12223

3556666

779

10

1011

1212

Table of Contents

Table of ContentsUsing the Sentaurus Materials Workbench for studying point defects

BackgroundGetting started

Material specifications

Setting up the calculationReplacing the material specification

Contents of the material specificationThe supercell parametersAtomic chemical potentialsHost material propertiesFormation entropy

Run the calculationAnalyzing the results

Expanding the data setDiscussion and summary

Including vibrational contributionsAnalyzing the results

ConclusionsReferences

Downloads & LinksDownloads & Links

PDF version SMW_ zero-entropies.py Sentaurus Materials Workbench Reference Manual Operat ing with defect lists Basic QuantumATK Tutorial ATK Reference Manual

Docs » Tutorials » New or Recent ly Updated Tutorials »Using the Sentaurus Materials Workbench for studying point defects

Using the Sentaurus Materials Workbench forUsing the Sentaurus Materials Workbench forstudying point defectsstudying point defectsVersion:Version: P-2019.03

In this tutorial, we will use the comprehensive, and highly-automated, framework provided by theQuantumATK module Sentaurus Materials Workbench (SMW) to calculate the format ion energies andtransit ion levels for a variety of charged defects in GaN. SMW is designed to make complex workflows ofab init io calculat ions more accessible, and is focused on specif ic applicat ions of interest . In this tutorial,we will use the defect list funct ionality to easily study several point defects in GaN, with 3 differentst ructure types and 2 charge states, for a total of 14 dist inct defects.

BackgroundBackground

The central feature of this tutorial is called Def ect List sDef ect List s and is explained in more detail here: Operat ingwith defect lists. It can be used to generate a list of specif ic defects of a part icular type, in a number ofcharge states, and calculate the format ion energies of these defects and the t ransit ion (or t rap) levelsbetween each of these charge states. After a type of defect is chosen, e.g. vacancies, QuantumATKrequires no input from the user to determine which defects exist in a part icular host material, as it willautomat ically determine all of them from symmetry analysis. However, SubstitutionalList andInterstitialList do require the user to specify the element that will be added to the host material as a

subst itut ional or interst it ial defect . QuantumATK will use the ChargedPointDefect study object for theindividual defect calculat ions, which is explained in detail in this tutorial: Format ion energies and t ransit ionlevels of charged defects.

Get t ing st ar t edGet t ing st ar t ed

Quant umAT KQuant umAT K

Try it !

QuantumATK

Contact

Open the QuantumATK GUI, NanoLab, and select Create New... in the Project Dialog. Create a new projectin an empty folder with an appropriate name, and make sure to select Sent aurus Mat erials WorkbenchSent aurus Mat erials Workbenchas the Type.

In QuantumATK, projects are a way to group related calculat ions together, and is closely related to thefolder/directory st ructure of the OS. The chosen type of project helps QuantumATK determine what kindof work you want to do, and modify the GUI accordingly. Specif ically, choosing the SMW project type willhide many of the, for this purpose, less-relevant plugins, allowing you to focus on these advanced features.

M at e r i al spe c i f i c at i o nsM at e r i al spe c i f i c at i o ns

Before we can do the defect calculat ions, we f irst need what is called a Material Specif icat ion. This is thedefinit ion of the material we wish to study and the computat ional model that will be used. QuantumATKincludes a database with example set t ings for some relevant materials, but if you wish to study a materialthat is not covered, you can provide your own specif icat ion as part of the input . In this case, we will use amaterial specif icat ion that has been generated part icularly for use in this tutorial, and tested to ensuregood results for the specif ic purpose we will look at here.

T ipT ip

Creat ing a good MaterialSpecifications requires ab init io expert ise to ensure that the computat ionalmodel is suff icient ly accurate. However, the philosophy behind the design of SMW is that it should notrequire ab init io expert ise to use it , simplifying collaborat ion between ab- init io and higher- level modeling.

Set t ing up t he calcu lat ionSet t ing up t he calcu lat ion

To set up the calculat ion, open the Def ect /Dif f usion Script erDef ect /Dif f usion Script er in the panel on the right .

Click the Dat abaseDat abase but ton to open the QuantumATK database of material specif icat ions for automateddefect calculat ions. It contains material specif icat ions for a total of 29 materials, with parameters chosento provide general applicability and high precision for studies of defects in this material. Choose theGaN_300_DFT_SCAN entry by double-clicking or select ing it and then clicking the OKOK but ton.

Now add three successive defects by clicking AddAdd and then select ing f irst Subst itut ional, then Interst it ial,and f inally Vacancy. We wish to add Magnesium atoms and invest igate the 0 and -1 charge states, soselect the subst itut ional defect , click on Phosphorous to open a window with the periodic table, andselect Mg there. After this window has closed, click on the downwards-point ing arrow in the left ChargeChargest at esst at es box to change the value to -1. The window should now look like this:

Now click on Interst it ial and do the same, then Vacancy and change the charge state here as well. Withthis, the script is ready to run, but let us f irst take a look at it . Click the and choose the Editor. You

should now see the following script :

from SMW import *

# Materialmaterial = MaterialSpecificationsDatabase.GaN_300_DFT_SCAN

# Defects# Defect list 0charge_states = [-1, 0]defect_list_0 = SubstitutionalList( material_specifications=material, substitutional_element=Magnesium, charge_states=charge_states)nlsave('GaN_300_DFT_SCAN.hdf5', defect_list_0)defect_list_0.update()

# Defect list 1charge_states = [-1, 0]defect_list_1 = InterstitialList( material_specifications=material, interstitial_element=Magnesium, charge_states=charge_states)nlsave('GaN_300_DFT_SCAN.hdf5', defect_list_1)defect_list_1.update()

# Defect list 2charge_states = [-1, 0]defect_list_2 = VacancyList( material_specifications=material, charge_states=charge_states)nlsave('GaN_300_DFT_SCAN.hdf5', defect_list_2)defect_list_2.update()

The script is rather simple, as the SMW module handles all details of the workflow without needing furtherinput from the user. First , it ext racts a material specif icat ion from the QuantumATK database, and thendefines the three defect lists that we set up previously. Note that they are run sequent ially, so it f irstcalculates the subst itut ions, then the interst it ials and then the vacancies.

R e pl ac i ng t he mat e r i al spe c i f i c at i o nR e pl ac i ng t he mat e r i al spe c i f i c at i o n

The material specif icat ions in the database are designed to be generally applicable and give high-precisionresults for a wide range of defects. However, this also makes them a bit t ime-consuming to use, and wewill therefore use a different material specif icat ion for GaN in this tutorial. It is specif ically designed andtested for the magnesium defects we are invest igat ing here, and should be used with care for otherdefects. In the original script , remove the line material = MaterialSpecificationsDatabase.GaN_300_DFT_SCANwith the material specif icat ion from the database, and replace it with the contents of this f ile: mat-spec-zero-ent ropies.py. The result ing script should be similar to this: SMW_zero-ent ropies.py.

C o nt e nt s o f t he m a t e r ia l s pe c if ic a t io nC o nt e nt s o f t he m a t e r ia l s pe c if ic a t io n

We will now go through the main points of this material specif icat ion. If you are not interested in thesedetails, you may skip ahead to the next sect ion: Run the calculat ion. We will look only at the materialspecif icat ion itself , which looks like this:

material = MaterialSpecifications( pristine_configuration=gan_primitive, supercell_repetitions=(3, 3, 3), formation_energy_calculator=calculator, atomic_chemical_potentials=[ga_mu, mg_mu], dielectric_constant=gan_dielectric_constant, bulk_modulus=173 * GPa, assumed_formation_entropy=0.0 * Joule/Kelvin,)

Some of the parameters are defined further up in the script , and you may consult the full materialspecif icat ion f ile for those details.

Not eNot e

For more informat ion, see the manual page: MaterialSpecifications

T he s upe rc e l l pa ra m e t e rsT he s upe rc e l l pa ra m e t e rs

material = MaterialSpecifications( pristine_configuration=gan_primitive, supercell_repetitions=(3, 3, 3), formation_energy_calculator=calculator,

The f irst few lines specify the host material and the calculator, or computat ional model, to be used for it .Specif ically, they define the unit cell of the prist ine host material, the number of t imes it is repeated tocreate a supercell containing a defect , and the main calculator to use when calculat ing the format ionenergy of the defects.

A t o m ic c he m ic a l po t e nt ia lsA t o m ic c he m ic a l po t e nt ia ls

atomic_chemical_potentials=[ga_mu, mg_mu],

This line specif ies the atomic chemical potent ials that will be used when calculat ing the format ionenergies for the defects. This can be given either as an energy and/or ent ropy per atom, a specif ic atomicconfigurat ion for the element , or left out ent irely. In all cases, QuantumATK will use the calculatorspecif ied above to calculate any missing propert ies.

H o s t m a t e r ia l pro pe rt ie sH o s t m a t e r ia l pro pe rt ie s

dielectric_constant=gan_dielectric_constant, bulk_modulus=173 * GPa,

These lines specify some propert ies of the host material which are used to correct f inite-size effects inthe results. For that reason, it is more important that they are consistent with the computat ional modelspecif ied above than with experimental results.

Fo rm a t io n e nt ro pyFo rm a t io n e nt ro py

assumed_formation_entropy=0.0 * Joule/Kelvin,)

Finally, it contains the definit ion of of the assumed format ion ent ropy. In this case, we do the calculat ionwithout ent ropic contribut ions and therefore define the format ion ent ropy as zero. If we had not definedit , it would be calculated, which is a rather t ime-consuming calculat ion. If we knew the value fromsomewhere else we could have defined it as that value instead of 0. We will revisit these contribut ionslater.

Run t he calcu lat ionRun t he calcu lat ion

The script is now ready to be run. Submit it to your favorite cluster - in our case, it ran in about 6.5 hours ona 24-core node with 256 GB of memory. It requires about 1.7 GB of disk space to store all the results.

T ipT ip

You can use the QuantumATK Job Manager for submit t ing jobs to clusters. See this tutorial for moredetails: Job Manager for remote execut ion of QuantumATK scripts.

The SMW framework will now run a series of individual defect calculat ions, and set up a folder st ructure tokeep t rack of them. If it does not f inish, either due to external circumstances, such as a power failure, orsimply running out of wallt ime, you can easily restart it by simply running the same script again.QuantumATK will check the status of the calculat ions and start from the interrupted task.

In the end, you should see a log-f ile containing blocks like these:

+------------------------------------------------------------------------------+| Defect List |+------------------------------------------------------------------------------+| 2 defect(s) will be calculated. |+------------------------------------------------------------------------------++------------------------------------------------------------------------------+| Calculating defect 1 / 2: || Results and log will be saved to the following folder: || substitutional/substitutional_Mg^Ga_0/000/3848cac9fcfea4adc57af73c58700111/|+------------------------------------------------------------------------------++------------------------------------------------------------------------------+| Calculation 1 / 2 finished. || Convergence status: Converged. All results will be available. |+------------------------------------------------------------------------------+

As could be seen in the script , each type of defect is defined as a separate list . We can see that the f irstdefect list contains subst itut ions, and that the f irst of two is a Mg subst itut ion at a Ga site. The locat ionof this part icular sub-calculat ion is also specif ied, so we know where to go if we want to take a closer lookat it .

Analyzing t he resu lt sAnalyzing t he resu lt s

After the calculat ions have f inished, we can now look at the results. Make sure to select theSMW_zero-entropies.hdf5 f ile in the panel on the left , so it appears on the LabFloorLabFloor in the center. Click that

line, and you should see something like this:

Not eNot e

If the project type is QuantumATK instead of Sentaurus Materials Workbench, you will see more pluginsin the panel on the right than what is shown above.

Select all three defect list objects and click on the Def ect List Analyz erDef ect List Analyz er. The following window will nowappear.

This window is composed of three main parts. On the left , there is a table showing the different defectsand their charge states, and the calculated format ion energy for each. Below this table, you can choosethe Fermi level to be used when calculat ing the format ion energy; the default is the midpoint of the bandgap. You also f ind f ilters that can be applied to the list of defects, in cases where the defect lists arelonger than those we are studying here. On the right , there is a plot showing the t rap levels for eachdefect type, with the valence and conduct ion bands indicated as blue areas and the Fermi level as thedotted line in the center.

If we look at the format ion energies, we quickly see that two values are close to 0 eV, while all the othersare much higher and no smaller than 3.5 eV. We will therefore focus on the f irst two, which are the neutraland negat ive charge states for a Mg subst itut ion at a Ga site. In the plot on the right , we see that thet ransit ion between them, which signif ies a t rap level, occurs slight ly above the top of the valence band. Ifyou hover over it , you will see that it is 249 meV above the top of the valence band. This is in excellentagreement with literature, where it has been found to be 260 meV above the top of the valence band[LJVdW12]. You may also click Subst it ut ionalListSubst it ut ionalList in the table, in which case the plot will show only thesubst itut ional defects, or select a subset of specif ic defects (hold down ctrl to add ent ries) to see onlythose in the plot . Click in the empty area at the bot tom of the table area to reset the plot , or press Esc .

We see that the t ransit ion between the same two charge states occur only a lit t le higher for the Gavacancy (hover over it to ident ify the vacancy site). However, we can see from the table that theformat ion energy for the Ga vacancy is much higher, so those defects will be much rarer under the

modeled condit ions.

The other defects also have t ransit ions between the two charge states, but they are not shown, as theyare outside the band gap. To f ind them, click the Edit but ton to change the propert ies. Find the y-axisand change the limits to -0.1 and 3.5, for example, and the x-axis limits to -0.5 and 7.5 to produce this plot :

We now see that the t rap levels for the other defects are (high) in the conduct ion band.

T ipT ip

You can also use the mouse scroll to quickly zoom out and get an overview.

E xpandi ng t he dat a se tE xpandi ng t he dat a se t

After taking a f irst look at your results, you might decide that you would like to expand the data set toinclude some more defects or charge states. This is quite easy to do, as there is intelligent restartfunct ionality in the SMW defect list and its const ituent features. Open the script ( SMW_zero-ent ropies.py) and edit lines 79, 89 and 99 to also include the +1 charge state, so they looklike this:

charge_states = [-1, 0, +1]

Now re-run the script in the same folder. QuantumATK will automat ically detect that some of thesecalculat ions have already been done, and only do the necessary new calculat ions. In this case, the newcalculat ions took about the same t ime as the original set , but it depends on the system.

Now look at the labfloor again - you will see that three more objects have appeared in the f ile. These arethe new defect lists, containing both the original results, and the new results for the +1 charge states.Select all three, and open them in the Def ect List Analyz erDef ect List Analyz er, as before. It should now look like this.

Note that the original t rap levels are st ill there, while 3 new ones appear, close to the band gap. In this way,we could easily expand the data set in the study, based on preliminary analysis of the original data.

Di sc ussi o n and summaryDi sc ussi o n and summary

In this sect ion, we have shown how to use the Sentaurus Materials Workbench (SMW) feature of Def ectDef ectList sList s to easily study several different point defects in GaN, and even consider them in different chargestates. Specif ically, we studied Mg subst itut ions and interst it ials, as well as vacancies in neut ral andnegat ively charged states. We found that the Mg subst itut ion at a Ga site has a low format ion energy anda t rap level 249 meV above the valence band maximum, consistent with literature.

Note that all of these calculat ions have been done without taking vibrat ional ent ropy and zero-pointenergy into account . These terms require the computat ion of a DynamicalMatrix and aPhononDensityOfStates for each sub-system, the f irst of which is very demanding. The computat ional cost

normally increases by more than an order of magnitude when including these terms, and they are oftensmall. If possible, it is therefore a good idea to evaluate whether their inclusion is relevant or not for thesystem at hand. In the next sect ion, we will include these terms and see how it changes the results.

Including v ibrat ional cont r ibut ionsIncluding v ibrat ional cont r ibut ions

It is quite st raight forward to change the original script to also include, and calculate, the vibrat ional terms.Simply delete the lines:

assumed_formation_entropy=0.0 * Joule/Kelvin, assumed_transition_prefactor=10**13*Second**(-1),

There are now two ways to run the script . One is to parallelize over the defects in each defect list , andthe other is to not do so. In this case, we choose to parallelize over defects, which is slight ly morecomplicated, but provides a faster t ime-to-result at full computat ional eff iciency. To achieve this, weneed to ensure that the choice of compute nodes is compat ible with the number of defects for eachdefect list . From before, we know that there are 2 subst itut ional defects, 2 vacancies and 3 interst it ials. Itwill therefore be most eff icient if we f irst run the subst itut ional defect list on 2 nodes, then the vacancylist on 2 nodes and f inally the interst it ial list on 3 nodes. This means that we will be running these threescripts in succession. In principle, they can also be run concurrent ly, but this would give a small risk ofcorrupt ing the cent ral .hdf5 f ile if more than one job wrote to it at the same t ime. We ran these threescripts in succession in a new and empty directory, using the hardware and computat ional t ime specif ied inthe table. This amounts to about a factor of 35 more CPU-t ime required for this calculat ion, compared tothe previous one without vibrat ional terms.

Not eNot e

Not eNot e

If you have already run the calculat ions without vibrat ions and wish to add these terms, you may save alit t le t ime by running it in the same directory. QuantumATK will detect that some calculat ions havealready been done, and not re-calculate them.

Table 1 Phonon calculations¶

S c riptS c ript CPU’sCPU’s Wallt im e (ho urs )Wallt im e (ho urs ) T o t al CPU- t im e (ho urs )T o t al CPU- t im e (ho urs )

smw-gan-mg-sub.py 2x24 42.0 2014

smw-gan-mg-vac.py 2x24 42.0 2017

smw-gan-mg-in.py 3x24 22.1 1593

After the calculat ions have run, the main results will be saved in the f ile SMW_with-entropies.hdf5 . Inaddit ion to the sub-folders and f iles created before, the phonon calculat ions will also produce severalthousand log-f iles, represent ing the many different displacements that are calculated along the way. Theycan be studied if needed for t roubleshoot ing or verif icat ion.

T ipT ip

For more details on how vibrat ional terms are included, see the manual page ofHarmonicChargedPointDefect .

Anal yz i ng t he re sul t sAnal yz i ng t he re sul t s

Go to the LabFloorLabFloor and make sure the f ile SMW_with-entropies.hdf5 is selected. As before, select thethree items in it , and click on the Def ect List Analyz erDef ect List Analyz er on the right . You should now see the followingwindow:

This looks very familiar, as the inclusion of vibrat ional quant it ies changes very lit t le for the defectsinvest igated here. It turns out that the 0/-1 t rap level moves 2 meV, for Mg subst ituted at a Ga site, whilethe underlying format ion energies change about 5 and 2 meV respect ively. Most other format ion energiesand t rap levels also change very lit t le, except for the format ion energy for neut ral Mg subst itut ion at a Nsite. This part icular format ion energy changes by more than 1 eV with the inclusion of vibrat ional terms.

When seeing surprising results, it is good pract ice to invest igate further, and in this case we can search

Next

through the log-f iles for warnings. It turns out that the log-f ile for elemental nit rogen( cpd_atomic_chemical_potential_Nitrogen.log ) contains this message:

################################################################################# ## WARNING ## ## ============================================================================ ## ## The sum rules are not obeyed in this PhononDensityOfStates calculation. ## There are 147 non-positive eigenmodes. Be careful if you want to calculate ## thermodynamic properties. ## #################################################################################

This means that the vibrat ional spect rum of nit rogen is, most likely, poorly described using thecomputat ional parameters in our current material specif icat ion. It follows that format ion energies whichcontain vibrat ional terms for nit rogen, such as the Mg subst itut ion at a nit rogen site, are a bit uncertain andshould be interpreted with care.

T ipT ip

For more informat ion on phonon calculat ions, see this tutorial: Silicon phonon bandstructure.

ConclusionsConclusions

We found that the Mg subst itut ion at a Ga site has a low format ion energy and a t rap level 249 meV abovethe valence band maximum, when not considering the vibrat ional terms. Including the vibrat ional termstakes approximately 35 t imes longer and changes the t rap level posit ion to 246 meV above the valenceband maximum. This means that inclusion of the vibrat ional terms was not important in this case, andcertainly not important enough to just ify the large computat ional cost .

ReferencesReferences

[LJVdW12] John L. Lyons, Anderson Janott i, and Chris G. Van de Walle. Shallow versus deep nature of mgacceptors in nit ride semiconductors. Phys. Rev. Lett ., 108:156403, Apr 2012. URL:https://link.aps.org/doi/10.1103/PhysRevLett .108.156403, doi:10.1103/PhysRevLett .108.156403.

Previous

© Copyright 2020 Synopsys, Inc. All Rights Reserved.