Computer modelling of defects and dopants in LiNbO 3 , with a look ahead to LiTaO 3 , and Li(Nb, Ta)O 3 solid solutions Robert A Jackson School of Physical & Geographical Sciences Keele University Keele, Staffordshire ST5 5BG, UK [email protected].uk http:// www.robajackson.com @robajackson http://www.slideshare.net/robajack
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Computer modelling of defects and dopants in LiNbO3, with a look ahead to LiTaO3, and Li(Nb, Ta)O3 solid solutions
Robert A JacksonSchool of Physical & Geographical Sciences
Formation energies for basic defects (in stoichiometric LiNbO3)
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Defect 0 K 293 K * [1] model II
VLi’ 9.81 9.71 9.8
VNb’’’’’ 127.56 127.45 117.3
VO 18.98 18.91 19.5
Lii -7.08 -7.12 -8.87**
Nbi -104.12 -104.25 -110.68**
Oi’’ -9.47 -9.64 -16.08**
NbLi -98.37 -98.49 -99.5
LiNb’’’’ -113.99
[1] Donnerberg et al, Phys. Rev. B.,40, 11909 (1989)
* Temperature taken into account via lattice expansion.
** Deduced values since paper does not report these values.
Frenkel, Schottky and pseudo-Schottky energies* (per defect)
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Defect 0 K 293 K [1]Li Frenkel 1.37 1.30 0.93
Nb Frenkel 11.72 11.60 6.26
O Frenkel 4.76 4.64 3.42
Schottky LiNbO3
3.95 3.85 3.91
Pseudo-Schottky Li2O
1.81 1.80 1.94
Pseudo-Schottky Nb2O5
5.09 5.07 2.85
* Calculated for information only since observed defects are more complex.
Expected trends in values are observed.
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Models to explain the observed experimental data
• The simple Frenkel and Schottky models do not explain the observed behaviour in LiNbO3.
• For example, the NbLi + 4VLi
’ defect cluster has a formation energy of –63.61 eV.
• We needed to consider possible reactions that give rise to such defects.
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Explaining the observed non-stoichiometry
• Following the work of Kovács and Polgár*, we considered models based on antisite or interstitial Nb compensated by Li or Nb vacancies.
• 3 possible reactions were considered (see next slide):
* L Kovács and K Polgár, Crystal Research and Technology, 21, K101 (1986)
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Possible defect reactions that give rise to Li deficiency
Antisite Nb compensated by Li vacancies5LiLi + ½Nb2O5 ® 4V’Li + NbLi
···· + 5/2Li2O
E(reaction) = -0.98 (-2.52*) eV per Li2O formula unit
Antisite Nb compensated by Nb vacancies5LiLi + 4NbNb + ½Nb2O5 ® 5NbLi
···· + 4VNb’’’’’ + 5/2Li2O E(reaction) = 29.8 eV per Li2O formula unit
Interstitial Nb compensated by Li vacancies5LiLi + ½Nb2O5 ® 5VLi’ + Nbi
····· + 5/2Li2O E(reaction) = 0.49 eV per Li2O formula unit
* ‘Bound’ defect configuration
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Conclusions from the reactions
• If the reaction energies are calculated, using the basic defect energies already obtained, we concluded that:– only the antisite Nb/Li vacancy model is energetically
favourable.– of the other two mechanisms, the interstitial Nb/Li
vacancy model is more favourable than the antisite Nb/Nb vacancy model.
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Divalent and trivalent dopants
• The incorporation of a range of dopant ions in LiNbO3 was modelled.
• Divalent, trivalent and tetravalent ion substitution was considered.
• Charge compensation is needed for substitution at either the Li+ or Nb5+ site.
• Reference [3] focused on M3+ dopants: Sc, Cr, Fe and In.• References [4] and [5] consider co-doping and Hf doping
respectively.[2] Journal of Physics: Condensed Matter, 19, 046211 (2007)[3] Journal of Physics: Condensed Matter, 20, 035201 (2008)[4] Proc. R. Soc. A 470, 20140406 (2014)[5] http://arxiv.org/abs/1505.01661
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Summary of modelling procedure
• The GULP code is used to calculate the substitution energies, e.g. M2+ at the Li+ site, denoted by MLi
in Kroger-Vink notation.
• The substitution energies are then converted into solution energies, which give the total energy involved in the process:
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Solution energies
• Assuming M2+ substitution at the Li+ site, a possible scheme could be (using Kröger-Vink notation):MO + 2 LiLi → MLi
+ VLi’ + Li2O• This assumes charge compensation by Li vacancies, but
other possibilities are considered.• The same idea is applied to M3+ dopants.
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Predicted doping schemes: M2+ ions
• From the calculations, the following predictions are made based on lowest energies:
• Co-doping at both Li+ and Nb5+ sites, except for Fe2+ and Cd2+ for which substitution at the Nb5+ site with charge compensation by Nb - Li anti-site substitution is preferred.
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Predicted doping schemes: M3+ ions
• The predicted scheme for all the lanthanide ions and Sc, Cr and Fe is self-compensation:M2O3 + LiLi + NbNb → MLi
+ MNb’’ + LiNbO3
• For In, the preferred scheme involves doping at the Nb5+ site with charge compensation by Nb-Li anti-sites.
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Some relevant experimental data
• Studies of M2+ & M3+ dopants in LiNbO3 have included:Mn2+ - LiNbO3: Darwish et al, NIMB, 141, 679-683 (1998)
Supports the idea of Mn2+ self compensation; does not give dopant concentration.Mg2+ - LiNbO3: González-Martínez et al, Opt. Comm., 282, 1212-1219 (2009)
Dopant concentration 0.0714-0.2422 mol%; suggests that self compensation occurs ‘after a certain dopant concentration level’.
Er3+, Cr3+ - LiNbO3: Dierolf & Sandmann, J. Lum., 125, 67-79 (2007) Mainly assumes Li site occupancy, but dopant concentration is unclear as several
samples have been used.
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‘EXAFS evidence for a primary ZnLi dopant in LiNbO3’
(F Bridges et al, Phys. Rev. B 85 064107 (2012))
• Doesn’t find Zn at the Nb site, but may not be directly comparable with the calculations (concentration effects, stoichiometry of sample?)– Measurements on a ‘stoichiometric’ sample give same result.– EXAFS measurements on In have also been performed, and
preliminary results suggest InLi dopants.
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General comments on comparison with experimental data
• The calculation results reported are at infinite dilution, so no concentration effects are considered.– Now we are looking at finite dopant concentrations in other materials,
and this could be done for dopants in LiNbO3 (needs persons and €€€).
• There may be issues with the stoichiometry of the older crystal samples (i.e. are we comparing ‘like with like’?)– But recently EXAFS was done on a stoichiometric sample and we are
comparing results.
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Hf4+ doping
• The lowest energy scheme again involves self-compensation:
• These results are supported by experimental studies:Marques J G, Kling A , de Jesus C M , Soares J C , da Silva M F, Dieguez E and Agulló-Lopez F 1998 Nuclear Instruments and Methods in Physics Research B 141 326-331Li S, Liu S, Kong Y, Deng D, Gao G, Li Y, Gao H, Zhang L, Hang Z, Chen S and Xu J 2006 J. Phys.: Condens. Matter 18 3527–3534
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Co-doping by transition metal ions
• TM co-doped LiNbO3 finds applications in holographic recording devices.
• We have modelled co-doping by Fe3+Cu+, Ce3+Cu+, Ce4+Mn2+, Rh3+Fe3+ and Ru4+Fe3+.
• In most cases the solution energy is reduced compared to doping with single ions.– Has implications for device development.
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Modelling LiTaO3: obtaining an (initial) Ta-O potential