# FAQ - Simulation¶

## nextnano Product related¶

### Which features have been implemented recently?¶

nn++: Added periodic repetition of quantum regions

nnm: New colormaps

nnm: Arrow showing difference value between two selected graphs

nnm: HTCondor support for mixed Linux/Windows pool

nn++: Added input files for GaN bulk k.p dispersion tutorial (has already existed for nn3)

nn++: Added input files for self-consistent k.p multi-QW intersubband tutorial (has already existed for nn3)

nn3: Bulk band structure with 14-band and 30-band k.p

nn++: Added electron injection (e.g. by electron beam) into structure definition

nn++: Integration of nextnano.MSB into nextnano++, incl. nextnano.MSB sample files into installer

nn++: Output reflection components of CBR transmissions

nn3: Improvements for CBR

nn++/nn3: New 2D CBR input files (QPC)

nn3: Improvement of 2DEG mobility input files (e.g. GaN)

nn++/nn3: Synonyms in material database (e.g. Al(x)In(x)As and In(x)Al(1-x)As)

nn++: Added input file for tutorial: “QCSE” (existed already for nn3)

nn++/nn3: Input files for tutorial: “Intersubband absorption in infinite QW”

nn3: Input files for intersubband absorption in Ge/SiGe QWs

nn++: Input files for absorption in Ge/SiGe QWs

nn++: Input files for absorption in Ge

nn++: Calculation of reflection and extinction coefficient

nn++: Gaussian and Lorentzian broadening for optical absorption

nn++: Improvements for optical absorption tutorial (k.p)

nn++: Improvements for optical absorption (k.p)

nn++: Improvements for k.p (speed: k=0 subspace expansion)

nn++/nn3: Added more tutorial input files to samples folder

nn++: New UVC LED AlGaN/GaN input files

nn++: Improvements for intersubband absorption (k.p)

nn3: Improvements for intersubband absorption (single-band, simple k.p model, k.p)

nnpy: Intersubband absorption script

nn++: Solar cell features, irradiation

nn++: Added quaternaries and quinternaries to database; AlScN, AlYN, …

nn3: Grid lines can be independent of region object boundaries (has always been the case for nn++)

nn++/nn3: Added XML support to input files

nn++/nn3: New region objects: circle/sphere

nn++/nn3: New region objects: triangle, polygonal_prism, regular_prism, hexagonal_prism, polygonal_pyramid, regular_pyramid, hexagonal_pyramid

nnpy: New Python tool: nextnanopy

nn++: Array of different biases is allowed in addition to bias sweep using steps

nn++: Output of emission spectrum for LEDs based on classical or quantum density

nn++: Output of energy resolved density n(E) and n(x,E)

nn++: Improved convergence and speed for current calculations

nn++: More intuitive setting in run{}

nn++/nn3: 2nd order piezo constants and 2nd order piezo tutorial

nn3: Bulk band structure with pseudopotential method

nn3: Bulk band structure with tight-binding method (improvements)

nn++/nn3: Piezo/pyro tutorial for arbitrary (hkil) in wurtzite

nn++: MOSFET tutorial

### What is the difference between nextnano³ and nextnano++?¶

The short answer is: Use the nextnano++ software.This is the software where we put on most effort in improving it by adding new features. The nextnano³ software is mainly distributed for historical reasons.nextnano³ is written in Fortran. It has been developed at the Walter Schottky Institute from 1999 to 2010. nextnano++ is written in C++. It has been developed at the Walter Schottky Institute from 2004 to 2008. The software packages have been written by different people that were working at the Walter Schottky Institute of the Technische Universität München in the Theoretical Semiconductor Physics group of Prof. Peter Vogl.

- Essentially, both software packages cover the same physics and methods, namely

the strain equation

the Poisson equation

the Schrödinger equation

the drift-diffusion current equation.

- Additionally, the nextnano³ software includes

solar cells

electrolytes

graphene

tight-binding (for bulk and one-dimensional superlattices)

the self-consistent CBR method (1D, 2D and 3D)

the NEGF method (1D only) which is particularly suited for quantum cascade lasers.

- In contrast to nextnano++, nextnano³ is not able to

treat the magnetic field within the \(\mathbf{k} \cdot \mathbf{p}\) approach

calculate the g tensor

include quaternary materials.

nextnano++ is much faster for drift-diffusion calculations and for 2D/3D simulations. For instance, if you work on LEDs, MOSFETs or Quantum Dots, nextnano++ is much better suited.

There are some applications where it is irrelevant which software to use. In this case we recommend to use both. This has the advantage that the results of one software can be compared to the results of the other software in order to gain more confidence in them. For some applications, one software package should be preferred. Please contact <support[at]nextnano.com> in order to find out which software to choose for your particular application.

- nextnano³ syntax

‘’$’’ character for the keywords:

`$regions ... $end_regions`

‘’%’’ character for the variables:

`%QuantumWellWidth = 5.0`

‘’!’’ character for comments:

`! This is a comment.`

(`#`

is supported by both nextnano++ and nextnano³ as a comment sign.)- nextnano++ syntax

‘’{}’’ brackets for the keywords:

`structure{ ... }`

‘’$’’ character for the variables:

`$QuantumWellWidth = 5.0``

‘’#’’ character for comments:

`# This is a comment.`

(`#`

is also supported by nextnano³.)

### Can I convert nextnano³ input files into nextnano++ input files?¶

Within nextnanomat, there is an experimental feature to convert a nextnano³ input file to a nextnano++ input file. How to use this automatic conversion:

In the menu select

`Tools ==> Convert nextnano³ input file to nextnano++`

When you use the automatic conversion of nextnano³ input file into nextnano++, you will find that it probably does not work completely.

If you save and run the nextnano++ input file that has been converted and that has the suffix

`_nnp.in`

, very likely some errors appear indicating which line(s) to change. Then some manual adjustments are needed, but the rough structure should help a lot for the conversion.

### How can I track how much memory is used during the simulations?¶

`Tools`

==>`Options`

==>`Expert settings`

==>`Include memory usage in log file (units: MB)`

### Can I pass additional command line arguments to the executable?¶

Yes, this is possible. Go to

`Tools`

==>`Options`

==>`Expert settings`

==>`Command line`

For nextnano³, one could use for instance:

`-database "D:\My folder\nextnano3\Syntax\my_database_nn3.in`

`-threads 4`

### How can I speed up my calculations with respect to CPU time?¶

The most obvious way is to reduce the

number of grid pointsyou are using. For instance, for the following pn junction simulation, a grid spacing of1 nmwas used (gray lines in Figure 7 ). If one is using a coarse grid of only10 nm, the calculated values (squares in Figure 7) agree very well with the calculated values of the thin lines.The difference in CPU time comes from the fact that for the 10 nm resolution the dimension of the matrix that is used for discretizing the Poisson equation is 30, while in the case for the 1 nm grid spacing it has the dimension 300. The proper choice of an optimal grid spacing is very relevant for 2D and 3D simulations, as can be seen in the following.

- 1D simulation (length of sample: x = 300 nm)

1 nm grid spacing: dimension of Poisson matrix: \(N=300\)

10 nm grid spacing: dimension of Poisson matrix: \(N=30\)

- 2D simulation (length of sample: x = 300 nm, y = 300 nm)

1 nm grid spacing: dimension of Poisson matrix: \(N=300 \cdot 300 = 90,000\)

10 nm grid spacing: dimension of Poisson matrix: \(N=30 \cdot 30 = 900\)

- 3D simulation (length of sample: x = 300 nm, y = 300 nm, z = 300 nm)

1 nm grid spacing: dimension of Poisson matrix: \(N=300 \cdot 300 \cdot 300 = 27,000,000\)

10 nm grid spacing: dimension of Poisson matrix: \(N=30 \cdot 30 \cdot 30 = 27,000\)

If a quantum mechanical simulation is performed, the numerical effort of eigenvalue solvers increases with the number of grid points \(N\) with order \(O\left(N^2\right)\).

### Can I take advantage of parallelization of the nextnano software on multi-core CPUs?¶

- The short answer is:
Some numerical routines are parallelized which is done automatically. These are the numerical routines, e.g. for calculating the eigenvalues with a LAPACK solver (which itself uses BLAS).

- The long answer is:
The nextnano software includes the Intel® Math Kernel Library (MKL). MKL includes the BLAS and LAPACK library routines for numerical operations. The MKL dynamically changes the number of threads.

nextnano++ - uses MKL (parallel version) The executables that are compiled with the Intel and Microsoft compilers use MKL (parallel version). The executable that is compiled with the GNU compiler (gcc/gfortran) uses the nonparallelized version of the BLAS and LAPACK source codes available from netlib webpage.

nextnano³ - uses MKL (parallel version) The executables that are compiled with the Intel and NAG (64-bit) compilers use MKL (parallel version). The executables that are compiled with the GNU compiler (gfortran) and NAG (32-bit) use the nonparallelized version of the BLAS and LAPACK source codes available from netlib webpage. There is a nextnano³ executable available that uses OpenMP parallelization for

CBR (parallelization with respect to energy grid)

NEGF (parallelization with respect to energy grid and further loops)

`number-of-MKL-threads = 8`

Calculation of eigenstates for each \(k_\parallel\) (1D and 2D simulations)

Matrix-vector products of numerical routines Note: Not all operations are thread-safe, e.g. one cannot combine \(k_\parallel\) parallelization with the ARPACK eigenvalue solver. Only for this executable, the flag

`number-of-parallel-threads = 4`

has an effect. The NEGF keyword also supports`number-of-MKL-threads = 4`

(`0`

meansdynamicwith is recommended) and`MKL-set-dynamic = yes`

/`no`

.nextnano.NEGF - uses MKL (parallel version)

nextnano.MSB - uses MKL (parallel version)

The NEGF algorithms (nextnano.NEGF, nextnano.MSB, CBR) include matrix-matrix operations which are well parallelized within the BLAS routines.

If e.g. 4 nextnano simulations are running in parallel on a quad-core CPU, i.e. 4 nextnano executables are running simultaneously and each of them is using calls to the parallelized MKL library simultaneously, the total performance might be slower compared to running these simulations one after the other. In this case using a nextnano executable compiled with the serial version of the Intel MKL could be faster.

In fact, it strongly depends on your nextnano application (e.g. 1D vs. 3D simulation, LAPACK vs. ARPACK eigenvalue solver, …) if you benefit from parallelization or not. In general, the best parallelization can be obtained if you run several nextnano simulations in parallel. For instance, you could do parameter sweeps (e.g. sweep over quantum well width) using nextnanomat’s

Templatefeature, i.e. if you run 4 simulations simultaneously on a quad-core CPU, e.g. for 4 different quantum well widths.

### Dirichlet vs. Neumann boundary conditions¶

There are three different boundary conditions that we use:

periodic: \(\psi(x=0) = \psi(x=L)\)

Dirichlet: \(\psi(x=0) = \psi(x=L) = 0\), and

Neumann: \(\frac{\text{d}\psi}{\text{d}x} = \text{const}\) at the left (\(x=0\)) and right (\(x=L\)) boundary. Typically, \(\text{const} = 0\).By specifying both Dirichlet and Neumann boundary conditions, the system would be over-determined.

### Quasi-Fermi level¶

So-called

quasi-Fermi levelswhich are different for electrons \(E_\text{F,n}\) and holes \(E_\text{F,p}\) are used to describe nonequilibrium carrier concentrations. In equilibrium the quasi-Fermi levels are constant and have the same value for both electrons and holes, \(E_\text{F,n}=E_\text{F,n}=0\text{ eV}\). The electron current is proportional to the electron mobility \(\mu_\text{n}(x)\), carrier density \(n(x)\) and the gradient of the quasi-Fermi level of the carriers, \(\nabla E_\text{F,n}(x)\), and analogously for the holes.

### I don’t understand the \(\mathbf{k} \cdot \mathbf{p}\) parameters¶

In the literature, there are two different notations used:

Dresselhaus–Kip–Kittel (DKK): \(L, M, N^+, N^-\) (zinc blende); \(L_1, L_2, M_1, M_2, M_3, N_1^+, N_1^-, N_2^+, N_2^-\) (wurtzite)

Luttinger parameters: \(\gamma_1, \gamma_2, \gamma_3, \kappa\) (zinc blende); Rashba–Sheka–Pikus (RSP) parameters \(A_1, A_2, A_3, A_4, A_5, A_6, A_7\) (wurtzite)

They are equivalent and can be converted into each other.

Some authors only use 3 parameters \(L, M, N\) (or \(\gamma_1, \gamma_2, \gamma_3\)) which is fine for bulk semiconductors without magnetic field but not for heterostructures because the latter require 4 parameters, i.e. \(N^+, N^-\) (instead of \(N\) only) or \(\kappa\). If these parameters are not known, they can be approximated.

There are different \(\mathbf{k} \cdot \mathbf{p}\) parameters for

6-band \(\mathbf{k} \cdot \mathbf{p}\) and

8-band \(\mathbf{k} \cdot \mathbf{p}\).

The 8-band \(\mathbf{k} \cdot \mathbf{p}\) parameters can be calculated from the 6-band parameters taking into account the temperature dependent band gap \(E_{\rm gap}\) and the Kane parameter \(E_{\rm P}\) (zinc blende). For wurtzite the parameters are \(E_{\rm gap}\) and the Kane parameters \(E_{{\rm P}1}\), \(E_{{\rm P}2}\).

The 8-band Hamiltonian also needs the conduction band mass parameter \(S\) (zinc blende) or \(S_1, S_2\) (wurtzite). They can be calculated from the conduction band effective mass \(m_{\rm c}\), the band gap \(E_{\rm gap}\), the spin-orbit split-off energy \(\Delta_{\rm so}\) and the Kane parameter \(E_{\rm P}\) (zinc blende). For wurtzite the parameters are \(m_{{\rm c},\parallel}\), \(m_{{\rm c},\perp}\), \(E_{\rm gap}\), \(\Delta_{\rm so}\), the crystal-field split-off energy \(\Delta_{\rm cr}\) and the Kane parameters \(E_{{\rm P}1}\), \(E_{{\rm P}2}\).

Finally there is the inversion asymmetry parameter \(B\) for zinc blende. For wurtzite there are \(B_1, B_2, B_3\).

For more details on these equations, please refer to Section

3.1 The multi-band\(\mathbf{k} \cdot \mathbf{p}\)Schrödinger equationin the PhD thesis of S. Birner.

- Spurious solutions
Some people rescale the 8-band \(\mathbf{k} \cdot \mathbf{p}\) in order to avoid

spurious solutions. The 8-band \(\mathbf{k} \cdot \mathbf{p}\) parameters can be calculated from the 6-band parameters taking into account the band gap \(E_{\rm gap}\), the spin-orbit split-off energy \(\Delta_{\rm so}\) and the Kane parameter \(E_{\rm P}\) (zinc blende). For wurtzite the parameters are \(E_{\rm gap}\), the spin-orbit split-off energy \(\Delta_{\rm so}\), the crystal-field split-off energy \(\Delta_{\rm cr}\) and the Kane parameters \(E_{{\rm P}1}\), \(E_{{\rm P}2}\).For more details, please refer to Section

3.2 Spurious solutionsin the PhD thesis of S. Birner.- Specific implementation nextnano++
See section

`quantum{ region{ kp_8band{} } }`

in Multi-band models in quantum{ region{} }.- Specific implementation nextnano³

See section

Choice of\(\mathbf{k} \cdot \mathbf{p}\)parametersin $numeric-control.See section \(\mathbf{k} \cdot \mathbf{p}\)

parametersin Which material parameters are used?.See section

Luttinger-parametersin $binary-zb-default.

### Can I add new materials to the database?¶

Sure!

- Option 1
The material parameters are contained in ASCII text files. You can find them in the installation folder:

nextnano³ software:

`C:\Program Files (x86)\nextnano\<date>\nextnano++\Syntax\database_nnp.in`

nextnano++ software:`C:\Program Files (x86)\nextnano\<date>\nextnano3\Syntax\database_nn3.in`

These files can be edited with any text editor such as notepad++ (available free of charge).It is best if you search for a material such as ‘’GaSb’’ and then simply use ‘’Copy & Paste’’ to reproduce all relevant entries and then you rename ‘’GaSb’’ to something like ‘’GaSb_test’’. Finally, you adjust the necessary material parameters that you need. In most cases, you don’t have to replace all material parameters. It is only necessary to replace the ones that you need in the simulation.

It is a good idea to save the new database to a new location such as

`C:\Users\<user name>\Documents\nextnano\My Database\database_nnp_GaSb_modified.in`

You can then read in the new nextnano++ (or nextnano³) database specifying the location within the Tools Options of nextnanomat.

`Tools`

=>`Options...`

=>`Material database`

=>`nextnano++/nextnano³ database file:`

- Option 2
A quicker way is the following. You can overwrite certain material parameters in the input file rather than entirely defining new materials. For instance if you need ‘’HfO2’’, you could use the material ‘’SiO2’’ and just change the static dielectric constant and conduction and valence band edges or any other relevant parameters that you need. So basically, you are using the material ‘’SiO2’’ a modified static dielectric constant and band edges.

Please note that we treat all materials to be either of the crystal structure

zinc blende (including diamond type) or

wurtzite.

Attention

More information on how to add materials

to nextnano++ can be found in Material Database

to nextnano³ can be found on How to add material parameters.

## GUI nextnanomat related¶

### How do I produce 1D slices through the 2D plots in the GUI?¶

Visualize horizontal and vertical slices:

Menu

`View`

=>`Show Horizontal and Vertical Slices`

(or click on appropriate button)Export horizontal or vertical slices:

Right-click on 2D graph,

`Export horizontal/vertical slice`

`as data (.dat)`

or`as image (.png)`

.

### Is there a way to produce a 1D (or 2D) plot of some result, for example the probability density with the conduction band edge superimposed?¶

### In other words, can the GUI show multiple plots at once?¶

Yes, this is possible. Multiple output files can be shown at once, see Overlay feature documentation.

### What is the difference between “List view” and “Tree view”?¶

In/For the Output tab of nextnanomat, you can switch between these options using:

`Tools ==> Options ==> View ==> Output folder browser`

`List view`

is the default and shows a list of the top level output folders.`Tree view`

additionally offers the possibility of showing the subfolders within the output folder panel.If you want to sort your output folders by date,

`List view`

is better suited.