Output-densities
The output of electron, hole and other charge densities is controlled by this
keyword.
!-------------------------------------------------------------------!
$output-densities
optional !
destination-directory
character
required !
electrons
character
optional !
holes
character
optional !
charge-density
character
optional !
intrinsic-density
character
optional !
ionized-dopant-density
character
optional !
piezo-electricity
character
optional !
pyro-electricity
character
optional !
interface-density
character
optional !
was previously called 'surface-density'
integrated-density
character
optional !
subband-density
character
optional !
spin-up-spin-down-kp-densities character
optional !
ion-density
character optional !
effective-density-of-states-Nc-Nv character
optional !
$end_output-densities
optional !
!-------------------------------------------------------------------!
Syntax:
destination-directory = my-directory/
e.g. = densities/
Name of directory to which the files should be written. Must exist
and directory name has to include the slash (\ for DOS and / for UNIX).
electrons = yes /
no
Flag whether to output electron density. More details, see below.
holes = yes / no
Flag whether to output hole density. More details, see below.
charge-density = yes /
no
Flag whether to output overall charge density. More details, see below.
intrinsic-density = yes /
no
Flag whether to output the intrinsic density. More details, see below.
ionized-dopant-density = yes /
no
Flag whether to output the ionized acceptor and donor densities. More
details, see below.
They are written to these files:
density1Ddopants_ionized.dat
density1Dacceptors_ionized.dat
density1Ddonors_ionized.dat
piezo-electricity = yes /
no
Flag whether to output the piezoelectric polarization charge density. This
file contains the piezoelectric interface and background charge densities. The
latter occur in graded materials, e.g. a ternary with a linear variation of
the x content. More details, see below.
pyro-electricity = yes /
no
Flag whether to output the pyroelectric polarization charge density. This
file contains the pyroelectric interface and background charge densities. The
latter occur in graded materials, e.g. a ternary with a linear variation of
the x content. More details, see below.
interface-density = yes /
no !
was previously called 'surface-density'
Flag whether to output information about the interface charge
densities, e.g. piezo- and pyroelectric interface charges as well as
interfaces states. More details, see below.
integrated-density = yes /
no
Flag whether to output the integrated electron or hole charge density
(applies also to space charge density, dopant density, ion densities).
1D: Units [e/cm2]
2D: Units [e/cm]
3D: Units [e]
subband-density = yes /
no
Flag whether to output the subband density. So far, this option works for
the single-band Schrödinger equation only and not for k.p.
The electron (hole) subband density of eigenstates that are far above (below)
the Fermi level should be zero.
The sum of all subband densities of the eigenstates must be equal to the
integrated quantum mechanical density.
- In a 1D quantum well one has several confined eigenstates forming
subbands.
The file 'subband1D_el_qc001_sg001_deg001_integrated.dat' contains the
electron density for each eigenstate in units of [e/cm²].
If four eigenvalues have been calculated, this file contains four values.
The file 'subband1D_el_qc001_sg001_deg001.dat' contains the
electron density for each eigenstate in units of [1 * 1018 e/cm³].
If four eigenvalues have been calculated, this file contains 1 + 4 = 5
columns where the first column is the grid coordinate.
Similar for the holes.
- In a 2D quantum wire one has several confined eigenstates forming
subbands.
The file 'subband2D_el_qc001_sg001_deg001_integrated.dat' contains the
electron density for each eigenstate in units of [e/cm].
If four eigenvalues have been calculated, this file contains four values.
The files 'subband2D_el_qc001_sg001_deg001_ev_001.fld',
'*.coord', '*.dat' contains the
electron density for the first eigenstate in units of [1
* 1018 e/cm³], similar for the second, third, ...
eigenstates.
Similar for the holes.
- In a 3D quantum dot one has several confined eigenstates.
The file 'subband3D_el_qc001_sg001_deg001_integrated.dat' contains the
electron density for each eigenstate in units of [e].
If four eigenvalues have been calculated, this file contains four values.
The files 'subband3D_el_qc001_sg001_deg001_ev_001.fld',
'*.coord', '*.dat' contains the
electron density for the first eigenstate in units of [1
* 1018 e/cm³], similar for the second, third, ...
eigenstates.
Similar for the holes.
1D example: The relevant files are:
densities1/subband1D_el_qc001_sg001_deg001_integrated.dat
(for Gamma conduction band)densities1/subband1D_hl_qc001_sg001_deg001_integrated.dat
(for heavy holes)densities1/subband1D_hl_qc001_sg002_deg001_integrated.dat
(for light holes)densities1/subband1D_hl_qc001_sg003_deg001_integrated.dat
(for split-off holes)
qc001 means "quantum cluster no. 1".
Note: If the electron bands at the L and X valleys are splitted due to
strain, the relevant output files should be interpreted carefully.
spin-up-spin-down-kp-densities = yes /
no
Flag whether to output the k.p densities
sorted into spin up and spin down contributions of the relevant
k.p spinors to the densities.
(Currently only 1D).
Relevant output files:
- densities1/density1Del_kpSpinUpSpinDown.dat (electrons)
- densities1/density1Dhl_kpSpinUpSpinDown.dat
grid points k.p density (spin
up) k.p
density (spin down) total
k.p density (spin up + spin down)
The last column (total density) is identical to the
quantum mechanical k.p density output in the files:
- densities1/density1Del.dat (electrons)
- densities1/density1Dhl.dat
(holes)
ion-density = yes /
no
Flag whether to output the ion charge density of the
electrolyte. Note that the units are [1*1018 cm-3].
The electrolyte contains i different ion species plus H3O+,
OH-, anion- and cation+
ions ($electrolyte-ion-content).
The density of electrolyte was calculated by the Poisson-Boltzmann
equation in FUNCTION
densities.
density1Dion001.dat - first ion species
density1Dion002.dat - second ion species
...
density1Dion00i+1.dat - H3O+ ions
density1Dion00i+2.dat - OH- ions
density1Dion00i+3.dat - anion- ions
related to concentration of H3O+
density1Dion00i+4.dat - cation+ ions related to
concentration of OH-
density1DIonConcentrationCorrection.dat - Correction due to H+
adsorbed or dissociated from the oxide/electrolyte interface.
density1Dion_total.dat - sum over all ion charge densities
effective-density-of-states-Nc-Nv = yes /
no !
default = no
Flag whether to output the effective density of states for the conduction
and valence bands.
Nc = valley_degeneracy * 2
(2 pi me
kBT / h² )3/2 = ... [1 * 1018 cm-3]
Nv = 2
(2 pi mh
kBT / h² )3/2 = ... [1 * 1018 cm-3]
==> 2 = spin degeneracy
The effective DOS depends on the temperature and on the effective mass.
(Note that for the derivation of this formula an isotropic and parabolic
energy dispersion E(k) is assumed).
The columns in the output files have the following meaning:
Nc_cb1D_ind001.dat: grid point [nm] Nc(Gamma)
Nc(L)
Nc(X)
Nv_cb1D_ind001.dat: grid point [nm] Nv(heavy
hole) Nv(light hole) Nv(split-off
hole)
The units of Nc, Nv
are [1 * 1018 cm-3].
So far, the 1D density output was the following:
I) -> density1Del.dat
-> density1Dhl.dat
Classical calculation:
- electrons: total classical density
- holes: total classical density
Quantum mechanical calculation:
- electrons: total density, quantum mechanical part, classical part
- holes: total density, quantum mechanical
part, classical part
Now there are additional output files named:
II) a) density1Dhh_lh_so.dat (holes)
b) density1DGamma_L_X.dat
a) The hole density in I) is the sum over all valence
band edges, i.e. heavy hole, light hole and split-off hole band.
The output file always has three columns: hh density,
lh density, split-off hole density
b) The electron density in I) is the sum over all
conduction band edges, i.e. Gamma band, L band and X band.
The output file only has three columns (Gamma density,
L density, X density) if there is no strain applied.
In case of strain, the L and X bands can be splitted
and thus additional columns arise for those grid points.
(Of course, if needed, one could split this output into classical and quantum
mechanical contributions to the density.)
This feature is only available for classical or single-band calculations (1D
only).
Output:
1D filenames and structure:
Electron density
[1018
cm-3]
filename:
density1Del_ind000.dat |
| |
_ind000 |
number of voltage step corresponding to
this output file (only if voltage sweep is turned on) |
structure:
For a quantum mechanical calculation:
position |
dens_el |
dens_el (quantum
mechanical
part only) |
dens_el (classical
part only) |
0.000000E+00 |
0.000000E+00 |
0.000000E+00 |
0.000000E+00 |
| position in space [nm] |
Electron density [1018 e/cm-3] |
Electron density [1018 e/cm-3] |
Electron density [1018 e/cm-3] |
For a classical calculation:
position |
dens_el |
0.000000E+00 |
0.000000E+00 |
| position in space [nm] |
Electron density [1018 e/cm-3] |
Hole density
[1018
cm-3]
filename:
density1Dhl_ind000.dat |
| |
_ind000 |
number of voltage step corresponding to
this output file (only if voltage sweep is turned on) |
structure:
For a quantum mechanical calculation:
position |
dens_hl |
dens_hl (quantum
mechanical part only) |
dens_hl (classical
part only) |
0.000000E+00 |
0.000000E+00 |
0.000000E+00 |
0.000000E+00 |
| position in space [nm] |
Hole density [1018 e/cm3] |
Hole density [1018 e/cm3] |
Hole density [1018 e/cm3] |
For a classical calculation:
position |
dens_hl |
0.000000E+00 |
0.000000E+00 |
| position in space [nm] |
Hole density [1018 e/cm-3] |
Space charge density
= -n + p -NA + ND
+ rhopiezo + rhopyro
[1018 cm-3]
Note: Here, the electron density
n and the acceptor density NA
have a negative sign.
Piezo and pyro charges are included as well.
filename:
density1Dspace_charge_ind001.dat |
| |
_ind000 |
number of voltage step corresponding to
this output file (only if voltage sweep is turned on) |
structure:
position |
dens_space |
0.000000E+00 |
0.000000E+00 |
| position in space [nm] |
Space charge density [1018 e/cm3] |
Intrinsic density
n_i = SQRT(n * p)
[cm-3]
filename:
structure:
position |
dens_space |
0.000000E+00 |
0.000000E+00 |
| position in space [nm] |
intrinsic density [e/cm3] |
Note: For the intrinsic density it is more transparent to output it in units
of [cm-3] rather than [1018 cm-3]
as is the case for the other densities.
Note: The output in 1D contains 3 columns.
- The 1st column is position in space in [nm].
- The 2nd column is the intrinsic density ni = SQRT(ni
* pi) for the bulk material at the relevant grid points.
(Note: Doping, the Poisson equation and heterostructure effects are not
considered!)
This is the value of the intrinsic density that enters the recombination
rates.
- The 3rd column is the quantity ni' = SQRT(n * p)
for the the relevant grid points.
Here, the densities n(x) and p(x) are the classical
electron and hole densities at the grid point x for the calculated
electrostatic built-in potential in equilibrium.
This quantity is just for information. It does not enter anywhere into
the actual calculation.
Piezoelectric
polarization charge density
filename:
structure:
position |
dens_piezo |
0.000000E+00 |
0.000000E+00 |
| position in space [nm] |
Piezo-charge density
[1018 e/cm3] |
Pyroelectric
polarization charge density
filename:
structure:
position |
dens_pyro |
0.000000E+00 |
0.000000E+00 |
| position in space [nm] |
Pyro-charge density [1018 e/cm3] |
Integrated density
filenames:
int_el_dens.dat
(Electron density)
int_hl_dens.dat (Hole density)
int_sp_dens.dat |
structure:
Pois_001 |
Cl_001 |
Total |
0.000000E+00 |
0.000000E+00 |
0.000000E+00 |
| Voltage at poisson cluster
[001] [V] |
Integrated density for
material cluster [001]
Units: 1D: [carriers/cm2]
2D: [carriers/cm]
3D: [carriers] |
Sum of all clusters |
Surface and interface
charge density
Filename:
interface_densities1D.txt |
Structure:
Information about interface/surface charge densities:
Scaling: n2d0= 1.000000000000000E+016
e.g.: n2d0=1d4 --> particles/cm^2
[C/m^2] => / |e| / n2d0 =>
|e|
10^16 m^-2
---------------------
PIEZOELECTRIC CHARGES
---------------------
Left boundary: 0.000000000000000E+000
Left boundary: 0.000000000000000E+000
Right boundary: 0.000000000000000E+000
Right boundary: 0.000000000000000E+000
Interface number 1 at position 100.000000000000 nm
piezoelectric charge: 2.762229388428833E-003 C/m^2
piezoelectric charge: 1.72403413480667
1E12 |e| / cm^2
Interface number 2 at position 117.000000000000 nm
piezoelectric charge: -2.762229388428833E-003 C/m^2
piezoelectric charge: -1.72403413480667
1E12 |e| / cm^2
--------------------
PYROELECTRIC CHARGES
--------------------
Left boundary: 0.000000000000000E+000
C/m^2
Left boundary: 0.000000000000000E+000
1E12 |e| / cm^2
Right boundary: 0.000000000000000E+000
C/m^2
Right boundary: 0.000000000000000E+000
1E12 |e| / cm^2
Interface number 1 at position 100.000000000000 nm
pyroelectric charge: 2.934399999999997E-003 C/m^2
pyroelectric charge: 1.83149371531894
1E12 |e| / cm^2
Interface number 2 at position 117.000000000000 nm
pyroelectric charge: -2.934399999999997E-003 C/m^2
pyroelectric charge: -1.83149371531894
1E12 |e| / cm^2
| 
