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Computational Study of the Deposition of Metal-Oxide Thin Films on Strontium Titanate

Permanent Link: http://ufdc.ufl.edu/UFE0024973/00001

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Title: Computational Study of the Deposition of Metal-Oxide Thin Films on Strontium Titanate Morphology and Growth Modes
Physical Description: 1 online resource (119 p.)
Language: english
Creator: Wohlwend, Jennifer
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2009

Subjects

Subjects / Keywords: deposition, growth, morphology, simulation, srtio3
Materials Science and Engineering -- Dissertations, Academic -- UF
Genre: Materials Science and Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: SrTiO3 and its component oxides have been deposited on SrTiO3 (100) using molecular dynamics simulations. SrO thin films have been shown to grow in a layer-by-layer fashion with highly ordered smooth morphology. TiO2 thin films exhibit island morphology with very little structural order. These differing growth modes have been explained by the differing mobilities of each incident particle as well as the interaction of each with the substrate. The higher mobility of SrO molecules with the substrate allows the species to move to favorable sites post deposition while the TiO2 molecules hit and stick where they land. Temperature accelerated dynamics was employed to further the time scale of the relaxation of the deposited films. While no significant structural ordering occurred, TAD has given insight into the surface diffusion mechanisms of SrO, O and TiO2 on STO.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Jennifer Wohlwend.
Thesis: Thesis (Ph.D.)--University of Florida, 2009.
Local: Adviser: Sinnott, Susan B.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2010-02-28

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Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2009
System ID: UFE0024973:00001

Permanent Link: http://ufdc.ufl.edu/UFE0024973/00001

Material Information

Title: Computational Study of the Deposition of Metal-Oxide Thin Films on Strontium Titanate Morphology and Growth Modes
Physical Description: 1 online resource (119 p.)
Language: english
Creator: Wohlwend, Jennifer
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2009

Subjects

Subjects / Keywords: deposition, growth, morphology, simulation, srtio3
Materials Science and Engineering -- Dissertations, Academic -- UF
Genre: Materials Science and Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: SrTiO3 and its component oxides have been deposited on SrTiO3 (100) using molecular dynamics simulations. SrO thin films have been shown to grow in a layer-by-layer fashion with highly ordered smooth morphology. TiO2 thin films exhibit island morphology with very little structural order. These differing growth modes have been explained by the differing mobilities of each incident particle as well as the interaction of each with the substrate. The higher mobility of SrO molecules with the substrate allows the species to move to favorable sites post deposition while the TiO2 molecules hit and stick where they land. Temperature accelerated dynamics was employed to further the time scale of the relaxation of the deposited films. While no significant structural ordering occurred, TAD has given insight into the surface diffusion mechanisms of SrO, O and TiO2 on STO.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Jennifer Wohlwend.
Thesis: Thesis (Ph.D.)--University of Florida, 2009.
Local: Adviser: Sinnott, Susan B.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2010-02-28

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2009
System ID: UFE0024973:00001


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1 COMPUTATIONAL STUDY OF THE DEPOSITION OF METAL OXIDE THIN FILMS ON STRONTIUM TITANATE : MORPHOLOGY AND GROWTH MODES By JENNIFER LYNNE WOHLWEND A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2009

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2 2009 Jennifer Lynne Wohlwend

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3 To my family

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4 ACKNOWLEDGMENTS I wish to thank my graduate advisor and mentor, Prof. Susan B. Sinnott who has given her kind guidance and advice throughout my time here. Dr. Sinnott has been a source of strength during difficult times and life changing events. I also wish to thank Dr. S imon Phillpot for his advice and for always having an open door when I struggled with writing code. Many thanks to the past and present members of the Computational Focus Group for their kindness and friendship. I came to UF without knowledge of coding o r simulation and my fellow group members were always willing to answer questions and offer support. Specifically to Rakesh Behera, who has been a never ending resource I also thank Cosima Boswell for her contributions to this work. Finally, I would like t o thank the professors at Clemson University in the ceramic and materials science and engineering department who laid the foundation and gave me inspiration to continue my education. I express my deepest thanks to my family. My parents, Gregory and Kather ine McKillip, made this accomplishment possible and have always been by my side. I thank my husband, Michael Wohlwend, for all he has given me. I am forever grateful for his never ending support especially during the past year.

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5 TABLE OF CONTENTS page ACKNOWLEDGMENTS .................................................................................................................... 4 LIST OF TABLES ................................................................................................................................ 7 LIST OF FIGURES .............................................................................................................................. 8 ABSTRACT ........................................................................................................................................ 11 CH A P T E R 1 INTRODUCTIO N ....................................................................................................................... 13 General Introduction ................................................................................................................... 13 Strontium Titanate and Component Oxides Structure and Applications ................................. 13 Experimental Strontium Titanate and Component Oxides Deposition and Growth ............... 17 Computational Studies of Deposition and Growth ................................................................... 20 Growth: Effects of Mobility and Diffusion ............................................................................... 23 2 COMPUTATIONAL METHODS ............................................................................................. 27 Molecular Dynamics ................................................................................................................... 27 Periodic Boundary Conditions ............................................................................................ 28 Velocity Rescaling Thermostat ........................................................................................... 29 Gear 5th Order Predictor Corrector ..................................................................................... 30 Interatomic Potenti al ............................................................................................................ 32 Buckingham potential .................................................................................................. 32 Coulomb potential ........................................................................................................ 33 Temperature Accelerated Dynamics .......................................................................................... 36 3 STRONTIUM OXIDE AND T ITANIUM DIOXIDE THIN FILM DEPOSITION ON STRONTIUM TITANATE ........................................................................................................ 41 Simulation Set up ........................................................................................................................ 41 Results .......................................................................................................................................... 42 Strontium Oxide Deposition ............................................................................................... 42 Titanium Dioxide Deposition .............................................................................................. 45 Discussion .................................................................................................................................... 46 Conclusions ................................................................................................................................. 52 4 PARTICULATE DEPOSITION OF HOMOEPITAXIAL STRONTIUM TITANATE THIN FILMS ............................................................................................................................... 54 Simulation Set up ........................................................................................................................ 54 Results .......................................................................................................................................... 55

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6 Alternating Particle Deposition .......................................................................................... 55 Alternating Monolayer Deposition ..................................................................................... 59 Discussion .................................................................................................................................... 61 Conclusions ................................................................................................................................. 64 5 STRONTIUM TITANATE CLUSTER DEPOSITION ........................................................... 65 Simulation Set up ........................................................................................................................ 65 Results .......................................................................................................................................... 68 Discussion .................................................................................................................................... 77 Conclusions ................................................................................................................................. 78 6 TEMPERATURE ACCELERATED DYNAMICS ................................................................. 79 Simulation Set up ........................................................................................................................ 79 Results .......................................................................................................................................... 82 Discussion .................................................................................................................................... 87 Conclusions ................................................................................................................................. 89 7 GENERAL CONCLUSIONS .................................................................................................... 91 A P P E N D I X : ANALYSIS CODES ................................................................................................... 93 REFERENCE LIST .......................................................................................................................... 107 BIOGRAPHICAL SKETCH ........................................................................................................... 119

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7 LIST OF TABLES Table page 2 1 Parameters used in the Buckingham and Coulombic potentials. ........................................ 34 2 2 Comparison of calculated and experimental structure and elastic properties for SrTiO3. .................................................................................................................................... 35 2 3 Comparison of the results of current calculations, experimental data, and previous calculations for the structural properties of anatase and rutile TiO2, a nd rocksalt SrO. .... 35 3 1 Nearest neighbor distances of Ti with O for bulk STO, rutile, and anatase. ...................... 46 3 2 Comparison of the works of adhesion of anatase TiO2, rutile TiO2, and rocksalt SrO, respectively, on STO. ............................................................................................................. 51 3 3 Diffusion coefficients (D) of an SrO or TiO2 p article on each STO termination .............. 53 5 1 Average Ti O bonding in STO clusters compared to bulk STO. ........................................ 67 5 2 Cluster d eposition schemes investigated ............................................................................. 68

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8 LIST OF FIGURES Figure page 1 1 SrTiO3 illustrating the alternating SrO/TiO2 planes. ........................................................... 15 1 2 Bulk SrO exhibits a structure similar to the SrO plane in SrTiO3 with a smaller Sr O bond. ........................................................................................................................................ 16 1 3 TiO2 polymorphs .................................................................................................................... 16 1 4 RHEED o scillations and the corresponding surface coverage. ........................................... 24 1 5 Schematic illustration of structures produced by differing growth modes ........................ 24 1 6 A tomic force microscopy images of SrTiO3 thin films illustrating different growth modes observed. ..................................................................................................................... 26 2 1 Schematic of simulation steps ............................................................................................... 27 2 2 Schematic of periodic boundary conditions. ........................................................................ 28 2 3 STO substrate illustrating thermostat and activ e regions. ................................................... 29 2 4 Schematic of transition state theory. ..................................................................................... 37 2 5 Schematic illustration of the extrapolation of Thigh time to Tlow time. ................................ 39 2 6 Flowchart illustrating the temperature accelerated dyanmics procedure. .......................... 40 3 1 SrO layers that are deposited with an incident energy of 1.0 eV/atom on TiO2terminated STO. ..................................................................................................................... 43 3 2 Sr O plannar pair distribution function for SrO layers on STO. ......................................... 44 3 3 Sr O plannar pair distribution function showing an obvious correlation between the STO termination layer and SrO deposited film structure. ................................................... 44 3 4 Sr O plannar pair distribution function showing the second SrO layer grown on TiO2terminated STO corresponding to the first SrO layer grow n on the SrO terminated STO. ..................................................................................................................... 45 3 5 TiO2 particle deposition. ........................................................................................................ 47 3 6 Ti O pair distribution function showing the influence of termination layer. ..................... 48 3 7 Mean square displacement curve for an SrO particle on TiO2 terminated STO at 973 K showing the adequate linearity needed to calculate the diffusion coefficient from the slope of the curve. ............................................................................................................ 53

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9 4 1 Alternating particle dep osition .............................................................................................. 56 4 2 A lternating particle deposition metal atom percentages. ..................................................... 57 4 3 Pair distribution functions for alternating particle deposition. ............................................ 58 4 4 Alternating monolayer deposition. ........................................................................................ 60 4 5 Metal atom percentages for alternating monolyaer deposited films. .................................. 61 4 6 Pair distribution function s for alternating monolyaer deposited films. .............................. 62 5 1 STO cluster geometries displaying bondlengths and symmetry. ....................................... 67 5 2 Representative snapshots of films deposited on SrO terminated STO showing layer segregation and order within the first layer. ......................................................................... 69 5 3 Pair distribution functio n of the second deposited layer comparing monoand mixed size cluster deposition on SrO terminated STO illustrating the similar structural order between the two deposition methods. ......................................................................... 70 5 4 Percentage of metal atoms in the first two deposited layers on SrO terminated STO. ..... 71 5 5 Representative snapshots of films deposited on TiO2terminated STO showing layer segregation and order within layers one and two shown in the lower figures .................. 72 5 6 Pair distribution function of the second deposited layer comparing monoand mixed size cluster deposition on TiO2termin ated STO illustrating the similar structural order between the two deposition methods. ......................................................................... 73 5 7 Percentages of metal atoms in the first two deposited layers on TiO2terminated STO. ........................................................................................................................................ 74 5 8 First layer of each film deposited on TiO2 termination illustrating the 4 -fold site vacancies, TiO2 inclusions and Ti substitutions. .................................................................. 75 5 9 Defects present in deposited films on TiO2 termination. ..................................................... 75 5 10 Defect percentages. ................................................................................................................ 76 6 1 Initial 2ML deposited on TiO2terminated STO structure ................................................... 80 6 2 Adsorption sites. ..................................................................................................................... 81 6 3 Final 2ML relaxed structure. ................................................................................................. 81 6 4 Oxygen adatom exchange mechanism on TiO2terminated STO. ...................................... 83 6 5 Oxygen adatom hop mechanism on SrO terminated STO. ................................................. 84

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10 6 6 SrO diffusion mechanism on TiO2-terminated STO. ........................................................... 85 6 7 SrO ad -dimer surface diffusion on SrO termination. ........................................................... 86 6 8 Structure formed when Ti, TiO or TiO2 is adsorbed, surface O bonds with Ti to make Ti 4 coordinated. .................................................................................................................... 87

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11 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy COMPUTATIONAL STUDY OF THE DEPOSITION OF METAL OXIDE THIN FILMS ON STRONTIUM TITANATE: MORPHOLOGY AND GROWTH MODES By Jennifer Lynne Wohlwend August 2009 Chair: Susan B. Sinnott Major: Materials Science and Engineering Thin films of strontium titanate, as well as one of its component oxides, TiO2, have been of great interest due to their applicability in electronic devices. Here, classical molecular dynamics simulations are used to examine the growth of SrTiO3 (STO), SrO and TiO2 thin films on STO. In particular, the simulations consider the deposition of SrO and TiO2 molecules and stoichiometric STO clusters at incident energies of 0.1, 0.5, and 1.0 eV/atom onto the (001) surface of STO. The role of surface termination layer (SrO vs. TiO2), incident ene rgy and in the case of STO deposition incident particle size and deposition scheme is investigated In the case of SrO deposition, smooth, ordered films are produced for all incident energies considered and for both surface terminations. In contrast, in the case of TiO2 deposition, three dimensional islands are formed under all conditions. Growth modes predicted are, as shown, a consequence of the mobility and interaction energy of each particle (SrO or TiO2) with the substrate. For STO thin film deposition three schemes are inv estigated, alternating particle deposition (APD), alternating monolayer deposition (AMD) and cluster deposition. For APD, a beam of alternating SrO and TiO2 molecules is deposited on the (001) surface of ST O with incident kinetic ener gies of 0.1, 0.5 or 1.0 eV/atom. AM D consists of the deposition of alternating SrO and TiO2 monolayers, where both have incident energies of 1.0 eV/atom. SrTiO3 cluster

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12 deposition considers t he deposition of 1, 2, 3, and 4 unit STO stoichiometric clusters having incident energies of 1.0 eV/atom. On the whole, some layer -bylayer growth is predicted to occur on both SrO and TiO2terminated STO for each type of deposition scheme. The prevalent defects observed in the first deposited layer on TiO2terminated STO are Sr vacancies, TiO2 inclusions and Ti substitutions, these are characterized and their effect on additional deposited layers is investigated. Temperature accelerated dynamics (TAD) is used to predict energy barriers associated with diffusion mechani sms of adatoms and ad-dimers on (100) SrTiO3 as well as energy barriers associated with the relaxation of a 2ML (1 SrO ML and 1 TiO2 ML) film deposited using traditional MD simulations. We observe two differing surface adatom/ad -dimer diffusion mechanisms depending on substrate termination. On TiO2 termination, an oxygen exchange mechanism is favored whereas on SrO termination, hopping mechanisms dominate. In summary, the major contributions of this work to the literature are the simulated thin film growt h of TiO2, SrO and STO using particulate and cluster deposition along with the investigation of ad -particle surface diffusion to elucidate the mechanisms involved during the first stages of deposition. This work has been published in Surface Science and th e Journal of Materials Research Society along with two additional publications in preparation.

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13 CHAPTER 1 INTRODUCTION General Introduction Strontium titanate is the archetype perovskite that has inspired countless experimental and theoretical studies. SrTiO3 (STO) possesses several properties that make it useful in electronic device applications. For example, STOs high dielectric constant and low dielectric loss make it an attractive material in ferroelectric thin film capacitors ,1, 2 microwave applications3, tunable resonant circuits4 and dynamic random access memory applications.5 Due to its lattice compatibility, STO is a desirable substrate material for high Tc superconductors; more over, the growth of atomically smooth films on these substrates is critically important for the epitaxy and performance of heterostructures.69 This has motivated extensive examination of thin film growth on STO. Of particular interest here, t he way in which STO and its components are deposited can be used to control its surface structure and t he properties of the resulting thin films.10 Strontium Titanate and C omponent O xides Structure and Applications STO is isostructural with the mineral pe rovskite (CaTiO3), hence the nomenclature11 and has a lattice constant of 0.3903 nm. This structure, having space group mPm3 is based on a cubic close -packed lattice of SrO3 (AO3) atoms with a Ti atom in the middle of the cubic configuration12, as shown in Figure 1 1 The large Sr2+ cations are 12 -fold coordinated and sit on the corner sites while the smaller Ti 4+ ion occupy all of the octahedral interstices surrounded by O2ions11. At room temperature, STO exists in the cubic phase with a transition to the tetragonal antiferrodistortive phase at temperatures below its Curie point of 105 K13 (110 K14). Thi s phase transition involves symmetry changes in the crystal structure as a consequence of lattice energy minimization11. This structural optimization typically leads to small lattice distortions, in the case of STO in the form of a rotation of the oxygen octahedral about a <001> axis in opposite

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14 directions in alternate unit cells. Experime ntally, this is shown by changes in lattice spacing and conductivity as a function of temperature. This behavior is characteristic of anti ferrodistortive materials13. Due to symmetry constraints arising from the c ubic structure, STO displays paraelectric behavior at room temperature. This eliminates the problem of fatigue and aging experienced with other materials in the ferroelectric class that display spontaneous polarization at regular operating temperatures; su ch as BaTiO3 with a Curie temperature of approximately 400K. STO plays a major role in electronic applications due to its excellent electronic properties15, 16. The most impressive property is its large dielectric constant at 300. Such a high constant allows high storage capacity that is almost an order of magnitude higher than other gate dielectrics such as SiO2 and Ta2O5 17. STO also has superior temperature, composition, and chemical stability compared to its fellow perovskites. These properties make STO an attractive material for use as Dynamic Random Access Memory (DRAM)18, 19, high -frequency integrated circuits20, and, due to its optical transparency, as insulating layers in thin film electroluminescent displays (TFELs) 21. STO thin films have also become the model material for use as substrates for the deposition high Tc superconductor thin films such as YBa2Cu3O7, ( YBCO ) due to the chemical and structural compatibility between STO and YBCO thereby reducing interfacial strain related to the lattice parameter mismatch of the YBCO thin film with the substrate .22 For use in high Tc superconductors, the interface quality is of utmost importance because of the ~2 nm coherence length where any precipitates or wrinkles can fatally impact the device.23 STO is comprised of alternating planes of SrO and TiO2 (illustrated in Figure 1 1) approximately 2 apart. Thin films of SrO and TiO2 have also been of interest Atomic layer

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15 deposition of SrO on STO is shown to create atomi cally smooth STO surface for use in heterostructures8, 24 as well as buffer layers25, 26. Buffer layers are utilized to suppress the strain created due to the lattice mismatch between substrate and film.27 Bulk SrO illustrated in Figure 1 2, has the rocksalt structure where each Sr atom is coordinated with 6 O atoms and each O atom is coordinated with 6 Sr atoms having an Sr O bond length of 2.58 Bulk SrO has a lattice constant of 5.16 and therefore has a lattice mismatch of ~24% with STO.28 TiO2 thin films, however, have significant applications in their own right. For example, TiO2 is important for catalytic applications .29 The two most stable TiO2 polymorphs are rutile and anatase, in both, each Ti atom is coordinated with 6 O atoms and each O atom is coordinated with 3 Ti atoms. Experimentally, anatase (its structure is shown in Figure 1 -3 A) is the dominant phase produced when TiO2 is deposited on STO (001) due to the smaller lattice mismatch of ~3% with the underlying substrate; in contrast, the m ore thermodynamically stable rutile phase (its structure is shown in Figure 1 3 B ) has a mismatch of ~15%.30 Anatase thin films are useful because of their efficiency in photocatalysis31 while rutile films are used in optical applications such as solar cells32 and anti reflective coatings.33 Figure 1 1 SrTiO3 illustrating the alternating SrO/TiO2 planes; Sr lime, Ti -silver, O red.

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16 Figure 1 2 Bulk SrO exhibits a structure similar to the SrO plane in STO with a smaller Sr O bond; Sr lime, O red. Figure 1 3 TiO2 polymorphs A) Anatase, B) Rutile. Ti -silver, O red.

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17 Experimental Strontium Titanate and C omponent O xides D eposition and G rowth In the semiconductor industry thin film deposition is central in device fabrication.34 Two key classes of thin film deposition are chemical vapor deposition (CVD) and physical vapor deposition (PVD). In CVD, reactive precursors are introduced to the subst rate surface where they undergo a chemical reaction forming the thin film. CVD can be characterized based on the type of chemical reactions by which the thin film is created and by the operating conditions. A few CVD methods include: aerosol assisted CVD ( precursors are atomized and transported to the substrate in a liquid or gas aerosol )35, metal organic chemical vapor deposition (MOCVD), (utilizing organometallic precursors )36, and ultra -high vacuum chemical vapor deposition (UHV CVD) ; the benefits of UHV include the ability to clean and characterize substrates prior to deposition as well as perform in situ characterization along with the reduction of impuritie s .37 The main benefits of most CVD methods ar e large area coverage ability to coat complex geometries, high deposition rates and epitaxial growt h ; the main limitations are high start up costs and toxicity or volatile nature of precursors and/or by products .38 Physical vapor deposition utilizes thermally activated particles which bombard the surface and condense. These methods are categorized based on the method of vaporization of the target. One class of PVD, sputter deposition, removes the target material by bombarding the target surface and ballistically removing material. It has the advantage of low substrate temperature regardless of the melting temperature of the target material and some disadvantages are the lack of atomic layer control and the incorporation of impurities in the film from the sputtering gasses. STO and component oxides have been successfully grown using excimer laser sputtering,39 magnetron sputtering40 42 and ion beam sputtering.43 As opposed to sputter techniques, the second class includes methods where the target material is evaporated instead of ballistically removed. Two main types of evaporation PVD

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18 meth ods used to deposit STO and its component oxides are pulsed laser deposition (PLD) and molecular beam epitaxy (MBE). PLD is a widely researched method for homogeneous thin film fabrication and is an attractive technique to produce in situ stoichiometric fe rroelectric thin films.5, 44 Deposition is accomplished by focusing short, high-energy laser pu lses onto a stoichiometric target in a vacuum chamber. The energy from the laser is transferred to the pa rticles and evaporation occurs creating a plume t hat contains species ranging from atoms and molecules to clusters having a range in size from 0.1 to 50 m.45, 46 Several advantages of using PLD when growth parameters have been optimized, include reproducibility47, single -phase purity and accurate stoichiometry48. MBE is also viable technique to deposit thin films. This method has the ability to deposit monolayers by utilizing elemental sources, allowing for high compositional accuracy of the deposited thin film ; these factors mak e it an attractive method for the design of complex systems.49 The disadvantages of both PLD and MBE are the difficulty in large -scale d eposition. Experimentally SrO thin films ha ve been successfully deposited on hydrogenterminated Si (100) for use as a buffer layer between Si and STO.25Also, o ne atomic layer of SrO has been deposited on TiO2terminated STO by MBE in order to change the surface termination50 and thereby eliminate precipitates during the deposition of YBCO.6 In addition, growth dynamics studies of epitaxial SrO films grown on STO (001) substrates carried out by Takahashi et al. indicated that after deposition of the first SrO layer, subsequent layer -by -laye r growth of SrO occurred with the atoms occupying positions consistent with bulk SrO.51 In situ reflection high-energy electron diffraction (RHEED) measurements during laser MBE of TiO2 films on STO (001) substrates performed by Ong and coworkers indicated various growth modes of TiO2 films.52 Well ordered and atomically flat anatase thin films have been

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19 successfully grown in a layer bylayer fashion on Nb -doped STO using oxygen plasma assisted molecular beam epitaxy at a growth ra te of approximately 0.03 /s.53 A study on the sputter deposition of TiO2 thin films discussed the presence of TiO2 clusters in the gaseous phase given that the separation distance between the target material and the substrate was larger than the mean free path of the sputtered species (which is the average distance a particle travels before colliding with another particle). This gives the atomic species and small molecules in the gas phase time to combine and form clusters.54 The size of the clusters and subsequently deposited film were shown to be dependent on the target to substrate distance. In particular, a larger distance (250 mm) promoted the growth of larger cluste rs (3 nm in diameter) and yielded an amorphous type TiO2 thin film whereas the shorter distance (50 mm) allowed only smaller clusters (less than 2 nm diameter) to form producing a crystalline film. This illustrates the impact of the type and size of the in cident species on the morphology of the resulting films. In addition to examining the deposition of the components of STO, numerous experimental studies have been conducted to better understand STO thin film growth under varying conditions. For example, Kh odan and coworkers55 investigate d the PLD of epitaxial STO films. They observed the formation of smooth multilayer films at temperatures above 873 K. Additionally, they concluded that, although annealing in an oxygen environment at 1373 K improves the functional properties of the STO fil ms significantly, only films deposited at pressures below 103 Pa exhibited low dielectric losses and high agility. Similar results were obtained by Ohtomo and Hwang56 who examined the dynamics of STO homoepitaxial films grown by PLD. They found that by controlling the oxygen partial pressure and growth temperature, two-dimensional layer -bylayer growth could be achieved.

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20 Computational S tudies of D eposition and G rowth Molecula r dynamics (MD) simulations are a powerful way to predict the deposition characteristics of STO and its component oxide s. MD allows one to view the atomic level mechanisms involved in the initial stages of deposition and will be discussed in detail in Chap ter 2 For example, MD simulations of epitaxial SrO film growth on STO indicated that only one layer of SrO can be deposited on TiO2terminated STO before a change in structure occurs.57 Such a change in structure corresponds to t he continuation of the SrO TiO2 stacking sequence found in STO. The effect of temperature and termination on SrO migration was also investigated, it was found that the higher the temperature, the more mobile the deposited particles on the SrO terminate d surface, and that SrO is not mobile on the TiO2-terminated substrate. TiO2 thin film deposition on Fe2O3, Al2O3, and SiO2 has been simulated using MD and predicted 3D island formation with a mixture of amorphous and polycrystalline structures within the 3 nm deposited film .58 MD simulations have also been carried out to elucidate the mechanisms involved during deposition of Ti4+, TiO2+, TiO2, and Sr4Ti4O12 on STO.59 When simulating the deposition of Ti4+, TiO2+, TiO2, the study includes a correspo nding vacancy on the substrate. This vacancy is then shown to be filled in by the incident species but the deposition of several TiO2 units was not investigated. In the same study, w hen looking into the homoepitaxial growth of STO, a 2unit STO cluster i s used. This cluster, however, has the unit cell geometry of bulk STO, thereby building the STO structure into the deposited film. Cluster deposition has been extensively simulated for metals60 63, investigating the impact of size, from 1 to hundre ds of thousands of atoms, and incident kinetic energy, from meV/cluster to MeV/cluster.64 Jrvi et al. utilized MD to study the effect of temperature on the maximum cluster size able to exhibit complete alignment between the cluster and the substrate (epitaxy).63 Small metallic clusters ( 0 atoms/cluster) are found to become epitaxial from the energy

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21 released by initial impact due to melting and resolidification. Larger clusters (100 1000 atoms/cluster) require additional thermal energy to enable the diffusion of twin dislocations within th e clusters which was found to be the mechanism responsible for attaining epitaxy. While MD simulations are able to predict the initial stages of deposition, including nonequilibrium structures created, they have two significant limitations: the time and length -scale s are many orders of magnitude smaller than those that are important in most experiment s To overcome this limitation other computational methods are used to determine the equilibrium structure of the deposited film, including Monte Carlo65 (MC), hybrid approaches66, 67, kinetic MC68, and accelerated dynamics .69 For example, STO thin film growth was investigated using the MC technique, a stochast ic method where SrO, TiO2 and STO units are randomly placed on an STO lattice and allowed to diffuse according to an Arrhenius relationship between hopping rate and temperature.70 While these simulations include an experimentally obtained diffusion barrier, as opposed to MD simulations, these results do not incorpo rate the physics of atomic interactions. The growth of the film is determined using statistical probabilities and therefore is insufficient to describe the mechanisms involved at the atomic scale during the initial stages of deposition. Hybrid approaches to study film growth are comprised of utilizing the benefits of MD during the initial deposition event and MC during the relaxation between deposition events.71 In this approach, an atom is chosen randomly and displaced by a distance, (where is the random number between 1 and 1 ). Next, the change in energy ( is ) it is accepted, if k T), where k is the Boltzman n constant and T is the temperature.72 This approach allows the non-equilibrium

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22 dynamics of the deposition event to be described adequately using MD while extending the time scale simulated using the stochastic, MC meth od. Kinetic Monte Carlo (kMC) is another simulation technique frequently utilized to model deposition and growth of thin films simulating deposition methods such as PLD7375 and MBE,76 the general process includes creating a list possible transition events then choosing an event based on a probability proportional to its rate. The list is then modified a ccording to the current configuration and the process continues.77 kMC parameters are based on rate con stants and sticking coefficients obtained from MD and experiment.78, 79 Such simulated deposition involves havin g a priori knowledge of the possible kinetic events and rate constants which could occur,80 this is one of the main drawbacks of kMC. Unless a mechanism is listed as a possible event it will not be predicted using kMC, this limitation was made evident after the discovery of the replacement (commonly known as exchange) mechanism for Al surface diffusion on Al (100) instead of the hopping mechanism previously believed to dominate.81 Therefore, kMC methods with out prior knowledge of the exchange mechanism would not predict the correct dynamics of diffusion.68 This has led to the development of accelerated MD simulations where there is no need for prior knowledge of possible events. Accelerated dynamics methods, in principle, increase the rate of transitions while accurately describing the physics of the system One such method, hyperdynamics, is based on incorporating a bias potential to the potential energy function in regions away from the potential dividing surfaces (or saddles) between two states, escalating the rate of transitions from one potential minima to another and thereby extending the simulated time scale.82 This method requires no pr evious knowledge of transition states but the development and implementation of the bias is nontrivial and many other studies have made modifications to reduce the

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23 complexity.83, 84 Another accelerat ed method is parallel replica dynamics that is similar, in principle, to parallel computing where the atoms of a system are spatially distributed between processers. In this technique the system is replicated and MD is performed simultaneously on each syst em therefore increasing the time -scale studied proportional to the number of processers used.69, 85 A third accelerated method is temperature accelerated dynamics (TAD) and is based on performing MD at high temperatures thereby increasing the rates of transitions while keeping the lower temperature dynamics of the system and will be discussed in detail in Chapter 2. Growth: Effects of Mobility and Diffusion Surface mobility of incident species have an impact on the growth mode and quality of film formed. Lower mobility, sometimes associated with lower temperatures, leads to the occurrence of defects in deposited films, while higher temperatures yield defect free smooth films due to the opposite trends in mobility.86 Reflection high -energy elect ron diffraction (RHEED) is commonly used, in -situ to monitor the growth -modes of deposited thin films. The period of RHEED oscillations corresponds to the time needed to go from a smooth surface to a rough surface and back to the smooth surface which indi cates the growth of one monolayer, this is depicted along with corresponding surface coverage in Figure 1 4.2 These provide a wealth of information enabling one to observe growth mode transitions and calculate surface diffusion parameters.87 kMC simulations have also been developed to simulate RHEED intensities to gain a better understanding of the surface morphology evolution.88, 89 Three main types of film growth are Frank -van der Merwe (FM), Stranski -Krastanov (SK), and Volmer -Weber (VW) along with two types of limited diffusion growth modes, polycrystalline and columnar, these are illustrated in Figure 1 5.90 FM is associated with 2D layer bylayer growth, SK is described as layer -bylayer with island growth and VW is characterized by 3D island growth. One RHEED oscillation corresponds to one u nit cell thereby

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24 indicating layer -bylayer growth. Three of the major processes occurring during the initial states of growth are adatom diffusion, nucleation, and interlayer mass transport of which adatom surface diffusion is considered the most important .91 Figure 1 4 RHEED oscillations and the corresponding surface coverage.2 Figure 1 5 Schematic illustration of structures produced by FW, S, VW, polycrystalline and columnar growth.90 Multiple studies have investigated the different growth modes exhibited by STO deposition. Atomic force microscopy (AFM) images of STO thin films exhibiting each growth mode are shown in Figure 1 6.92 One study of the impact of substrate temperature on growth mode during the deposition of STO using PLD93 shows that island growth prevails for low

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25 temperature deposition due to the decreased mobility of the incoming species this is indica ted by a lack of clear RHEED oscillations. Temperatures between 560 and 770 C produce layer -bylayer growth and step-flow growth occurs at temperatures above 800 C. Step-flow growth is characterized by the recovery of the RHEED intensity after deposition has ceased. In this study, the time required for recovery is approximately 7 seconds illustrating the time -scale needed for complete relaxation of the deposited films. Step-flow growth has been shown to produce STO homoepitaxial films which are indistingu ishable from the substrate and therefore yield higher quality films.94 One study of STO homoepitaxial deposition found columnar structures which were attributed to diffusion limited mobility.95 This illustrates the importance of surface diffusion in thin film grow th therefore understanding the mechanisms involved on the atomic level are essential. In this work, MD simulations are used to examine the deposition of STO, SrO and TiO2 on the (100) surface of STO at incident energies of 0.1, 0.5 and 1.0 eV/atom. Of par ticular interest is the resulting morphology of thin films after deposition. Under consideration are the effects of surface termination (SrO vs. TiO2), incident energy of the deposited particles, and beam composition on the morphology and growth of STO, Sr O and TiO2 thin films. Included in this work is the deposition of SrO dimers, TiO2 trimers as well as stoichiometric STO clusters. To better correlate STO thin film growth with experiment, we relax the clusters in vacuum where the resulting structure has little to no comparison to bulk STO. Temperature accelerated dynamics (TAD) is then used to extend the time -scale reached by the annealing of the deposited STO thin films. TAD is also utilized to understand the diffusion mechanisms involved with adatom and ad -dimer surface diffusion on (100) STO. The diffusion barriers obtained are able to explain the differing growth modes observed.

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26 Figure 1 6 AFM images of SrTiO3 thin films illustrating different growth modes observed. A) lay er bylayer growth mode, B) Stranski -Krastanov (S.K.) growth mode (layer bylayer plus 3D island growth) and C) 3D island growth mode.92

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27 CHAPTER 2 COMPUTATIONAL METHODS Molecular Dynamics (MD) has progressed by leaps and bounds since it was introduced in 1957 where Alder and Wainwright stated The [MD] met hod consists of solving exactly (to the number of significant figures carried) the simultaneous classical equations of motion of several hundred particles by means of fast electronic computers.96 Their study reported that large systems of 108, 256, and 500 particles took one hour for 2000, 1000, and 500 collisions, respectively, to occur using the first commercial computer, the UNIVersal Automatic Computer (UNIVAC ).96 This study is archaic by todays standards where 5 billion particles have been simulated by Roth on a CRAY T3E 1200.97 Molecular D ynamics The main goal for classical MD simulation s is to evolve a system of interacting atoms through time while describing the atoms in a classical manner .98 It is a computer simulation technique w hich numerically solves Newtons equations of motion and, for this study, can be outline d as illustrated in Figure 2 199: Figure 2 1 Schematic of simulation steps This method allows a systems time dependent properties to be determined, thus enabling the study of complex, dynamic processes such as deposition. Here, Newtons equations of

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28 motion, ma F are integrated using the G ear 5th order predictor -corrector algorithm with a time t, of 1 fs. The time step is a pivotal parameter in MD simulations. It must be small enough so as to encompass the phonon relaxation process of the system on an atomic scale, but large enough to be computationally efficient. Periodic Boundary Conditions The system considered consists of two components, an STO substrate and a beam of incident particles. The free surface for deposition is simulated by adding vacuum along the depositing direction <100>. T o minimize substrate size effects and to simulate an infinite surface, periodic boundary conditions100 (PBCs) are imposed along the <010> and <001> directions. The system of interest is placed in a central cell which is replicated in all directions forming an infinite lattice. If a particle leaves its primitive cell, it is translated to the opposite face thereby keeping the number of atoms constant. A schematic of two -dimensional PBCs is shown in Figure 2 2 where the primitive cell is shaded. The central parti cle within the circle interacts with all other particles within the cutoff Rc, chosen based on parameterization of the potential, all other interactions are neglected. The system size, L, must be at least twice Rc to ensure a particle does not interact wi th its replicated image. Figure 2 2 Schematic of periodic boundary conditions .101

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29 Velocity Rescaling Thermostat Deposition involves the transfer of energy from the incident particles to the deposition site. This transferred kinetic energy can cause undesirable te mperature increases in the system over time. For this reason a thermostat was utilized to simulate energy dissipation and to better model experimental conditions, where energy dissipation occurs through phonon vibrations over distances larger than those available in the simulation system. The thermostat involves rescaling the velocities of the atoms outside the region in which deposition takes place so as to maintain the desired temperature in this region. The arrangement of thermostat atoms relative to ac tive atoms, i.e., atoms which are allowed to evolve in time with no constraints, is shown schematically in Figure 2 3 The lateral dimensions of the unit cell are fixed to those determined for STO described by this potential at the simulation temperature. Figure 2 3 STO substrate illustrating thermostat and active regions

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30 In MD, temperature is defined in terms of the kinetic energy of the system, (Eq uation 2 1) = 1 2 2 = 1 = 3 2 (2 1) Here, mi and vi ar e the mass and velocity, respectively, of atom I, N is the total number of atoms in the system, kB is the Boltzmann constant Temperature is determined by rearranging equation (2 1) as follows: = 1 3 2 = 1 (2 2) The desired temperature is maintained by multiplying the velocity of the thermostated atoms by Gear 5th Order Predictor-Corrector In this work Newtons equations of motion are integrated utilizing the Gear 5th order predic tor -corrector algorithm. This integrator propagates particle positions and velocities from time, t, to a time, t t by utilizing a finite difference scheme.97 The order of the predictor corrector algorithm corresponds to the order of the Taylor expansion used to integrate the equations of motion. The higher the order, the less energy fluctuation there is in the system ; this results in higher accuracy for the predictor. By this integration, positions and accelerations are predicted to allow the time evolution of the system to be observed. The integration scheme begins with the prediction of positions, xp, velocities vp, and accelerations, ap, at = + from the initial positions, x (t) and velocities v (t) (Eq uation 2 3)101: ( + ) = ( ) + ( ) + 1 2 ( ) 2 + 1 3 3 3 ( ) 3 + 1 4 4 4 ( ) 4 + 1 5 5 5 ( ) 5 (2 3)

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31 = ( ) + ( ) + 1 2 ( ) 2 + 1 3 ( ) 3 = ( ) + ( ) +1 2 ( ) = ( ) + ( ) w here, ( ) = ( ) ( ) = 2 2 ( ) ( ) = 3 3 ( ) ( ) = 4 4 ( ) ( ) = 5 5 ( ) The second step is the calculation of the force acting on each atom by calculating the potential function at the predicted positions giving the correct acceleration. After evaluating the forces of the particles at the predicted positions, accelerations are computed and compared to the predicted acceleration. The error (Eq uation 2 4) in the predicted values is proportional to the difference between the pre dicted and correct acceleration. ( + ) = ( + ) ( + ) (2 4) The corrections imposed are proportional to this error. The final step is the correction of the predicted positions and velocities101 (Eq uation 2 5): ( + ) = ( + ) + 3 2 16 ( + ) ( + ) = ( + ) +251 360 ( + ) ( + ) = ( + ) + 11 18 ( + ) ( + ) = ( + ) + 1 6 2 ( + ) ( + ) = ( + ) + 1 60 3 ( + ) (2 5)

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32 Interatomic Potential Particles within the system interact with each other through interatomic interactions and forces. Such forces are obtained by using a n expression that describes the potential energy between and among atoms (the potential) and are the gradient of the potential with respect to atomic displacements .100 In order to validate a model, it must be compared to experimental data and crystal properti es. There are parameters within the potential that are fitted to experimental data; this is the necessary link between simulation and experimentation. The interatomic potentials used here take the traditional form for ionic materials of long ranged elect rostatic interactions plus a short ranged empirical interaction term. Short range forces can be described as van der Waals and repulsive interactions resulting from electron-cloud overlap. Long range forces dominate when particles are beyond a predetermine d cutoff They can be further subdivided into electrostatic, induction and dispersion contributions. The first of which is due to the permanent charge distribution and the other two encompass fluctuation charge contributions.102 In this work these forces are represented by a Coulombic term. In ionic systems, short ranged interactions are commonly modeled using the Buckingham potential.103 The potential energy is the sum of both the long and short range contributions. After the interactions in the STO system are parameterized, it i s possible to generate a list of energies at different separation distances which can consequently be used during the simulation increasing the computational efficiency. Buckingham potential The Buckingham (Eq uation 2 6) potential is comprised of two par ts, a short -ranged repulsive term and an attractive term.104 = 6 (2 6)

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33 Here, rij is the distance between any pair of atoms of species i and j. The first term corresponds to the repulsive interactions resulting from electron cloud overlap and the second term corresponds to attractive van der Waals interactions.103 The potential pa rameters, Aijij and Cij, are related to the ionic stiffness, radii, and strength of the van der Waals interactions between ions. Several parameter sets were tested; the potential parameters from Sekiguchi et al .105 (see Table 2 1) were chosen as the most approp riate for the system of interest. Of particular importance for these simulations, within this partial charge model the SrO and TiO2 formula units are individually charge neutral; thus the deposited particles and substrate are at all times charge neutral. P ertinent material properties calculated with this potential are compared to experimental values and previous computational calculations (see Tables 2 -2 and 2 3). The current potential produces bulk lattice parameters which are in good agreement with exper imental results; the elastic properties, however, show a rather large deviation from experimental results in the case of rutile and anatase. These differences are a consequence of using a potential developed for STO as opposed to a potential parameterized specifically for TiO2. It is also noted that this potential predicts the bulk moduli of SrO fairly well. Coulomb potential Long range forces can be further subdivided into electrostatic, induction and dispersion contributions. The first of which is due to the permanent charge distribution and the other two encompass fluctuation charge contributions.102 In this study these forces are represented by a Coulombic term, (Eq uation 2 7). = 1 2 = 1 = 1 (2 7) Here, qi and qj correspond the charges on atoms i and j, respectively, rij is the distance between them, and N is the total number of atoms.

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34 It is wellknown that the pairwise r1 sum in the Coulomb potential is conditionally converegent,100 meaning in order for the potential to converge to zero there must be an infinite value for rij. This is not possible for the simulated system sizes, thus the potential requires special treatment. Traditionally the Ewald summation106 technique is used to carry out this sum; it is accurate but scales, at best, as O(N3/2), where N is the number of atoms in the system. For this reason, the charged neutralized direct summation technique107 is used (Eq uation 2 8). = 1 2 ( ) < = 1 (2 8) T he first term is the 1/r pairwise potential in Eq uation 2 7 and the second term is the Coulomb interaction of ion i i(Rc) is the net charge within the cutoff sphere (Rc) of ion i ; here Rc is chosen to be 10.148 This approach creates equ al and opposite counter charges for each ion within this cutoff, thereby allowing the spherical truncation to be charged neutralized. The total potential energy is the sum of both the longand short range contributions; the forces used to predict the atom ic trajectory are simply the first derivative of the potential energy. To improve convergence, an additional damping term is added in the manner described by Wolf et al.107 Table 2 1 Parameters used in the Buckingham and Coulombic potentials obtained from Sekiguchi et al. 105 Inte raction A (eV) ) C (eV*6) Sr 1.331+ O 1.331 139621.961934 0.1963 2.33222 Ti2.662+ O1.33118476.946631 0.1963 0.0 O1.331-O1.33121943.289277 0.2226 4.14616

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35 Table 2 2 Comparison of calculated and experimental structure and elastic properties for SrTiO3. Calculated Experimental Error Lattice Parameter STO () 3.918 3.905 0.3% C 11 (GPa) 405.18 335 21% C 12 (GPa) 131.1 105 25% C 44 (GPa) 131.1 127 3% Table 2 3 Comparison of the results of current calculations, experimental data, and previous calculations for the structural properties of anatase and rutile TiO2, and rocksalt SrO. Where GULP is the General Utility Lattice Program a Ref. 108 b Ref. 109 c Ref. 110 d Ref 111 e Ref. 112 f Ref. 113 g Ref. 114 h Ref. 115 Anatase TiO 2 Calculated (this work) Calculated Experiment b Lattice Parameter () 9.779 9.063 (GULP) a 9.514 3.783 3.85 (GULP) a 3.786 Bulk(GPa) 231 176 (GULP) a 36020 Cohesive energy (eV/TiO 2 ) 56.13 21.54 (PBE) d 24.46 (LDA) d Rutile TiO 2 Calculated (this work) Calculated Experiment b Lattice Parameter () 4.528 4.587(GULP) a 4.593 3.038 2.958(GULP) a 2.958 Bulk(GPa) 298 229(GULP) a 2117 Cohesive energy (eV/TiO 2 ) 44.34 21.44 (PBE) d 24.44 (LDA)d 20.27 (BLYP)d 19.9 d Rocksalt SrO Calculated (this work) Calculated Experiment c,f Lattice Parameter () 5.257 5.19 (GGA) e 5.16 Bulk(GPa) 96 85.9 (GGA) e 91 Cohesive energy (eV/SrO) 12.54 11.80 (LDA) g 10.45 h

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36 Temperature A ccelerated D ynamics Thin film growth is mainly comprised of phenomena occurring in two time scale regimes. The first enco mpasses the initial kinetic behavior of the depositing particles: collision and short term relaxation, which occurs in the ps time range. The second involves the subsequent relaxation and diffusion of the deposited particles between deposition events, this happens on a time -scale of s -s.71 Convent ional MD simulations are limited by a time -scale of ns therefore restricting the comprehensive modeling of thin film growth. Recently, there has been considerable attention to accelerated MD methods which have been able to extend the time -scale studied to orders -of -magnitude larger than traditional MD.116 The basic event examined is the transition from one state to another connecte d by a minimum energy pathway (MEP) as illustrated in Figure 2 4 This pathway contains a transition state at a maximum along the MEP, also known as a saddle configuration. Temperature accelerated dynamics (TAD) enlists two main assumptions: events of inte rest are considered infrequent or rare and harmonic transition state theory is applicable for the system of interest. This method takes advantage of accelerated transitions at higher temperatures in order to accelerate the pace of system evolution, yet s till preserving the correct order of transitions at the temperature of interest. This is done by filtering the transitions to only allow those that would occur at the actual temperature of interest.117 Infrequent event systems are characterized by well defined transitions between states occurring on a time -scale of se veral vibrational periods. While the actual transition event occurs rapidly, the time between events can be orders of magnitude longer .118 Since h armonic tran sition state theory is also assumed (no correlated events) an Arrhenius expression for the rate constant going from state A to B, kA B (Eq uation 2 9) is obtained.117

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37 = 0 exp ( 1 ) (2 9) where Ea, is the energy barrier between the saddle configuration and the minimum (State A) and v0 is a pre -exponential factor calculated using the Vineyard formula ( Equation 2 10).119 0 = 3 = 1 / 3 1 = 1 (2 10) Here, {vi} is the set of vibrational frequencies at the minimum (State A) and {vj} are the set of real -frequencies at the saddle point configuration.120 This relationship is a consequence of assuming HTST, that the frequencies of both minimum and saddle configurations can be approximated by a harmonic oscillator. It is a measure of the width of the harmonic oscillators at the saddle versus the minimum. Figure 2 4 Schematic of transition state theory TAD utilizes basin -constrained MD, confining the trajectory to a particular potential energy basin. If the particle attempts to leave the basin it is reflected back to the original state and the time of the attempted escape is documented creating a list of waiting times of attempted escapes.117 At each state the syst em is evolved at Thigh until a transition (or escape) is detected noting the waiting times and the saddle point, corresponding to the energy maximum of the MEP from state A to B, is found.69 The nudged elastic band method was used to find the MEPs

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38 between known initial and final states by first optimizing the initial and final state and then systematically creating and optimizing structures along the reaction pathway. Using the energy barrier between the initial state and saddle configuration, t he waiting times at Thigh (thigh), are then extrapolated to corresponding waiting times a t Tlow (the temperature of interest), (tlow) given by (Equation 2 1 1 ). = 1 1 (2 11) This procedure is illustrated in Figure 2 5 The simulation continues following the dashed line to the first detected transition at thigh, denoted by the red star. This time is then extrapolated along the line with a slope of Ea (for said event) into a corresponding tlow, denoted by the black star. An additional assumption that there exists a minimum pre -exponential fact or, vmin, enables one to impose a stopping time, thigh,stop, where the probability that a shorter tlow would replace the shortest 69 Both vmin and are input parameter s on the order of 1012 and 0.01 respectively This continues until thigh,stop, (Eq uation 2 1 2 ), is reached (indicated by the open circle) and the event with the shortest time at the low temperature is accepted, blue circle, and the process repeats with the new position. ln ( 1 ) ln ( 1 ) / (2 12)

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39 Figure 2 5 Schematic illustration of the extrapolation of Thigh time to Tlow time .121

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40 Figure 2 6 Flowchart illustrating the TAD procedure

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41 CHAPTER 3 STRONTIUM OXIDE AND TITANIUM DIOXIDE THIN FILM DEPOSITION ON STRONTIUM TITANATE To understand the deposition of STO, it is first beneficial to evaluate the growth of the component oxides, SrO and TiO2. By understanding the processes which dominate during the growth of these thin films, one can better understand the reasoning behind the morphology and growth of STO thin films. This w ork has been published in Surface Science.122 Simulation Set up The system considered consists of two components, an STO s ubstrate and a beam of incident particles. To model the substrate, a 16 x 16 x 16 cubic STO lattice is primarily used; this contains a total of 20,480 atoms. The free surface for deposition is simulated by adding vacuum along the depositing direction <100> Before deposition begins, the substrate is equilibrated until minimum energy fluctuations are observed (corresponding to 100 ps) at the desired temperature of 973 K, which has been shown experimentally to produce crystalline films.123 TiO2 deposition was also carried out on an expanded substrate with dimensions of 30 x 30 x 16 to evaluate the impact of surface size. To model deposition, each incident particle is assigned a velocity directly towards the surface along the [100] direction that corresponds to a kinetic energy of 0.1, 0.5, or 1.0 eV/atom. The particles in the beam are initially given random orientations an d random positions over the substrate. Along the deposition direction they are approximately 30 apart, which corresponds to roughly 3 ps between each deposition event. This interval between deposition events allows the structure of the deposited film to, at least partially, equilibrate before the next particle is deposited, and gives the thermostat time to dissipate the excess energy. Each particle is deposited individually in a manner similar to that in MBE which, as mentioned in Chapter 1, is a widely u sed method to deposit STO. After depositing 60 incident particles (of either SrO or TiO2) the

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42 system is annealed at an elevated temperature of 1100 K for approximately 50 ps to allow the films to equilibrate. Although the energies of individual deposited particles are consistent with experimental values, the short time scales available to MD simulation require that the interval between deposition events is much shorter than in experiment. As a result the total particle flux, 1 X 1011 particles/sec, is much higher than in experiment. Thus, while the deposited structures analyzed are in equilibrium on the timescales of tens of picoseconds, any experimental structural equilibrations associated with longer timescales are absent in the simulations. Results Stro ntium Oxide Deposition A typical deposited SrO film is shown in Figure 3 1. Figures 3 1 A B and C of the three partially grown layers show the extremely high level of order within each layer. The quality of the grown surface and the absence of any ions in any layer above the third indicate that there must be a significant amount of surface transport taking place. This is also a strong indication that the system has been able to reach equilibrium despite the high flux and short equilibration time. To quanti tatively analyze the structure of the SrO deposited films, a planar pair distribution function (PPDF) is determined for each deposited layer after a high temperature annealing (2000 K) and subsequent quench to remove thermal fluctuations. The PPDF is then compared with the corresponding PPDF for SrO layers in the bulk STO and in the bulk SrO. The analysis shown in Figures 3 2 and 33 shows distribution of distances of the oxygen neighbors of the strontium within each SrO layer. The first peak (between 2.5 a nd 3.5 ) is the nearest neighbors, the second peak (between 5.5 and 6.0 ) is the second neighbor peak. Previous computational work has shown that only one epitaxial SrO layer can be deposited on TiO2terminated STO before the structural order of the SrO film breaks down.57

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43 Figure 3 1 SrO layers that are deposited with an incident energy of 1.0 eV/atom on TiO2terminated STO A ) first deposited layer B) second deposited layer C ) third d eposited layer D ) side view. As seen in Figure 3 2, we find that the first deposited layer (denoted by the number 1) on a TiO2terminated STO substrate displays Sr O distances that are almost the same as in STO; however, even for this layer the first nearest neighbor peak contains a smaller peak at the distance corresponding to the Sr -O distance in rocksalt. The second deposited layer nearest neighbor peaks (denoted 2) is shifted towards the rocksalt peaks and the third deposited layer (denoted 3) shif ts even more. This shift is illustrated by the arrow, and is consistent with Kubos earlier simulation results.57 Figure 3 3 illustrates the effect of surface termination on the structure of the first deposited layer. In contrast to SrO on the TiO2 surface (Peak A, which is the same as Peak 1 in Figure 32), the first SrO layer grown on the SrO terminated surface (Peak B) exhibits a structure in between that of the SrO layer in STO and the SrO layer in bulk rocksalt SrO.

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44 Figure 3 2 Sr O PPDF for SrO layers on STO. As the deposited layers increase, the nearest neighbor distances approach that of bulk SrO. Figure 3 3 Sr O PPDF showing an obvious correlation between the STO te rmination layer and SrO deposited film structure. Crystallographically, the second SrO layer grown on TiO2terminated STO (shown in red) should be identical to the first SrO layer grown on the SrO -terminated STO (shown in black) as Figure 3 4 shows. The re duction in peak height is due to the smaller number of Sr atoms present

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45 in the second SrO layer grown on TiO2terminated compared to the first layer deposited on the SrO termination. This again indicates that the kinetics of the system are rapid and that t he structures generated are in good thermal equilibrium. Figure 3 4 Sr O PPDF showing the second SrO layer grown on TiO2-terminated STO corresponding to the first SrO layer grown on the SrO -terminated STO. Titanium Dioxide Dep osition The corresponding simulations have been performed for the deposition of TiO2. As can be seen from Figure 3 5 the growth morphology for the TiO2 films is very different from the SrO films. In particular, there is no obvious ordering in the deposited layer and no obvious layering. Q uantitative structural analysis was also performed for the case of TiO2 deposition. The Ti O first nearest neighbor distances for rutile, anatase, and STO are very similar (see Table 3 1), and thus do not provide a sensitive probe of the structure. Indeed, as Figure 3 6 shows, the Ti O nearest neighbor distances are sharply p eaked around the expected values. In contrast, the second and third nearest Ti O neighbor distances are very different in the three structures (see Table 3 1 ), and thus should constitute a more sensitive probe of the crystallographic structure.

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46 The most obvious feature of the PDFs in Figure 3 6 is the strong broadening of the 2nd and 3rd neighbor peaks; indeed, for the TiO2-terminated surface, the third neighbor peak is almost completely washed out. These broad peaks are indicative of the absence of a we lldefined crystallographic TiO2 phase. Another feature in Figure 3 6 B is the emergence of a shoulder at approximately 3.7 ; this distance is similar to that of the second neighbor peak of bulk anatase. Table 3 1 Nearest neighbo r distances of Ti with O for bulk STO, rutile, and anatase Bulk Structure First Nearest Neighbor Distance(s) () Second Nearest Neighbor Distance(s) () Third Nearest Neighbor Distance(s) () STO 1.96 4.38 5.87 Rutile (TiO 2 ) 1.95, 1.99 3.49, 3.57 4.09 Anatase (TiO2) 1.94, 1.98 3.86 4.26, 4.28 Discussion For SrO depositio n, all incident energies examined (0.1, 0.5, and 1.0 eV/atom) and both terminations (SrO and TiO2) yield layer -bylayer growth with no clustering or agglomeration, as illustrated in Figure 3 1 In Figure 3 2 it is apparent that the termination of the substrate influences the structure of the deposited film There is no noticeable difference between the structures of the first deposited layer for the different incident energies for eit her termination These findings are consistent with the results found by Kubo et al .57 and with experiment .6, 50 The SrO deposition results in Frank -Van der Merwe growth where the SrO particles impact the substrate and subsequently move to prefer red adsorption sites and grow in a layer bylayer manner. The TiO2 deposited films also do not show a structural orde r dependence on incident energy or surface size, for the energies and size studied. The lack of variance with system size is an indication of the adequacy of the primary s ystem size of 16 x16. As with the SrO films, the TiO2 films illustrate a termination effect with the SrO termination yielding a longer ranged ordered film.

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47 Figure 3 5 TiO2 particle deposition: A ) C ) represent plots of Ti atom s in the deposited film showing variations of island height with incident energy: A ) 15.9 B) 13.6 and C) 11.5 for 0.1, 0.5 and 1.0 eV/atom, respectively for films deposited on SrO terminated STO D ) and E ) illustrate the top and side view morphology of the deposited film at 0.1 eV/atom on TiO2terminated STO which is characteristic of the morphology found in all the deposited films.

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48 Figure 3 6 Ti O PDF showing the influence of termination layer, A ) SrO termination and B) TiO2 termination, on film structure where the TiO2 film on SrO terminated substrate has a longer ranged order compared to the deposited film on the TiO2terminated substrate It has been experimentally demonstrated that TiO2 deposited on STO does not pr oduce smooth, layer -bylayer, ordered, single -crystalline films at high growth rates; indeed, the exact form of the deposited TiO2 varies with deposition conditions. For example, one study found

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49 rough surfaces and possible rutile inclusions present for ana tase TiO2 thin films deposited on STO substrates; in contrast, surfaces were smooth and films had higher crystallinity for deposition on LaAlO3 using MBE in pure ozone ambients.124 One study depositing TiO2 on STO using laser -MBE found a transition from island growth to 2D growth around 3 nm, illustrating a possible link between the current observations and experiment.125 Deposition rate is known to have a large effect on film quality.126 Layer -bylayer growth of anatase films were successfully grown on Nb -doped STO in an oxygen rich atmosphere using OPAMBE with a growth rate of 0.03 /sec 53. Comparing to the simulated growth rate of 1 X 1010 /s, this gives insight into the impact of deposition rate on the morphology and growth modes seen in this study. Additionally, it was found that the presence of islands is expected and consistently observed127 for anatase TiO2 grown on STO(001) using oxygen plasma assisted MBE. Furthermore, with higher growth rates, multiphase, polycrystalline films are created.127 Even though single crystalline anatase TiO2 films have been successfully grown on LaAlO3, approximately 2 nm thick amorphous regions were observed.127 Each of these experimental studies indicates a strong dependence on gro wth rate and therefore can indicate the importance of diffusion between deposition events; however, the experimental growth rates are considerably slower than are accessible to simulation. Moreover, the simulations show strong adhesion of the TiO2 particle s to the STO substrate on impact. The TiO2-deposited film morphology observed in the simulations corresponds to island build up which is analogous to the three -dimens ional, Volmer Weber growth mode, as illustrated in Figure 3 6 Although the films appear to have amorphous qualities, the structural analysis indicates some crystalline behavior due to the presence of additional neighbor peaks not seen in

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50 amorphous bulk phase PDF. The morphology of the deposited films is consistent with the growth of polycrys talline, multiphase films found in experiment.124 When the inciden t particles begin to interact with the substrate, both TiO2 and SrO particles reorient within the beam such that the oxygen atom faces the metal atom and vice versa However, following initial impact the particles behave in vastly different ways. The simulations indicate that Volmer Weber growth mode dominates because the deposited TiO2 particles move very little from their initial, random impact site. In contrast, the SrO particles are mobile enough following impact to produce layer -bylayer growth. In order to further analyze the differences between the growth modes of SrO and TiO2 thin films, the work of adhesion ( Wad) of each on STO were calculated. The work of adhesion is the energy required to separate a perfect thin film of material from the su bstrate, and is calculated by subtracting the total energy of the thin film on the substrate in vacuum from the total energies of the thin film in vacuum and substrate in vacuum: = + + (3 1) For this analysis it is sufficient to treat the film and film/substrate systems as ideal and only relax the system at 0 K. Due to statistical variations among the total energies of the relaxed systems, a linear fit of layer thickness versus energy is used to obtain Esubstrate and Efilm +substrate. The larger the Wad the more work needed to separate the film from the substrate. The calculated works of adhesion are given in Table 3 2. Not surprisingly, the results indicate that the anatase film adheres more strongly to STO than does rutile; this is due to the smaller lattice mismatch between anatase and the substrate (anatase ~3%, rutile ~15%) The SrO film has a higher Wad on the TiO2terminated substrate than on the SrO terminated substrate. It also has an overall lower Wad than anatase, which is an indicator of the higher wettability of TiO2

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51 with the STO substrate. However, the larger calculated cohesive energy associated with the TiO2 polymorphs, seen in Table 2 3 (Anatase: 56.13 eV/TiO2; Rutile: 44.34 eV/TiO2), compared to the cohesive energy of SrO (12.54 eV/SrO) is believed to be responsible for the three dimensional growth of deposited TiO2 particles. The difference in the interaction of a single TiO2 particle with the substrate and a single SrO par ticle with the substrate is calculated to be approximately 0.7 eV, with the TiO2 particle having a considerably stronger interaction of 2.5 eV. The energy barriers associated with particle motion on the substrate were also examined. TiO2 is predicted to have larger diffusion barriers with a minimum of 0.5 eV compared to SrO, which has a minimum diffusion barrier of 0.1eV. Table 3 2 Comparison of the works of adhesion of anatase TiO2, rutile TiO2, and rocksalt SrO, respectively, on STO. Anatase Rutile 3.09% Strain 4.97% Strain SrO Termination TiO2 Termination SrO Termination TiO2 Termination 6.71 J/m 2 4.93 J/m 2 0.750 J/m 2 1.10 J/m 2 Rocksalt 6.54% Strain 1.24% Strain SrO Termination TiO 2 Termination SrO Termination TiO 2 Termination 0.429 J/m2 1.33 J/m2 Dissociated 0.297 J/m2 To further elucidate the growth modes exhibited in SrO and TiO2 deposition, the mobility of a single SrO or TiO2 particle on both SrO and TiO2 terminations was calculated for several temperatures. Diffusion coefficients were calculated from the slope of the mean square displacement (MSD) curve shown in Figure 3 7. These coefficients are reported in Table 3 3, which confirms that the SrO molecule s are more mobile than the TiO2 particles. In fact, starting at a temperature of 1800 K, which is lower than the experimental melting temperature of 2353 K the SrO particle desorbs from the SrO -terminated STO. The data in Table 3 -3 coincide with the

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52 inter action energies of the two particles, with the higher interaction energies giving lower particle mobility. The higher mobility of the SrO is the origin of the layer -bylayer growth observed in the simulations for the SrO thin-film deposition while the lowe r mobility of the TiO2 particle explains the three -dimensional growth seen in TiO2 deposition. Conclusions In conclusion, MD simulations have been used to examine the growth of SrO and TiO2 thin films on STO substrates. The results indicate that SrO grows in a layer -by -layer manner that agrees well with experimental data. Structural analysis illustrates a shift from the perfect SrO layer structure found in STO to the SrO rocksalt planar structure as the number of deposited layers increase. Surface terminat ion has been shown to significantly correlate to the deposited film structural order, with the SrO film deposited on the TiO2 termination having a structure more closely resembling an SrO layer in STO. In contrast, TiO2 deposition yields three dimensional island/agglomerate growth at all incident energies for both STO terminations This type of growth is consistent with experimental results for films grown at high deposition rates. Mobility data, work of adhesion results, and particle interaction energies e lucidate the causes of the differing growth modes exhibited in SrO and TiO2 deposition. The stronger interaction of the TiO2 particle with the substrate explains the predicted three -dimensional growth, while the weaker interaction of the SrO particle permi ts the deposited SrO to move, upon deposition, about the substrate to preferable adsorption sites and grow in a layer -bylayer fashion.

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53 Table 3 3 Diffusion coefficients (D) of an SrO or TiO2 particle on each STO termination. U nits are D x 109 m2/s. SrO Particle TiO 2 Particle Temperature (K) TiO 2 Termination SrO Termination TiO 2 Termination SrO Termination 973 2.75 3.62 1.75 3.00 1100 3.50 3.70 1.75 2.75 1300 4.17 4.30 1.92 3.88 1500 4.58 5.25 2.42 4.00 1700 5.33 5.75 2.92 4.38 1800 6.50 Desorption 3.17 5.00 1900 6.63 3.58 5.13 2000 6.67 4.00 5.50 2100 7.13 4.00 5.60 2200 7.25 4.25 5.63 2300 7.75 4.25 6.50 2400 8.13 4.75 8.00 2500 8.00 5.75 6.50 Figure 3 7 Mean square displacement (MSD) curve for an SrO particle on TiO2 terminated STO at 973 K showing the adequate linearity needed to calculate the diffusion coefficient from the slope of the curve.

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54 CHAPTER 4 PARTICULATE DEPOSITION OF HOMOEPITAXIAL STRONTIUM TITANATE T HI N FILMS After gaining an understanding of the fundamental processes that occur during the deposition of STO component oxides, homoepitaxial STO thin films are deposited using SrO and TiO2 particles. Two deposition schemes are evaluated, depositing alternat ing particles in a single beam and depositing alternating monolayers. The following deposition simulations were performed under my supervision and guidance by an undergraduate I mentored, Cosima Boswell. Simulation Set up Similar to the previous study of SrO and TiO2 thin film deposition, STO deposition involves a substrate and beam of incident particles. The beam consists of a column of SrO and TiO2 particles that land randomly on the deposition area and are separated from each other by ~ 30 in the direc tion perpendicular to the surface, such that there is some time for equilibration between each impact event. To model deposition conditions with incident energies of 0.1, 0.5, or 1 .0 eV/atom, the particle s are assigned corresponding velocities normal to the substrate as with the previous study. Two types of beams are created to model different deposition schemes, one where SrO and TiO2 particles alternate within the beam (alternating particle deposition, APD) and one that consists of alternating monolayers of SrO and TiO2 (alternating monolayer deposition, AMD). Each case results in stoichiometric STO thin films. For APD, 60 particles are deposited, after which the system is equilibrated at 1100 K for 50 p s which is sufficient time for the substrate to dissipate excess kinetic energy. This process is then repeated until a total of 200 particles (100 SrO and 100 TiO2) are deposited on the substrate which would correspond to approximately 4 layers of STO if perfect layer -bylayer growth was achieved. Following deposition, the system temperature is increased to a final temperature of 2000 K ramping from 1000 K to 2000 K at 100 degree intervals This process takes

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5 5 approximately 340 ps including a hold at 2000 K for ~100 ps with subsequent quenching of the sys tem to remove thermal fluctuations, thereby simplifying the subsequent structural analysis. As with the APD AMD results in an overall 1:1 composition of SrO:TiO2. This is achieved by depositing alternating monolayers of SrO and TiO2. The first monolayers deposited consists of those that would continue the layering sequence of bulk STO, i.e., SrO particles are deposited on the TiO2terminated substrate and TiO2 particles are deposited on the SrO terminated substrate. After one monolayer is deposited, the fi lm is relaxed at 1100 K for 50 ps and then the second monolayer is deposited. This process is repeated until a total of 4 monolayer s are deposited (2 TiO2 monolayer s and 2 SrO monolayer s), and the system is equilibrated as described previously. Some simula tions were repeated to determine statistical differences in the simulated depositions. The structures of the films, as determined with pair distribution functions, are essentially identical for the repeated simulations. However, the difference in the catio n layering, described by the percentage of metal atoms (either Sr or Ti) located within each layer of each film, ranges from approximately 5 to 20% between the repeated simulations. Results Alternating Particle D eposition The simulations of APD were perfor med at multiple incident energies on both SrO and TiO2terminated STO substrates R epresentative films that were deposited at 0.1 eV/atom incident energy are shown in Figure 4 1, where the layers are rendered separated from one another to better illustrate their composition and ordering Visual inspection of these layers provides an initial indicatio n of the degree of ordering and cation layering of the deposited films.

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56 Figure 4 1 Alternating particle deposition exhibits cation layering. A ) SrO termination: (i) Side view and assigned layers of 200 species deposited wit h an incident energy of 0.1 eV/atom. (ii) Bottom up view of layers 1 5. B) TiO2 termination: (i) Side view and assigned layers of 200 species deposited with an incident energy of 0.1 eV/atom. (ii) Bottom up view of layers 1 3. As illustrated in F ig ure 4 1, the thin film on the SrO -terminated substrate consists of five layers, whereas although the film deposited onto the TiO2terminated substrate contains the same number of particles, it consists of only three layers This is attributed to the fact that the first layer on TiO2-terminated STO is comprised primarily of SrO particles that have higher mobility than TiO2 particles. This was discussed in the previous chapter. The SrO particles therefore

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57 spread over a relatively larger surface area, reducing the num ber of layers in the film deposited on the TiO2 termination but increasing the number of atoms within each layer. In contrast, the first layer on the SrO -terminated substrate is comprised of mainly TiO2 particles that are more likely to adhere to wherever they first impact the surface due to their higher interaction energy. Consequently, the resulting film will have more layers with fewer atoms within each layer relative to the film on the TiO2terminate d substrate. Figure 4 2 APD metal atom percentages. A ) Percentage of the identity of the alternating particles deposited onto SrO -terminated STO starting with layer 1 (Ti percentage) and ending with layer 4 (Sr percentage). B ) Percentage of the identity of the alternating particles deposited onto TiO2terminated STO starting with layer 1 (Sr percentage) and ending with layer 3 (Sr percentage). Cation layering is quantified by calculating the percentage of each type of metal ato m within each layer; these results for a representative case of 1.0 eV/atom incident energy are provided in Figure 4 2. In each case, the percentage of metal atoms (Sr or Ti) present in each layer is used as a measure of layer segregation within the film a nd the extent to which the atomic arrangement in the films matches that of bulk STO which consists of alternating planes of SrO and TiO2. In particular, Figure 4 2 A displays the percentages of cations expected in layers 1 4 (Ti Sr, Ti, and Sr, respectiv ely) for the film deposited on TiO2terminated STO. Figure 4 2 B

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58 displays the percentages of Sr Ti, and Sr atoms in layers 1 3, respectively, for films deposited on SrO terminated STO. The results indicate that the expected majority metal atom in each layer is consistent with what one would expect in bulk STO Figure 4 3 Pair distribution functions for alternating particle deposition. A) Sr O PDF for first layer APD film that shows the highest degree of order for the film deposited on TiO2terminated STO. B) Ti O PDF for first layer APD film that shows the film on SrO terminated STO yields an ordered structure similar to that of bulk STO. C) Sr O PDF for the second layer APD film that shows that neither termination yields or dering similar to that of bulk STO. D) TiO PDF for second layer APD film that shows that only the film deposited on TiO2terminated STO yields an ordered structure similar to that of bulk STO. To illustrate the degree of structural order within the layers in more detail, three dimensional plane -by-plane pair distribution functions (PDFs) are determined within each deposited layer. A Sr -O PDF, for example, shows the distances between each Sr atom in that

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59 layer and neighboring O atoms. Each PDF is then compared to the PDF of the corresponding layer in bulk STO. Figure 4 3 summarizes the Sr O and Ti O PDFs for both the first and second APD layers that were deposited with representative energies of 0.1 eV/atom. As illustrated in F igure 4 3 A layer 1 of the fil m deposited on the TiO2-terminated substrate shows close agreement with the Sr -O PDF of bulk STO, whereas layer 1 of the SrO terminated deposition (F igure 4 3 B ) matches the Ti O nearest neighbor peaks in bulk STO Resulting PDFs for layer 2 also show the expected trend. Here, the SrO terminated deposition (F igure 4 3 C) Sr -O PDF shows closer agreement to bul k STO, while in the TiO2terminated deposition the Ti O PDF (F igure 4 3 D ) correlates with the Ti O PDF of bulk STO These results are consistent with the natural layering sequence of STO and are an indication of layer -by -layer growth of the deposited films. However, closer agreement with the corresponding bulk PDFs is observed within the film deposited on the TiO2terminated substrate indicating superi or layer -by -layer growth on this termination. Alternating Monolayer D eposition Next, the simulations considered alternating monolayer deposition (AMD). AMD is analogous to molecular beam epitaxy (MBE) due to the similarities in incident species with MBE d epositing elemental species in a monolayer fashion. Representative films produced by AMD with incident energies of 1.0 eV/atom on SrO and TiO2terminated STO are shown in Figure 4 4 Similar to APD, the film deposited on the TiO2 termination covers a larg er surface area compared to the film on SrO termination. The percentages of m etal atom s in each layer are indicated in Figure 4 5 The metal atoms in l ayer 1 of the film deposited on SrO terminated STO, which is expected to consist of 100% Ti in the form of TiO2, is in fact 69% Ti Interestingly, l ayer 2 has a smaller majority (58%) of Sr atoms in the form of SrO T he metal atom percentages of the film deposited on the TiO2-

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60 terminated STO indicate that this film is substan tially more ordered. In particular, 89% of the metal atoms in the first layer are Sr in the form of SrO, while 100% of the metal atoms in the second layer are Ti in the form of TiO2. Figure 4 4 Alternating monolayer deposition. A) SrO terminated STO: i) Side view and assigned layers; ii) Bottom up views. B) TiO2terminated STO: i) Side view and assigned layers; ii) Bottom up view. Green Sr; Red O; Silver Ti

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61 PDFs of the first layer of each monolayer deposition are given in Figures 4 -6 A and 4 6 B. As expected, the first layer of the film deposited on the TiO2terminated substrate shows close agreement with the nearest neighbor Sr O peaks of bulk STO, whereas t he first layer of the SrO terminated deposition shows closer agreement with the Ti O nearest neighbor peaks. PDFs of layer 2 are given in Figures 4 6 C and 4 6 D Since the second layer of the film deposited on the TiO2 termination consists of only Ti and O atoms, no Sr O PDF is observed. However, it can be seen from Figure 4 6 D that this layer exhibits Ti -O peaks that closely correspond to the TiO2 layer in bulk STO. On the SrO -terminated substrate, the expected second layer is SrO; however as seen in Fig ure 4 6 C this layer does not yield an ordered structure. This once again indicates superior ordering of the depositions on the TiO2terminated substrate. Figure 4 5 Metal atom percentages for AMD films. A ) Percentage of the identity of alternating monolayers onto SrO terminated STO starting with layer 1 (Ti percentage). B) Percentage of the identity of alternating monolayers onto TiO2terminated STO starting with layer 1 (Sr percentage). Discussion The first layer of the APD films deposited on both substrate terminations shows a majority of the expected metal atoms and shows structural ordering that is illustrated in the PDFs. Layer 2 of the film deposited on the SrO termination shows a smaller percentage of the expected meta l

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62 atom (Sr) compared to the second layer on the TiO2 termination; this is attributed to the relatively poor quality of layer 1. The first layer deposited on the TiO2 termination is SrO; due to the aforementioned difference in mobility, this layer is more ordered than the first TiO2 layer deposited on the SrO termination. This is consistent with experimental evidence of the importance of substrate surface quality on the deposited films128: if the surface quality is low, the quality of the deposited film will also be low. Also, although some ordering is observed in all APD films, the depositions on the TiO2 termination exhibit superior ordering over SrO termination at all incident energies suggesting a higher quality film is more likely produced when depositing on a TiO2 termination due to the higher ordering of the first deposited layer Figure 4 6 PDFs for AMD films. A ) Sr O PDF for the first layer on TiO2t erminated STO. B ) Ti O PDF for the first layer on SrO -terminated STO C ) Sr O PDF for the second layer on TiO2terminated STO. D ) Ti O PDF for the second layer on TiO2terminated STO

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63 The first two l ayer s of the AMD film on SrO terminated STO consist of a majority of expected metal atoms indicating STO type cation layering Additionally, the pair distribution functions of the first two layers coincide with the bulk structure found in STO. However, s ubsequent layers show little correlation to bulk STO, possi bly due to limited diffusion of the atoms post deposition The influence of incident kinetic energy on the resulting APD films was also examined. The simulations indicate that the considered range of incident energy, 0.1, 0.5 and 1.0 eV/atom, has no signi ficant effect on the overall structure of the deposited films as evidenced by the PDFs. Additional simulations were performed on select incident energy depositions; these resulted in essentially identical PDFs but a 5 20% spread in the metal atom percentag es within each layer. It was also noted that the SrO termination exhibited a ~6% standard deviation in the metal atom percentage in layer one whereas TiO2 termination had a ~4% standard deviation. The overall film structure is qualitatively described as pa rtially ordered with significant variation in the cation ordering within the film being observed for alternating particle depositions. However, there is no evidence that incident energy controls segregation, which is mainly controlled by substrate terminat ion and whether alternating particles or alternating monolayers are deposited. The large percentages of expected metal atoms present in each layer of the film deposited on TiO2terminated STO and the high degree of order illustrated in the PDFs indicates that monolayer deposition on TiO2terminated substrates results in layer -bylayer growth within the first few deposited monolayers. Once again this is attributable to the higher mobility of the Sr O particles Overall, better agreement with bulk -like struc tures is found for AMD compared to APD. The difference in mobility is also a reason for the higher quality films produced when depositing in a monolayer fashion as opposed to an alternating particle method. Several

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64 experimental studies indicate the presence of islands at the initial stage of growth and the importance of diffusion and migration of the particles on the resultant films.95, 129 As previously mentioned, molecular dynamics sim ulations are kinetically limited to 100s of ps as opposed to the seconds used to relax films experimentally as seen in RHEED analysis93, 130, 131; this is the reason only the first two layers exhibit an or dered structure similar to that of bulk STO. Co nclusions Both in monolayer and alternating particle depositions, the films deposited on TiO2terminated STO show superior layer -by -layer growth. This is attributed to the difference in the intrinsic mobilit y of the two metal -oxide particles. TiO2, which has a lower mobility due to its stronger interaction with the surface, sticks wherever it impacts the substrate, whereas the higher mobility of SrO allows it to move and reorient into the preferred STO positi ons. This gives rise to the highest quality films deposited with AMD on TiO2terminated STO since the first deposited species are the more mobile SrO particles Additionally, subsequent layers deposited in this scheme are of higher quality due to the super ior first layer. This work thus gives insight into the importance of surface quality on film production

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65 CHAPTER 5 STRONTIUM TITANATE CLUSTER DEPOSITION To further elucidate the initial deposition processes which occur during STO deposition, stoichiometric STO clusters of varying size are deposited on STO. Little examination of STO cluster deposition exists59, 70 and the processe s involved during the deposition of energetic STO clusters would provide significant insight into the pulsed laser deposition (PLD) of STO thin films. PLD involves evaporation of an STO target producing species ranging from atomic species to large molecules. Dimer and trimer (SrO and TiO2, respectively) deposition was discussed in Chapter 3 and 4; here, we continue the study to incorporate the effect of clusters on the morphology and growth of STO thin films. Simulation Set up The system utilized in the cur rent study is consistent with the previous deposition simulations and uses the same substrate. Although clusters of metals and some oxides are prevalent in the literature60 64, 132 137, information on stoichiometric STO clusters is lacking. The existing studies of STO deposition use bulk-like STO clusters with similar structural parameters.59, 70 Experimentally, TiOx clusters produced during Ti sput tering exist in a range of sizes with both spherical and cubic shapes depending on the oxygen partial pressure133, therefore depositing clusters with a bulk -like structure is believed to be an inadequate representation of the clusters involved in depositio n. To further elucidate the initial deposition processes, stoichiometric STO clusters of varying size are deposited on the STO slab. To create the clusters that are ultimately deposited, an STO crystal was cut into one, two, three, and four unit STO cluste rs. To attempt to ensure the cluster geometry is comparable to that found in the plume created during PLD, they were then equilibrated until minimal energy fluctuations were detected. This process reduces the possibility of building the STO crystal structu re into the growing film

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66 as the equilibrated clusters exhibit unique symmetry and surface induced bond length variations as shown in Figure 5 1 The average Sr O bond distance in all clusters is 2.6 compared to a bulk Sr O distance of 2.77 Clusters co nsisting of 2 or more STO units include two types of Ti O bonds, Type I and Type II as shown in Table 5 1 and Figure 5 1. For all deposition schemes studied, an incident kinetic energy of 1.0 eV/atom was allocated to each incident cluster by assigning a c orresponding velocity. The particles in the beam were deposited at random orientations and positions, with respect to their center of mass, and the distance between particles was varied to better understand the effect of deposition rate. The various systems studied are described in Table 5 2 including 6 unique deposition beams for each termination resulting in 12 unique systems To analyze the effect of cluster size distribution, films were deposited by mono-sized clusters and mixtures of one two three and four unit STO clusters along with SrO and TiO2 particles in a random sequence. In addition to the unique beams, some systems were repeated changing the distance between each deposition event, as indicated in Table 5 2 to evaluate t he impact of deposition rate For 3 -STO clusters the distance between particles was varied from 20 to 90 and 200 Furthermore, 1 and 4 unit STO mono -beam deposition and the mixed-beam depositions were repeated for a total of 5 simulations each. No st ructural variance was seen and the quantitative film composition analysis yielded a 4 18% variance between the repeated simulations on TiO2 termination and 8 25% variance between repeated simulations on SrO termination. After depositing approximately 200 atoms (40 1unit STO, 20 2 unit STO, 15 3unit STO, 5 4unit STO) the system was allowed to equilibrate at an elevated temperature of 1100 K for approximately 50 ps to allow the films to relax and after approximately 100-STO units,

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67 corresponding to 4 ML (2 SrO, 2 TiO2), were deposited the system was ramped to 2000 K and held for 300 ps and then quenched to 0 K to eliminate thermal effects for analysis purposes. Figure 5 1 STO cluster geometries displaying bondlengths and symm etry. A) 1 unit STO, B) 2 unit STO, C) 3 unit STO, D) 4 Unit STO (i: side, ii: top -down) Table 5 1 Average Ti O bonding in STO clusters compared to bulk STO. Ti O Type I Ti O Type II Ti O in Bulk STO Bond Length 1.9 1.7 1.95 Coordination of O with Ti 2 1 2

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68 Table 5 2 Cluster deposition schemes investigated. Each scheme was repeated for each termination. Subsections indicate simulations comparing different separation distances between incident clusters to evaluate the impact of deposition rate. Deposition Scheme Mono Cluster S ize Cluster Size (STO units) Separation Distance 1 30 2 30 3 20, 30, 60, 90 and 200 4 30 Mixed Cluster S ize 1 4 without SrO/TiO2 particles 30 and 60 1 4 with SrO/TiO2 particles 30 and 60 Results Various analysis methods have been used to both qualitatively and quantitatively describe the deposited thin films. First, snapshots of the films with layer separation qualitatively illustrate the structural order and are compared to the layering sequence in bulk STO. The percentages of metal atoms present in each layer is also calculated as an indication of mixing within each layer and illustrate possible layer composition dependence on the differing deposition schemes studied. Since STO consists of alternating SrO/TiO2 pl anes, the metal percentages of the first deposited layer on SrO termination should have predominately Ti cations whereas the first layer on TiO2 termination should contain Sr cations.

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69 Figure 5 2 Representative snapshots of fi lms deposited on SrO terminated STO showing layer segregation and order within the first layer. To quantitatively analyze the structural order of the deposited films, pair distribution functions (PDF) were calcul ated for each deposited layer. Ti O PDF, for example, illustrates the nearest neighbor distances of Ti within each film with surrounding O atoms. For all film depositions, the first deposited layer produced PDFs consistent with bulk STO, meaning they had the same Sr -O and Ti O neighbor distances as the corresponding SrO and TiO2 planes in STO. The second deposited layer, however, showed deviation from bulk like structure. Therefore, the PDFs for the second deposited layer for all schemes investigated are analyzed and discussed. STO thin films deposited on the SrO terminat ed STO produced similar morphologies for each scheme, and a representative snapshot is shown in Figure 5 2 with the layers separated for visual impact. Each layer is approximately 2 thick, corresponding to half the lattice parameter. The figure shows areas of TiO2 ordering separated by SrO molecules in the first layer with no

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70 visually apparent order in the second deposited layer. PDFs were constructed comparing all the variables studied including particle size, deposition rat e and size distribution. A representative PDF of the second deposited layer comparing two different deposition schemes, mono-sized and mixed -sized deposition, is illustrated in Figure 5 3. Figure 5 3 Pair distribution functio n of the second deposited layer comparing monoand mixed size cluster deposition on SrO terminated STO illustrating the similar structural order between the two deposition methods. Films deposited by all schemes on SrO -terminated STO have similar peaks t o the Sr O layer in bulk STO up to the second nearest neighbor, damping out significantly afterwards. Metal atom percentages, shown in Figure 5 4, also indicate no trend based on the deposition schemes studied with a 9% spread in Ti atom percentages within the first layer (Figure 5 4 A) and a 26% spread of Sr atoms present in the second deposited layer (Figure 54 B).

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71 Figure 5 4 Percentage of metal atoms in the first two deposited layers on SrO terminated STO. A) Ti atoms in first layer, B) Sr atoms in second layer.

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72 Next, we examine films deposited on TiO2-terminated STO. A representative snapshot of the film is illustrated in Fi gure 5 5 where the layers are again separated to illustrate the ordering and composition of each layer. Representative Ti O PDFs comparing films produced from mono -sized versus mixed -sized beams (shown in Figure 5 6) illustrate similar peak positions, heig hts and widths for each scheme. The Ti O peaks describing the second layer are the same as those representing the TiO2 planes in bulk STO. Figure 5 5 Representative snapshots of films deposited on TiO2terminated STO showing layer segregation and order within layers one and two shown in the lower figures. The circled areas depict effect of first layer TiO2 inclusions on the subsequently deposited second layer. Metal atom percentages within the first two layers are given in Fig ure 5 7. The percent of Sr atoms in the first layer and Ti atoms in the second layer deviates 20% between the deposition schemes illustrated with mixed beam deposition having the highest percentage of expected metal atoms for both layers.

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73 Upon further inspection of the snapshots of the first deposited layer of each film on TiO2terminated STO (Figure 5 8 ), the most prevalent defects observed are 4 -fold site vacancies, Ti substitutions and TiO2 inclusions ; these are provided in Figure 5 9 To evaluate the im pact of deposition scheme on the defects described in Figure 5 9, the percentage of each defect present compared to the total 4 -fold sites available is calculated and sho wn in Figure 5 10. Taking all defects into consideration within the first deposited la yer is an indication of its structural quality and can affect the second deposited layer. This is indicated in the circled areas in Figure 5 6 where the TiO2 inclusions create regions of disorder in the second layer. Figure 5 6 Pair distribution function of the second deposited layer comparing monoand mixed size cluster deposition on TiO2terminated STO illustrating the similar structural order between the two deposition methods.

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74 Figure 5 7 Perc entages of metal atoms in the first two deposited layers on TiO2-terminated STO. A) Sr atoms in first layer, B) Ti atoms in second layer.

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75 Figure 5 8 First layer of each film deposited on TiO2 termination illustrating the 4 -fol d site vacancies TiO2 inclusions and Ti substitutions A) 1 -Unit STO, B) 2 -Unit STO, C) 3 Unit STO, D) 4 -Unit STO, E) 3 -Unit STO with 200 separation, E) Mixed-size distribution beam with SrO and TiO2 particles. Figure 5 9 Defects present in deposited films on TiO2 termination. Triangle: Ti substitution. Oval: TiO2 inclusions. Square: 4 -fold vacancy.

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76 Figure 5 10 Defect percentages. A) Ti substitution. B) 4 -fold site vacancy. C) TiO2 inclusions.

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77 Discussion Films deposited on SrO terminated STO for all schemes investigated yield a partially ordered first layer with very little structural order within the second layer and no dependence on cluster size distribution or deposition rate is predicted. The overall film structure on the TiO2 termination is described as having regions of order similar to that in bulk STO with three structural defects: Ti substitution for Sr, TiO2 inclusions, and 4 -fold site vacancies. The first deposited layer on both termi nations has a structural order comparable to bulk STO, as indicated in the percentage of metal atoms within the layer and the PDFs. STO films deposited on TiO2terminated STO, however, illustrate two ordered (or semi -ordered) layers before its structural o rder deteriorates making the layers fully disordered, whereas films deposited on SrO -terminated STO only retains structural order in the first deposited layer. The PDFs also indicate films deposited on SrO termination only correspond to the bulk nearest ne ighbor distances up to the second nearest neighbor whereas the PDFs for the films deposited on TiO2 termination exhibit longer ranged order. Comparing the metal atom percentages with respect to termination indicates films deposited on the TiO2 terminatio n have an overall higher percentage of expected metal atoms within each layer compared to films deposited on SrO terminated STO. The impact of deposition scheme on layer composition was not conclusive since the differences are within the statistical varian ce between repeated simulations. The PDFs comparing monoand mixed -beam deposition shows the same peak position and width, which also indicates that the differing schemes have minimal effect on the deposited film structure. Looking at the defects observed within the first deposited layer, Ti substation is the most prevalent defect for the 1 unit STO beam and TiO2 inclusions dominate with 4 unit STO beam. Also looking at the defect percentages, it appears TiO2 inclusions increase with increasing cluster siz e but there is no apparent trend for the

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78 occurrence of Ti substitutions. Four -fold site vacancies are also an indication of the planar density of the deposited films. The cluster size and deposition rate within the ranges studied illustrate no apparent inf luence on vacancies but the mixed-beam deposition including SrO/TiO2 particles, contains fewer vacancies compared to the mixed -beam deposition without these particles. Conclusions Analyzing the effects of incident particle size was accomplished by differing -sized stoichiometric cluster deposition. To determine the effect of cluster size distribution within the beam, films were also grown by depositing beams comprised of 1 to 4 unit STO clusters with and without SrO and TiO2 particles. It is apparent that TiO2-terminated STO yields films with ordered first and second layers while the SrO -termination only has an ordered first deposited layer. Defects in the first layer deposited on TiO2 termination showed a slight dependence on deposition scheme with the mixed-sized beam including SrO/TiO2 particles having the lower overall defects present when compared to both mixed -size beams without SrO/TiO2 and mono sized beams A nalysis of the deposited films reveals that cluster size and deposition rate within the studied ranges does not affect the structure of the deposited film. Termination effect is shown to impact the resulting film structure as was seen in the previous deposition studies where films deposited on TiO2terminated STO exhibit a more highly ordered film as compared to SrO terminated STO.

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79 CHAPTER 6 TEMPERATURE ACCELERA TED DYNAMICS Due to the time -scale limitations of MD simulations and the time -scale needed for deposite d films to relax, temperature accelerated dynamics (TAD) has been employed to further the relaxation time of deposited thin films. Surface adatom and ad-dimer diffusion mechanisms are also investigated. This work was carried out in collaboration with Blas P. Uberuaga a nd Arthur F. Vote r of Los Alamos National Laboratory. Simulation Set up As with all of our studies, the Buckingham potential with parameterization from Sekiguchi et al.105 was used to describe the short range interactions. As discussed in Chapter 2, T AD performs basin constrained MD at a high temperature, Thigh, and records the time at which a transition occurs, thigh. The thigh is then interpolated to a corresponding waiting time, tlow, at Tlow (the temperature of interest) based on Equation 2 11. The transition with the lowest tlow is accepted after continuing the MD until thigh,stop, Equation 2 12 is reached. As discussed, thigh,stop depends on two factors, a minimum pre probability that a transitio n would occur with a shorter tlow uncertainty 0.05 and the minimum prefactor was chosen to be 1012. For a sample system the normal mode frequencies were calculated to obtain the vineyard prefactor for each transi tion and it was shown to be 1013. This implies our simulations were a bit less conservative but still adequate since the same events and barriers were predicted with both prefactor values. This means, with a certainty of 95%, continuing the high -temperatu re MD would not produce a transition which would extrapolate to a shorter, low temperature, waiting time. The low temperature for most simulations was 1000 K which was the temperature of interest and the high temperature was varied depending on the system under consideration.

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80 Unlike the MD studies discussed in the previous chapters, TAD has system size restrictions due to the complexity and serial nature of the code. Therefore, to extend the time scale of the relaxation of deposited films, partially deposi ted films consisting of 2 ML coverage on a smaller surface area is extracted from the MD simulation results, as illustrated in Figure 6 1. This system was chosen due to its simplicity, one ML of SrO was already relaxed with an island of TiO2 (1ML equivalen t) above. To further increase the efficiency of the simulations, only the four layers below the film were allowed to relax during the simulations, while the remaining five layers were held fixed. For this system the high temperature was 3000 K. Figure 6 1 Initial 2ML deposited on TiO2terminated STO structure To determine the mechanisms involved in adatom and ad dimer surface diffusion, one SrO/Sr/TiO2/Ti/TiO/O particle or atom was placed above each STO (001) termination on v arying adsorption sites, indicated in Figure 6 2. The high temperature for each simulation depended on the temperature at which transition events were observed. The high temperature for the diffusion of O and SrO was 2400 K and for the Ti containing specie s a high temperature of 2900 K was

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81 used The star is noted as a bridge site (Br), triangle is a 4 -fold site, and Tx indicates an adsorption site above x atom. This notation will be utilized throughout the following sections. Multiple adsorption sites were evaluated as the starting position and had no effect on the diffusion barriers and mechanisms observed since each possible adsorption site was also either a minimum or transition state found in the TAD simulations. Figure 6 2 Adsorption sites. A) TiO2 termination B) SrO Termination Figure 6 3 Final 2ML relaxed structure.

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82 Results Initially, we expected TAD to relax the TiO2 island (equivalent to 1ML) above the 1ML SrO, deposited with traditional MD, to a structure similar to bulk STO by overcoming the kinetic limitations of our classical MD simulations. However, increasing the time -scale of the relaxation process proved to b e less revolutionary than expected. Due to small barriers associated with many transitions taking place within the film, on the order of a few meV, TAD would become less efficient due to the higher probability of reverse transitions (where state B reverts back to state A). Additional TAD features were utilized that reduces such back and forth from occurring but the system has an overabundance of such small barriers and therefore slows down the simulation. The resulting film is shown in Figure 6 3 The figur e indicates that TiO2 units comprising the TiO2 island atop the SrO deposited layer are beginning to form a TiO2 layer and the island has smoothed out such that the height is reduced by approximately 5 O adatom diffusion proved to be more interesting. T he minimum state predicted for both terminations is atop a surface cation, TT i or TS r. On the SrO termination, O diffusion occurred through a hopping mechanism while on the TiO2 termination, the diffusion mechanism was an exchange of the ad-oxygen with a s urface oxygen; the latter mechanism is depicted in Figure 6 4. The O exchange begins by pulling an O from the surface and moving to an intermediate state where both pulled O and ad -oxygen sit on adjacent TTi (image 3 in Figure 6 -4) The ad -oxygen then moves into the vacancy created by pulling out the surface O and the pulledO is now the diffusing adatom (image 5) The barrier associated with pulling out a surface O (images 1 to 3) is 1.4 1 eV while the barrier to put the original ad -oxygen into the vaca ncy (images 3 to 5) is 0.18 eV where images 2 and 4 are saddle configurations In addition to a complete exchange, where translation occurs the surface oxygen pulled out was also put back in its original position with a coinciding barrier of 0.116 eV.

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83 It is important to note that TAD records the transitions which are not accepted (they were not the transitions with the lowest Tlow waiting time). In some of these cases, a n additional hopping mechanism was attempted where the O adatom moves from TT i to an a djacent TO, to another TT i; this transition has a barrier of 2.4 eV or 1 eV higher than the barrier associated with the exchange mechanism Figure 6 4 Oxygen adatom exchange mechanism on TiO2terminated STO. Th e hopping mechanism of the O adatom upon SrO termination is illustrated in Figure 6 5. This mechanism involves the O adatom hopping from TSr across a bridge site, Br, to an adjacent TSr. The energy barrier associated with the ad -o xygen going from TSr to Br (images 1 to 3 in Figure 6 5) is 0.19 eV and, completing the translation, from the Br to an adjacent TSr (images 3 to 5), is 0.06 eV where images 2 and 4 are saddle configurations

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84 Figure 6 5 Oxygen adatom hop mechanism on SrO -terminated STO. SrO ad -dimer diffusion also exhibited varying mechanisms between the two STO terminations. SrO atop the TiO2 termination diffused via an oxygen exchange mechanism similar to that observed in the O/TiO2terminated system, illustrated in Figure 6 6. In the minimum energy configuration for SrO atop TiO2 termination, the Sr sits at the four -fold site while the O in the dimer rests at TTi (Figure 6 6, image 1). SrO diffusion begins by pulling out a surface O (images 1 to 3) then moving to an intermediate state where both surface O and dimer O sit at adjacent TTi (image 3). The original O associated with the ad -dimer is then placed into the vacancy created and the Sr moves to an adjacent four -fold site (images 3 to 5), making the removed surfa ce O now part of the diffusing dimer. The barrier associated with taking surface oxygen is 1.18 eV and to place the original ad oxygen in the vacancy from the surface oxygen is 0.18 eV thereby completing the SrO translation.

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85 Figure 6 6 SrO diffusion mechanism on TiO2-terminated STO A) initial structure, B) exchange and C) final structure. The minimum energy configuration of the SrO ad dimer atop the SrO termination consists of Sr on TO and O on TSr, which is i llustrated as image 1 in Figure 6 7. The addimer diffused atop the surface by a walking mechanism, which is simply a combination of two consecutive hops, one by each member of the dimer. The Sr hop (Figure 6 7, A) involves moving the Sr from TO to a Br site (images 1 to 3) having an associated barrier of 0.24 eV then to an adjacent TO (3 to 5) after overcoming a barrier of 0.22 eV. The O hop (Figure 6 7, B) begins by moving from TSr to a Br site (images 6 8) then back to an adjacent TSr (images 8 to 10) with a barrier of 0.24 eV. This completes the full translation.

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86 Figure 6 7 SrO ad dimer surface diffusion on SrO termination. A) Sr hop, B) O hop.

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87 Ti -containing adsorbates were also examin ed, including Ti, TiO and TiO2. Howev er, compared to the other ad -species considered, adsorbates containing Ti did not exhibit any translation. The Ti adatom bonded with four surface oxygen atom s making it four coordinated as in bulk TiO2. This was also predicted for TiO and TiO2 ad particles where they bonded with three and two surface oxygen atoms, respectively. The preferred structure is shown in Figure 6 8 where the yellow oxygen atoms are bonded to the adsorbed Ti. It is believed that the additional bonding with the surface leads to the immobility of the Ti -containing ad -species. Discussion The relaxation of the 2 ML film produced using the classical MD simulations discussed in Chapter 4 did not vary appreciably in the TAD simulations. Rather than transforming to bulk like STO structures the deposited structures only exhibited the beginning signs of TiO2 ordering above the SrO deposited layer and some smoothing of TiO2 islands. The TAD simulations do provide tremendous insight into the mechanisms by which individual deposited particles diffuse on STO surfaces. Figure 6 8 Structure formed when Ti, TiO or TiO2 is adsorbed, surface O bonds wit h Ti to make Ti 4 coordinated.

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88 Surface diffusion was seen to produce differing mechanisms depending on the termination of the (100) STO surface. Similar to the literature on metal adatoms on MgO(001)138, 139 and NiO(001)140, Sr and Ti sit on TO sites in the minimum energy configurations when adsorbed on SrO terminated STO. On TiO2 termination, however, the cations pr efer the four -fold sites to maximize the distance between the adsorbed cation and surface Ti. Adsorbates on the SrO termination exhibited a hopping mechanism also seen for Au surface self diffusion along terraces.141 This is also comparable to Henkelman et al.s work on MgO ad -dimer diffusion on MgO (001).142 In their study, the Mg f rom the ad dimer exhibits a hop similar our Sr hop in Figure 6 7 A and they also describe a O hop similar to Figure 6 7 B. The advantages of TAD are exploited in this study The first part of their study involved static calculations minimizing initial, fi n al and intermediate structures. F rom this standpoint, the collaborative cation and O hop we describe as walking was not verified. However the second part of the study involved using TAD to describe the MgO ad -dimer diffusion and predicted the same walk outlined in the previous section for the SrO ad-dimer. The adatoms or ad -particles on TiO2terminated STO diffused via an oxygen exchange mechanism. The presence of an exchange (or replacement) mechanism was first discovered theoretically in 1990 by Feibelman for Al diffusion on Al (001)81 and experimentally by Kellogg and Feibelman also in 1990 in the surface self diffusion on Pt (001).143 The exchange mechanism has an overall higher barrier when compared to the hopping mechanism on SrO termination. This coincides with earlier mobility analysis that showed particulate mobility is high er on the SrO termination seen using traditional MD.122 The behavior of Ti containing species can be compared to a theoret ical study of Ni3+ on NiO due to the difference in oxidation state of the adatom with the surface cation. In this case, as

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89 with our study, Ni3+ pulls oxygen atoms from the surface and, compared to a Ni2+ adatom on NiO, has a stronger interaction with the s urface.144 The difference in diffusion mechanisms between the two terminations is believed to be due to the difference in atomic density of the two planes. The TiO2 terminated surface is more closely packed and contains twice the oxygen present on the SrO termination; therefore instead of O hopping along the surface (and getting nearer to surface O) it forces the surface O to vacate its lattice site to be replaced by the original O. This p rocess is predicted to occur for both SrO and O diffusion. Evidence of this is demonstrated in the attempted O hop on TiO2terminated STO (TTi TO TTi) exhibiting a significant energy barrier when compared to the exchange process (1 eV difference). Conclusions Utilizing TAD to extend the relaxation time -scale for the 2ML STO film (1ML SrO and 1 ML TiO2) produced some smoothing of the TiO2 island but, due to the abundance of back and forth transitions, the simulation was not able to overcome the kinet ic limitations of our traditional MD simulations. O and SrO are predicted to diffuse via exchange on TiO2terminated STO and via a hopping mechanism on SrO terminated STO. Overall, ad -species have a lower barrier to diffusion on SrO -terminated (100) STO al lowing particles a higher mobility on this surface. The barriers calculated in this work can be utilized to parameterize the kMC simulations discussed in Chapter 1. These results also complement the classical MD simulations discussed in Chapters 3 through 5 to elucidate the atomistic mechanisms occurring after an initial deposition event. These findings are comparable to the study of SrO and TiO2 particulate mobility on each termination discussed in Chapter 3 where it was shown that SrO particles are more mobile overall and that mobility was higher on SrO termination compared to TiO2 termination.

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90 An additional benefit of TAD is the ability to capture saddle configurations and possible complex diffusion mechanism since, while a transition from one state to another is infrequent, the actual passing is quite fast and what as appears to be a simple hop in MD could actual be a more complicated walk. TAD enables the calculation of energy barriers as well as intermediate and saddle geometries. In future studies of thin -film deposition it is recommended that classical MD be utilized to deposit a single incident species while TAD be used to describe the relaxation occurring between events. This approach is predicted to make use of the strengths of each approach to most accurately describe the dynamics and relaxation of deposited particles.

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91 CHAPTER 7 GENERAL CONCLUSIONS In this dissertation, MD simulations were performed to study the deposition and growth of metal -oxide thin films on STO (100) at the atomistic level. The results obtained for each system were compared to experimental results and elucidate the processes involved in the first stages of deposition. The first section investigates SrO and TiO2 thin film growth to gain a fundamen tal understanding of the different growth modes exhibited by each. These films exhibited significantly different morphologies and proceeded in two different growth modes. While SrO thin films grew in a layer -by -layer fashion and have smooth highly ordered structure, TiO2 thin films grew in a three -dimensional growth mode producing an island/agglomerate morphology. TiO2 films in this study are consistent with experimental results for films grown at high deposition rates. Mobility data, work of adhesion resul ts, and particle interaction energies explain the causes of the differing growth modes exhibited in SrO and TiO2 deposition. Next, STO thin films were grown using two deposition methods, alternating TiO2/SrO particles in an ABAB arrangement, and alternating TiO2/SrO monolayers. Alternating monolayer deposition on TiO2terminated STO produced superior films based on the structural analysis performed. As outlined in SrO/TiO2 thin film deposition, SrO particles exhibit higher mobility and can grow in a layer b y layer fashion. Therefore, since the first deposited layer is SrO, it has the higher structural quality. Additionally, subsequent layers deposited in this scheme produce a higher quality film due to the superior quality of the first layer. While the prev ious study is more analogous to MBE due to the size of the incident particles, PLD involves species of larger sizes. To better simulate species produced during PLD, stoichiometric STO clusters of varying sizes were created. These clusters were equilibrated in

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92 vacuum and as a result relaxed into structures having little to no bulk like structural properties. While no particle size dependence was found, substrate termination yet again impacted the resulting thin film. Films deposited on TiO2-terminated STO produced the longer ranged ordered films compared to films deposited on SrO terminated STO; this result was also observed in AMD. Defects present in the first deposited layer on TiO2termination were also analyzed. Three main defects were seen: TiO2 inclu sions, Ti substitution and Sr vacancies. Modifying the incident particle -size distribution resulted in a reduction of the overall occurrence of defects within the first layer. TAD results on the adatom and ad-dimer surface diffusion revealed the mechanisms involved following each deposition event. As with our thin film deposition studies using classical MD, termination had an important impact on the diffusion mechanisms. Ad -species on SrO termination move along the surface by hopping. SrO diffusion occurs w ith consecutive hops by each atom in the dimer. On the TiO2 termination, however, diffusion progresses by oxygen exchange with a higher overall diffusion barrier compared to the hopping observed on SrO termination. In summary, t his is the first study to d eposit relaxed STO clusters and investigate surface diffusion on perovskite substrates. In addition to investigating thin film growth, analysis codes were developed to analyze the resulting films, these are included in Appendix A. In future work to model thin -film growth the mechanisms and diffusion barriers calculated here can be used to parameterize kMC simulations. Also, a hybrid approach is recommended for the simulation of thin-film growth, combining a classical MD description of the initial depositi on event and utilizing TAD to simulate the subsequent relaxation between events.

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93 APPENDIX ANALYSIS CODES Planar pair distribution (Sr -O given as example) c********************* c Last modified 7/19/08 Jennifer Wohlwend c Program to generate the pair distribution funciton c for Strontium Oxygen for deposited species. c PDF is for atom i within layer of upper limit ul c and lower limit ll with neighboring j in 3D c Language: Fortran c********************* imp licit real (a h,oz) parameter (max=50000) real::x(max),y(max),z(max),ll,lu integer::natoms,counting(30000000),tnrtot,kt(max) integer::igo(max),ithermo(max),No,Nti,Nsr real::th(3,3),binw,rbd,rx1,ry1,rz1,ro,dvr2,dvr1 integer::tbin,nn open(unit=18,f ile='SrO_pdf.xls',status='unknown') !output open(unit=35,file='structure_in', status='unknown') !input No=0 Nti=0 Nsr=0 ll=63.6 !lower limit of i layer (A) ul=66.0 !upper limit of i layer (A) read(35,*) natom do 5 i=1,natom read(35,*) k,kt(k), x(k), y(k), z(k),igo(k), ithermo(k) if ((x(k).gt.ll).and.(x(k).lt.ul)) then if (kt(k).eq.8) No=No+1 if (kt(k).eq.22) Nti=Nti+1 if (kt(k).eq. 38) Nsr=Nsr+1 endif 5 continue tnrtot=natom binw=0.01 rbd=7 tbin=rbd/binw nn=0 do k=1,tbin counting(k)=0 enddo do i=1,tnrtot if (kt(i).eq.38) then !sr if ((x(i).gt.ll).and.(x(i).lt.ul)) then nn=nn+1 do j=1,t nrtot

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94 if (i.ne.j) then if (kt(j).eq.8) then !OXYGEN if (ithermo(j).eq.0) then rx1=x(j) x(i) ry1=y(j) y(i) rz1=z(j) z(i) c****************periodic boundary conditions if analyzing bulk c if (rx1.gt.(th(1,1)/2)) rx1=rx1th(1,1) c if (rx1.lt.( th(1,1)/2)) rx1=rx1+th(1,1) c if (ry1.gt.(th(2,2)/2)) ry1=ry1th(2,2) c if (ry1.lt.( th(2,2)/2)) ry1=ry1+th(2,2) c if (rz1.gt.(th(3,3)/2)) rz1=rz1 th(3,3) c if (rz1.lt.( th(3,3)/2)) rz1=rz1+th(3,3) c************************************************************* r3=((rx1*rx1)+(ry1*ry1)+(rz1*rz1)) r2=sqrt(r3) do k=1,tbin if (((k 1)*binw.Lt.r2).and.(r2.LE.(k*binw )))then counting(k)=counting(k)+1 endif enddo endif endif endif enddo endif endif enddo write(18,*) Nsr,nn do k=1,tbin write(18,*)(k*0.01),float(counting(k))/Nsr enddo stop end program

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95 Coordination Analysis c********************* c Last modified 3/ 12/09 Jennifer Wohlwend c Program to calculate the coordination of O, Sr, and Ti atoms c coordination is planar, i is within each layer j is 3D c Language: Fortran c**************** ***** parameter (max=40000) parameter (max2=40000) parameter (max4=6) implicit real*8 (a h) real x(max),y(max),z(max) integer iOTi(max),nOTi(max4),iOSr(max),nOSr(max4),nCNOTi8(max4), 1 nCNOTi7(max4),nCNOTi6(ma x4),nCNOTi5(max4),nCNOTi4(max4), 1 nCNOTi3(max4),nCNOTi2(max4),nCNOTi1(max4),nCNOTi0(max4), 1 nCNOSr14(max4),nCNOSr13(max4),nCNOSr12(max4),nCNOSr11(max4), 1 nCNOSr10(max4),nCNOSr9(max4),nCNOSr8(max4),nCNOSr7(max4), 1 nCNOSr6(max4),nCNOSr5(max4),nCNOSr4(max4),nCNOSr3(max4), 1 nCNOSr2(max4),nCNOSr1(max4),nCNOSr0(max4) real blat,diagonal,dx,dy,dz integer kt(max),natom,nframe,ithermo(max),igo(max),nl, 1 iSrO(max),iTiO(max),nSrO(max4),nTiO(max4),p integer ncellx,ncelly,ncellz,maxdist,No,Nti,Nsr integer nCNTi6(max4),nCNTi8(max4),nCNTi7(max4), 1 nCNTi5(max4),nCNTi4(max4),nCNTi3(max4),nCNTi2(max4), 1 nCNTi1(max4),nCNTi0(max4),layer(max) integer nCNSr12(max4),nCNSr11(max4),nCNSr10(max4), 1 nCNSr9(max4),nCNSr8(max4),nCNSr7(max4),nCNSr6(max4), 1 nCNSr5(max4),nCNSr4(max4),nCNSr3(max4),nCNSr2(max4), 1 nCNSr1(max4),nCNSr13(max4),nCNSr14(max4),nCNSr0(max4) real dist,temp integer count,lay ,CNOTI(max),CNOSR(max),CNSRO(max), 1 CNTIO(max),osr,oti,sro,tio integer Nolayer6,Nsrlayer6,Ntilayer6 integer Nolayer1,Nsrlayer1,Ntilayer1 integer Nolayer2,Nsrlayer2,Ntilayer2 integer Nolayer3,Nsrlayer3,Ntilayer3 integer Nolayer4,Nsrlayer4,Ntilayer4 integer Nolayer5,Nsrlayer5,Ntilayer5 open (unit=11, file='structure_in', status='old') open (unit=6, file='output1', status='unknown') !verbose open (unit=7, file='outputlist',status=' unknown') !short open (unit=10, file='pos_CN_layer',status='unknown') !surface atomic positions with corresponding coordination numb write (10,*)' i ',' kt ',' x ',' y ',' z ', 1 OTi ',' OSr ',' TiO ',' SrO No=0 Nti=0 Nsr=0 layer1=0 layer2=0 layer3=0

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96 layer4=0 layer5=0 layer6=0 c******************************************************************** c reads the input file c******************************************************************** read(11,*) natom do 10 i=1,na read(11,*) k,kt(k), x(k), y(k), z(k), igo(k),ithermo(k) igo(k)=6 if (imass(k).eq.3) kt(k)=8 if (imass(k).eq.2) kt(k)=22 if (imass(k).eq.1) kt(k)=38 c*****************Input layer parameters, coordination is found for each deposited layer if(x(k)*blat.ge.68.2) igo(k)=0 !top layers if((x(k)*blat.ge.62.0).and.(x(k)*blat.lt.64.2)) igo(k)=1 !layer(k)=1 if((x(k)*blat.ge.64.2).and.(x(k)*blat.lt.66.2)) igo(k)=2 !layer(k)=2 if((x(k)*blat.ge.66.2).and.(x(k)*blat.lt.68.2)) igo(k)=3 !layer(k)=3 if((x(k)*blat.lt.60.0).and.(x(k)*blat.gt.58.5)) igo(k)=4 !Subsurface layer if((x(k)*blat.lt.62.0).and.(x(k)*blat.gt.60.0)) then if ((y(k)*blat.gt. 15.0).and.(y(k)*blat.lt.20)) then if ((z(k)*blat.gt. 20.0).and.(z(k)*blat.lt.19)) igo(k)=5 !layer=surface if (kt(k).eq.8) No=No+1 if (kt(k).eq.22) Nti=Nti+1 if (kt(k).eq.38) Nsr=Nsr+1 if ((igo(k).eq.0).AND.(ithermo( k).eq.0)) layer(k)=5 !top if ((igo(k).eq.1).AND.(ithermo(k).eq.0)) layer(k)=1 !first layer deposited film if ((igo(k).eq.2).AND.(ithermo(k).eq.0)) layer(k)=2 !second layer deposited film if ((igo(k).eq.3).AND.(ithermo(k).eq.0)) layer(k)=3 !third layer deposited film if ((igo(k).eq.4).AND.(ithermo(k).eq.0)) layer(k)=4 !sub surface layer if ((igo(k).eq.5).AND.(ithermo(k).eq.0)) layer(k)=6 !THIS IS THE SURFACE ATOMS if ((igo(k).eq.0).AND.(ithermo(k).eq.0)) layer5=layer5+1 if ((igo(k).eq.1).AND.(ithermo(k).eq.0)) layer1=layer1+1 if ((igo(k).eq.2).AND.(ithermo(k).eq.0)) layer2=layer2+1 if ((igo(k).eq.3).AND.(ithermo(k).eq.0)) layer3=layer3+1 if ((igo(k).eq.4).AND.(ithermo(k).eq.0)) layer4=layer4+1 if ((igo(k).eq.5).AND.(ithermo(k).eq.0)) layer6=layer6+1 !TO CHECK THE SURFACE COORDINATION endif endif 10 Continue write(6,*)'No=',No,' Nti=',Nti,' Nsr=',Nsr write(6,*)'Reading is done' write(6,*)'layer1= ',layer1,' ','layer2= ', 1 layer2,' ','layer3= ',layer3,' ','layer4= ',layer4, 1 'layer5= ',layer5 write(7,*)'layer1= ',layer1,' ','layer2= ', 1 layer2,' ','l ayer3= ',layer3,' ','layer4= ',layer4, 1 'layer5= ',layer5 nframe=1 blat=3.9087 ncellx=16 ncellz=ncellx ncelly=ncellx c******************************************************************** c initializes all the varibales to zero

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97 c******************************************************************** do k=1,6 nCNOTi8(k)=0 nCNOTi7(k)=0 nCNOTi6(k)=0 nCNOTi5(k)=0 nCNOTi4(k)=0 nCNOTi3(k)=0 nCNOTi2(k)=0 nCNOTi1(k)=0 nCNOTi0(k)=0 nCNOSr14(k)=0 nCNOSr13(k)=0 nCNOSr12(k)=0 nCNOSr11(k)=0 nCNOSr10(k)=0 nCNOSr9(k)=0 nCNOSr8(k)=0 nCNOSr7(k)=0 nCNOSr6(k)=0 nCNOSr5(k)=0 nCNOSr4(k)=0 nCNOSr3(k)=0 nCNOSr2(k)=0 nCNOSr1(k)=0 nCNOSr0(k)=0 nCNTi8(k)=0 nCNTi7(k)=0 nCNTi6(k)=0 nCNTi5(k)=0 nCNTi4(k)=0 nCNTi3(k)=0 nCNTi2(k)=0 nCNTi1(k)=0 nCNTi0(k)=0 nCNSr14(k)=0 nCNSr13(k)=0 nCNSr12(k)=0 nCNSr11(k)=0 nCNSr10(k)=0 nCNSr9(k)=0 nCNSr8(k)=0 nCNSr7(k)=0 nCNSr6(k)=0 nCNSr5(k)=0 nCNSr4(k)=0 nCNSr3(k)=0 nCNSr2(k)=0 nCNSr1(k)=0 nCNSr0(k)=0 enddo N olayer1=0 Nolayer2=0 Nolayer3=0 Nolayer4=0 Nolayer5=0

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98 Nolayer6=0 Nsrlayer1=0 Nsrlayer2=0 Nsrlayer3=0 Nsrlayer4=0 Nsrlayer5=0 Nsrlayer6=0 Ntilayer1=0 Ntilayer2=0 Ntilayer3=0 Ntilayer4=0 Ntilayer5=0 Ntilayer6=0 do i=1,natom iOTi(i)=0 iOSr(i)=0 iTiO(i)=0 iSrO(i)=0 if (layer(i).EQ.1) then if(kt(i).EQ.8) Nolayer1=Nolayer1+1 if(kt(i).EQ.22) Ntilayer1 =Ntilayer1+1 if(kt(i).EQ.38) Nsrlayer1=Nsrlayer1+1 elseif (layer(i).EQ.2) then if(kt(i).EQ.8) Nolayer2=Nolayer2+1 if(kt(i).EQ.22) Ntilayer2=Ntilayer2+1 if(kt(i).EQ.38) Nsrlayer2=Nsrlayer2+1 elseif (layer(i).EQ.3) then if(kt(i).EQ.8) Nolayer3=Nolayer3+1 if(kt(i).EQ.22) Ntilayer3=Ntilayer3+1 if(kt(i).EQ.38) Nsrlayer3=Nsrlayer3+1 elseif (layer(i).EQ.4) then if(kt(i).EQ.8) Nolayer4=Nolayer4+1 if(kt(i).EQ.22) Ntilayer4=Ntilayer4+1 if(kt(i).EQ.38) Nsrlayer4=Nsrlayer4+1 elseif (layer(i).EQ.5) then if(kt(i).EQ.8) Nolayer5=Nolayer5+1 if(kt(i).EQ.22) Ntilayer5=Ntilayer5+1 if(kt(i).EQ.38) Nsrlayer5=Nsrlayer5+1 elseif (layer(i).EQ.6) then if(kt(i).EQ.8) Nolayer6=Nolayer6+1 if(kt(i).EQ.22) Ntilayer6=Ntilayer6+1 if(kt(i).EQ.38) Nsrlayer6=Nsrlayer6+1 endif e nddo write(6,*)'' write(6,*)'Total Number of atoms of each type in layer1' write(6,*)'O = ',Nolayer1,' Sr= ',Nsrlayer1,' Ti= ',Ntilayer1 write(6,*)'' write(6,*)'Total Number of atoms of each type in layer2' write(6,*)'O = ',Nolayer2,' Sr= ',Nsrlayer2,' Ti= ',Ntilayer2 write(6,*)'' write(6,*)'Total Number of atoms of each type in layer3' write(6,*)'O = ',Nolayer3,' Sr= ',Nsrlayer3,' Ti= ',Ntilayer3 write(6,*)'' write(6,*)'Total Number of atom s of each type in layer4'

PAGE 99

99 write(6,*)'O = ',Nolayer4,' Sr= ',Nsrlayer4,' Ti= ',Ntilayer4 write(6,*)'' write(6,*)'Total Number of atoms of each type in layer5' write(6,*)'O = ',Nolayer5,' Sr= ',Nsrlayer5,' Ti= ',Ntilayer5 write( 6,*)'' write(6,*)'Total Number of atoms of each type in surface layer' write(6,*)'O = ',Nolayer6,' Sr= ',Nsrlayer6,' Ti= ',Ntilayer6 c******************************************************************** c calculates the coordination of Oxygen with Sr and Ti c******************************************************************** do lay=1,6 do i=1,natom if (layer(i).eq.lay) then if (kt(i).EQ.8)then nOTi(lay)=0 nOSr(lay)=0 count=0 do j=1,natom if(layer(j).eq.lay) then if ((i.NE.j).AND.(kt(j).NE.8)) then dx=ABS(x(j)x(i)) dy=ABS(y(j) y(i)) dz=ABS(z(j) z(i)) c IF (dx.GT.0.5*ncellx) dx=ncel lx dx !PBC if looking at bulk c IF (dy.GT.0.5*ncelly) dy=ncelly dy c IF (dz.GT.0.5*ncellz) dz=ncellz dz temp=dx*dx+dy*dy+dz*dz dist=sqrt(temp) if (kt(j).EQ.22) then for O Ti if (dist.LE.0.55*blat) then nOTi(lay)=nOTi(lay)+1 iOTi(i)=iOTi(i)+1 endif elseif (kt(j).eq.38) then !for O Sr if (dist.LE.0.80*blat) then nOSr(lay)=nOSr(lay)+1 iOSr(i)=iOSr(i)+1 endif endif endif endif enddo if (nOTi(lay).eq.8) nCNOTi8(lay)=nCNOTi8(lay)+1 if (nOTi(lay).eq.7) nCNOTi7(lay)=nCNOTi7(lay)+1 if (nOTi(lay).eq.6) nCNOTi6(lay)=nCNOTi6(lay)+1 if (nOTi(lay).eq.5) nCNOTi5(lay)=nCNOTi5(lay)+1 if (nOTi(lay).eq.4) nCNOTi4(lay)=nCNOTi4(lay)+1 if (nOTi(lay).eq.3) nCNOTi3(lay)=nCNOTi3(lay)+1 if (nOTi(lay).eq .2) nCNOTi2(lay)=nCNOTi2(lay)+1 if (nOTi(lay).eq.1) nCNOTi1(lay)=nCNOTi1(lay)+1 if (nOTi(lay).eq.0) nCNOTi0(lay)=nCNOTi0(lay)+1 if (nOSr(lay).eq.14) nCNOSr14(lay)=nCNOSr14(lay)+1 if (nOSr(lay).eq.13) nCNOSr1 3(lay)=nCNOSr13(lay)+1 if (nOSr(lay).eq.12) nCNOSr12(lay)=nCNOSr12(lay)+1

PAGE 100

100 if (nOSr(lay).eq.11) nCNOSr11(lay)=nCNOSr11(lay)+1 if (nOSr(lay).eq.10) nCNOSr10(lay)=nCNOSr10(lay)+1 if (nOSr(lay).eq.9) nCNOSr9(lay)=nCNOSr9(lay)+1 if (nOSr(lay).eq.8) nCNOSr8(lay)=nCNOSr8(lay)+1 if (nOSr(lay).eq.7) nCNOSr7(lay)=nCNOSr7(lay)+1 if (nOSr(lay).eq.6) nCNOSr6(lay)=nCNOSr6(lay)+1 if (nOSr(lay).eq.5) nCNOSr5(lay)=nCNOSr5(lay)+1 if (nOSr(lay).eq.4) nCNOSr4(lay)=nCNOSr4(lay)+1 if (nOSr(lay).eq.3) nCNOSr3(lay)=nCNOSr3(lay)+1 if (nOSr(lay).eq.2) nCNOSr2(lay)=nCNOSr2(lay)+1 if (nOSr(lay).eq.1) nCNOSr1(lay)=nCNOSr1(lay)+1 if (nOSr(lay).eq.0) nCNOSr0(lay)=nCNOSr0(lay)+1 elseif (kt(i).eq.22) then !i is a Ti nTiO(lay)=0 do j=1,natom if (layer(j).eq.lay) then if ((i.NE.j).AND.(kt(j).NE.22)) then if (kt(j).EQ.8) then !Ti O dx=ABS(x(j)x(i)) dy=ABS(y(j) y(i)) dz=ABS(z(j) z(i)) c IF (dx.GT.0.5*ncellx) dx=ncellxdx c IF (dy.GT.0.5*ncelly) dy=ncelly dy c IF (dz.GT.0.5*ncellz) dz=ncellz dz temp=dx*dx+dy*dy+dz*dz dist=sqrt(temp) if (dist.LE.0.55*blat) then nTiO(lay)=nTiO(lay)+1 iTiO(i)=iTiO(i)+1 endif endif endif endif enddo if (nTiO(lay).eq.8) nCNTi8(lay)=nCNTi8(lay)+1 if (nTiO(lay).eq.7) nCNTi7(lay)=nCNTi7(lay)+1 if (nTiO(lay).eq.6) nCNTi6(lay)=nCNTi6(lay)+1 if (nTiO(lay).eq.5) nCNTi5(lay)=nCNTi5(lay)+1 if (nTiO(lay).eq.4) nCNTi4(lay)=nCNTi4(lay)+1 if (nTiO(lay).eq.3) nCNTi3(lay)=nCNTi3(lay)+1 if (nTiO(lay).eq.2) nCNTi2(lay)=nCNTi2(lay)+1 if (nTiO(lay ).eq.1) nCNTi1(lay)=nCNTi1(lay)+1 if (nTiO(lay).eq.0) nCNTi0(lay)=nCNTi0(lay)+1 c**************************** elseif (kt(i).EQ.38)then !i is Sr nSrO(lay)=0 do j=1,natom if (layer(j).eq.lay) then if ((i.NE.j).AND.(kt(j).NE.38)) then if (kt(j).EQ.8) then Sr O dx=ABS(x(j)x(i)) dy=ABS(y(j) y(i)) dz=ABS(z(j) z(i)) c IF (dx.GT.0.5*ncellx) dx=ncellxdx

PAGE 101

101 c IF (dy.GT.0.5*ncelly) dy=ncelly dy c IF (dz.GT.0.5*ncellz) dz=ncellz dz temp=dx*dx+dy*dy+dz*dz dist=sqrt(temp) if (dist.LE.0.80*blat) then nSrO(lay)=nSrO(lay)+1 iSrO(i)=iSrO(i)+1 endif endif endif endif enddo if (nSrO(lay).eq.14) nCNSr14(lay)=nCNSr14(lay)+1 if (nSrO(lay).eq.13) nCNSr13(lay)=nCNSr13(lay)+1 if (nSrO(lay).eq.12) nCNSr12(lay)=nCNSr12(lay)+1 if (nSrO(lay).eq.11) nCNSr11(lay)=nCNSr11(lay)+1 if (nSrO(lay).eq.10) nCNSr10(lay)=nCNSr10(lay)+1 if (nSrO(lay).eq.9) nCNSr9(lay)=nCNSr9(lay)+1 if (nSrO(lay).eq.8) nCNSr8(lay)=nCNSr8(lay)+1 if (nSrO(lay).eq.7) nCNSr7(lay)=nCNSr7(lay)+1 if (nSrO(lay).eq.6) nCNSr6(lay)=nCNSr6(lay)+1 if (nSrO(lay).eq.5) nCNSr5(lay)=nCNSr5(lay)+1 if (nSrO(lay).eq.4) nCNSr4( lay)=nCNSr4(lay)+1 if (nSrO(lay).eq.3) nCNSr3(lay)=nCNSr3(lay)+1 if (nSrO(lay).eq.2) nCNSr2(lay)=nCNSr2(lay)+1 if (nSrO(lay).eq.1) nCNSr1(lay)=nCNSr1(lay)+1 if (nSrO(lay).eq.0) nCNSr0(lay)=nCNSr0(lay)+1 endif if((igo(i).eq.5).and.(ithermo(i).eq.0)) then write(10,104)i,kt(i),x(i),y(i),z(i), & iOTi(i),iOSr(i),iTiO(i),iSrO(i) endif endif enddo c************************************************** write(6,*)'layer ',lay write(6, *)'Coordination of Oxy with Ti and Sr' write(6,*) '# Ti 8 coordinated (around Oxy) = ',nCNOTi8(lay) write(6,*) '# Ti 7 coordinated (around Oxy) = ',nCNOTi7(lay) write(6,*) '# Ti 6 coordinated (around Oxy) = ',nCNOTi6(lay) write(6,*) '# Ti 5 coordinated (around Oxy) = ',nCNOTi5(lay) write(6,*) '# Ti 4 coordinated (around Oxy) = ',nCNOTi4(lay) write(6,*) '# Ti 3 coordinated (around Oxy) = ',nCNOTi3(lay) write(6,*) '# Ti 2 coordinated (around Oxy)** = ,nCNOTi2(lay) write(6,*) '# Ti 1 coordinated (around Oxy) = ',nCNOTi1(lay) write(6,*) '# unbonded Ti (around Oxy) = ',nCNOTi0(lay) write(6,*) '# Sr 14 coordinated (around Oxy) = ',nCNOSr14(lay) write(6,*) '# Sr 13 coordinated (around Oxy) = ',nCNOSr13(lay) write(6,*) '# Sr 12 coordinated (around Oxy) = ',nCNOSr12(lay) write(6,*) '# Sr 11 coordinated (around Oxy) = ',nCNOSr11(lay) write(6,*) '# Sr 10 coordinated (around Oxy) = ',nCNOSr10(lay) write(6,*) '# Sr 9 coordinated (around Oxy) = ',nCNOSr9(lay) write(6,*) '# Sr 8 coordinated (around Oxy) = ',nCNOSr8(lay) write(6,*) '# Sr 7 coordinated (around Oxy) = ',nCNOSr7(lay)

PAGE 102

102 write(6,*) '# Sr 6 coordinated (around Oxy) = ',nCNOSr6(lay) write (6,*) '# Sr 5 coordinated (around Oxy) = ',nCNOSr5(lay) write(6,*) '# Sr 4 coordinated (around Oxy)** = ',nCNOSr4(lay) write(6,*) '# Sr 3 coordinated (around Oxy) = ',nCNOSr3(lay) write(6,*) '# Sr 2 coordinated (around Oxy) = ',nCNOSr2(la y) write(6,*) '# Sr 1 coordinated (around Oxy) = ',nCNOSr1(lay) write(6,*) '# unbonded Sr (around Oxy) = ',nCNOSr0(lay) write(6,*) write(6,*)'Coordination of Ti with Oxygen' write(6,*) '# Ti 8 coordinated (Ti with Oxy) = ',nCNTi8(lay) write(6,*) '# Ti 7 coordinated (Ti with Oxy)= ',nCNTi7(lay) write(6,*) '# Ti 6 coordinated (Ti with Oxy)=** ',nCNTi6(lay) write(6,*) '# Ti 5 coordinated (Ti with Oxy)= ',nCNTi5(lay) write(6,*) '# Ti 4 coordinated (Ti with Oxy)= ',nCNTi4(lay) write(6,*) '# Ti 3 coordinated (Ti with Oxy)= ',nCNTi3(lay) write(6,*) '# Ti 2 coordinated (Ti with Oxy)= ',nCNTi2(lay) write(6,*) '# Ti 1 coordinated (Ti with Oxy)= ',nCNT i1(lay) write(6,*) '# unbonded Ti (Ti with Oxy)= ',nCNTi0(lay) write(6,*) write(6,*) write(6,*)'Coordination of Sr with Oxygen' write(6,*) '# Sr 14 coordinated (Sr with Oxy)= ',nCNSr14(lay) write(6,*) '# Sr 13 coordinated (Sr with Oxy)= ',nCNSr13(lay) write(6,*) '# Sr 12 coordinated (Sr with Oxy)=** ',nCNSr12(lay) write(6,*) '# Sr 11 coordinated (Sr with Oxy)= ',nCNSr11(lay) write(6,*) '# Sr 10 coordinated (Sr with Oxy)= ',nCNSr10(lay) wr ite(6,*) '# Sr 9 coordinated (Sr with Oxy)= ',nCNSr9(lay) write(6,*) '# Sr 8 coordinated (Sr with Oxy)= ',nCNSr8(lay) write(6,*) '# Sr 7 coordinated (Sr with Oxy)= ',nCNSr7(lay) write(6,*) '# Sr 6 coordinated (Sr with Oxy)= ',nCNSr6(lay) write(6,*) '# Sr 5 coordinated (Sr with Oxy)= ',nCNSr5(lay) write(6,*) '# Sr 4 coordinated (Sr with Oxy)= ',nCNSr4(lay) write(6,*) '# Sr 3 coordinated (Sr with Oxy)= ',nCNSr3(lay) write(6,*) '# Sr 2 coordinated (Sr with Oxy)= ',nCNS r2(lay) write(6,*) '# Sr 1 coordinated (Sr with Oxy)= ',nCNSr1(lay) write(6,*) '# unbonded Sr (Sr with Oxy)= ',nCNSr0(lay) write(6,*) enddo !****************************finished each layer write(7,100)'O Ti 6',float(nCNOTi6(6))/Nolayer6, & float(nCNOTi6(1))/Nolayer1, & float(nCNOTi6(2))/Nolayer2,float(nCNOTi6(3))/Nolayer3, & float(nCNOTi6(4))/Nolayer4,float(nCNOTi6(5))/Nolayer5 write(7,100)'O Ti 5',float(nCNOTi 5(6))/Nolayer6, & float(nCNOTi5(1))/Nolayer1, & float(nCNOTi5(2))/Nolayer2,float(nCNOTi5(3))/Nolayer3, & float(nCNOTi5(4))/Nolayer4,float(nCNOTi5(5))/Nolayer5 write(7,100)'O Ti 4',float(nCNOTi4(6))/Nolayer6, & float(nCNOTi4(1 ))/Nolayer1, & float(nCNOTi4(2))/Nolayer2,float(nCNOTi4(3))/Nolayer3, & float(nCNOTi4(4))/Nolayer4,float(nCNOTi4(5))/Nolayer5

PAGE 103

103 write(7,100)'O Ti 3',float(nCNOTi3(6))/Nolayer6, & float(nCNOTi3(1))/Nolayer1, & float(nCNOTi3(2))/ Nolayer2,float(nCNOTi3(3))/Nolayer3, & float(nCNOTi3(4))/Nolayer4,float(nCNOTi3(5))/Nolayer5 write(7,100)'O Ti 2',float(nCNOTi2(6))/Nolayer6, & float(nCNOTi2(1))/Nolayer1, & float(nCNOTi2(2))/Nolayer2,float(nCNOTi2(3))/Nolayer3, & float(nCNOTi2(4))/Nolayer4,float(nCNOTi2(5))/Nolayer5 write(7,100)'O Ti 1',float(nCNOTi1(6))/Nolayer6, & float(nCNOTi1(1))/Nolayer1, & float(nCNOTi1(2))/Nolayer2,float(nCNOTi1(3))/Nolayer3, & float(nCNOTi1(4))/Nolayer4,float(nCNOTi1(5))/Nolayer5 write(7,100)'O Ti 0',float(nCNOTi0(6))/Nolayer6, & float(nCNOTi0(1))/Nolayer1, & float(nCNOTi0(2))/Nolayer2,float(nCNOTi0(3))/Nolayer3, & float(nCNOTi0(4))/Nolayer4,float(nCNO Ti0(5))/Nolayer5 write(7,*)' write(7,101)'O Sr 13',float(nCNOSr13(6))/Nolayer6, & float(nCNOSr13(1))/Nolayer1, & float(nCNOSr13(2))/Nolayer2,float(nCNOSr13(3))/Nolayer3, & float(nCNOSr13(4))/Nolayer4,float(nCNOSr13(5))/Nolayer5 write(7,101)'O Sr 12',float(nCNOSr12(6))/Nolayer6, & float(nCNOSr12(1))/Nolayer1, & float(nCNOSr12(2))/Nolayer2,float(nCNOSr12(3))/Nolayer3, & float(nCNOSr12(4))/Nolayer4,float(nCNOSr12(5))/Nolayer5 write(7,101)'O Sr 11',fl oat(nCNOSr11(6))/Nolayer6, & float(nCNOSr11(1))/Nolayer1, & float(nCNOSr11(2))/Nolayer2,float(nCNOSr11(3))/Nolayer3, & float(nCNOSr11(4))/Nolayer4,float(nCNOSr11(5))/Nolayer5 write(7,101)'O Sr 10',float(nCNOSr10(6))/Nolayer6, & float(nCNOSr10(1))/Nolayer1, & float(nCNOSr10(2))/Nolayer2,float(nCNOSr10(3))/Nolayer3, & float(nCNOSr10(4))/Nolayer4,float(nCNOSr10(5))/Nolayer5 write(7,101)'O Sr 9',float(nCNOSr9(6))/Nolayer6, & float(nCNOSr9(1))/Nolayer1, & float(nCNOSr9(2))/Nolayer2,float(nCNOSr9(3))/Nolayer3, & float(nCNOSr9(4))/Nolayer4,float(nCNOSr9(5))/Nolayer5 write(7,101)'O Sr 8',float(nCNOSr8(6))/Nolayer6, & float(nCNOSr8(1))/Nolayer1, & float(nCNOSr8(2))/Nolayer2,floa t(nCNOSr8(3))/Nolayer3, & float(nCNOSr8(4))/Nolayer4,float(nCNOSr8(5))/Nolayer5 write(7,101)'O Sr 7',float(nCNOSr7(6))/Nolayer6, & float(nCNOSr7(1))/Nolayer1,

PAGE 104

104 & float(nCNOSr7(2))/Nolayer2,float(nCNOSr7(3))/Nolayer3, & float(n CNOSr7(4))/Nolayer4,float(nCNOSr7(5))/Nolayer5 write(7,101)'O Sr 6',float(nCNOSr6(6))/Nolayer6, & float(nCNOSr6(1))/Nolayer1, & float(nCNOSr6(2))/Nolayer2,float(nCNOSr6(3))/Nolayer3, & float(nCNOSr6(4))/Nolayer4,float(nCNOSr6(5))/N olayer5 write(7,101)'O Sr 5',float(nCNOSr5(6))/Nolayer6, & float(nCNOSr5(1))/Nolayer1, & float(nCNOSr5(2))/Nolayer2,float(nCNOSr5(3))/Nolayer3, & float(nCNOSr5(4))/Nolayer4,float(nCNOSr5(5))/Nolayer5 write(7,101)'O Sr 4',flo at(nCNOSr4(6))/Nolayer6, & float(nCNOSr4(1))/Nolayer1, & float(nCNOSr4(2))/Nolayer2,float(nCNOSr4(3))/Nolayer3, & float(nCNOSr4(4))/Nolayer4,float(nCNOSr4(5))/Nolayer5 write(7,101)'O Sr 3',float(nCNOSr3(6))/Nolayer6, & float(nCNOSr3(1))/Nolayer1, & float(nCNOSr3(2))/Nolayer2,float(nCNOSr3(3))/Nolayer3, & float(nCNOSr3(4))/Nolayer4,float(nCNOSr3(5))/Nolayer5 write(7,101)'O Sr 2',float(nCNOSr2(6))/Nolayer6, & float(nCNOSr2(1))/Nolayer1, & f loat(nCNOSr2(2))/Nolayer2,float(nCNOSr2(3))/Nolayer3, & float(nCNOSr2(4))/Nolayer4,float(nCNOSr2(5))/Nolayer5 write(7,101)'O Sr 1',float(nCNOSr1(6))/Nolayer6, & float(nCNOSr1(1))/Nolayer1, & float(nCNOSr1(2))/Nolayer2,float(nCNOSr1 (3))/Nolayer3, & float(nCNOSr1(4))/Nolayer4,float(nCNOSr1(5))/Nolayer5 write(7,101)'O Sr 0',float(nCNOSr0(6))/Nolayer6, & float(nCNOSr0(1))/Nolayer1, & float(nCNOSr0(2))/Nolayer2,float(nCNOSr0(3))/Nolayer3, & float(nCNOSr0(4) )/Nolayer4,float(nCNOSr0(5))/Nolayer5 write(7,*)' write(7,102)'Ti O 8',float(nCNTi8(6))/Ntilayer6, & float(nCNTi8(1))/Ntilayer1, & float(nCNTi8(2))/Ntilayer2,float(nCNTi8(3))/Ntilayer3, & float(nCNTi8(4))/Ntilayer4,float(nCNTi8( 5))/Ntilayer5 write(7,102)'Ti O 7',float(nCNTi7(6))/Ntilayer6, & float(nCNTi7(1))/Ntilayer1, & float(nCNTi7(2))/Ntilayer2,float(nCNTi7(3))/Ntilayer3, & float(nCNTi7(4))/Ntilayer4,float(nCNTi7(5))/Ntilayer5 write(7,102)'Ti O 6',float(nCNTi6(6))/Ntilayer6, & float(nCNTi6(1))/Ntilayer1, & float(nCNTi6(2))/Ntilayer2,float(nCNTi6(3))/Ntilayer3, & float(nCNTi6(4))/Ntilayer4,float(nCNTi6(5))/Ntilayer5 write(7,102)'Ti O 5',float(nCNTi5(6))/Ntilayer6, & float(nCNTi5(1))/Ntilayer1,

PAGE 105

105 & float(nCNTi5(2))/Ntilayer2,float(nCNTi5(3))/Ntilayer3, & float(nCNTi5(4))/Ntilayer4,float(nCNTi5(5))/Ntilayer5 write(7,102)'Ti O 4',float(nCNTi4(6))/Ntilayer6, & float(nCNTi4(1) )/Ntilayer1, & float(nCNTi4(2))/Ntilayer2,float(nCNTi4(3))/Ntilayer3, & float(nCNTi4(4))/Ntilayer4,float(nCNTi4(5))/Ntilayer5 write(7,102)'Ti O 3',float(nCNTi3(6))/Ntilayer6, & float(nCNTi3(1))/Ntilayer1, & float(nCNTi3(2))/N tilayer2,float(nCNTi3(3))/Ntilayer3, & float(nCNTi3(4))/Ntilayer4,float(nCNTi3(5))/Ntilayer5 write(7,102)'Ti O 2',float(nCNTi2(6))/Ntilayer6, & float(nCNTi2(1))/Ntilayer1, & float(nCNTi2(2))/Ntilayer2,float(nCNTi2(3))/Ntilayer3, & float(nCNTi2(4))/Ntilayer4,float(nCNTi2(5))/Ntilayer5 write(7,*)' write(7,103)'Sr O 14',float(nCNSr14(6))/Nsrlayer6, & float(nCNSr14(1))/Nsrlayer1, & float(nCNSr14(2))/Nsrlayer2,float(nCNSr14(3))/Nsrlayer3, & float(nCNSr14(4))/Nsrlayer4,float(nCNSr14(5))/Nsrlayer5 write(7,103)'Sr O 13',float(nCNSr13(6))/Nsrlayer6, & float(nCNSr13(1))/Nsrlayer1, & float(nCNSr13(2))/Nsrlayer2,float(nCNSr13(3))/Nsrlayer3, & float(nCNSr13(4))/Nsrlayer4,fl oat(nCNSr13(5))/Nsrlayer5 write(7,103)'Sr O 12',float(nCNSr12(6))/Nsrlayer6, & float(nCNSr12(1))/Nsrlayer1, & float(nCNSr12(2))/Nsrlayer2,float(nCNSr12(3))/Nsrlayer3, & float(nCNSr12(4))/Nsrlayer4,float(nCNSr12(5))/Nsrlayer5 write(7,103)'Sr O 11',float(nCNSr11(6))/Nsrlayer6, & float(nCNSr11(1))/Nsrlayer1, & float(nCNSr11(2))/Nsrlayer2,float(nCNSr11(3))/Nsrlayer3, & float(nCNSr11(4))/Nsrlayer4,float(nCNSr11(5))/Nsrlayer5 write(7,103)'Sr O 10',float(nCN Sr10(6))/Nsrlayer6, & float(nCNSr10(1))/Nsrlayer1, & float(nCNSr10(2))/Nsrlayer2,float(nCNSr10(3))/Nsrlayer3, & float(nCNSr10(4))/Nsrlayer4,float(nCNSr10(5))/Nsrlayer5 write(7,103)'Sr O 9',float(nCNSr9(6))/Nsrlayer6, & float( nCNSr9(1))/Nsrlayer1, & float(nCNSr9(2))/Nsrlayer2,float(nCNSr9(3))/Nsrlayer3, & float(nCNSr9(4))/Nsrlayer4,float(nCNSr9(5))/Nsrlayer5 write(7,103)'Sr O 8',float(nCNSr8(6))/Nsrlayer6, & float(nCNSr8(1))/Nsrlayer1, & float(nCNSr8(2))/Nsrlayer2,float(nCNSr8(3))/Nsrlayer3, & float(nCNSr8(4))/Nsrlayer4,float(nCNSr8(5))/Nsrlayer5 write(7,103)'Sr O 7',float(nCNSr7(6))/Nsrlayer6, & float(nCNSr7(1))/Nsrlayer1,

PAGE 106

106 & float(nCNSr7(2))/Nsrlayer2,float(nCNS r7(3))/Nsrlayer3, & float(nCNSr7(4))/Nsrlayer4,float(nCNSr7(5))/Nsrlayer5 write(7,103)'Sr O 6',float(nCNSr6(6))/Nsrlayer6, & float(nCNSr6(1))/Nsrlayer1, & float(nCNSr6(2))/Nsrlayer2,float(nCNSr6(3))/Nsrlayer3, & float(nCNSr6( 4))/Nsrlayer4,float(nCNSr6(5))/Nsrlayer5 write(7,103)'Sr O 5',float(nCNSr5(6))/Nsrlayer6, & float(nCNSr5(1))/Nsrlayer1, & float(nCNSr5(2))/Nsrlayer2,float(nCNSr5(3))/Nsrlayer3, & float(nCNSr5(4))/Nsrlayer4,float(nCNSr5(5))/Nsrlayer5 write(7,103)'Sr O 4',float(nCNSr4(6))/Nsrlayer6, & float(nCNSr4(1))/Nsrlayer1, & float(nCNSr4(2))/Nsrlayer2,float(nCNSr4(3))/Nsrlayer3, & float(nCNSr4(4))/Nsrlayer4,float(nCNSr4(5))/Nsrlayer5 write(7,103)'Sr O 3',float(nCN Sr3(6))/Nsrlayer6, & float(nCNSr3(1))/Nsrlayer1, & float(nCNSr3(2))/Nsrlayer2,float(nCNSr3(3))/Nsrlayer3, & float(nCNSr3(4))/Nsrlayer4,float(nCNSr3(5))/Nsrlayer5 100 format(1A6,1X,6F15.6) 101 format(1A6,1X,6F15.6) 102 format(1A6,1X,6F15.6) 103 format(1A6,1X,6F15.6) 104 format(i7,1x,i5,3(1x,f11.6),4(i5,1x)) c,5F15.6) c100 format(1X,1X,5(I12,1X)) stop end

PAGE 107

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119 BIOGRAPHICAL SKETCH Jennifer Wohlwend was born and predominately raised in Summerville, South Carolina. She attended Clemson University in Clemson, South Carolina where she attained a Bachelor of Science in ceramic and materials science and engineering, in 2004. In the fall of 2004, she arrived at the University of Florida under the advisory of Dr. Susan B. Sinnott and became part of the Computational Materials Science Focus Group (CMSFG). Jennifer worked on the simulation of particulate and cluster deposition of SrTiO3.