Understanding of Preferred Orientation Formation in Rock-Salt

Synopsis. We developed a kinetic model to predict the preferred orientation for the case of rock-salt MgO crystal by assuming random walk diffusion of...
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Understanding of Preferred Orientation Formation in Rock-Salt Materials: The Case of MgO Hak Ki Yu† and Jong-Lam Lee* Division of Advanced Materials Science and Department of Materials Science and Engineering, Pohang University of Science and Technology (POSTECH), Pohang, 790-784, Korea ABSTRACT: We developed a kinetic model to predict the preferred orientation for the case of rock-salt MgO crystal by assuming random walk diffusion of the adatom between (111) and (100) planes during growth. This model suggests that the tendency of the (111) preferred orientation increases under high deposition rate and low activation energy for diffusion of the adatom between (111) and (100) grains because the adatoms on the (111) surface stick to the surface more strongly compared to those on the (100) plane. The theoretical model was confirmed experimentally by growing several polycrystalline MgO films using the electron beam evaporation method. We could easily control the flux and energy of MgO adatoms by modulating the emission current of the electron gun, substrate temperature, and extra energy source such as ion beam assisted deposition. Our experimental results show good qualitative agreement with the model for the various polycrystalline MgO films deposited at several growth conditions.

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INTRODUCTION Formation of polycrystalline films with increasing film thickness even though a well lattice matched heteroepitaxial system, under vacuum conditions, is a general phenomenon.1−4 Moreover, control of preferred orientation in the polycrystalline film has been of great importance not only in physical origin but also in engineering applications because it is deeply related to a lot of material properties (mechanical, electrical, magnetic, and optical properties).5−9 Although a lot of preliminary studies have been done in polycrystalline metal film,10,11 ionic compound materials have a difficulty due to a lot of variables to consider based on strong anisotropic properties between crystal planes such as Madelung constant, surface energy, polarity, etc. Meanwhile, control of preferred orientation in simple rock-salt structured (Fm3m) ionic materials such as TiN, TiC, TaN, CrN, and MgO continuously has been studied for the application of mechanical barrier in electronic and plasma devices.12−19 In the early works, some studies focused on the surface energy minimization of polycrystalline systems during competitive growth.12,13 However, due to strong polar properties in ionic compound materials, the surface energy of rock-salt (111) is difficult to measure and surface reconstruction such as octopole (anion termination or cation termination) formation and hydroxyl (come from residual water molecule) termination should be considered during growth.20−23 Moreover, this thermo-dynamical approach is too macroscopic to understand the detailed growth process because preferred orientation could happen even at room temperature.14−16 Later, some groups explained the preferred orientation phenomena of TiN using a © XXXX American Chemical Society

kinetic approach, adatom diffusion and hopping during growth. For the case of TiN, the Ti adatom on the neutral (100) plane has lower activation energy for lateral movement than that on the polar (111) plane.14−16 On the basis of this anisotropic property in activation energy for lateral movement, the final preferred orientation could be determined. In this previous study, reactive sputtering was mainly used to synthesize those rock-salt materials due to the high melting points (TiN: 2930 °C, TiC: 3160 °C, MgO: 2852 °C, and TaN: 3090 °C) and strong corrosion resistance to the plasma environment. However, it is very difficult to control the flux and energy of adatoms due to complex intercollision between buffer gas for plasma (such as Ar) and reactive atoms,14,15 resulting in uncertainty to predict the preferred orientation. Electron beam can melt such high melting point materials and avoid the complex interference between adatoms. Moreover, the flux and energy of adatoms could be controlled easily by modulating the emission current of the electron gun, substrate temperature, and extra energy source such as ion beam assisted deposition (IBAD). In this work, we developed a theoretical kinetic model to predict the preferred orientation of MgO film by assuming random diffusion of the adatom between the (111) and (100) planes. To reduce the complexity of the adatom, we evaporated a MgO pellet using the electron beam evaporation (EBE) method. The diffusion between (111) and (100) planes was Received: November 5, 2015 Revised: February 18, 2016

A

DOI: 10.1021/acs.cgd.5b01564 Cryst. Growth Des. XXXX, XXX, XXX−XXX

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Figure 1. (a) Large surface diffusion from the (100) plane to the (111) plane due to strong anisotropic properties makes the (111) preferred orientation, and it could be controlled by modulating the surface diffusion and sticking factor. (b) XRD patterns of MgO films grown on SiO2/ Si(100) substrate as a function of film thickness (constant growth temperature and deposition rate at 250 °C, 10 Å/s) by EBE.

controlled experimentally by adjusting the substrate temperature, deposition rate, and diffusion barrier energy by using IBAD. The adhesion of the adatom was assumed to be proportional to the sticking factor of the adatom based on the Hartman and Perdok model.24

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⎞

dn dtdA ∬ {S111(1 + K100) − K111}⎝ dtdA ⎠

V100 =

dn dtdA ∬ {S100(1 + K111) − K100}⎝ dtdA ⎠

⎜

⎛ ⎜

⎟

(1-1)

⎞ ⎟

(1-2)

where Khkl, n, t, and A represent the diffusion constant of the hkl plane, the number of adatoms, time, and area. Because the diffusion constant strongly depends on the temperature, the Khkl could be defined as the Arrhenius equation like this25

EXPERIMENTAL SECTION

An n-type (100) silicon wafer (doped with Arsenic) covered by thermal oxide with a 150 nm thickness was used as a starting substrate. The substrate was cleaned with acetone, ethyl alcohol, and deionized water. MgO films were deposited by EBE using high-purity MgO pellets. The MgO pellets were produced by pressing 99.995% purity MgO powder (from Mitsubishi Materials Co.) and heat-treating. MgO films were grown at a base pressure on the order of 10−7 Torr. The chamber pressure was maintained at about 10−6 Torr during deposition, and the substrate temperature was controlled from room temperature to 750 °C using a SiC based heating element. For the IBAD, nitrogen gas was inserted and the gas pressure was set at 0.2 mTorr, the ion beam voltage was set at 150 V, and beam flux was 0.2 mA/cm2. The film thickness was measured using a quartz microbalance monitoring system during growth. Powder X-ray diffractometry was performed by an XRD difractometer Mac Science M18XHF22 (18 kW) using monochromated Cu Kα radiation and a scintillation detector. The HRTEM images were collected using a Cscorrected JEM 2200FS operated at 200 kV.

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⎛

V111 =

Khkl = exp{−Ea, hkl /kBT }

(2)

where Ea,hkl, kB, and T represent the activation energy for diffusion of the adatom on the hkl plane, the Boltzmann constant, and temperature. In the case of the rock-salt structure, a Mg or O adatom arriving at the (111) or (100) plane has 3 or 1 of the nearest atom, respectively. Therefore, the Ea,111 has higher values than Ea,100, resulting in easy diffusion of the adatom on the (100) surface. There are several reconstructions of the MgO (111) surface with respect to oxygen chemical potential such as 2 × 2 octopole, 2 × 2 alpha, 1 × 1 hydroxyl (OH), etc.26 Although Mg-octopole or O removed O-octopole (Mg-alpha) are quite stable reconstructions at the environment of low oxygen chemical potential such as 10−7 Torr vacuum (some reports say that these octopole related reconstructions are more stable than OH termination.27), the adatom on this reconstructed surface also has the 3 nearest neighbors. Therefore, we can apply the same nearest neighbor number in this case. Although the 1 × 1 hydroxyl termination could happen during growth due to residual water vapor in the chamber, the H atom helps the Mg or O atoms to grow epitaxially by partially desorbing from the surface during growth.20 In this case, the Ea,111 could be a little different, but it does not mean the unnecessariness of this kinetic model. Figure 1b shows XRD patterns of MgO films with respect to film thickness deposited at 250 °C and 10 Å/s by EBE. At the early stage of growth below 400 nm, all kinds of major orientations in the rock-salt crystal including (111), (200), and (220) come

RESULTS AND DISCUSSION

First, we start the theory at the condition of the Volmer− Weber growth mode (3D random island growth mode), meaning an equated existence between MgO (111) and (100) planes by using an amorphous substrate. The volume of the (hkl) orientation Vhkl could be defined simply as Shkl × Nhkl, where Shkl is the sticking factor and Nhkl is the number of adatoms that arrived on the hkl plane. If we consider the interdiffusion of the adatom between (111) and (100) planes as shown in Figure 1a, the Vhkl could be expressed like this based on the mass balance equation B

DOI: 10.1021/acs.cgd.5b01564 Cryst. Growth Des. XXXX, XXX, XXX−XXX

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Figure 2. (a) XRD patterns of MgO films (700 nm thickness) grown on the SiO2/Si(100) substrate as a function of deposition rate (constant growth temperature at 250 °C) and substrate temperature (constant deposition rate 20 Å/s) by EBE. (b) XRD patterns of MgO films (700 nm thickness) grown on the SiO2/Si(100) substrate as a function of deposition rate (constant growth temperature at 250 °C) and substrate temperature (constant deposition rate 20 Å/s) by IBAD.

tendency for the (111) preferred orientation formation at high deposition rate and high growth temperature is similar, a relatively lower intensity in the (111) orientation happened compared to EBE. These results could be understood as blocking of adatom diffusion, which means the changes in Khkl by increasing Ea,hkl in eq 3. Generally, the ion energy below 1 eV does not have an effect on the film growth and that between 10 and 100 eV could enhance the mobility of adatom.28 However, the ion energy more than 100 eV could induce sputtering and readsorption of adatoms and makes some defects such as point defects or dislocation sometimes.28 The ion energy used in this experiment is about 150 eV, which is strong enough to block the adatom diffusion by the sputtering and readsorption process. Moreover, the high flux of ions also could have an effect on the decrease of adatom mobility due to multiple scattering on the surface. The flux of ions used in this experiment is 0.2 mA/cm2 (measured by Faraday cup), and this value is high enough to cause this effect.29 In other words, energetic ions during growth block the lateral movement of adatoms arriving at the (100) surface and (111) grains could not overgrow (100) grains easily until the growth system reaches enough high temperature. To compare the macroscopic XRD patterns with the atomic schematics as shown in Figure 1a, a cross-sectional view of samples based on the electron micrograph is needed. Therefore, we selected two samples: one with the most strong (111) diffraction grown at 450 °C, 20 Å/s, EBE, and the other with the most weak (111) diffraction grown at room temperature, 3 Å/s, and IBAD. Figure 3a shows a crosssectional SEM micrograph of MgO film with strong (111) preferred orientation (grown at 450 °C, 20 Å/s, EBE). There are strong columnar structures above the 400 nm region from the substrate, which will be the (111) preferred orientation, as shown in Figure 3c (detailed HR-TEM micrograph of rectangular area in Figure 3a). From the clear Fourier transformed diffraction pattern (inset of Figure 3c) and well aligned MgO (111) orientation with lattice spacing of 0.243 nm

up and the (111) preferred orientation developed with respect to film thickness above 400 nm thickness. This means that the (111) orientation that is the fastest growth plane could overwhelm the other orientations such as (200) and (220) during growth, as shown in Figure 1a. Because the MgO films grown in this study tend to have the (111) preferred orientation, we can define the (111) preferred orientation factor f111 by adopting the sticking factor ratio r = S111/S100 (we can assume the S100 as 1.0 for the convenience) like this f111 =

(V111 − V100) (V111 + V100)

=

[S111(1 + K100) − K111] − [S100(1 + K111) − K100] [S111(1 + K100) − K111] + [S100(1 + K111) − K100]

≅

r(1 + K100) − K111 − (1 + K111) + K100 r(1 + K100) − K111 + (1 + K111) − K100

=

(r − 1) + K100(r + 1) − 2K111 (r + 1) + K100(r − 1)

(3)

On the basis of this kinetic factor model, we can modulate the tendency for the (111) preferred orientation by controlling several growth parameters that have influence on the r and Khkl, as shown in Figure 1a. Figure 2a shows XRD patterns of MgO films (700 nm, EBE) with respect to deposition rate and growth temperature. The tendency for the (111) preferred orientation appeared more strongly as the deposition rate and growth temperature increased. The deposition rate strongly affects the r because the diffusion of the adatom could be blocked by additionally evaporated adatoms, resulting in a strong sticking factor at high deposition rate. This phenomenon happens on the (111) surface more significantly due to close packing properties, which means that the r increased at the high deposition rate. Moreover, the growth temperature acts to increase the Arrhenius interdiffusion term in eq 3. Figure 2b shows XRD patterns of MgO films (700 nm) by IBAD. Although the C

DOI: 10.1021/acs.cgd.5b01564 Cryst. Growth Des. XXXX, XXX, XXX−XXX

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major diffraction pattern of cubic system) were randomly distributed with the ring diffraction patterns in the inset of Figure 3d. By comparing these two samples in cross-sectional view, we could know that the (111) preferred orientation was formed as the film thickened by overwhelming the other orientations and those tendencies could be controlled by changing deposition variables. The quantitative matching of our kinetic model with the experimental results was done by analyzing XRD data numerically. The tendency of the preferred orientation of materials could be expressed as some parameters such as the Lotgering factor and March−Dollase factor.30,31 The Lotgering factor is defined as30 fL = (p − p0 )/(1 − p0 )

(4)

where p is the ratio of specific preferred orientation intensity compared to all the diffraction intensity and p0 is the ratio for the nonpreferred samples (from the JCPDS data, intensity ratio between (111) and (200) diffraction peaks; 4 of (111) and 100 of (200)32). The March−Dollase factor is defined as31 fM − D = {(1 − m)3 /(1 − m3)}1/2 Figure 3. Cross-sectional SEM micrographs of MgO film (700 nm thickness) for the (a) EBE and (b) IBAD. (c) HR-TEM micrograph of near top of MgO film, rectangular area in (a). Inset: detailed HR-TEM micrograph with (111) preferred orientation and its corresponding Fourier diffraction pattern. (d) HR-TEM micrograph of near top of MgO film, rectangular area in (b). Inset: its corresponding Fourier diffraction pattern.

(5)

where m comes from ⎡ ⎤1/3 sin 2 α ⎥ m=⎢ ⎢⎣ (n/n0)2/3 − cos2 α ⎥⎦

(6)

where n and n0 represent the intensity ratio between (111) and (100) orientations from XRD measurement and the JCPDS table, respectively. The α is the angle between the two planes (54.7° for the angle between MgO (111) and (100) planes). To compare the f L and f M−D with our kinetic model, we have to know the Khkl and the activation energy for diffusion. We used a constraint about the ratio between Ea,111 and Ea,100 as 3.0 based on the theoretical calculation (this value is related to the neighbor atom number ratio on the surface for each orientation).33 By using this constraint, we optimized the parameter after fitting, Ea,100 = 0.07 eV, Ea,111 = 0.21 eV, and r as

prove the strong (111) preferred orientation formation. Moreover, the columnar structure looks like an inverted triangle, and it means that the (111) preferred orientation overwhelmed the other orientations during growth. On the other hand, the MgO film with weak (111) preferred orientation (grown at RT, 3 Å/s, and IBAD) has smaller and relatively parallel columns, as shown in Figure 3b. In the detailed HR-TEM view in Figure 3d, polycrystalline MgO grains with (111), (200), and (220) orientations (showing all

Figure 4. (111) preferred orientation factors with respect to (a) growth temperature and (b) deposition rate. The fsimul, f L, and f M−D mean the simulation based on our kinetic model, Lotgering factor, and March−Dollase factor, respectively. Each plot is composed of EBE and IBAD. D

DOI: 10.1021/acs.cgd.5b01564 Cryst. Growth Des. XXXX, XXX, XXX−XXX

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2.5. For the case of IBAD, the r = 1.5 (best fit to our kinetic model), Ea,100 = 0.17, and Ea,111 = 0.31, which means that the ion beam blocks the interdiffusion of the adatom between (111) and (200) surfaces by increasing the barrier 0.1 eV, and it also has an effect on the r from 2.5 to 1.5. As shown in Figure 4a, the kinetic model is located between f L and f M−D with well matched (111) preferred orientation factor. The effect of deposition rate in the (111) preferred orientation factor was calculated in Figure 4b. For the fitting of our kinetic model to the values of f L and f M−D, we used the empirical exponential function of r with respect to deposition rate. The boundary condition of r is 2.5 for 20 Å/s and 1 for 0 Å/s (for the case of EBE) and 1.5 for 20 Å/s and 1 for 0 Å/s (for the IBAD). Then, the r could be written as

by assuming random walk diffusion of the adatom species between (111) and (100) planes. This model suggests that the tendency of the (111) preferred orientation increases under low activation energy for diffusion of adatoms and high deposition rate. Our experimental results show good qualitative agreement with the model for the various MgO films deposited at several growth conditions. This theoretical model opens the fundamental understanding of MgO film growth and could be applied to other rock-salt-type material growth systems.

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AUTHOR INFORMATION

Corresponding Author

*Tel: +82-54-279-2152. Fax: +82-54-279-5242. E-mail: jllee@ postech.ac.kr.

⎧ ⎛ ln 1.6 ⎞ ⎫ rEB = 2.5⎨exp⎜ R ⎟ − 0.6⎬ ⎭ ⎩ ⎝ 20 ⎠

(7-1)

⎧ ⎛ ln 1.33 ⎞ ⎫ rIB = 1.5⎨exp⎜ R ⎟ − 0.33⎬ ⎠ ⎭ ⎩ ⎝ 20

Dept. of Materials Science and Engineering and Dept. of Energy Systems Research, Ajou University, Suwon, 443-749, Korea.

(7-2)

Notes

Present Address †

The authors declare no competing financial interest.

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where the R is the growth rate (Å/s). As we mentioned before, the deposition rate strongly affects the r because the diffusion of the adatom could be blocked by additionally evaporated adatoms, resulting in a strong sticking factor at high deposition rate. This phenomenon happens on the (111) surface more significantly due to close packing properties, which means that the r increased at the high deposition rate. The f L is the absolute population ratio of specific orientation in the whole polycrystalline film without considering the distribution of other orientations, whereas the f M−D can be obtained by calculating the relative intensity of a specific orientation compared to the competitive orientation. Because our suggested model is competitive growth between (111) and (200) of the MgO crystal, the tendency of the (111) preferred orientation factor (slope with respect to growth parameter such as temperature and growth rate) is closer to f M−D. The deviation in absolute value from the f M−D is due to the existence of partial (220) orientations and experimental error due to deviation from the Gaussian fitting function for the intensity calculation of the diffraction peak. However, the influence of this error on the tendency of preferred orientation formation is small enough to ignore. Considering the experimental results mentioned above, it is obvious that the tendency of the MgO (111) preferred orientation could be adjusted by controlling adatom diffusion between (111) and (100) planes. Moreover, it is well matched with our kinetic model. The diffusion of the adatom could be adjusted by the two main factors: activation energy and sticking factor. First, the activation energy is strongly affected by substrate temperature due to the Arrhenius term in our model. In addition, the extra energy applied in the adatom could also control the activation energy. In this study, we could increase the activation energy for diffusion using the IBAD method. Energetic ions block the lateral movement of the adatom by increasing the activation energy for diffusion. The sticking factor could be controlled easily by adjusting adatom flux using different deposition rates.

ACKNOWLEDGMENTS This work was supported in part by the Priority Research Centers Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2010-0029711), and in part by the WCU (World Class University) program through the Korea Science and Engineering Foundation funded by the Ministry of Education, Science and Technology (Project No. R31-2008-000-10059-0). This work was also partially supported by the new faculty research fund of Ajou University.

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CONCLUSION In conclusion, we investigated the mechanism that determines the preferred orientation of polycrystalline MgO films and developed a kinetic model to predict the preferred orientation E

DOI: 10.1021/acs.cgd.5b01564 Cryst. Growth Des. XXXX, XXX, XXX−XXX

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DOI: 10.1021/acs.cgd.5b01564 Cryst. Growth Des. XXXX, XXX, XXX−XXX