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Output files of the simulation

Note: The output of a simulation can easily exceed 1 GB. So 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.
All files that have the file extension .gnu.plt can be plotted with Gnuplot.
All files that have the file extension .fld     can be plotted with nextnanomat or AVS/Express.

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 in units of []
    Position [nm]   Relative Static Permittivity []
  • EpsOptic.dat
    optical dielectric constant in units of []
    Position [nm]   Relative Optical Permittivity []
  • MaterialDensity.dat
    sound velocity in units of [m/s]
    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 ongitudinal optical phonon energy (LO phonon energy) in units of [eV]
    For an explanation, see Material database.
    Position [nm]   LO Phonon Energy [eV]
    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 []
    Position [nm]   Probe Values []

 

BandProfile

  • BandEdge_conduction.dat
    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, Ec(x) = Ec,0 - e phi(x), is known, the eigenenergies Ei and wave functions psii(x) of the single-band Schrödinger equation are calculated.
phi(x) is the electrostatic potential.

H psi(x) = E psi(x)

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

  • periodic: psi(x=0) = psi(x=L)
  • Dirichlet: psi(x=0) = psi(x=L) = 0, and
  • Neumann boundary conditions: d psi / d x = 0 at the left (x=0) and right (x=L) boundary.

There are files for the

  • amplitudes psii(x) in units of [nm-1/2]
    Amplitudes_Dirichlet.dat          / *_Neumann.dat / *_Periodic.dat
  • amplitudes psii(x) shifted by their eigenenergies Ei
    Amplitudes_shift_Dirichlet.dat    / *_Neumann.dat / *_Periodic.dat
  • probability densities psii2(x) in units of [nm-1]
    Probabilities_Dirichlet.dat       / *_Neumann.dat / *_Periodic.dat
  • probability densities psii2(x) shifted by their eigenenergies Ei
    Probabilities_shift_Dirichlet.dat / *_Neumann.dat / *_Periodic.dat
  • eigenvalues Ei in units of [eV]
    Eigenvalues_Dirichlet.dat         / *_Neumann.dat / *_Periodic.dat

 

Carrier density

  • 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)
  • CarrierDensity.dat / *.gnu.plt
      Position [nm]  Density [1/cm^3]
      0              5.74416
      ...            ...

 

DOS

  • DOS_position_resolved.avs.fld   (or the corresponding *.gnu.plt / *.dat file)
    The position and energy resolved density of states DOS(z,E) in units of [eV-1 nm-1].
  • DOS.dat / *.gnu.plt
    Energy [eV]  DOS [1/eV]
    The density of states DOS(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 DOS(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 = BAC + BLO.
    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 spectral function Aprobe(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 µ, e.g. the probe at grid point #5 has µ5. Then the LDOSprobe#5(z,E) is occupied everywhere with this chemical potential µ5.
    In our algorithm, we only have one probe at each grid point having the combined scattering potential B = BAC + BLO.
    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(E) due to the Büttiker probes only (probe-connected DOS).
  • DOS_Lead_Source_position_resolved.fld   (or the corresponding *.gnu.plt / *.dat file)
    The position and energy resolved density of states DOS(z,E) due to the source contact only in units of [eV-1 nm-1].
  • DOS_Lead_Source.dat / *.gnu.plt
    Energy [eV]  DOS [1/eV]
    The density of states DOS(E) due to the source contact only (lead-connected DOS).
  • DOS_Lead_Drain_position_resolved.fld   (or the corresponding *.gnu.plt / *.dat file)
    The position and energy resolved density of states DOS(z,E) due to the drain contact only in units of [eV-1 nm-1].
  • DOS_Lead_Drain.dat / *.gnu.plt
    Energy [eV]  DOS [1/eV]
    The density of states DOS(E) due to the drain contact only (lead-connected DOS).
  • DOS_Leads_position_resolved.fld   (or the corresponding *.gnu.plt / *.dat file)
    The position and energy resolved density of states DOS(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(E) due to the  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>

    a)
    <ProbeMode   Comment="Specify method to calculate current conservation."> iterative </ProbeMode>

    local Büttiker probe virtual chemical potentials µp (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.

    b)
    <ProbeMode   Comment="Specify method to calculate current conservation."> direct </ProbeMode>

    local Büttiker probe coefficients cp (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> here.

    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: BOP ~ e2 zeta ELO / ( 32 pi epsilon0) (epsilonoptic-1 - epsilonstatic-1)
    For AC, the prefactor is given after eq. (7.8) of the PhD thesis of P. Greck. It reads: BAP ~ VD2 kBT ( 8 pi rhoM vs2 EAP )
    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 BOP is given in eq. (7.9) of the PhD thesis of P. Greck.
    The scattering potential for acoustic phonons BAP 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 is 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 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,ν) in units of [THz-1 cm-1].
    Here, frequency 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,λ) in units of [µm-1 cm-1].
    Here, wavelength 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(ν) 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(λ) 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 [1/cm]. 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

  • The position and energy resolved current density j(z,E) is contained in this file:
    current_density_energy_resolved.avs.fld   (or the corresponding *.gnu.plt / *.dat file)
  • current_density.dat / *.gnu.plt
      Position [nm]  Current Density [A/cm^2]
      0              5.74416
      ...            ...

 

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.

 

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