nextnano³ - FAQ

Frequently asked questions

General

• Command line arguments
• Program window closes immediately upon finishing
• Program doesn't work at all
• Downloads / Additional tools
• d0

Materials

• Where can I find a list of all materials?

Simulation

• Alloy composition 2D
• Conduction/valence band plots
• Band structure
• Contacts
• Database - Band gaps
• Database- Conduction/Valence band nonparabolicities
• Database - Effective masses
• Database - Strain
• Dirichlet/Neumann boundary conditions
• Doping concentration
• Errors
• Fermi level
• Growth direction
• Materials
• Matlab
• Piezoelectric charges
• Quaternaries
• Orientation in 2D (simulation system)
• Output files
• Strain (band shifts and deformation potentials) / Database
• Strain (pseudomorphic and relaxed in one structure simultaneously)
• Substrate
• Superlattice
• Temperature
• Units - electron density, elastic constants
• Voltage sweep
• Warning: Warning define_poisson_clusters: Boundary conditions fixed manually, not by input.
• Calculating eigenvalues for 8-band k.p

General

Program window closes immediately upon finishing

Question

Unfortunately, the program window that opens after I started nextnano3.exe by double-clicking on it, closes immediately upon finishing, so I can't see the stuff that is written on the screen during program execution. Is there a way to prevent this?

Answer

Yes, there is. In Windows go to the Start button, select Run ... and type in cmd and press Enter.
This opens the command shell. Switch to the directory where nextnano3.exe is located by using the change directory command and type in  nextnano3.exe and then press Enter.
You can redirect the screen output into a file by using the command: nextnano3.exe > out.log.

doesn't work at all

Question

I get a strange message in my command prompt. Something with "keyword", "optional", "required".

Answer

You are probably trying to run a UNIX formatted ASCII file on a PC (or vice versa). Save it in PC/DOS mode or download the PC formatted input files from the download section.

Downloads / Additional tools

Question

Where can I get the Perl script to convert output AVS/Express files (*.fld, *.dat, *.coord) into xyz files?

Answer

Follow this link to our download page: Downloads / Additional tools

d0

Question

What is the meaning of d0 in the input file?

Answer

d0 or  D0 is a Fortran like syntax and means 10⁰ = 1 in "double precision". You can also use e0 or E0 in the input file which is single-precision.
In fact, nextnano³ converts e0 (single precision) automatically into d0 (double precision) when parsing the input file.

1d-3 means 10^-3 = 0.001
50d-3 means 50 * 10^-3 = 0.050
2.0d18 means 2.0 * 10¹⁸

Meanwhile, d0 is optional, so intead of specifing 0.067d0, you can use 0.067 for newer versions of nextnano³.

Materials

Where can I find a list of all materials?

Open the database file "database_nn3.in" with a text editor (e.g. WordPad) and search for the string "$default-materials". Then you can see a list of all materials.

You can add new materials into the database very easily. Just "copy and paste" the entries of a previously defined material and modify them appropriately.

Simulation

Alloy composition 2D

Question

I have to simulate a 2D system where in certain regions I have alloy composition fluctuations. From experiment I have  the alloy content given in a two-dimensional grid (that is in a file with three columns: x y and alloy composition). The grid consists of 60x187 points.

Is there any simple way to input these alloy composition or do I have to define in the input file all these 60x187 numbers?

Answer

Unfortunately, it is currently not possible to read in the alloy content from a file but we are certainly planning to do so in the future.
(However, it is possible to read in a doping profile.)

You have to specify it as indicated here: $alloy-function

Band structure

Question

I am only familiar with band structures like E(k_x,k_y,k_z), i.e. energy as a function of the k vectors in the Brillouin zone (energy dispersion). Is it true that nextnano³ plots the band structure as a function of real space (device geometry in x, y and z direction) for the minimum of the conduction and maximum of the valence bands?

Answer

Yes, it is. We are interested in the values at the Gamma point E(k=0) for the conduction band (minimum) and valence band (maxium; heavy, light and split-off hole). These energy values (which represent extrema) are plotted as a function of real space E(r) over the whole device geometry (i.e. for each material including doping effects aso.)
The same applies to the conduction band minima at the L point and X point (k≠0).

Conduction/valence band plots

Question

Instead of a sharp edge in the bands at the interface of a semiconductor heterostructure from one material to the other, there is always a grid point in between with the value  0.5 * band offset. This seems wrong to me.

Answer

You are absolutely right. To save the amount of data points necessary for a 2D or 3D plot, we take the average value of the 8 points of the corresponding 8 octants (boxes) for each grid point, thus the plotted value lies in the "middle" of the real boundary values. (In 2D, average of 4 "octants".)
You can change this default assignement by including in your input file the keyword $output-file-format. If you make your grid denser at the heterointerface, you can also modify the appearance of the resulting plot.

 !--------------------------------------------------!
 $output-file-format                                !
  simulation-dimension = 3                          ! 2D or 3D
  file-format          = AVS-ASCII                  !
  resolution           = all                        ! all/average
 $end_output-file-format                            !
 !--------------------------------------------------!

Contacts

Question

Output file for the potential (bandstructure/potential1D.dat):
I noticed that the electrostatic potential in the (metal) contact is zero.

Answer

If a region is assigned to be a Poisson boundary cluster ($poisson-boundary-conditions) then it is not considered to be contained inside the quantum or current region any more although the quantum or current region could in principle extend over the Poisson boundary cluster (by definition as specified in the input file) (-> setup_quantumregion).
Note: No Schrödinger or current equation will be solved in regions that are specified as Poisson boundary conditions.
In addition, the Poisson equation is not solved in these regions either. In the output, the value of the contact regions is set to zero, or to the applied voltage, respectively.

Database - Bandgaps and band offsets

Question

How are the band gaps and band offsets determined?

Answer

There are two ways:

• Option a) (default)
  
  $numeric-control
 ...
 use-band-gaps = no    ! use conduction-band-energies = ... of the material parameters section
                         ! (band-gaps = ...                       of the material parameters section are ignored)
  
  The conduction band edge energy is taken from conduction-band-energies but this value is finally altered by taking into account the Varshni parameters, a and b, to obtain a temperature dependent band gap.
  
  The band gap is calculated as: band_gap = conduction-band-energies -  a T²  /  ( T + b) - ( valence-band-energies + 1/3 Delta_split_off )
   
• Option b) (same as nextnano++ implementation)
  
  $numeric-control
 ...
 use-band-gaps = yes   ! use band-gaps = ...                of the material parameters section
                         ! (conduction-band-energies = ...       of the material parameters section are ignored)
  
  The conduction band energies are calculated as: E_c = ( valence-band-energies + 1/3 Delta_split_off ) + band-gaps -  a T²  /  ( T + b)
  
   

Conduction and valence band offsets

The values of the conduction band minima and valence band maxima are given with respect to a common reference level of energy (0 eV).
In this way, the band edge values for two adjacent semiconductors automatically include the respective band discontinuity.

For the valence-band-energies we take the calculated valence band maximum values (E_VBM) of
S.-H. Wei and A. Zunger, Appl. Phys. Lett. 72 (16), 2011 (1998)
"Calculated natural band offsets of all II-VI and III-V semiconductors: Chemical trends and the role of cation d orbitals"
and shift them by -1/3 Delta_SO to get an average of all three valence band maxima (Delta_SO = split-off energy).

valence-band-energies = E_v,av = E_VBM - 1/3 Delta_SO

If use-band-gaps = no (default), the conduction band energies for the Gamma, L and X valley are calculated as

conduction-band-energies = E_gap(Gamma) + E_v,av+ 1/3 Delta_SO         E_gap(X) + E_v,av + 1/3 Delta_SO           E_gap(L) + E_v,av + 1/3 Delta_SO

The conduction band energies are given for 0 Kelvin in the nextnano³ database.
Varshni parameters should be used to get the temperature dependent conduction band energies for e.g. 300 K.

With the specifier band-shift [eV], you are able to shift the absolute values of valence and conduction band edges simultaneously by a certain amount (default: 0.0 eV).

For zinc blende, the three hole energies E_hh, E_lh and E_so (heavy, light and spin-orbit split-off energy) are related as follows:
(E_hh + E_lh + E_so)/3 = E_v,av

For wurtzite, the three hole energies E_A, E_B and E_C (heavy, light and crystal-field split-off energy) are related as follows:
(E_A + E_B + E_C)/3 = 2/3 * Delta_cr + E_v,av

Summary

VBO: You can adjust valence-band-energies and/or band-shift to adjust the valence band offset.
CBO: Option a) You can adjust conduction-band-energies (if use-band-gaps = no) and/or band-shift to adjust the conduction band offset.
         Option b) You can adjust band-gaps (if use-band-gaps = yes) and/or band-shift and/or valence-band-energies adjust the conduction band offset.

Ternaries

The situation for ternaries is essentially the same.
Bowing parameters can be used to tune the band gaps and band offsets. Additionally, a band-shift can be used.
(bow-conduction-band-energies, bow-valence-band-energies, bow-band-shift, band-shift)
For ternaries, the Varshni parameters are not interpolated. Instead, the conduction-band-energies (if use-band-gaps = no) are interpolated (default) or the band-gaps (if use-band-gaps = yes).

In order to get the valence band edges for ternaries, the following procedure applies.

1. The following parameters are interpolated (including taking into account bowing parameters): [eV]
- average valence band edge energy E_v,av: valence-band-energies = ... [eV]
- split-off energy Delta_so: 6x6kp-parameters = . . . DeltaSO [eV]
- absolute deformation potential: absolute-deformation-potential-vb = ... [eV]
- uniaxial deformation potentials: uniax-vb-deformation-potentials   = ... [eV]
- band-shift: band-shift = ... [eV] (Typically, the default value is zero.)
2. The 6-band k.p Hamiltonian is set up including strain tensor.
   It is diagonalized and the 6 eigenenergies are called heavy hole, light hole and split-off hole (each of them is two-fold degenerate).
3. Note that the band gap is defined with respect to the unstrained valence band edge maximum. The program takes shifts and splittings of the conduction band edges due to strain automatically into account, i.e. changes of the band gap due to strain are included automatically.

Database - Conduction/Valence band nonparabolicities

Question

How is nonparabolicity treated?

Answer

The following parameters of the database refer to a hyperbolic dispersion, k2 ~ E(1+aE) where a = nonparabolicity [1/eV].

 conduction-band-nonparabolicities = 0d0 0d0 0d0 !
 valence-band-nonparabolicities    = 0d0 0d0 0d0 !

They are only used in regions where the density is calculated classically.
The do not enter the Schrödinger equation.
In order to treat nonparabolicty in quantum regions, a 6-band k.p or 8-band k.p model is required.

A common problem is that for the smaller band gap semiconductors like InAs, the nonparabolicity is so large that the calculated Fermi levels (to be precise: the calculated alignment of the band edges with respect to the Fermi level) are quite inaccurate.
For example, when looking at a case with n~1.5x10¹⁸ cm^-3, the Fermi level calculated without nonparabolicity is about 0.214 eV. It is 0.143 eV when nonparabolicty is taken into account. Here is an example of how one can modify the Fermi-Dirac integral for free carrier concentration in 3D for a single band from parabolic to nonparabolic using the Van Halen-Pulfrey functions. The nonparabolicity modifies the SQRT(E) density of states in the simple way shown.

Database - Effective masses

Question

How are effective hole masses determined in the database? By k.p parameters (6x6/8x8kp-parameters) or by effective masses (valence-band-masses)?

Answer

In the database when we describe material we specify

• k.p parameters and
• hole effective masses.

But they are not consistent: k.p parameters are used only when 6-band or 8-band k.p quantum model is selected and hole effective masses are used only when 1-band Schrödinger equation is solved.
(Exception: The k.p parameter Delta_so for spin-orbit splitting energy is used in any case including if no strain is considered. The k.p parameters in the database are also used to determine band shifts due to strain. Program computes the k.p and strain dependent Hamiltonian for each grid point, diagonalizes it, and takes the eigenvalues for the band edges. So, band edges for single band calculations are k.p parameter dependent. More information ...)

There is also the option under $numeric-control to calculate the effective valence band masses from the 6-band k.p parameters (L, M, N) specified in the database.

Dirichlet/Neumann boundary conditions

Question

For the quantum calculation there is a possibility to choose either Dirichlet or Neumann boundary conditions. Which function is a subject for such boundary conditions? Wave function? If yes, do Dirichlet conditions mean that wave function is equal to zero on the boundaries?

Answer

Yes, at the boundaries of the quantum region, the wave function is zero if Dirichlet is chosen.
Neumann:
- Physically, it means zero current normal to the boundary surface (3D), boundary line (2D) or boundary point (1D).
- Mathematically, it means if a Hamiltonian contains a term like
  [d/dx_i m_ij d/dx_j + b_i d/dx_i + c] Psi
  then the boundary condition is
  [n_i m_ij d/dx_j + b_i n_i] Psi = 0
  where n_i is a normal vector to a surface (line).
More details about boundary conditions can be found here: Boundary conditions

Doping concentration

Question 1

In 1D, what is the unit of doping concentration? If I have an experimental value of 2*10¹⁸ cm^-3 for 3D, is it then 2^1/3*10⁶ cm^-1 for 1D?

Answer 1

No, it is still 2*10¹⁸ cm^-3 for 1D. Please look at this example for more details: $doping-function

Errors

Error message Error linesearch: Round-off problem.

Solution

This error occurs in the Newton routine (subroutine linesearch) when solving the 1D/2D/3D nonlinear Poisson equation with the Newton method.

Possible solutions (depending on your input file geometry):

• $numeric-control
 ...
 nonlinear-poisson-stepmax    = 1.0d-0
 nonlinear-poisson-iterations = 100
$end_numeric-control
• Try to set different starting values for the initial guess of the potential phiV under the keyword $numeric-control (specifier initial-potential).

Error message (on Windows only)
forrtl: error (74): floating underflow
forrtl: error (74): floating underflow
forrtl: info (300): 9 floating underflow traps

Explanation

An underflow indicates that the absolute value of a floating point number has become smaller than about 1e-150 and that it has been replaced by a zero. For many algorithms this replacement does not cause any harm, for others the effects will be disastrous. Unfortunately, in simulation codes like nextnano³ both cases occur depending on where in the code the underflow happened.

Fermi level

Question

I want to manually adjust the Fermi level. How can I do this?

Answer

There are several possibilites.

• Read in Fermi levels from an ASCII file.
  $import-data-on-material-grid
  You can use different Fermi levels for electrons and holes.
• Assign a Fermi level to a region cluster.
  $region-cluster
  You can use different Fermi levels for electrons and holes.
• Assign a Fermi level to a quantum cluster.
  $quantum-cluster
  You can use different Fermi levels for electrons and holes.
• Use "Poisson boundary condition" to assign to a certain region a "Fermi level boundary condition". You can choose a constant Fermi level (Fermi) or a linear Fermi level profile (Fermi-linear).
  $poisson-boundary-conditions
  The same Fermi level is applied to both electron and hole Fermi levels.

These four options can also be combined.

An example is shown here: Double quantum well heterostructure

1DAlGaAs_GaAs_DQW_read_in_Fermi_level.in
1DAlGaAs_GaAs_DQW_apply_Fermi_level_to_region_cluster.in
1DAlGaAs_GaAs_DQW_apply_Fermi_level_to_quantum_cluster.in
1DAlGaAs_GaAs_DQW_apply_Fermi_level_to_contact.in

If you are interested in examples, please submit a support ticket.

Growth direction

Question

I have to simulate a quantum dot with [N 1 1] growth direction. But in the database I have only:

axes-possible = 0 0 1 !
                0 1 0 !
                1 0 0 !

Is it possible to simulate [N 1 1] growth direction?

Answer

Yes, but don't confuse the axes-possible specifier with the Miller indices. Change these to [N 1 1] for other directions. The specifier axes-possible is only applicable to the growth direction which must be x, y or z as indicated. However, you can choose [3 1 1] to be the Miller x axis and then choose x axis as growth direction which will then be [3 1 1].
More details can be found under keyword $domain-coordinates.

Materials

Question

What should I pay attention to?

Answer

• You can define new materials for certain temperatures that consider a change in the band gap due to temperature (e.g. GaAs-4K in addition to GaAs in the database).
• Al_xGa_1-xAs
  You should adjust the bowing factor manually:
    bow-conduction-band-energies  =  0.305d0  0.055d0  0d0
The bowing factor for the Gamma band (according to Vurgaftman is)
      -0.127+1.310x   for E_gap(Gamma)
  e.g.   0.384d0 for Al_0.39Ga_0.61As    ->  Crossover for minimum (Gamma -> L) at x=0.39   (300 K)
      0.305d0 for Al_0.33Ga_0.67As    -> (Gamma)
      0.070d0 for Al_0.15Ga_0.85As    -> (Gamma)

Matlab

Question

Can I use Matlab to visualize the 3D output files (AVS format)?

Answer

Not directly, but you should be able to convert the AVS data to Matlab format if you write a script that does it for you. For an explanation of the AVS format, please consult the 2D/3D Tutorials.

Piezoelectric charges

Question

I want to "switch-off" piezoelectrical effects. Should I put piezo-electric-constant e₁₄  in the database_nn3.in file to be 0, or  can I specify it somewhere in the input file?

Answer

Option 1: You have to adjust e₁₄ for the appropriate materials in the database_nn3.in file to:
 piezo-electric-constants = 0d0  0d0 0d0 0d0 ! [C/m²] e14,B114,B124,B156

Option 2: You can specify it here:
  $numeric-control
   piezo-constants-zero = no

The pyroelectric constants can be switched on and off similarly.

Quaternaries

Question

Are quaternaries included? If not, how can I interpolate them?

Answer

Only lattice matched-quaternaries (e.g. In_xGa_yAl_1-x-yAs with only one free parameter x or y but not quaternaries with two free parameters like A_xB_1-xC_yD_1-y) are included in our database. See database comments and quaternaries documentation.

You can define a new material in the database_nn3.in file with linearly interpolated values of the binary constituents of the quaternary.

Strain (band shifts and deformation potentials)

Question

How do you incorporate strain into the calculation? What is the meaning of the deformation potentials in the database?

Answer

In order to get the band edge shifts due to strain, we diagonalize numerically on each grid point the strain dependent k.p Hamiltonian for k=0. More information ...

Van de Walle (PRB 39, 1871 (1989)) describes the dependence on strain of the valence and conduction band edges (zinc blende). In this paper strain is described along [001] and [111] directions. In a general case, when we have [a b c] growth direction please have a look here.

Pseudomorphic (or commensurate) growth of strained layers on a substrate subjects these layers to a biaxial strain (epsilon_||) parallel to the plane of the interface and a uniaxial strain (epsilon_{|_}) perpendicular to it.

                              (1)

where    a_||=a₀                                      (2a)
       .      (2b)

So we can also write

Here a₀ denotes the lattice constant of the substrate and a the equilibrium lattice constant of the layer material. D depends on the elastic constants c of the layer material and on the interface orientation. (Often, 1/D⁰⁰¹ is called the Poisson ratio, denoted as sigma).

                                      (3a)

               (3b)

             (3c)

In the database we specify:

The lattice constants are temperature dependent. More information...

The effect of strain on energy levels can be decomposed into hydrostatic and shear contributions. The hydrostatic strain component leads to a shift of the average valence band energy E_v,av=(E_hh+E_lh+E_so)/3, i.e. of the average of the energies of the heavy hole, light hole and spin-orbit split-off bands (see picture for details):

        (4a)

and similarly for the conduction band energy

          (4b),

where a_v and a_c are the hydrostatic (=absolute) deformation potentials for the valence band and conduction band, respectively.

In the database we specify:

The shear contribution couples to the spin-orbit interaction and leads to an additional splitting of the valence band energies. In the case of growth on a (001) or (111) substrate, the energy shifts relative to E_hh=E_v,av+Delta_so/3  (Delta_so is the spin-orbit splitting in the absence of strain) are given by

                                                                                               (5a)

          (5b)

           (5c)

The strain dependent shift delta E^sh depends on the interface orientation:

                  (6a)        or    

           (6b)        or    

                                                                         Here,
                                                                                     .

The quantities b and d are the tetragonal and rhombohedral shear deformation potentials, respectively. In the absence of strain, equation (5) leads to the correct spin-orbit splitting Delta_so. Conduction bands at Gamma are not affected by the shear contribution to the strain. However, at L and X they are affected.

In the database we specify:

Once E_v,av are known on an absolute scale (only physically meaningful relative to E_v,av in related semiconductors), the valence band and conduction band edge energies E_v and E_c, respectively, are obtained on an absolute scale from

        (7a)

                                         (7b)   (for Gamma)

where E_v,av, Delta_so, and E_g (band gap energy) refer to unstrained bulk properties. The strain contribution is incorporated into the other properties.
Now we can calculate the band offset at the interface directly comparing the values of E_v and and E_c of the semiconductors constituting the heterojunction.

Equations (4), (5) and (6) were arrived at by treating the effect of strain as a small perturbation, and are therefore only valid in the case of small lattice mismatch. The mismatch attainable in pseudomorphic heterojunctions composed of III-V alloys is expected to fall within this range of validity.

(Most of this text was taken from M.P.C.M. Krijn, Semicond. Sci. Technol. 6, 27 (1991))

More information ...

Strain (pseudomorphic and relaxed in one structure simultaneously)

Question

Is it possible to have some of the layers of the heterostructure to be pseudomorphic and then at some point higher up in the structure have the layers be relaxed? Currently, I have the entire structure with homogeneous-strain.

Answer

Yes, it is. Have a look at this keyword: $material
For each material one can specify its own substrate. If this substrate is identical to the material name, then one has a "relaxed" and not a strained material, even with option homogeneous-strain.

Substrate

Question

How can I specify the substrate or its lattice constant?

Answer

$domain-coordinates
 ...
 pseudomorphic-on = <material-name>
 ...
$end_domain-coordinates

Superlattice

Question

I want to simulate a superlattice of quantum wells in 1D. For this I want to build a cluster consisting of a well and a barrier, i.e. this cluster would contain 2 different materials. Is this possible?

Answer

No. You can define one huge cluster that consists of the barrier material for the whole superlattice and set region-priority=1. Then you can put several wells on it with region-priority=2. Alternatively, open two windows of the 1D Input file generator (Step 1) and define in the first the barrier and in the second the well and press the "Submit" buttons alternately.

Temperature

Question

What physical properties or equations are affected if I change the lattice-temperature in the input file?

Answer

• Band gap?
  Yes! The latest version includes temperature dependent band gaps based on the Varshni parameters that are specified in the database. (Actually only the conduction band energy is changed. The valence band energy remains constant.)
  You can switch it off: varshni-parameters-on = no.
  No! (Previous versions) The band gap is specified by values on an absolute scale which can be changed manually in the database_nn3.in file to get the correct band gap for the corresponding temperature of interest (more information on band gap). You can even specify your own materials as was already done for GaAs-4K, AlAs-4K, InAs-4K, Al(x)Ga(1-x)As-4K, In(x)Ga(1-x)As-4K, Al(x)In(1-x)As-4K (in addition to GaAs, AlAs, ...).
• Doping?
  Yes! To what degree are the donors or acceptors ionized or not? This is clearly a function of temperature. The keyword $impurity-parameters specifies how far a donor/acceptor lies below/above the conduction/valence band. If the temperature is around 4 K, almost no donors/acceptors are ionized. In this case - if you still want all donors/acceptors to be fully ionized - you need to specify a value of say -10 eV instead of +0.03 eV.
• Mobility?
  Yes!
• Lattice constants?
  Yes!
  You can switch in on or off under keyowrd $numeric-control (lattice-constants-temp-coeff-on = no/yes).
No! (Previous versions)

Orientation in 2D (simulation system)

Question

When we have 2D simulation we can specify as simulation domain [1 0 1] or [1 1 0 ] or [0 1 1]. What is x and what is y in the simulation domain?

Answer

Output files

Question 1

How to plot 2D AVS/Express output data with Origin?  ->  Answer

Units - electron density, elastic constants

Question 1

What is the unit of the electron density (output)? What is the units of the elastic constants in the database?

Answer 1

The electron/hole density output will be given in the following units [1018 cm-3]. These units are the same for 1D, 2D and 3D simulations.
The elastic constants are given in GPa.
 

Question 2

The numbers of the electron density on my plot looks different to what I expected.

Answer 2

You could try to adjust your energy-levels-relative in impurity-parameters to -10d0 instead of e.g. 0.02d0 and check if it makes a difference.
 

Question 3

I get three different columns for my electron density output (1D) when I run a quantum mechanical calculation. Which one is the electron density?

Answer 3

The second column in the electron density which is the sum of classical and quantum mechanical density.
 - second column: sum of quantum mechanical and classical density
 - third column:     quantum mechanical density
 - forth column:     classical density

Warning: Warning define_poisson_clusters: Boundary conditions fixed manually, not by input.

Question

I get the following warning:
Warning define_poisson_clusters: Boundary conditions fixed manually, not by input.
What does it mean?

Answer

It simply means that for the boundary conditions of the Poisson equation ($poisson-boundary-conditions) by default Neumann boundary conditions with electric field = 0 V/m are assumed when calling SUBROUTINE define_poisson_clusters. This is just a reminder that these boundary conditions cannot be specified in the input file yet. However, Ohmic and Schottky boundary conditions are implemeted correctly.

Calculating eigenvalues for 8-band k.p

Question

Why does it take so long to calculate the eigenvalues of an 8-band k.p calculation?

Answer

Mathematically speaking, 8-band k.p requires a different eigenvalue solver (“finding eigenvalues in the interior of the spectrum”) than single-band and 6-band (“finding eigenvalues at the end of the spectrum”), so it is much harder (both with respect to time and stability) to find a solution.

An 8-band matrix has 8 times the size of a single-band matrix and the mathematical problem gets harder the more eigenvalues are sought.

We have implemented different eigenvalue solvers for 8-band k.p, e.g. the ARPACK solver (shift-invert mode) or the FEAST solver.

Degeneracy: For instance, if 4 eigenvalues are degenerate (e.g. due to spin and/or geometry) and you are looking for only 3, the eigenvalue solver will very likely fail. In such a case, it could be that certain eigenvalues are misisng.

Adjusting the resdiual might help you for debugging, e.g. by using a larger value for the residual (accuracy) one should get solutions more quickly althouth they might not be accurate enough.

Another interesting strategy could be to divide the input file into two, e.g. if one needs 6 electron eigenvalues and 12 hole eigenvalues.
- One input file calculates only the electron eigenvalues. Then you have in total 6 eigenvalues instead of 18 which should be much faster.
- The other input file calculates only the hole eigenvalues. (12 instead of 18)