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The End<br />

Growth Simulations of Single Crystal Perovskite Alloys; Charles <strong>Tahan</strong> Slide 32


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Future Work<br />

Growth Simulations of Single Crystal Perovskite Alloys; Charles <strong>Tahan</strong> Slide 31


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Results/Analysis<br />

Growth Simulations of Single Crystal Perovskite Alloys; Charles <strong>Tahan</strong> Slide 30


Results/Analysis<br />

Growth Simulations of Single Crystal Perovskite Alloys; Charles <strong>Tahan</strong> Slide 29


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Growth Simulations of Single Crystal Perovskite Alloys; Charles <strong>Tahan</strong> Slide 28


Results/Analysis<br />

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Growth Simulations of Single Crystal Perovskite Alloys; Charles <strong>Tahan</strong> Slide 27


E<br />

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Growth Simulations of Single Crystal Perovskite Alloys; Charles <strong>Tahan</strong> Slide 26<br />

KLK<br />

Results/Analysis<br />

R, growth rate (# adatoms/MC time)<br />

0.2<br />

0.1<br />

0<br />

kT=0.025<br />

kT=0.1<br />

kT=0.2<br />

kT=0.6<br />

kT=1.0<br />

kT=1.4<br />

kT=1.8<br />

kT=2.0<br />

Zoom in: Long−Range Model, Rock Salt: F<br />

Growth Rate vs. Change in Chemical Potential G<br />

20x20x60<br />

Hsubstrate=20, salt<br />

JI5 runs/data point<br />

−0.1<br />

−0.75 −0.65 −0.55 −0.45 −0.35 −0.25<br />

∆µ


NM O M O <br />

E<br />

0Q<br />

Results/Analysis<br />

R, growth rate (# adatoms/MC time)<br />

0.5<br />

0<br />

−0.5<br />

kT=0.025<br />

kT=0.05<br />

kT=0.1<br />

kT=0.2<br />

kT=0.6<br />

kT=1.0<br />

kT=1.4<br />

kT=1.8<br />

kT=2.0<br />

Long−Range Model, Rock Salt: S<br />

Growth Rate vs. Change in Chemical Potential G<br />

20x20x60 lattice<br />

Hsubstrate=20, salt<br />

JI5 runs/data point<br />

−1<br />

−2.5<br />

−2 P<br />

−1.5 −1 −0.5<br />

∆µ<br />

R Q<br />

Growth Simulations of Single Crystal Perovskite Alloys; Charles <strong>Tahan</strong> Slide 25


Results/Analysis<br />

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Growth Simulations of Single Crystal Perovskite Alloys; Charles <strong>Tahan</strong> Slide 24


NM O M O <br />

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Results/Analysis<br />

Nearest−Neighbor Model, Rock Salt:<br />

Growth Rate vs. Change in Chemical Potential G<br />

R, growth rate (# adatoms/MC time)<br />

0.3<br />

0.2<br />

0.1<br />

0<br />

kT=0.025<br />

kT=0.05<br />

kT=0.1<br />

kT=0.2<br />

kT=0.6<br />

kT=1.0<br />

kT=1.4<br />

kT=1.8<br />

kT=2.0<br />

20x20x60 latice<br />

Hsubstrate=20, salt<br />

I10 runs/data point<br />

−0.1<br />

−2.5<br />

−2 P<br />

−1.5 −1 −0.5<br />

∆µ<br />

Q<br />

Growth Simulations of Single Crystal Perovskite Alloys; Charles <strong>Tahan</strong> Slide 23


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Results/Analysis<br />

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Growth Simulations of Single Crystal Perovskite Alloys; Charles <strong>Tahan</strong> Slide 22<br />

Y[Z


i i h<br />

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Development & Implementation<br />

k<br />

Species 1: 1-<br />

Species 2: 1+<br />

}substrate<br />

j<br />

i<br />

Growth Simulations of Single Crystal Perovskite Alloys; Charles <strong>Tahan</strong> Slide 21


i kt `<br />

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Development & Implementation<br />

k<br />

Species 1: 1-<br />

Species 2: 1+<br />

}substrate<br />

j<br />

i<br />

k®M~”¦M~”M t ›«ª¬‰š wv†|„y M ‰ƒ wvx„{}…ƒ¯{ ³<br />

Growth Simulations of Single Crystal Perovskite Alloys; Charles <strong>Tahan</strong> Slide 20<br />

ƒ


i k„t `<br />

d»x»f»¼d½ ` ¾ ¸ ¿¸ i•¸º¹ ¸ ¾<br />

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k ” ”|¯t ¨§~© ¡‰uz¢ ~v†‰|zy}|z|zy ~v†‰zy}|w ~v†‰zy<br />

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k®M¬” ”M t ›Îª¬‰š ~v†‰ƒzy}…Š‡# ~v†«‡‡¯zƒ… ~vÏy<br />

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y<br />

k ”M¬”M t ›Îª¬‰š ~v†‰ƒzy}…Š‡# ~v†«‡‡¯zƒ… ~vÐ{y}<br />

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k®M¬”M¬”|¯t ¨§~© ¡‰uz¢ ~v†‰|zy}|z|zy ~v†‰zy}|w ~vxƒ„yy<br />

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Growth Simulations of Single Crystal Perovskite Alloys; Charles <strong>Tahan</strong> Slide 19<br />

u‰Ñ<br />

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Development & Implementation


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h k„t `<br />

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zvxƒ M | M { ‚ vxƒ M | M { ‚<br />

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Development & Implementation<br />

k<br />

Species 1: 1-<br />

Species 2: 1+<br />

}substrate<br />

j<br />

i<br />

Growth Simulations of Single Crystal Perovskite Alloys; Charles <strong>Tahan</strong> Slide 18


¢YÖÕ£¢¸¥¤§¦<br />

r <br />

Growth Simulations of Single Crystal Perovskite Alloys; Charles <strong>Tahan</strong> Slide 17<br />

Development & Implementation<br />

(i) list,í Generate a , of all possible events per time step; There<br />

possible events: an evaporation or an adsorption could happen on<br />

each<br />

are¨©î<br />

of sites;<br />

ï<br />

theî<br />

surface<br />

(ii) Calculate the<br />

ðÊñ<br />

rates ) of adsorption and evaporation for each site on<br />

the surface rates); (¨©î (ò<br />

(iii) Normalize these¨óî<br />

rates, giving probabilities,ô£õ, for<br />

evaporation/adsorption on site 1, on site 2, . . . on site N, which all add<br />

to unity;<br />

(iv) Generate a random numberöø÷_ùûúü¤¦ý<br />

choose the first eventí õ<br />

such that þ ¿<br />

An event will always be chosen;<br />

and<br />

ö.<br />

(v) Generate new<br />

ô£õ˜ÿ<br />

based on chosen<br />

õ<br />

configuration¡<br />

eventí<br />

õ.


g<br />

g<br />

Y[Z<br />

such that þ ¿<br />

õ ô õ ÿ ö;<br />

¢YÖÕ£¢<br />

s<br />

Growth Simulations of Single Crystal Perovskite Alloys; Charles <strong>Tahan</strong> Slide 16<br />

r<br />

¢YÖÕ£¢¸@¤§¦<br />

possible<br />

¢YÖÕ?¢¸@¤§¦<br />

Methodology<br />

(i) Randomly select theð<br />

from surface sites;<br />

(ii) Generate a<br />

an¨©nüý<br />

, of possible events at¨©nüý.<br />

ñ<br />

list,í<br />

pair<br />

In our case,í<br />

ï<br />

#";<br />

(iii) Define the probability each event will occur by normalizing the event<br />

ü! ö© ü ö©<br />

(iv) Generate a random and numberöø÷_ùûúü¤¦ý<br />

choose the first eventí õ<br />

rates$&%'()*,+-%.),/0),12%435(6*,38723 92/-:;:;*='%4$&()%:.<br />

(v) Generate new configuration¡<br />

based on chosen eventí<br />

õ;


BDC E GFH A<br />

YÖÕ ` Ißç`<br />

ŽŽŽ<br />

ŽŽŽ<br />

ò<br />

C EDA B<br />

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¿ àèåá ¹ çæ Y_^‰çY_^èå ª„èNMzkPO ‚ QRt ” ”<br />

J<br />

O Y_^ ç ¡ ` k£”#]z”¡ t<br />

BDC E SUT ¤è,VUWçYX&Z[\XÚ¤è A<br />

YÖÕ<br />

Methodology<br />

‚ QRt<br />

Growth Simulations of Single Crystal Perovskite Alloys; Charles <strong>Tahan</strong> Slide 15<br />

ª„èNMzkPO


YÖÕ<br />

¾ ¤V_^çMa` Y[Z<br />

b cUdfe>gihkj l mon prqksut<br />

YÖÕ<br />

ì ›«’„š xìzy à,{ æ Ão | w<br />

}~ c € l mƒ‚ n „ qksut b<br />

¾ Zv¤W<br />

Methodology<br />

Growth Simulations of Single Crystal Perovskite Alloys; Charles <strong>Tahan</strong> Slide 14


k£”#] t<br />

¸ çV_Zcè<br />

` ‡0ˆC EDA B<br />

A BDC E † g Y[Z àÚÝÜæ ÚÝÜ v k… t<br />

E BDC A X“çX¤è‰Zcè,ZŠ‹XM¦ç^X¤XÚŠfZ[ŒZMY§Ž<br />

ÚÝÜ<br />

Õ k… t<br />

…<br />

¤èè¤V_^çMWDXÚç[‰^<br />

Methodology<br />

Growth Simulations of Single Crystal Perovskite Alloys; Charles <strong>Tahan</strong> Slide 13


Background<br />

Only discrete placement<br />

on our perfect 3-d lattice.<br />

Solid-on-Solid (SOS)<br />

restriction for<br />

adatom placement<br />

on the crystal surface.<br />

Periodic Boundary Conditions (PBC)<br />

real adatom in crystal matrix<br />

"images"<br />

Growth Simulations of Single Crystal Perovskite Alloys; Charles <strong>Tahan</strong> Slide 12


‘<br />

‘<br />

` Zf^ ‚ Z è Y[Z<br />

M’ “’<br />

|”’<br />

Background<br />

k<br />

MELT<br />

adsorbed adatom at site (i,j,k)<br />

H<br />

L<br />

}<br />

substrate<br />

j<br />

i<br />

L<br />

2<br />

N = L = # of surface sites (w/ SOS)<br />

Growth Simulations of Single Crystal Perovskite Alloys; Charles <strong>Tahan</strong> Slide 11


–˜— •<br />

›š— œ – — ž •<br />

•<br />

Background<br />

1:1 1:2<br />

• –˜Ÿ¡ œ ¢¤£ ¥ ›šŸ¡ œ ¦£<br />

[111]<br />

[001]<br />

1<br />

2<br />

1<br />

2<br />

( -n ) + ( +n) -2n ( +n)<br />

3 ( ) + 3<br />

Species: quantity([color]charge)<br />

1<br />

2<br />

Growth Simulations of Single Crystal Perovskite Alloys; Charles <strong>Tahan</strong> Slide 10<br />


•<br />

•<br />

•<br />

¥ ¥ •<br />

•<br />

— œ œ ¨ ©«ª ¬ ©®­<br />

§<br />

² ›š°¯<br />

›š°¯&›š°¯­<br />

²´± ±³²<br />

Background<br />

Growth Simulations of Single Crystal Perovskite Alloys; Charles <strong>Tahan</strong> Slide 9


•<br />

Background<br />

Perovskite Unit Cell<br />

Crystal Lattice<br />

B Sublattice<br />

B Sublattice with pretty cubes<br />

B atom<br />

=<br />

Growth Simulations of Single Crystal Perovskite Alloys; Charles <strong>Tahan</strong> Slide 8


•<br />

•<br />

 ÃÅÄ ÆÃÅÄ<br />

· ¸¹Dº» µ<br />

¿¾ ¼½i¾<br />

Ä<br />

ÁÀa½<br />

ÂÃÆ Â ÃÆ<br />

Ä<br />

Background<br />

Unit Cell, Perovskite Alloy - ABO 3<br />

A atom: fixed Group II metal<br />

B atom: fractional, metals from<br />

O atom: Oxygen<br />

Groups II-VII<br />

can be different elements, ie fractional<br />

fixed: always the same element<br />

no matter the location<br />

within the crystal matrix<br />

Growth Simulations of Single Crystal Perovskite Alloys; Charles <strong>Tahan</strong> Slide 7<br />

¹Dº » Ç‹È#É ÊÈ#É ¸<br />

¹Dº » Ç«È;Ê Ç‹È#Ê ¸


Background<br />

Growth Simulations of Single Crystal Perovskite Alloys; Charles <strong>Tahan</strong> Slide 6


•<br />

•<br />

•<br />

•<br />

Introduction & Motivation<br />

Growth Simulations of Single Crystal Perovskite Alloys; Charles <strong>Tahan</strong> Slide 5


•<br />

•<br />

Ë<br />

Introduction & Motivation<br />

Growth Simulations of Single Crystal Perovskite Alloys; Charles <strong>Tahan</strong> Slide 4


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è˜ÖìëUÑ,íÔ°ÕÅáãÛÜ߉â¥Ù æ<br />

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T-PLOTT: <strong>Tahan</strong> Pain-Level-of-Talk Topography<br />

why?<br />

ðñáãÍÏòaÔ°Í“Ñ,Í“ç_ÛÜÕÅáãç ÖkÕØ×ÚÙÛÜÒ°ÑÙ Ð.ÍÏÑÒ°Ó°ÔÕ4ÖkÕØ×ÚÙÛÜÒ°ÑÙ ÌfÍÏÎ<br />

how?<br />

ðñÍ“ÕÅÔ°ï°Ù÷öáãÛÜÍ4ëUÑÑÔG×ÚÙ<br />

ÖkÕØ×ÚÙÛÜÒ°ÑÝ ÕÅÔ°ÎÞÛPß<br />

ÕÅÔ°ÎÞÛPߥàÚáãâ¥äŒÑÒ°ÛÜáãÔ°å‰Ù Ý<br />

new!<br />

ÌfÍÏÎóëUÑí°Ô°ÕÅáãÛÜ߉âõôHàöáãâ¥ä‰Ñ,Ò°ÛPáãÔ°å<br />

àöáãâ¥ä‰Ñ,Ò°ÛPÍÏøûÖêÕ#×ÚÙÛÜÒ°ÑÙ<br />

Ò°å‰ø8â¥Ô°ÕÍÏùúùúù Ð.Ôç_÷8àÚÒ°Ñ,Û<br />

joy<br />

pain<br />

Growth Simulations of Single Crystal Perovskite Alloys; Charles <strong>Tahan</strong> Slide 3


¥<br />

Preliminary Overview<br />

Growth Simulations of Single Crystal Perovskite Alloys; Charles <strong>Tahan</strong> Slide 2

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