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 !
 dopant-energy-levels                    character         optional !
 piezo-electricity                       character         optional !
 pyro-electricity                        character         optional !
 interface-density                       character         optional !
 integrated-density                      character         optional !
 subband-density                         character         optional !
 spin-up-spin-down-kp-densities          character         optional !
 ion-density                             character         optional ! for electrolyte
 effective-density-of-states-Nc-Nv       character         optional !
 detailed-output                         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.
They are written to these files:
density1Ddopants_ionized.dat   - acceptors (negative) + donors (positive)
density1Dacceptors_ionized.dat - acceptors only, for each impurity number and total density. Here, the density is plotted with a positive sign.
density1Ddonors_ionized.dat    - donors     only, for each impurity number and total density

dopant-energy-levels = yes / no 

Flag whether to output the energy levels (energy-levels-relative, see $impurity-parameters) of the donors and acceptors relative to the lowest conduction band edge and highest valence band edge.
They are written to this file:
dopant_level_profile.dat

   position[nm]  donor_001[eV]  acceptor_001[eV]
   ...           ...            ...
It makes sense to plot this file together with the conduction and valence band edges.

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

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.
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.
   
• 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.
   
• 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.
Similar for k.p.

1D example: The relevant files are:

• densities/subband1D_el_qc001_sg001_deg001_integrated.dat (for Gamma conduction band)
• densities/subband1D_hl_qc001_sg001_deg001_integrated.dat (for heavy holes)
• densities/subband1D_hl_qc001_sg002_deg001_integrated.dat (for light holes)
• densities/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 split due to strain, the relevant output files should be interpreted carefully.
Note: The single-band eigenstates are two-fold spin-degenerate. Thus the subband density is twice as high as in the case of k.p.

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:
- densities/density1Del_kpSpinUpSpinDown.dat (electrons)
- densities/density1Dhl_kpSpinUpSpinDown.dat (holes)

Contains the following four colums for the quantum mechanical densities:
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:
- densities/density1Del.dat (electrons)
- densities/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.

N_c = valley_degeneracy * 2 (2 pi m_e k_BT / h² )^3/2 = ... [1 * 10¹⁸ cm^-3]
N_v =                              2 (2 pi m_h k_BT / 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].

detailed-output = yes / no   ! default = yes (1D)
                             ! default = no  (2D/3D)

Flag whether to output additional densities with respect to
- Gamma band
- L band
- X band
- heavy hole (hh) band
- light hole (lh) band
- split-off hole (so) band

- classical density (cl)
- quantum mechanical density (qm)

electrons = yes  ! contains the sum of Gamma, L and X bands
holes     = yes  ! contains the sum of heavy hole, light hole and split-off hole band

By default, the sum of classical and quantum mechanical densities is contained in the density output for the electrons and holes.

This flag is useful if one is interested in the contribution of each band to the total density.

The relevant 1D output is
- density1Del.dat - contains total electron density, quantum mechanical part of the density and classical part of the density:
  The columns are labeled with el[1e18/cm3] el_qm[1e18/cm3] el_cl[1e18/cm3].
    The electron density in is the sum over all conduction band edges, i.e. Gamma band, L band and X band.
- density1Dhl.dat - contains total hole       density, quantum mechanical part of the density and classical part of the density:
  The columns are labeled with hl[1e18/cm3] hl_qm[1e18/cm3] hl_cl[1e18/cm3].
  The hole density in is the sum over all valence band edges, i.e. heavy hole, light hole and split-off hole band.
- density1DGamma_L_X.dat - densities of Gamma, L and X bands
  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 split and thus additional columns arise for those grid points.
- density1Dhh_lh_so.dat  - densities of heavy hole, light hole and split-off hole band
  The output file always has three columns: hh density, lh density, split-off hole density
  If one does k.p for holes, one cannot distinguish between hh, lh, and so densities. Therefore this output is omitted.
  (The only disadvantage is if there are regions in the device where the classical hole density dominates,
  or if there are several quantum regions with different hole quantum models,
  then there will be no way to see if the density originates from hh, lh or so classical or single-band densities.)
  (Of course, if needed, one could split this output into classical and quantum mechanical contributions to the density.)

Output:

1D filenames and structure:

Electron density

[1018 cm-3]

filename:

structure:

For a quantum mechanical calculation:

For a classical calculation:

Hole density

[1018 cm-3]

filename:

structure:

For a quantum mechanical calculation:

For a classical calculation:

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.
So this file contains the total density present in the device.

filename:

structure:                          

Intrinsic density

n_i = SQRT(n * p) [cm-3]

filename:

structure:                          

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 1^st  column is position in space in [nm].
- The 2^nd column is the intrinsic density n_i = SQRT(n_i * p_i) 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 3^rd column is the quantity n_i' = 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:                          

Pyroelectric polarization charge density

filename:

structure:                          

Integrated density

filenames:

structure:                          

Surface and interface charge density

Filename:

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

Full-band density approach (k.p)

The following file contains the background charge density when using the full-band envelope-function approach (broken-gap = full-band-density).
density1DFullBandBackground.dat

If using $quantum-model-electrons, this number contains the positive background charge density.
If using $quantum-model-holes    , this number contains the negative background charge density.

For the same structure, using $quantum-model-electrons, the positive background charge density is three times larger than the negative background charge density (when using $quantum-model-holes).