep current graph as overlay*.

## 5.1. Input¶

In this folder, all material and input parameters are contained.

### Material parameters¶

`BandEdge_conduction_input.dat`

This is the conduction band edge profile that has been specified in the

*input file*.`BandEdge_conduction_adjusted.dat`

This is the conduction band edge profile that has been used in the

*simulation*.The suffix

`_adjusted`

indicates that the well and barrier widths, as well as heights, had been adjusted automatically by the program.Why do the band edges for

`*_input.dat`

and`*_adjusted.dat`

differ? See`AdjustBandedge`

in Input file documentation for more information.conduction band edge in units of

`[eV]`

`Position [nm] Conduction Band Edge [eV]`

`EffectiveMass.dat`

electron effective mass in units of

`[m0]`

`Position [nm] Effective Mass [m0]`

`EpsStatic.dat`

static dielectric constant in units of

`[]`

`Position [nm] Relative Static Permittivity []`

`EpsOptic.dat`

optical dielectric constant in units of

`[]`

`Position [nm] Relative Optical Permittivity []`

`MaterialDensity.dat`

material density or mass density in units of

`[kg/m^3]`

`Position [nm] Material Density [kg/m^3]`

`PhononEnergy_acoustic.dat`

acoustic phonon energy in units of

`[eV]`

`Position [nm] Acoustic Phonon Energy [eV]`

`PhononEnergy_LO.dat`

longitudinal optical phonon energy (LO phonon energy) in units of

`[eV]`

`Position [nm] LO Phonon Energy [eV]`

`PhononEnergy_LO_width.dat`

width of longitudinal optical phonon energy (LO phonon energy) in units of

`[eV]`

For an explanation, see Material database.

`Position [nm] LO Phonon Energy Width [eV]`

`VelocityOfSound.dat`

sound velocity in units of

`[m/s]`

`Position [nm] Velocity of Sound [m/s]`

### Input parameters¶

`AlloyContent.dat`

alloy profile in units of

`[]`

`Position [nm] Alloy Content []`

`DopingConcentration.dat`

doping concentration in units of

`[cm^-3]`

.It is assumed that all dopants are ionized (

*fully ionized*). An ionization model is not included.`Position [nm] Doping Concentration [1/cm3]`

`ProbeValues.dat`

profile of the Büttiker probes in units of

`[]`

, value is between`0`

and`1`

`Position [nm] Probe Values []`

## 5.2. Output¶

### BandProfile¶

`BandEdge_conduction.dat`

conduction band edge in units of

`[eV]`

`Position [nm] Conduction Band Profile [eV]`

`ElectrostaticPotential.dat`

electrostatic potential in units of

`[V]`

`Position [nm] Electrostatic Potential [V]`

`ElectricField.dat`

electric field in units of

`[kV/cm]`

`Position [nm] Electric Field [kV/cm]`

### Eigenstates¶

The data contained in this folder is not used inside the actual MSB algorithm. It is merely a post-processing feature. Once the self-consistently calculated conducton band edge,

\(E_{\text{c}}(x) = E_{\text{c,0}}(x) - e \phi(x)\)

is known, the eigenenergies \(E_i\) and wave functions \(\psi_i(x)\) of the single-band Schrödinger equation are calculated.

\(\phi(x)\) is the electrostatic potential which is the solution of the Poisson equation.

\({\mathbf{H}} \psi(x) = E \psi(x)\)

The Schrödinger equation is solved three times, i.e. with three different boundary conditions

*periodic*: \(\psi(x=0) = \psi(x=L)\)*Dirichlet*: \(\psi(x=0) = \psi(x=L) = 0\), and*Neumann*: \(\frac{\text{d}\psi}{\text{d}x} = 0\) at the left (\(x=0\)) and right (\(x=L\)) boundary.

There are files for the

amplitudes \(\psi_i(x)\) in units of

`[nm^-1/2]`

`Amplitudes_Dirichlet.dat`

/`*_Neumann.dat / ``*_Periodic.dat`

amplitudes \(\psi_i(x)\)

*shifted*by their eigenenergies \(E_i\)`Amplitudes_shift_Dirichlet.dat`

/`*_Neumann.dat`

/`*_Periodic.dat`

probability densities \(\psi_i^2(x)\) in units of

`[nm^-1]`

`Probabilities_Dirichlet.dat`

/`*_Neumann.dat`

/`*_Periodic.dat`

probability densities \(\psi_i^2(x)\)

*shifted*by their eigenenergies \(E_i\)`Probabilities_shift_Dirichlet.dat`

/`*_Neumann.dat`

/`*_Periodic.dat`

eigenvalues \(E_i\) in units of

`[eV]`

`Eigenvalues_Dirichlet.dat`

/`*_Neumann.dat`

/`*_Periodic.dat`

### CarrierDensity¶

The position and energy resolved electron density \(n(z,E)\) is contained in this file:

`CarrierDensity_energy_resolved.avs.fld`

(or the corresponding`*.gnu.plt`

/`*.dat`

file)The electron density \(n(z)\) is contained in this file:

`CarrierDensity.dat`

/`*.gnu.plt`

`Position [nm] Density [1/cm^3]`

### DOS¶

`DOS_position_resolved.avs.fld`

(or the corresponding`*.gnu.plt`

/`*.dat`

file)The position and energy resolved local density of states (LDOS) \(\rho(z,E)\) in units of

`[eV-1 nm-1]`

.`DOS.dat`

/`*.gnu.plt`

`Energy [eV] DOS [1/eV]`

The density of states (DOS) \(n(E)\).

The density of states is the sum of the DOS due to source, drain and Büttiker probes, i.e.

`DOS = DOS_Source + DOS_Drain + DOS_Probes.`

`DOS_Probes_position_resolved.avs.fld`

(or the corresponding`*.gnu.plt`

/`*.dat`

file)The position and energy resolved density of states (LDOS) \(\rho(z,E)\) due to the Büttiker probes only in units of

`[eV-1 nm-1]`

.This DOS is induced by scattering events. Like the lead-connected DOS enters the device through the source or drain contacts, respectively, the probe DOS is due to scattering.

Here we plot the LDOS for the probes, i.e. all probes are summed up, and the LDOS of the probes is determined by the self-energies of the probes. A probe has the scattering strength \(B = B_{\text{AC}} + B_{\text{LO}}\).

From this plot one cannot see if the DOS is due to LO or AC scattering events as both scattering potentials are added to obtain \(B\).

In fact, as one considers the probes for each grid point individually, one could print out the LDOS for each grid point. So each probe grid point produces a probe spectral function \(A_\text{p}(z,E)\), e.g. the probe at grid point 5 produces the

*grid point 5 connected local density of states*which is nonzero not only on grid point #5 but everywhere.Each probe has its own chemical potential \(\mu\), e.g. the probe at grid point 5 has \(\mu_5\). Then the LDOS of probe 5 \(\rho_5(z,E)\) is occupied everywhere with this chemical potential \(\mu_5\). In our algorithm, we only have one probe at each grid point having the combined scattering potential \(B = B_{\text{AC}} + B_{\text{LO}}\). In principle, each grid point could have 2 probes, one for AC and one for LO phonon scattering. However, this is not the case in our algorithm so far.

`DOS_Probes.dat`

/`*.gnu.plt`

`Energy [eV] DOS [1/eV]`

The density of states (DOS) \(n(E)\) due to the

*Büttiker probes*only (probe-connected DOS).`DOS_Lead_Source_position_resolved.fld`

(or the corresponding`*.gnu.plt`

/`*.dat`

file)`DOS_Lead_Drain_position_resolved.fld`

(or the corresponding`*.gnu.plt`

/`*.dat`

file)The position and energy resolved local density of states (LDOS) \(\rho(z,E)\) due to the

*source*and*drain*contact only in units of`[eV-1 nm-1]`

.`DOS_Lead_Source.dat`

/`*.gnu.plt`

`DOS_Lead_Drain.dat`

/`*.gnu.plt`

`Energy [eV] DOS [1/eV]`

The density of states (DOS) \(n(E)\) due to the

*source*and*drain*contact only (lead-connected DOS).`DOS_Leads_position_resolved.fld`

(or the corresponding`*.gnu.plt`

/`*.dat`

file)The position and energy resolved local density of states (LDOS) \(\rho(z,E)\) due to the

*drain*and*source*contacts in units of`[eV-1 nm-1]`

.This corresponds to the sum of

`DOS_Lead_Source_position_resolved.fld`

`+`

`DOS_Lead_Drain_position_resolved.fld`

.`DOS_Leads.dat`

/`*.gnu.plt`

`Energy [eV] DOS [1/eV]`

The density of states (DOS) \(n(E)\) due to the

*drain*and*source*contacts (lead-connected DOS). This corresponds to the sum of`DOS_Lead_Source.dat`

`+`

`DOS_Lead_Drain.dat`

.

### Probes¶

`ProbeLevels.dat`

This output depends on the probe model used:

`ProbeMode`

`ProbeMode = iterative # Comment="Specify method to calculate current conservation."`

local Büttiker probe

*virtual chemical potentials*\(\mu_\text{p}\)`[eV]`

related to the occupation of the probes`Position [nm] Local Probe Levels [eV]`

For zero applied bias, the local probe levels are

`0`

`[eV]`

which is the same value as the chemical potentials of the source and drain contacts as there is no current flowing. The probe levels indicate the occupation of the scattering states.`ProbeMode = direct # Comment="Specify method to calculate current conservation."`

local Büttiker probe

*coefficients*\(c_\text{p}\)`[]`

(dimensionless)`Position [nm] Local Probe Levels (% of Drain) [0..1]`

Here, the units are dimensionless and the numbers are between

`0`

and`1`

.`0`

means 100 % occupation of the probes by the*source*contact.`1`

means 100 % occupation of the probes by the*drain*contact.For zero applied bias, the local probe levels are

`0.5`

, i.e. 50 % occupation due to source and 50 % due to drain contact.

See also the comments on

`ProbeMode`

in the documentation of the Input file.

There is only one \(B(z,E)\) for which current conservation holds. Once this quantity has been calculated, one cannot distinguish any more between optical and acoustic phonon scattering.

If the command line argument `-debug 1`

is provided, additional output is written to this folder.

`NumericalPrefactor_MSB_AC.dat`

`NumericalPrefactor_MSB_LO.dat`

The numerical prefactors for the MSB scattering potentials for acoustic phonon (AC) and LO phonon scattering are given in units of

`[...]`

. (Add correct units here.)

For LO, the prefactor is given in eq. (7.9) of the PhD thesis of P. Greck. It reads:

\(B_\text{OP} \sim \frac{e^2 \zeta E_\text{LO}} { 32 \pi \varepsilon_0} \left( \varepsilon_{\text{optic}}^{-1} - \varepsilon_{\text{static}}^{-1} \right)\)

For AC, the prefactor is given after eq. (7.8) of the PhD thesis of P. Greck. It reads:

\(B_\text{AP} \sim \frac{V_\text{D}^2 k_\text{B}T}{8 \pi \rho_\text{M} v_\text{s}^2 E_\text{AP}}\)

The prefactors are independent of applied bias voltage.

`ScatteringPotential_MSB_AC.dat`

`ScatteringPotential_MSB_LO.dat`

The scattering potentials for MSB for acoustic phonon (AC) and LO phonon scattering are given in units of

`[...]`

.It is not`[nm]`

as written in the output file.The scattering potential for LO phonons \(B_\text{OP}\) is given in eq. (7.9) of the PhD thesis of P. Greck.

The scattering potential for acoustic phonons \(B_\text{AP}\) is given after eq. (7.8) of the PhD thesis of P. Greck.

`ScatteringPotential_MSB_AC_position_resolved.dat`

`ScatteringPotential_MSB_LO_position_resolved.dat`

The position resolved scattering potentials for MSB for acoustic phonon (AC) and LO phonon scattering are given in arbitrary units.

### Gain¶

`gain_energy_resolved.avs.fld`

(or the corresponding`*.gnu.plt`

/`*.dat`

file)The position and energy resolved optical gain \(g(z,E)\) in units of

`[eV-1 cm-1]`

.Here, energy \(E\) is the photon energy.

`gain_frequency_resolved.avs.fld`

(or the corresponding`*.gnu.plt`

/`*.dat`

file)The position and frequency resolved optical gain \(g(z,\nu)\) in units of

`[THz-1 cm-1]`

.Here, frequency \(\nu\) is the photon frequency.

`gain_wavelength_resolved.avs.fld`

(or the corresponding`*.gnu.plt`

/`*.dat`

file)The position and wavelength resolved optical gain \(g(z,\lambda)\) in units of

`[µm-1 cm-1]`

.Here, wavelength \(\lambda\) is the photon wavelength.

`gain_energy.dat`

/`*.gnu.plt`

The optical gain as a function of photon energy \(g(E)\) in units of

`[cm^-1]`

.`Photon Energy [eV] Optical Gain [1/cm]`

`gain_frequency.dat`

/`*.gnu.plt`

The optical gain as a function of frequency \(g(\nu)\) in units of

`[cm^-1]`

.`Photon Frequency [THz] Optical Gain [1/cm]`

`gain_wavelength.dat`

/`*.gnu.plt`

The optical gain as a function of photon wavelength \(g(\lambda)\) in units of

`[cm^-1]`

.`Photon wavelength [µm] Optical Gain [1/cm]`

Negative values of the *gain* correspond to *optical absorption*.

### Gain-voltage characteristics¶

`GainMaxFrequency-Voltage.dat`

/`*.gnu.plt`

`Source [V] Drain [V] Frequency of Max. Gain [THz]`

`0 0 2.41798940e-001`

This file shows the frequency of the maximum value of the gain as a function of voltage. The first two columns contain the source and drain voltages. The third column is the frequency of the maximum gain at this voltage.

`GainMaxFrequency-Voltage_Source.dat`

`GainMaxFrequency-Voltage__Drain.dat`

These files contain the same as discussed above but here only the source or drain voltages are contained, respectively, i.e. only one column for the voltages instead of two. It is easier to plot the data from one of these files compared to

`GainMaxFrequency-Voltage.dat`

.`GainMax-Voltage.dat`

/`*.gnu.plt`

`Source [V] Drain [V] Max. Gain [1/cm]`

`0 0 -1.46451103e+000`

This file shows the maximum value of the gain as a function of voltage in units of

`[cm^-1]`

. The first two columns contain the source and drain voltages. The third column is the maximum gain at this voltage. From this file, one can extract the voltage for threshold of gain.`GainMax-Voltage_Source.dat`

`GainMax-Voltage__Drain.dat`

These files contain the same as discussed above but here only the source or drain voltages are contained, respectively, i.e. only one column for the voltages instead of two. It is easier to plot the data from one of these files compared to

`GainMax-Voltage.dat`

.

### Transmission¶

`Transmission.dat`

Transmission \(T(E)\) in units of

`[eV]`

`Energy [eV] Transmission (Source->Drain)`

Does the transmission have a meaning in the actual calculation? Yes, it adds the ballistic part, i.e. the tunneling from source to drain to the current (compare with Landauer formula (

*insert reference*)), see thesis page 65ff in PhD thesis of Peter Greck (*check this*).It has been calculated from the self-consistently obtained conduction band profile. The transmission function is only the coherent ballistic contribution to the current, i.e. the current that goes directly from source to drain. The meaning of this output should be interpreted with care. There is also a noncoherent contribution to the current.

If one does a ballistic calculation then the total current is based on this transmission function (see Landauer formula).

### Current density¶

`current_density_energy_resolved.avs.fld`

(or the corresponding`*.gnu.plt`

/`*.dat`

file)position and energy resolved current density \(j(z,E)\)

`current_density.dat / *.gnu.plt`

current density \(j(z)\)

`Position [nm] Current Density [A/cm^2]`

### Current-voltage characteristics (I-V curve)¶

`Current-Voltage.dat / *.gnu.plt`

`Source [V] Drain [V] Current [A/cm^2]`

`0 0 0.00000000e+000`

This file contains the current through the device (current-voltage or I-V characteristics). The first two columns contain the source and drain voltages. The third column is the current density.

`Current-Voltage_Source.dat`

`Current-Voltage_Drain.dat`

These files contain the same as discussed above but here only the source or drain voltages are contained, respectively, i.e. only one column for the voltages instead of two. It is easier to plot the I-V characteristics from one of these files compared to

`Current-Voltage.dat`

.