 
nextnano.MSB
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 [m_{0}]
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/cm^{3}]
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]
The data contained in this folder is not used inside the actual MSB
algorithm. It is merely a postprocessing feature.
Once the selfconsistently calculated conducton band edge, E_{c}(x) = E_{c,0}
 e phi(x), is known, the eigenenergies E_{i} and wave functions psi_{i}(x)
of the singleband 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 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
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 leadconnected 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 selfenergies of the probes.
A probe has the scattering strength B = B_{AC} + B_{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 spectral function A_{probe}(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 µ_{5}. Then the LDOS_{probe#5}(z,E) is occupied
everywhere with this chemical potential µ_{5}.
In our algorithm, we only have one probe at each grid point having the
combined scattering potential B = B_{AC} + B_{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(E) due to the Büttiker probes only
(probeconnected 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
(leadconnected 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
(leadconnected 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
(leadconnected 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 µ_{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.
b)
<ProbeMode Comment="Specify
method to calculate current conservation.">
direct </ProbeMode> local Büttiker probe
coefficients c_{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>
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: B_{OP} ~ e^{2} zeta E_{LO} / ( 32
pi epsilon_{0}) (epsilon_{optic}^{1}
 epsilon_{static}^{1})
For AC, the prefactor is given after eq. (7.8) of the PhD thesis of
P. Greck. It reads: B_{AP} ~ V_{D}^{2} k_{B}T
( 8 pi rho_{M} v_{s}^{2} E_{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_{OP} is given in
eq. (7.9) of the PhD thesis of P. Greck.
The scattering potential for acoustic phonons B_{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 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.
Gainvoltage characteristics
GainMaxFrequencyVoltage.dat / *.gnu.plt
Source [V] Drain [V] Frequency
of Max. Gain [THz]
0 0
2.41798940e001
...
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.
GainMaxFrequencyVoltage_Source.dat
GainMaxFrequencyVoltage__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 GainMaxFrequencyVoltage.dat .
GainMaxVoltage.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.
GainMaxVoltage_Source.dat
GainMaxVoltage__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 GainMaxVoltage.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 selfconsistently 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
... ...
Currentvoltage characteristics (IV curve)
CurrentVoltage.dat / *.gnu.plt
Source [V] Drain [V] Current [A/cm^2]
0 0
0.00000000e+000
...
This file contains the current through the device (currentvoltage or
IV characteristics). The first two
columns contain the source and drain voltages. The third column is the
current density.
CurrentVoltage_Source.dat
CurrentVoltage_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 IV characteristics from one of these files
compared to CurrentVoltage.dat .
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