These example input files demonstrate how to calculate the current of a
resonant tunnerling diode (RTD).
An RTD is a device where quantum mechanical effects are essential.
We use the same structure as outlined in Section 8.2 of [GreckPhD2012]
.
We perform two simulations:
> RTD_PhDthesis_PeterGreck_ballistic.xml

calculation without scattering (ballistic calculation)
> RTD_PhDthesis_PeterGreck.xml

calculation including scattering
The RTD structure consists of 48 nm GaAs.
In the central region, there are two 4 nm wide AlGaAs barriers.
These two AlGaAs barriers are separated by a 4 nm intrinsic region.
Outside the barriers, the structure is doped with a concentration of 10^{17}
cm^{3}.
The following figure shows the calculated currentvoltage characteristics. It
corresponds to Fig. 8.2 of [GreckPhD2012]
.


Fig. 8.2 of PhD thesis of Peter Greck 
Calculated currentvoltage characteristics
of the ballistic calculation (gray)
and
the calculation including scattering (red).
The peak current density is at 100 mV
for the ballistic calculation but is shifted to
140 mV for the calculation that includes scattering.
The file that is plotted is called CurrentVoltage_Drain.dat . 
The relevant lines are "gray (Ballistic)"
for the ballistic calculation and "blue
(MSB)" for the calculation including scattering.
The peak current density of the ballistic calculation is reached at about 100 mV
where the chemical potential of the source contact is aligned with the lowest
quantum well state.
However, this result is physically wrong. This is due to the fact that a
ballistic calculation neglects any kind of incoherent scattering.
In a realistic device the carriers do not ballistically reach the RTD.
Instead, a bound state is formed by the triangular shaped potential in front of
the RTD and inelastic scattering processes lead to a capture of carriers within
this state.
Since the energy of this bound state is lower than the chemical potential of the
source contact, the alignment with the RTD resonance is realized at higher bias
voltages.
For the calculated RTD, the peak currenty density is shifted from 100 mV to 140
mV.
Results
The following figures shows the conduction band edges (BandProfile/BandEdge_conduction.dat
)
together with the
 local density of states rho(x,E) (
DOS/DOS_position_resolved.avs.fld
)
 electron density n(x,E) (
CarrierDensity/CarrierDensity_energy_resolved.avs.fld
)
 current density j(x,E) (
CurrentDensity/CurrentDensity_energy_resolved.avs.fld
)
at the peak current densities of 100 mV (left figures, ballistic
calculation) and 140 mV (right figures, calculation including scattering).
Note that the peak current densitiy of the ballistic calculation (100 mV)
deviates from the peak current density (140 mV) of the calculation including
scattering.
Local density of states rho(x,E):
For the ballistic calculation (left figure), the quantum well state is aligned
energetically with the chemical potential of the left contact (source).
For the scattering calculation (right figure), the quantum well state is aligned
energetically with the triangular quantum well state left of the barrier.
Electron density n(x,E):
For the ballistic calculation (left figure), the quantum well state is aligned
energetically with the chemical potential of the left contact (source).
For the scattering calculation (right figure), the quantum well state is aligned
energetically with the triangular quantum well state left of the barrier.
Current density j(x,E):
For the ballistic calculation (left figure), the quantum well state is aligned
energetically with the chemical potential of the left contact (source).
For the scattering calculation (right figure), the quantum well state is aligned
energetically with the triangular quantum well state left of the barrier.
On the right figure one can nicely see that the carriers that are injected from
the left contact (source) scatter into the triangular quantum well state and
then tunnel through the double barrier into the right contact (drain).
Further comments regarding the MSB input file
 In order to calculate the current ballistically we switched of
scattering by using the following flag.
<BallisticCalculation Comment="yes
or no (default is no)">yes</BallisticCalculation>
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.
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