APPLIED PHYSICS LETTERS 98, 031904 共2011兲
Probing the atomic structure of amorphous Ta2O5 coatings R. Bassiri,1,a兲 K. B. Borisenko,2 D. J. H. Cockayne,2,b兲 J. Hough,1 I. MacLaren,1 and S. Rowan1 1
SUPA, School of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ, United Kingdom Department of Materials, University of Oxford, Oxford OX1 3PH, United Kingdom
2
共Received 16 August 2010; accepted 16 December 2010; published online 19 January 2011兲 Low optical and mechanical loss Ta2O5 amorphous coatings have a growing number of applications in precision optical measurements systems. Transmission electron microscopy is a promising way to probe the atomic structure of these coatings in an effort to better understand the causes of the observed mechanical and optical losses. Analysis of the experimental reduced density functions using a combination of reverse Monte Carlo refinements and density functional theory molecular dynamics simulations reveals that the structure of amorphous Ta2O5 consists of clusters with increased contribution from a Ta2O2 ring fragment. © 2011 American Institute of Physics. 关doi:10.1063/1.3535982兴 A number of optical applications are critically dependent on highly reflective mirrors of low optical and/or mechanical loss, including ring laser gyroscopes in inertial guidance systems,1 frequency stabilization using laser cavities relevant to, e.g., frequency comb techniques,2,3 and high precision interferometers for gravitational wave detection such as the Laser Interferometer Gravitational-wave Observatory 共LIGO兲.4 It is essential in all such techniques that the mirrors have losses that are as low as possible and introduce as little noise as possible into the system. The list of suitable materials for such mirrors is rather short. Very frequently the mirrors in such applications consist of multilayers of a low refractive index 共low dielectric constant兲 material, such as amorphous SiO2, alternating with a high refractive index material, which is often amorphous Ta2O5 or a doped composition based on Ta2O5. Additionally Ta2O5 has been investigated for use in microelectronics as a high dielectric constant coating,5 and as a corrosion resistant coating for biomedical uses.6 Unfortunately, while a large number of studies exist on the structures of the numerous crystalline polymorphs of tantalum oxides, both from experimental diffraction-based studies and from modeling using density functional theory,7–11 there is little published information about the structure of amorphous Ta2O5. Such information is essential to any attempt to understand the properties of this important material, and no property modeling efforts can be expected to yield reliable information until the local structure in the amorphous phase is better understood.12 The study described in the present work aims to rectify this deficit. We use the combination of experimental diffuse electron diffraction and modeling, which involves density functional theory and reverse Monte Carlo 共RMC兲 refinements, as recently applied to study the structures of amorphous Ge2Sb2Te5 and N-doped Ge2Sb2Te5,13,14 to probe the atomic structure of coatings of amorphous Ta2O5. Using electron diffraction data to study amorphous materials is an area of active research, described in detail in a review article by Cockayne,15 and there have also been comparable studies a兲
Electronic mail:
[email protected]. This paper is dedicated to the memory of Professor David J. H. Cockayne FRS, 1942–2010. He will be well remembered for his very significant contributions to science, as well as his warm and engaging manner.
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from x-ray and neutron diffraction data that use similar RMC refinements.16–18 The coating investigated here was manufactured by the Commonwealth Scientific and Industrial Research Organisation 共CSIRO, Materials Science and Engineering Division, West Lindfield, NSW, Australia兲 by argon-ion-beamsputtering onto an amorphous SiO2 substrate, followed by heat-treatment in air for 24 h at 400 ° C. This coating was one of a range of similar coatings heat-treated at different temperatures in order to examine the effects on mechanical loss and possible improvements to optical loss in high precision interferometry.19 Samples of the Ta2O5 thin film were prepared for transmission electron microscopy studies using a standard crosssection method and were thinned using Ar ion irradiation at 4 kV in a Gatan precision ion polishing system 共PIPS兲 共Gatan Inc., Pleasanton, CA, USA兲. They were then characterized in a FEI Tecnai T20 transmission electron microscope 共TEM兲 共FEI Corp., Eindhoven, The Netherlands兲, operated with an accelerating voltage of 200 kV and equipped with a SIS Megaview III charge-coupled device camera 共Olympus SIS, Garching, Germany兲 for data collection. Electron diffraction patterns, recorded with a convergence semiangle of ␣ = 1.89 mrad, were collected from the thin film and then used in the subsequent analysis.20 The diffraction patterns azimuthally averaged out to at least q = 10 Å−1, this then being used as the raw data for calculating the reduced scattering intensities and reduced density functions 共RDFs兲. The RDF itself is a statistical representation of where atoms sit with regard to a central atom and can be effectively described as the Fourier transform of the averaged reduced scattering factor, 共q兲: G共r兲 = 4
冕
⬁
共q兲sin共qr兲dq,
共1兲
0
where q = 4 sin / , r is the distance from a central atom, is half of the scattering angle, and is the wavelength of electrons 共 = 2.5 pm兲. In order to accurately probe the atomic structure further and gain a fuller understanding of the information stored in the RDF we performed RMC refinements of atomistic models using the experimentally obtained scattering intensities. Information from density func-
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tional theory molecular dynamics 共MD兲 simulations of liquid quenching was used in the RMC refinements in order to ensure that we obtain a physically meaningful model of the amorphous material, which fits both the theoretical and experimental data. The procedure is described below. Initially, a small model of 77 randomly packed atoms in a cubic cell was prepared and then refined using the RMC software to fit the experimental electron diffraction intensities for amorphous Ta2O5. The size of the model was chosen to provide an acceptable balance between containing enough atoms to allow a reasonable representation of the structure and few enough to still allow the MD simulations to run in a reasonable period of time. The size of the cell was chosen so that it gave a density close to the experimentally measured density of 7.68 g / cm3. This initial model was refined using a RMC approach by comparing 共q兲 calculated from the model structures with the experimental 共q兲 and moving random atoms until an acceptably good match was achieved. Before the refinement, contributions of the scattering intensity components that gave peaks below 1.33 Å in the experimental RDF, where no contribution from the interatomic distances is expected, were removed from the experimental data using a Fourier filter. In the refinements periodic boundary conditions were used in three dimensions. O–O and Ta–Ta distances closer than 2.9 Å were excluded and the minimal approach between Ta and O atoms was flexibly restrained to the sum of the respective covalent radii using a penalty term from a soft sphere potential. In the second stage, CASTEP 共Ref. 21兲 was used to perform MD simulations based on density functional theory 共DFT兲 that allowed us to ensure that all the atoms sat in physically reasonable positions. This utilized norm-conserving pseudopotentials of Lee et al. provided with the code21 within the generalized gradient approximation using the Perdew–Burke–Ernzerhof exchangecorrelation functional22 where an energy cutoff was set at 200 eV. To test how the selected pseudopotentials and the energy cutoff would describe the known crystalline structure of Ta2O5 an energy optimization of a crystalline model23 was performed relaxing the cell parameters using a series of cutoff energies of 200, 300, and 400 eV. The computed cell parameters were found to be within 1% of the experimental values for the 200 eV cutoff which was selected for the MD simulations. The RMC refined small model was used as a starting structure for melting and cooling simulations using MD within a canonical 共constant NVT兲 ensemble. The model was first melted at 3000 K for 5 ps, then cooled down to 2000 K and equilibrated for 10 ps. The melt was then cooled down to 500 K in steps of 300 K, allowing 5 ps equilibration at each step. Finally, the structure was equilibrated at 300 K for 10 ps. Total simulation time was thus 50 ps with the time step of 2 fs. Although several high frequency vibrational modes 共for instance, including bonded vibrations兲 can be anticipated in the material, a longer time step is used here as a reasonable compromise between describing atomic diffusion and vibrations. The temperature was controlled using an implementation of the Nose–Hoover thermostat.24 The electron density was sampled only at the gamma point, which was thought to be a reasonable approximation considering the material is an insulator. In the simulations periodic boundary conditions were used with fixed lattice constants.20 To better understand the amorphous Ta2O5 structure over a longer range, a final large model for RMC refinement was
Appl. Phys. Lett. 98, 031904 共2011兲
FIG. 1. 共Color兲 共a兲 Comparison between final amorphous Ta2O5 model and experimental RDFs. 共b兲 Partial RDFs showing individual nearest neighbor distances within the model. In both cases the y-axis. G共r兲 represents the normalized probability of finding an atom at a particular distance r 共x-axis兲 from a central atom.
then prepared by assembling together 27 randomly oriented small models obtained from the MD simulations of liquid quenching. This model was then refined using a small 0.1 Å maximum displacement step per iteration in the RMC routine, to preserve the simulated bond length and angle distributions as much as possible, while at the same time fitting the model to the experimental diffraction data and avoiding any unphysical distances.20 The comparison between experimental and refined RDFs is shown Fig. 1共a兲. The partial RDFs computed from the final large RMC refined model are compared to the experimental RDF in Fig. 1共b兲. The first peak position in the RDF corresponds to the Ta–O distances found at 1.93 Å. The shoulder of the second peak at about 3.2 Å can be attributed to the Ta–Ta distances. The RDF also shows that there is no order beyond the second peak 共r ⬎ 4 Å兲. It was found that the refined amorphous structure had a considerable contribution from the planar or nearly planar Ta2O2 fragments with a relatively short average Ta–Ta distance of 3.2 Å 共Ref. 20兲 although not in the amounts suggested by the MD simulations. These results accord well with the manufacturing method of ion-beam sputtering the coating material, where we can expect stable ring fragments and ring clusters to form in the gas phase in the moments before it is randomly deposited onto the substrate. Hence there is only order in the coating at the size of the Ta2O2 ring fragments.
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A search in the Cambridge Crystal Structure Database25,26 revealed a number of compounds containing similar fragments with the Ta–Ta distance varying from 2.71 Å 共Ref. 27兲 to 3.64 Å 共Ref. 28兲 with the average at about 3.2 Å in good agreement with the value obtained in the present study. The average Ta–O bond length in the refined structure was also found to be in a good agreement with the corresponding bond in these clusters and also in crystalline phases of pure Ta2O5.9 The average coordination numbers computed from the refined model are 6.53 for Ta and 2.09 for O 共using covalent radii of 1.7 and 0.73 Å, respectively, where a bond is defined as an atom to atom distance of less than the sum of the covalent radii plus a tolerance factor of 0.1 Å兲. This is in good accord with published high temperature structures for Ta2O5 where tantalum is usually six or seven coordinated to oxygen and oxygen is either two or three coordinated.9,29 This observation confirms that the suggested building block of the amorphous phase of Ta2O5 is an energetically stable configuration and the good agreement between refined and previously reported experimental bond lengths lends further credibility to the refined structure. The DFT simulated structure suggests considerable presence of Ta–Ta interactions, which although not as pronounced in the final refined structure, are still noticeable. The normal coordinate analysis of 8− infrared and Raman spectra of octahedral oxyanion Ta6O19 −1 has attributed a weak band at 245 cm to the stretching Ta–Ta vibrations.30 Its low intensity was interpreted as a sign of absence of any direct metal-metal interactions in this anion, as would be expected from a rare gas d0 electronic configuration of Ta in this case. The Ta–Ta distance in this anion was 3.30 Å. The spread of the Ta–Ta distance observed in the various compounds suggests that this distance is very sensitive to the surrounding atoms and their electronic properties. In the simulated amorphous structure, a range of Ta nearest neighbor configurations have been observed, and consequently the Ta–Ta distance was also found in a substantial range between 2.78 and 3.3 Å. These observations will be an important factor to consider when building models of mechanical loss in the amorphous Ta2O5. This will be invaluable in further studies on the structural origins of differences in mechanical loss depending on heat-treatment temperature19 and the effect of Ti-doping on mechanical loss31 and studies are now focused on the development of DFT models based on experimental data in a similar manner to those discussed in this initial study of the structure of amorphous ion-beam-sputtered Ta2O5. It was demonstrated that through experimental RDFs and DFT modeling we can produce an atomic structure that represents an amorphous Ta2O5 coating. Atomic structure measurements from this model produce a wealth of information including nearest atomic neighbor distances, coordination numbers, and observed similarities between crystalline and amorphous phases, such as clusters with increased contribution from a Ta2O2 ring fragment. This work represents an important step toward understanding the atomic properties of these coatings.
We would like to thank our colleagues at the IGR, GEO, and LIGO Scientific collaborations for useful discussions, especially Professor M. M. Fejer. We wish to acknowledge the use of the Chemical Database Service at Daresbury. We would also like to thank STFC 共Grant No. PP/F00110X/1兲, SFC, and the University of Glasgow in the U. K. and the NSF 共Grant No. PHY-0757058兲 in the USA for financial support. RB is grateful to the EPSRC for the provision of a DTA studentship. 1
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