4.5. 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 nextnanomat or any other visualization software like e.g. Origin.
.gnu.plt can be plotted with Gnuplot.
.fld can be plotted with nextnanomat or AVS/Express.
.vtr can be plotted with nextnanomat, ParaView or VisIt.

Note

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

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

Position [nm] Relative Static Permittivity []
EpsOptic.dat

optical dielectric constant

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

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, value is between 0 and 1

Position [nm] Probe Values []

Output

Energy profile

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
1. 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.
2. 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 spectrum as a function of photon wavelength \(g(\lambda)\) in units of (cm^-1).

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

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

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.