PEROVSKITE結構系統與簡單金屬氧化物的介面穩定性與成長(II)

1

行政院國家科學委員會補助專題研究計畫成果 報告

※※※※※※※※※※※※※※※※※※※※※※※※※

※ ※

※ PEROVSKITE 結構系統與簡單金屬氧化物 ※

※ 的介面穩定性與成長(II) ※

※ ※

※※※※※※※※※※※※※※※※※※※※※※※※※

計畫類別：□個別型計畫 □整合型計畫 計畫編號：NSC 89－2112－M－006－015－

執行期間：1999 年 8 月 1 日至 2001 年 7 月 31 日

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執行單位：國立成功大學物理系

2

中 華 民 國 90 年 10 月 15 日

3

行政院國家科學委員會專題研究計畫成果報告

國科會專題研究計畫成果報告撰寫格式說明 Preparation of NSC Project Reports

計畫編號：NSC

89-2112-M-006-015

執行期限：88 年 8 月 1 日至 90 年 7 月 31 日 主持人：鄭靜 國立成功大學物理系

一、中文摘要

我 們 使 用 第 一 原 理 計 算 方 法 研 究 等 結 晶 常 數 成 長 的 SrTiO3/MgO(001) 和 MgO/SrTiO3(001)系 統。探討的內容包括一層層上加五至六層覆蓋層 與不同的介面結構。同時也研究其相對應的自由 懸空薄膜，包括塊材與基底結晶常數的考量。研 究發現 SrTiO3/MgO(001)的介面效應影響範圍要比 MgO/SrTiO3(001) 的長程得多。在應力上也發現二

項有趣的結果：一為在有應變的 SrTiO3薄膜應力

主要分佈在 TiO2原子層，二為在 SrTiO3/MgO(001)

系統中若介面結構為 TiO2/MgO 則應力改變量在

前五層薄膜為正負符號交替變化。

關鍵詞：介面結構，pervovskite，鹼金屬氧化物，

第一原理計算

Abstract

First-principles calculations are employed to study the pseudomorphically grown systems of SrTiO3/MgO(001) and MgO/SrTiO3(001). Different interface structures and up to 5 or 6 layers in the film thickness added layer by layer are considered in the present studies. The corresponding free-standing slabs in the lattice constants of the substrate and that of the bulk film materials are also treated for comparison. The variation in adsorption energy and stress due to different film thickness are evaluated and discussed. It was found that the interface effect in the SrTiO3/MgO(001) systems is much longer range than that in the MgO/SrTiO3(001) systems. We also observe two interesting phenomena related to stresses.

Firstly, in the free-standing strained films of SrTiO3 the strain effect is found to distribute mainly on the TiO2

atomic layer. Secondly, the interface effect causes the stress changes alternating in sign in the first 5 added film layers of the SrTiO3/MgO(001) systems with TiO2/MgO interface.

Keywords: interface structure, perovskite, alkaline earth oxide, ab initio calculations

二、結果與討論

如所附論文。

free-standing strained films Strained films on a 7-layer, SrO-terminated SrTiO ₃ substrate

M1 M M/SrO-SrTiO ₃ sub./M

M2 M/M/M M/M/SrO-SrTiO ₃ sub./M/M

M3 M/M/M/M/M M/M/M/SrO-SrTiO ₃ sub./M/M/M

M4 M/M/M/M/M/M/M M/M/M/M/SrO-SrTiO ₃ sub./M/M/M/M

M5 M/M/M/M/M/M/M/M/M M/M/M/M/M/SrO-SrTiO ₃ sub./M/M/M/M/M

Free-standing strained films Strained films on a 7-layer MgO(001) substrate

S1 S S/MgO substrate/S

T2 T/S/T T/S/MgO substrate/S/T

S3 S/T/S/T/S S/T/S/MgO substrate/S/T/S T4 T/S/T/S/T/S/T T/S/T/S/MgO substrate/S/T/S/T S5 S/T/S/T/S/T/S/T/S S/T/S/T/S/MgO substrate/S/T/S/T/S T6 T/S/T/S/T/S/T/S/T/S/T T/S/T/S/T/S/MgO substrate/S/T/S/T/S/T

Free-standing strained films Strained films on a 7-layer MgO(001) substrate

T1 T T/MgO substrate/T

S2 S/T/S/ S/T/MgO substrate/T/S

T3 T/S/T/S/T T/S/T/MgO substrate/T/S/T

S4 S/T/S/T/S/T/S S/T/S/T/MgO substrate/T/S/T/S

T5 T/S/T/S/T/S/T/S/T T/S/T/S/T/MgO substrate/T/S/T/S/T

S6 S/T/S/T/S/T/S/T/S/T/S S/T/S/T/S/T/MgO substrate/T/S/T/S/T/S

Sr Sr

Sr Sr

Mg Mg

Mg Mg

Mg

Mg Mg

Mg

Mg

O O

O

O O

O O

O O

O Ti

Mg Mg

Mg Mg

Mg Mg

Mg Mg Mg

O

O

O

O O

O

O O O

O O

O O SrTiO film

MgO (001) Substrate

SrTiO /MgO(001) interfaces ₃

The preferred, lower-energy interface structures

S-on-M systems T-on-M systems

Sr

Sr Sr

Sr

Ti

Mg

Mg

Mg Mg

Mg

O O

O O O

O

O O

O

Sr

Sr Sr

Sr Ti

Mg Mg

Mg

Mg

O O

O O O

O O O O

SrTiO (001) O Substrate

3

MgO film

MgO/SrTiO (001) interfaces ₃

The preferred, lower-energy interface structures

M-on-S systems M-on-T systems

SrTiO3/MgO(001) and MgO/SrTiO3(001) Systems:

Energetics and Stresses

C. Cheng,

K. Kunc,

G. Kresse

and J. Hafner

¤

Department of Physics, National Cheng Kung University, Tainan, Taiwan, R.O.C.

y

Laboratoire d'Optique des Solides associ¶ e au CNRS, T13 - C80, 4 pl. Jussieu, 75252 Paris - Cedex 05, France

z

Institut fÄ ur Material Physik and Center for Computational Material Science, Sensengasse 8, A-1090 Wien, Austria

Abstract

First-principles calculations are employed to study the pseudomorphically grown systems of SrTiO3/MgO(001) and MgO/SrTiO3(001). Di® erent interface structures and up to 5 or 6 layers in the ¯lm thickness added layer by layer are considered in the present studies. The corresponding free-standing slabs in the lattice constants of the substrate and that of the bulk ¯ lm materials are also treated for comparison. The variation in adsorption energy and stress due to di® erent ¯ lm thickness are evaluated and discussed. It was found that the interface e® ect in the SrTiO3/MgO(001) systems is much longer range than that in the MgO/SrTiO3(001) systems. We also observe two interesting phenomena related to stresses. Firstly, in the free-standing strained

¯lms of SrTiO3 the strain e® ect is found to distribute mainly on the TiO2atomic layer.

Secondly, the interface e® ect causes the stress changes alternating in sign in the ¯ rst 5 added ¯lm layers of the SrTiO3/MgO(001) systems with TiO2/MgO interface.

PACS: 77.84-s, 77.84.Bw, 68.10.Cr, 68.35.Bs

1corresponding author, E-mail: [email protected]

1

1 Introduction

The heterogrowth between oxides exhibits very di®erent physical properties from those between semiconductors. For example, the lattice mismatch between observed heteroepi- taxially grown oxides can be much larger than those between semiconductors. However, considerably fewer studies have been dedicated to the heterosystems between oxides.

In the present work, we carry out systematic studies of SrTiO

¯lms pseudomor- phically grown onto MgO(001) (denoted as SrTiO

/MgO(001) hereafter) and its inverted systems, i.e. MgO ¯lms onto SrTiO

(001) (denoted as MgO/SrTiO

(001)), by investigat- ing the ab initioly evaluated adsorption energy and stresses of these systems in various ¯lm thickness and di®erent interface structures. The SrTiO

(001) surface is frequently used as substrate for growing epitaxial ¯lms of high-T

superconductors

1

while MgO(001) is widely used as substrate for di®erent materials such as metals

2

, superconductors

3

and optoelectronic devices

4

. Bulk SrTiO

stays paraelectric in the cubic perovskite structure at ¯nite temperatures down to 105K

5

. This structure allows two types of (001) termina- tion, viz. the SrO- or the TiO

-terminated surface. MgO is a prototype of ionic rocksalt solid with neutral (001) surface consisting both Mg and O atoms. Experimental

6

stud- ies of growing SrTiO

on MgO(001) observed very di®erent ¯lm properties for the growth with di®erent interfaces, i.e. SrO/MgO and TiO

/MgO interfaces. With SrO/MgO inter- face the grown SrTiO

¯lms have 'island-like' nucleation and surface roughening while with TiO

/MgO interface, the psdudomorphically and optical-quality epitaxially grown thin ¯lm was observed. On the other hand, incommensurate growth was found in the inverted system of MgO grown on SrTiO

(001)

7

. The growth gave high quality single crystalline MgO

¯lm with nearly relaxed lattice constant from the ¯rst monolayer, i.e. no pseudomorphic growth.

Due to the limit in the method we use, both the SrTiO

/MgO(001) and MgO/SrTiO

(001) will be studied in the pseudomorphic condition. The adsorption energy and macroscopic stresses of di®erent interface structures with di®erent ¯lm thickness are obtained from ab initio calculations. These results and their implications to the experimental observations

2

will be discussed. For comparison, the free-standing ¯lms in the lattice constants of the substrate and that of the bulk ¯lm materials are also treated. The interface e®ect can be easily deduced from the comparison between the interface systems and their corresponding free-standing ¯lms. It was found that the SrTiO

/MgO(001) systems have much longer- ranged interface e®ect than the MgO/SrTiO

(001) systems. The analysis of system stresses also lead to unexpected new and interesting results.

The present paper is organized as follows: The details of the calculations are ex- plained in Section 2. Section 3 speci¯es the systems included in the present studies for ab initio calculations and Section 4 the preferred interface structures obtained from calcula- tions. The calculated results of adsorption energy and stresses for the SrTiO

/MgO(001) and MgO/SrTiO

(001) systems are presented in the section 5 and 6 respectively. Finally the conclusion is in Section 7.

2 Calculational details

The calculations are based on Density Functional Theory

8

within the Local Density Approximation

9

using the Ceperley-Alder form

10

for exchange-correlation. We use the ab-initio total-energy and molecular-dynamics Vienna ab-initio simulation program (VASP), developed at the Institut fÄ ur Material Physik of the UniversitÄ at Wien

11

.

The one-electron wavefunctions are expanded in a plane-wave basis limited by the kinetic energy cuto® E

=495eV. Integration over the ¯rst Brillouin zone uses the discrete k-point sampling according to Monkhost-Pack

12

(see further). The ultrasoft pseudopotentials

13

are used to describe the interactions between valence electrons and ions; the number of valence electrons considered is 8, 10, 8, and 6 for Sr, Ti, Mg and O atoms respectively.

The calculated lattice constants for bulk SrTiO

and MgO are 3.866º A and 4.1605º A respectively, well compared to the experimental values of 3.905

14

and 4.21

15

. The k-

3

point set used corresponds to the Monkhost-Pack parameters (4 4 4) for bulk SrTiO

in the primitive unit cell and bulk MgO in the conventional cubic cell (consisting of 4 Mg and 4 O atoms). Previous studies

16

have shown that this k-point set is su± cient for the Brillouin zone integration.

Periodic slabs separated by vacuum are used to simulate the surface systems. We use periodic cells with vacuum size at least as large as 12º A. For the interface systems, slab consisting of 7 atomic planes are used to simulate the substrate. It have been checked that it gives similar surface properties as previous calculations

16

which used up to 11 atomic layers for studying the SrTiO

(001) surfaces. All the slabs studied are symmetric with respect to the mirror plane passing through the center of the supercell as shown in Fig. 1 and 2. The k-point set used in the supercell corresponds to (4 4 2) Monkhost- Pack parameters, i.e. the same accuracy as that for the bulk in the lateral direction and higher accuracy in the ¯lm-growing direction. For relaxing atomic positions in the surface structures, we use the forces due to the Hellmann-Feynman theorem

17

to move the atoms to positions at which all forces become smaller than ± = 0.02eV/ºA.

3 The Studied Systems

Four interface systems are studied: (1) SrTiO

¯lms grown on the MgO(001) substrate with SrO/MgO interface, (2) similar as (1) but with TiO

/MgO interface, (3) MgO ¯lms grown on the SrO-terminated SrTiO

(001) substrate, and (4) similar as (3) but on the TiO

-terminated SrTiO

(001) substrate. They are denoted as the S-on-M, T-on-M, M-on- S and M-on-T systems respectively. As stated in the section 2, the systems are simulated by using periodic slabs separated by vacuum of thickness greater than 12º A and the substrates contain 7 atomic layers of substrate bulk materials. The thickness of the ¯lms considered is up to 6 layers for the S-on-M and T-on-M systems and up to 5 layers for the M-on-S and M-on-T systems. All systems considered are symmetric with respect to mirror plane passing through the center of the slab as shown in ¯gures 1 and 2. The interface systems are calculated using the theoretical lattice constants of the substrates. For comparison,

4

the free-standing ¯lms in the lattice constants of the substrates and the bulk of the ¯lm materials are also studied. We shall denote the former as the free-standing strained ¯lms and the latter as the free-standing ¯lms.

4 Interface Structures

The preferred, lower-energy interface structures for the pseudomophophically grown SrTiO

on the MgO(001) surface and those for MgO on the SrTiO

(001) surface obtained from cal- culations are shown in ¯gures 3 and 4. The lattice mismatch between the bulk SrTiO

(3.866 º A) and MgO (4.1605 º A) is around 7% while that between the SrTiO

(001) (3.866 º A) and MgO(001) surfaces (4:1604= p

2) is more than 23% as the surface unit cell of MgO is ro- tated 45

relative to its bulk unit cell. Considering the large lattice mismatch between the SrTiO

(001) and MgO(001) surfaces, it is expect that the more realistic interface con- struction is from the 45

rotated ( p

2 £ p

2) MgO(001) surface structure which reduces the lattice mismatch back to that between the two bulks.

Theoretically there are two di®erent interface structures for each of the interface systems. In addition to the interface structures shown in ¯gures 3 and 4, the other inter- face structures can be obtained by horizontally shifting half unit cell of the grown ¯lms along (100) direction relative to the substrate. For the TiO

/MgO (T-on-S systems) and MgO/TiO

(M-on-T systems) interfaces, the relative shift results in anion-on-anion and cation-on-cation interfaces whose interface energy are much higher than the shown pre- ferred structures which have anion-on-cation bonds. Calculations give energy di®erences in the order of 5 eV/(TiO

interface area). For the SrO/MgO (S-on-M systems) and MgO/SrO (M-on-S systems) interfaces, the relative shifted interfaces have adsorption energies of 0.3 and 0.3 eV (per SrO interface area) higher than those of the shown structures in the ¯rst adsorption layer. The preference is still present when the ¯lm thickness is increased to 2, about 0.3 and 0.4 eV lower in the adsorption energy of the two-layer ¯lms. Notice that for the SrO/MgO and MgO/SrO interfaces, the preferred interfaces have O-on-Mg and Sr- on-Mg bonds (or Mg-on-O and Mg-on-Sr bonds) while the shifted ones have O-on-O and

5

Sr-on-O bonds. These results show that the interface structures which avoid O-on-O bonds are more favoured than those avoid anion-on-anion. From now on the studied systems will have the preferred, lower-energy interface structures as those shown in Fig. 3 and 4.

5 Results for the SrTiO3/MgO(001) systems

For the SrTiO

/MgO(001) systems, up to six layers in ¯lm thickness were considered for both the S-on-M and T-on-M systems. The corresponding free-standing strained ¯lms and free-standing ¯lms, as shown in Fig. 1, are also considered in the calculations. We evaluate the adsorption energy of an added SrO or TiO

layers to the system and the change in lateral stresses (¾

= ¾

) caused by the additional layer. The results are listed in the Tables 1 and 2 for the adsorption energy and Tables 3 and 4 for the stress changes. The adsorption energy are with respect to the corresponding atomic energy. Only lateral stresses are considered as the stresses along the ¯lm-growing direction is at least one-order smaller than the lateral stresses, due to the atomic relaxation in the ¯lm-growing direction.

From the adsosrption-energy results of both kinds of free-standing ¯lms (3rd col- umn in Tables 1 and 2) we see that the adsorption energy converges to constants (-14.7 eV for an added SrO layer and -29.7 eV for an added TiO

layer) from the 3rd added layers, i.e. when the thickness of the ¯lms is 5 atomic layers (Fig. 1). Our assumption that 7 atomic layers are thick enough to simulate SrTiO

(001) substrates is again con¯rmed. For the free-standing strained ¯lms, they take two more layers in thickness to the same con- vergence, i.e. from the 4th added layers which corresponds to ¯lms of 7-layer thickness.

We notice that the converged adsorption energy of an added SrO layer are the same for the free-standing and free-standing strained ¯lms. That is, the strain has e®ect mainly on the TiO

layers. This fact also can be seen in the results of stress changes (Tables 3 and 4). In the free-standing strained ¯lms, the stresses hardly change when the added layer is SrO layer. It is an interesting phenomenon that a lateral strain applied to the materials consisting of two di®erent atomic layers have the e®ect mainly on one kind of them.

6

The adsorption energies for the heterosystems are expected to converge to the same values as the free-standing strained ¯lms converge. Only from the 6th added layer in the heterosystems that the convergence are approached. This much slower convergence is the e®ect of the substrate, i.e. the interface e®ect. The lower adsorption energies of the T-on-M systems than the S-on-M systems is consistent with the experimental observations that the T-on-M system gives pseudomorphic-growing epitaxial ¯lms. The T-on-M systems have not only lower adsorption energy of the 1st added ¯lm layer than the S-on-M system, but the preference is kept throughout the pseudomorphic growth. When the same number of each kinds of atoms in the overlayers are considered for the S-on-M and T-on-M systems, i.e. considering the systems with 2, 4... layers of SrTiO

¯lms, the energy preference is about 1.7 eV per (4.1604 £ 4.1605) MgO(001) surface area, as can be seen from the last column of Tables 1 and 2.

The stress results are shown in Tables 3 and 4. Positive and negative stresses of a system indicate the system is under tensile and compressive stresses respectively. Although the stress changes can be positive or negative in these systems, their system stresses are all found tensile.

For the free-standing ¯lms at large thickness, the non-zero stresses correspond to their surface stresses. For the free-standing strained ¯lms, the stresses include the surface stresses and the stresses of the strained layers. As the strain in the free-standing strained

¯lms of SrTiO

is positive, i.e. the ¯lms are in the lattice constant of bulk MgO (4.1605 º A) rather than in that of the bulk SrTiO

(3.866º A), the changes in stress are positive and the systems are getting under more tensile stresses. The convergence in the stress changes for the free-standing strained ¯lms are much slower than that in the adsorption energy. This is expected as stresses correspond to the 1st derivative of energy with respect to strain.

As mentioned previously, the stress increment is mainly on the TiO

layers. It seems that the convergence has not been achieved even after the 6th added layers, i.e. thickness of 13 layers in the free-standing strained ¯lms.

The interface e®ect makes the stress changes extends to even longer range than

7

that for the free-standing strained ¯lms. It is expected to take a few more layers beyond the 6th added layer for the stress changes converging to the values of the free-standing strained

¯lms. The interface e®ect on stress changes show very di®erent patterns on the S-on-M systems from those on the T-on-M systems. In the S-on-M systems, the stress changes for the added SrO layers start with large positive values and decrease as ¯lm thickness increase while those for the added TiO

layers increase as ¯lm thickness increases. In the T-on-M systems, the stress changes for the added SrO layers start with negative values and decrease in magnitude as ¯lm thickness increases while those for the added TiO

layers seem to be oscillating. Note that in the T-on-M systems, the ¯rst two added SrO layers actually reduce the system's tensile lateral stresses. Accordingly, the stress changes alternate in sign in the T-on-M systems for the ¯rst ¯ve added SrTiO

layers. Therefore, the interface e®ect in the T-on-M systems do not only modify the stress changes, but actually changes the sign of the stress changes.

6 Results for the MgO/SrTiO₃(001) systems

The free-standing and free-standing strained MgO ¯lms have their adsorption energy con- verge to constants at the 2nd and 3rd added layers respectively (3rd and 4th column in Table 5). These are faster than those in the free-standing SrTiO

(001) ¯lms. One interest- ing point about the free-standing MgO ¯lms is that the energy of the one-layer free-standing strained ¯lm (of lattice constant 3.866 º A) is actually lower than that of the one-layer free- standing ¯lm (of lattice constant 4.1605 º A). Calculations show that the most stable lateral lattice constant of the single-layer MgO ¯lm is 3.9298º A which is 5.5% smaller than the theoretical lattice constant of bulk MgO (4.1605º A).

The adsorption energy for the heterosystems converge at the 4th and 3rd added MgO layer for the M-on-S and M-on-T systems respectively. The interface e®ect in the MgO/SrTiO

(001) systems is therefore much shorter ranged than that in the SrTiO

/MgO(001) systems. In fact, one would say that in the M-on-T system the interface e®ect is not longer in range than that of the free-standing ¯lms, both of their adsorption energy are converged

8

from the 3rd added layer. Similarly to the SrTiO

/MgO(001) systems, the MgO/TiO

interface is more favored than the MgO/SrO interface. The adsorption energy is about 1 eV/(per SrTiO

(001) surface unit cell) lower for the M-on-T systems throughout the pseudomorphic growth.

The surface stress for the free-standing MgO ¯lms is tensile, similar to most sur- faces. The system stresses for the free-standing strained MgO ¯lms are compressive as the

¯lms are at the lattice constant of bulk SrTiO

which is about 7% smaller than that of bulk MgO. Although the SrTiO

(001) surfaces are under tensile stress as most surfaces do, the system stresses become compressive after 1st MgO layer is added pseudomorphically.

Therefore, all the M-on-S and M-on-T systems we considered here are under compressive stresses. The magnitude in the stress changes of both the M-on-S and M-on-T systems seem to be oscillating. In the experiment of MgO growing on the SrTiO

(001) surface

7

, it was not identi¯ed which surface of the SrTiO

(001) surfaces was the MgO ¯lms grow- ing on. However, it is usually believed that most of the surface area

18

is occupied by the TiO

-terminated SrTiO

(001) surface as it is more stable than the SrO-terminated one. The experimental observation of the non-pseudomorphic growth of MgO on the SrTiO

(001) surface with nearly relaxed lattice constant from the ¯rst monolayer might be related to the very short-ranged interface e®ect and/or the compressive surface stresses of the pseudomorphic grown systems. Compressive surface stresses are rarely found on stable surfaces.

7 Conclusions

We have carried out systematic ab initio studies of the SrTiO

/MgO(001) and MgO/SrTiO

(001) systems. The adsorption energy and changes in stress of up to 5- or 6-layer ¯lms added layer by layer onto the substrates were considered. The corresponding free-standing ¯lms in the lattice constants of the substrates and the bulk ¯lm materials were considered for deducing the interface e®ect. It was found the the interface e®ect in the SrTiO

/MgO(001) systems is much longer range than that in the MgO/SrTiO

(001) systems. Several interesting phe-

9

nomena related to stresses were found: the strain e®ect is mainly on the TiO

atomic layer in the free-standing strained ¯lms and the interface e®ect in the T-on-M systems causes the stress changes alternate in sign in the ¯rst 5 added ¯lm layers.

Acknowledgements

We are grateful to G. Chern for having suggested this study and useful discus- sions. This work was supported by the National Science Council in Taiwan (ROC) and the CNRS (Centre National de la Recherche Scienti¯que) in France. The computer resources were partly provided by the National Center for High-Performance Computing in HsinChu, Taiwan.

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11

Figure Captions:

Figure 1. The structures of the studied SrTiO

/MgO(001) systems and their corre- sponding free-standing ¯lms. All simulated structures are symmetric in the ¯lm-growing direction. The 'S' and 'T' corresponds to the SrO and TiO

atomic layer respectively. The notation, e.g. T4, speci¯es the top atomic layer (i.e. the surface layer) of the structure (TiO

in T4) and the number of layers in the ¯lm thickness on top of the substrate (4 in T4). The same notation is used for the corresponding free-standing ¯lms whose similarity to the interface systems can be seen from the shaded letters of the structures.

Figure 2. Similar as ¯gure 1, but for the MgO/SrTiO

(001) systems and their corre- sponding free-standing ¯lms. The 'M' denotes the MgO layer.

Figure 3. The preferred, lower-energy interface structures for the S-on-M and T-on-M systems. The strain in the SrTiO

¯lm casued by pseudomorphic growth is 7.6%.

Figure 4. As ¯gure 3, but for the M-on-S and M-on-T systems. The strain in the MgO

¯lm casued by pseudomorphic growth is -7%.

12

Tables:

Table 1. The adsorption energy of an added SrO or TiO

layer for the S-on-M systems and the corresponding free-standing and free-standing strained ¯lms (Fig.1). The energy is in units eV/(SrO formula unit) or eV/(TiO

formula unit). The results of the SrO added layer and TiO

added layer are left- and right- aligned for clarity. Also listed are the accumulated adsorption energy for even number of layers in the adsorbed ¯lms.

overlayer free-standing free-standing S-on-M §

thickness ¯lms strained ¯lms systems

S1 0+1 -11.3 -10.1 -11.0

T2 1+1 -30.0 -29.5 -30.9 -41.9

S3 2+1 -14.8 -14.8 -13.7

T4 3+1 -29.7 -29.0 -29.5 -85.1

S5 4+1 -14.7 -14.7 -14.4

T6 5+1 -29.7 -29.0 -29.1 -128.6

Table 2. The adsorption energy for the T-on-M systems. Details as in Table 1.

overlayer free-standing free-standing T-on-M §

thickness ¯lms strained ¯lms systems

T1 0+1 -25.6 -24.0 -27.5

S2 1+1 -15.3 -15.5 -16.0 -43.5

T3 2+1 -29.7 -29.1 -28.3

S4 3+1 -14.7 -14.7 -15.0 -86.8

T5 4+1 -29.7 -29.0 -28.8

S6 5+1 -14.7 -14.7 -14.8 -130.4

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Table 3. The change in stress (average macroscopic stress ¾

= ¾

) caused by an additional SrO or TiO

layer for the S-on-M systems and their corresponding free-standing and free-standing strained ¯lms. Stress are in units eV/(SrO formula unit) or eV/(TiO

formula unit).

overlayer free-standing free-standing S-on-M

thickness ¯lms strained ¯lms systems

S1 0+1 +6.7 +8.5 +8.3

T2 1+1 -0.9 +6.5 +1.1

S3 2+1 -0.7 -0.2 +4.8

T4 3+1 +0.4 +8.6 +5.5

S5 4+1 -0.4 +0.1 +2.5

T6 5+1 +0.5 +8.9 +7.4

Table 4. As in table 3, but for the T-on-M systems and their corrsponding free-standing and free-standing strained ¯lms.

overlayer free-standing free-standing T-on-M

thickness ¯lms strained ¯lms systems

T1 0+1 +6.9 +15.3 +7.5

S2 1+1 -1.3 -0.6 -3.4

T3 2+1 +0.1 +7.8 +11.8

S4 3+1 -0.5 +0.1 -1.6

T5 4+1 +0.3 +8.8 +10.6

S6 5+1 -0.4 +0.1 +0.1

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Table 5. The adsorption energy of an added MgO layer for the M-on-S and M-on-T systems and the corresponding free-standing and free-standing strained ¯lms (Fig. 2). The energy is in unit eV/(two MgO formula unit).

overlayer free-standing free-standing M-on-S M-on-T thickness ¯lms strained ¯lms systems systems

M1 0+1 -24.0 -24.4 -25.5 -26.5

M2 1+1 -26.6 -26.1 -25.9 -25.8

M3 2+1 -26.6 -26.0 -25.9 -26.0

M4 3+1 -26.6 -26.0 -26.0 -26.0

M5 4+1 -26.6 -26.0 -26.0 -26.0

Table 6. The change in stress caused by an added MgO layer for the M-on-S and M-on-T systems and the corresponding free-standing and free-standing strained ¯lms. Stress are in unit eV/(two MgO formula unit).

overlayer free-standing free-standing M-on-S M-on-T thickness ¯lms strained ¯lms systems systems

M1 0+1 +7.9 -2.7 -1.3 -5.6

M2 1+1 -0.2 -8.3 -4.7 -8.4

M3 2+1 +0.0 -8.4 -11.1 -9.2

M4 3+1 +0.0 -8.5 -8.7 -8.8

M5 4+1 +0.1 -8.3 -9.1 -8.5

15