# 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 ! ```(optional, only needed for electric field sweep)
``` 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                                             ! !---------------------------------------------------------------!```

### 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             ! ``` 1D only```  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 ```and
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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