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Electric field
- 1D: Electric field must be oriented parallel to simulation axis.
- 2D: Electric field must be oriented in plane of simulation area.
- 3D: arbitrary
!----------------------------------------------------------------------!
$electric-field
optional !
electric-field-on
character required !
electric-field-strength
double required !
electric-field-strength-from-applied-voltage
character optional !
1D only
electric-field-direction
integer_array required !
!
electric-field-sweep-active
character optional !
electric-field-sweep-step-size
double
optional ! (optional, only needed for
electric field sweep)
electric-field-sweep-number-of-steps integer
optional ! (optional, only needed for
electric field sweep)
$end_electric-field optional !
!----------------------------------------------------------------------!
Syntax
!---------------------------------------------------------------!
$electric-field !
electric-field-on =
yes ! yes/no
electric-field-strength = 7.0d5
! [V/m], i.e. in this case 7.0 * 105 V/m
electric-field-direction = 1 0 0 !
!
electric-field-sweep-active =
yes
! yes/no
electric-field-sweep-step-size =
0.5d5 !
[V/m], i.e. in this case 0.5 * 105 V/m
electric-field-sweep-number-of-steps = 10
! number of electric field sweep steps
$end_electric-field !
!---------------------------------------------------------------!
Note: The origin of the electric field is
chosen automatically to be the center of the structure. This makes it possible
to compare energies by varying the applied electric field as shown in the
Tutorial "Quantum Confined Stark
Effect".
electric-field-strength =
7.0d5 ! [V/m], i.e. in this case 7.0 * 105 V/m
The units are [V/m]: 1 kV/cm = 1 * 105 V/m
= 1d5 V/m
electric-field-direction = 1 0 0
The direction of the electric field
vector is with respect to the
simulation coordinate system, i.e. 1 0 0
means along x direction [100], 0 0 1
along the z direction [001].
Additional option for 1D simulation
If one has two contacts at the left and right device boundaries,
one can calculate the electric field from the difference of the two applied
voltages (assuming a linear potential drop).
This can be combined with a voltage sweep ($voltage-sweep).
In that case, the electric field is calculated automatically, and thus the value
of electric-field-strength will be ignored.
!---------------------------------------------------------------!
$electric-field !
electric-field-on =
yes ! yes
electric-field-strength =
0d0
! [V/m] will be ignored in this case
electric-field-strength-from-applied-voltage
=
yes !
electric-field-direction = 1 0 0 !
$end_electric-field !
!---------------------------------------------------------------!
This feature electric-field-strength-from-applied-voltage
only works if
'applied-voltage = 0.0 V' at the left contact and
'applied-voltage /= 0.0 V' at the right contact.
If 'applied-voltage /= 0.0 V' at left contact and
'applied-voltage = 0.0 V' at the right contact,
then the sign of the electric field has to be reversed.
If none of the contacts is zero, then the electric field is not calculated
correctly.
Electric field sweep
It is possible to sweep over the electric field strength, i.e. to vary the
strength of the electric field stepwise. This is similar to magnetic field
sweeps ($magnetic-field), voltage
sweeps ($voltage-sweep) and doping
concentration sweeps ($doping-function).
The output is labeled with ..._ind000.dat, ..._ind001.dat,
..._ind002.dat, ... where the index refers to the number of the
electric field sweep step.
The output for the eigenvalues as a function of applied electric field can be
found here:
Schroedinger_1band / electric_ev1D_cb001_qc001_sg001_deg001_dir_Kx001_Ky001_Kz001.dat.
In this particular example, the Gamma conduction band edge electron energies ('cb001')
that have been obtained with the one-dimensional ('1D') single-band
('sg') Schrödinger equation with Dirichlet ('dir')
boundary conditions have been written out as a function of electric field.
The first column contains the strength of the electric field in units of
[kV/cm].
The second column contains the 1st eigenvalue for the specified
electric field in units of [eV],
the third column contains the 2nd
eigenvalue for the specified electric field in units of [eV], ...
For details, please have a look into the
Quantum Confined Stark Effect
(QCSE) tutorial.
Restrictions:
- Can only be used in connection with
flow-scheme =
20
1. Calculate electrostatic potential.
2. Apply electric field.
3. Calculate eigenstates.
flow-scheme =
21 so far.
1. Do not calculate electrostatic potential.
2. Apply electric field.
3. Calculate eigenstates.
- Electric field direction so far refers to x, y or z-coordinate axis (and
not to Miller indices), i.e.
1D: only possible: 1 0 0
or 0 1 0
or 0 0 1
2D: only possible: 1 0 0
or 0 1 0
or 0 0 1
3D: only possible: 1 0 0
or 0 1 0
or 0 0 1
- Outlook: The following should be implemented in the future:
Arbitrary electric field orientation in 3D: e.g. 3
1 1
Arbitrary electric field orientation in 2D: e.g. 0
1 1
(1D restriction: Electric field must still be oriented parallel to simulation
axis.
2D restriction: Electric field must still be oriented in plane of
simulation area.)
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