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Sanaullah I, Khan HN, Sajjad A, Khan S, Sabri AN, Naseem S, Riaz S. Improved osteointegration response using high strength perovskite BaTiO 3 coatings prepared by chemical bath deposition. J Mech Behav Biomed Mater 2023; 138:105635. [PMID: 36603524 DOI: 10.1016/j.jmbbm.2022.105635] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/10/2022] [Revised: 12/15/2022] [Accepted: 12/18/2022] [Indexed: 12/24/2022]
Abstract
A wide range of bioactive materials have been investigated for tissue engineering and regeneration. Barium titanate is a promising smart material to be used as scaffold for bone tissue engineering. Barium titanate coatings are prepared in the present study using chemical bath deposition technique. Coatings are prepared at room temperature with the variation in solution molarity from 0.1 to 1.2 M. Perovskite tetragonal phase is observed after annealing the samples at 300 °C using 1.0-1.2 M solutions. Normal-anomalous dielectric response is observed for annealed coatings. Maximum transmission of ∼55% and ∼82% is observed under as-prepared and annealed coatings, respectivly. Variation in direct band gap, i.e. 3.45-3.64 eV, is observed with varying molarity. High hardness of the coatings (∼1180 HV) is observed at 1.2M with fracture toughness of ∼22 MPam-1/2. Biodegradation studies show smaller values of weight loss even after immersion in simulated body fluid (SBF) after 26 weeks. Barium titanate coatings also show high antioxidant activity. BaTiO3's antibacterial reaction is evaluated against microorganisms such as Escherichia coli (E. coli) and Staphylococcus aureus. Antibacterial activity shows highest zone of inhibition (∼31 mm) against Staphylococcus aureus bacteria. Quantitative real-time PCR is used to assess the gene expression profile in cultivated cells. Thus, coatings produced without the use of hazardous solvents/reagents utilizing CBD technique are a potential material for biomedical applications.
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Affiliation(s)
- Ifra Sanaullah
- Centre of Excellence in Solid State Physics, University of the Punjab, Lahore, 54590, Pakistan
| | - Hera N Khan
- Centre of Excellence in Solid State Physics, University of the Punjab, Lahore, 54590, Pakistan; Institute of Microbiology and Molecular Genetics, University of the Punjab, Lahore, Pakistan
| | - Amna Sajjad
- Department of Zoology, Government College University Faisalabad, Faisalabad, 38000, Pakistan
| | - Sidra Khan
- Centre of Excellence in Solid State Physics, University of the Punjab, Lahore, 54590, Pakistan
| | - Anjum N Sabri
- Institute of Microbiology and Molecular Genetics, University of the Punjab, Lahore, Pakistan
| | - Shahzad Naseem
- Centre of Excellence in Solid State Physics, University of the Punjab, Lahore, 54590, Pakistan
| | - Saira Riaz
- Centre of Excellence in Solid State Physics, University of the Punjab, Lahore, 54590, Pakistan.
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2
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Fernandez A, Acharya M, Lee HG, Schimpf J, Jiang Y, Lou D, Tian Z, Martin LW. Thin-Film Ferroelectrics. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2022; 34:e2108841. [PMID: 35353395 DOI: 10.1002/adma.202108841] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/02/2021] [Revised: 03/03/2022] [Indexed: 06/14/2023]
Abstract
Over the last 30 years, the study of ferroelectric oxides has been revolutionized by the implementation of epitaxial-thin-film-based studies, which have driven many advances in the understanding of ferroelectric physics and the realization of novel polar structures and functionalities. New questions have motivated the development of advanced synthesis, characterization, and simulations of epitaxial thin films and, in turn, have provided new insights and applications across the micro-, meso-, and macroscopic length scales. This review traces the evolution of ferroelectric thin-film research through the early days developing understanding of the roles of size and strain on ferroelectrics to the present day, where such understanding is used to create complex hierarchical domain structures, novel polar topologies, and controlled chemical and defect profiles. The extension of epitaxial techniques, coupled with advances in high-throughput simulations, now stands to accelerate the discovery and study of new ferroelectric materials. Coming hand-in-hand with these new materials is new understanding and control of ferroelectric functionalities. Today, researchers are actively working to apply these lessons in a number of applications, including novel memory and logic architectures, as well as a host of energy conversion devices.
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Affiliation(s)
- Abel Fernandez
- Department of Materials Science and Engineering, University of California, Berkeley, Berkeley, CA, 94720, USA
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, 94720, USA
| | - Megha Acharya
- Department of Materials Science and Engineering, University of California, Berkeley, Berkeley, CA, 94720, USA
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, 94720, USA
| | - Han-Gyeol Lee
- Department of Materials Science and Engineering, University of California, Berkeley, Berkeley, CA, 94720, USA
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, 94720, USA
| | - Jesse Schimpf
- Department of Materials Science and Engineering, University of California, Berkeley, Berkeley, CA, 94720, USA
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, 94720, USA
| | - Yizhe Jiang
- Department of Materials Science and Engineering, University of California, Berkeley, Berkeley, CA, 94720, USA
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, 94720, USA
| | - Djamila Lou
- Department of Materials Science and Engineering, University of California, Berkeley, Berkeley, CA, 94720, USA
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, 94720, USA
| | - Zishen Tian
- Department of Materials Science and Engineering, University of California, Berkeley, Berkeley, CA, 94720, USA
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, 94720, USA
| | - Lane W Martin
- Department of Materials Science and Engineering, University of California, Berkeley, Berkeley, CA, 94720, USA
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, 94720, USA
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3
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Kim B, Jeon YU, Lee C, Kim IS, Lee BH, Kim YH, Kim YD, Han IK, Lee K, Kim J, Kang J. Controlling of lattice strains for crack-free and strong ferroelectric barium titanate films by post-thermal treatment. Sci Rep 2022; 12:5363. [PMID: 35354865 PMCID: PMC8967881 DOI: 10.1038/s41598-022-09182-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/21/2021] [Accepted: 03/17/2022] [Indexed: 11/09/2022] Open
Abstract
In this study, we experimentally demonstrate fabrication of ultra-smooth and crystalline barium titanate (BTO) films on magnesium oxide (MgO) substrates by engineering lattice strain and crystal structure via thermal treatment. We observe that oxygen-depleted deposition allows growth of highly strained BTO films on MgO substrates with crack-free surface. In addition, post-thermal treatment relaxes strain, resulting in an enhancement of ferroelectricity. Surface roughening of the BTO films caused by recrystallization during post-thermal treatment is controlled by chemical–mechanical polishing (CMP) to retain their initial ultra-smooth surfaces. From Raman spectroscopy, reciprocal space map (RSM), and capacitance–voltage (C–V) curve measurements, we confirm that the ferroelectricity of BTO films strongly depend on the relaxation of lattice strain and the phase transition from a-axis to c-axis oriented crystal structure.
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Posadas AB, Park H, Reynaud M, Cao W, Reynolds JD, Guo W, Jeyaselvan V, Beskin I, Mashanovich GZ, Warner JH, Demkov AA. Thick BaTiO 3 Epitaxial Films Integrated on Si by RF Sputtering for Electro-Optic Modulators in Si Photonics. ACS APPLIED MATERIALS & INTERFACES 2021; 13:51230-51244. [PMID: 34669388 DOI: 10.1021/acsami.1c14048] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
Thick epitaxial BaTiO3 films ranging from 120 nm to 1 μm were grown by off-axis RF magnetron sputtering on SrTiO3-templated silicon-on-insulator (SOI) substrates for use in electro-optic applications, where such large thicknesses are necessary. The films are of high quality, rivaling those grown by molecular beam epitaxy (MBE) in crystalline quality, but can be grown 10 times faster. Extraction of lattice parameters from geometric phase analysis of atomic-resolution scanning transmission electron microscopy images revealed how the in-plane and out-of-plane lattice spacings of sputtered BaTiO3 changes as a function of layer position within a thick film. Our results indicate that compared to molecular beam epitaxy, sputtered films retain their out-of-plane polarization (c-axis) orientation for larger thicknesses. We also find an unusual re-transition from in-plane polarization (a-axis) to out-of-plane polarization (c-axis), along with an anomalous lattice expansion, near the surface. We also studied a method of achieving 100% a-axis-oriented films using a two-step process involving amorphous growth and recrystallization of a seed layer followed by normal high temperature growth. While this method is successful in achieving full a-axis orientation even at low thicknesses, the resulting film has a large number of voids and misoriented grains. Electro-optic measurement using a transmission setup of a sputtered BTO film grown using the optimized conditions yields an effective Pockels coefficient as high as 183 pm/V. A Mach-Zehnder modulator fabricated on such films exhibits phase shifting with an equivalent Pockels coefficient of 157 pm/V. These results demonstrate that sputtered BTO thick films can be used for integrated electro-optic modulators for Si photonics.
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Affiliation(s)
- Agham B Posadas
- Department of Physics, The University of Texas at Austin, Austin, Texas 78712, United States
| | - Hyoju Park
- Materials Science and Engineering Program and Texas Materials Institute, The University of Texas at Austin, Austin, Texas 78712, United States
- Walker Department of Mechanical Engineering, The University of Texas at Austin, Austin, Texas 78712, United States
| | - Marc Reynaud
- Department of Physics, The University of Texas at Austin, Austin, Texas 78712, United States
| | - Wei Cao
- Optoelectronics Research Centre, Faculty of Engineering and Physical Sciences, University of Southampton, SO17 1BJ Southampton, United Kingdom
| | - Jamie D Reynolds
- Optoelectronics Research Centre, Faculty of Engineering and Physical Sciences, University of Southampton, SO17 1BJ Southampton, United Kingdom
| | - Wei Guo
- Department of Physics, The University of Texas at Austin, Austin, Texas 78712, United States
| | - Vadivukkarasi Jeyaselvan
- Optoelectronics Research Centre, Faculty of Engineering and Physical Sciences, University of Southampton, SO17 1BJ Southampton, United Kingdom
| | - Ilya Beskin
- Department of Physics, The University of Texas at Austin, Austin, Texas 78712, United States
| | - Goran Z Mashanovich
- Optoelectronics Research Centre, Faculty of Engineering and Physical Sciences, University of Southampton, SO17 1BJ Southampton, United Kingdom
| | - Jamie H Warner
- Materials Science and Engineering Program and Texas Materials Institute, The University of Texas at Austin, Austin, Texas 78712, United States
- Walker Department of Mechanical Engineering, The University of Texas at Austin, Austin, Texas 78712, United States
| | - Alexander A Demkov
- Department of Physics, The University of Texas at Austin, Austin, Texas 78712, United States
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Kormondy KJ, Popoff Y, Sousa M, Eltes F, Caimi D, Rossell MD, Fiebig M, Hoffmann P, Marchiori C, Reinke M, Trassin M, Demkov AA, Fompeyrine J, Abel S. Microstructure and ferroelectricity of BaTiO 3 thin films on Si for integrated photonics. NANOTECHNOLOGY 2017; 28:075706. [PMID: 27973350 DOI: 10.1088/1361-6528/aa53c2] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/14/2023]
Abstract
Significant progress has been made in integrating novel materials into silicon photonic structures in order to extend the functionality of photonic circuits. One of these promising optical materials is BaTiO3 or barium titanate (BTO) that exhibits a very large Pockels coefficient as required for high-speed light modulators. However, all previous demonstrations show a noticable reduction of the Pockels effect in BTO thin films deposited on silicon substrates compared to BTO bulk crystals. Here, we report on the strong dependence of the Pockels effect in BTO thin films on their microstructure, and provide guidelines on how to engineer thin films with strong electro-optic response. We employ several deposition methods such as molecular beam epitaxy and chemical vapor deposition to realize BTO thin films with different morphology and crystalline structure. While a linear electro-optic response is present even in porous, polycrystalline BTO thin films with an effective Pockels coefficient r eff = 6 pm V-1, it is maximized for dense, tetragonal, epitaxial BTO films (r eff = 140 pm V-1). By identifying the key structural predictors of electro-optic response in BTO/Si, we provide a roadmap to fully exploit the linear electro-optic effect in novel hybrid oxide/semiconductor nanophotonic devices.
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Affiliation(s)
- Kristy J Kormondy
- Department of Physics, The University of Texas at Austin, Austin, TX 78712, USA
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6
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Zhang Y, Chen Y, Mietschke M, Zhang L, Yuan F, Abel S, Hühne R, Nielsch K, Fompeyrine J, Ding F, Schmidt OG. Monolithically Integrated Microelectromechanical Systems for On-Chip Strain Engineering of Quantum Dots. NANO LETTERS 2016; 16:5785-5791. [PMID: 27574953 DOI: 10.1021/acs.nanolett.6b02523] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Elastic strain fields based on single crystal piezoelectric elements represent an effective way for engineering the quantum dot (QD) emission with unrivaled precision and technological relevance. However, pioneering researches in this direction were mainly based on bulk piezoelectric substrates, which prevent the development of chip-scale devices. Here, we present a monolithically integrated Microelectromechanical systems (MEMS) device with great potential for on-chip quantum photonic applications. High-quality epitaxial PMN-PT thin films have been grown on SrTiO3 buffered Si and show excellent piezoelectric responses. Dense arrays of MEMS with small footprints are then fabricated based on these films, forming an on-chip strain tuning platform. After transferring the QD-containing nanomembranes onto these MEMS, the nonclassical emissions (e.g., single photons) from single QDs can be engineered by the strain fields. We envision that the strain tunable QD sources on the individually addressable and monolithically integrated MEMS pave the way toward complex quantum photonic applications on chip.
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Affiliation(s)
| | | | | | - Long Zhang
- Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences , 110016, Shenyang, China
- Institute for Complex Materials, IFW Dresden , Helmholtzstraße 20, 01069 Dresden, Germany
| | | | - Stefan Abel
- IBM Research GmbH , Säumerstraße 4, 8803 Rüschlikon, Switzerland
| | | | | | - Jean Fompeyrine
- IBM Research GmbH , Säumerstraße 4, 8803 Rüschlikon, Switzerland
| | | | - Oliver G Schmidt
- Material Systems for Nanoelectronics, Technische Universität Chemnitz , 09111 Chemnitz, Germany
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Meunier B, Largeau L, Regreny P, Penuelas J, Bachelet R, Vilquin B, Wague B, Saint-Girons G. Chemical reactivity between sol–gel deposited Pb(Zr,Ti)O3layers and their GaAs substrates. CrystEngComm 2016. [DOI: 10.1039/c6ce01276k] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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8
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Castera P, Tulli D, Gutierrez AM, Sanchis P. Influence of BaTiO3 ferroelectric orientation for electro-optic modulation on silicon. OPTICS EXPRESS 2015; 23:15332-15342. [PMID: 26193513 DOI: 10.1364/oe.23.015332] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
The influence of BaTiO(3) ferroelectric domain orientations for high efficiency electro-optic modulation has been thoroughly analyzed. The Mach-Zehnder modulator structure is based on a CMOS compatible silicon/BaTiO(3)/silicon slot waveguide that supports both TE and TM polarizations whereas the Pockels effect is exploited by the application of a horizontal electric field with lateral electrodes placed on top of the BaTiO(3) layer. The influence of the waveguide parameters has been optimized for each configuration and the lowest V(π) voltage combined with low losses has been determined. A V(π)L as low as 0.27 V·cm has been obtained for a-axis oriented BaTiO(3) and TE polarization by rotating the waveguide structure to an optimum angle.
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9
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Mazet L, Yang SM, Kalinin SV, Schamm-Chardon S, Dubourdieu C. A review of molecular beam epitaxy of ferroelectric BaTiO 3 films on Si, Ge and GaAs substrates and their applications. SCIENCE AND TECHNOLOGY OF ADVANCED MATERIALS 2015; 16:036005. [PMID: 27877816 PMCID: PMC5099853 DOI: 10.1088/1468-6996/16/3/036005] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/06/2015] [Revised: 05/14/2015] [Accepted: 05/14/2015] [Indexed: 06/05/2023]
Abstract
SrTiO3 epitaxial growth by molecular beam epitaxy (MBE) on silicon has opened up the route to the monolithic integration of various complex oxides on the complementary metal-oxide-semiconductor silicon platform. Among functional oxides, ferroelectric perovskite oxides offer promising perspectives to improve or add functionalities on-chip. We review the growth by MBE of the ferroelectric compound BaTiO3 on silicon (Si), germanium (Ge) and gallium arsenide (GaAs) and we discuss the film properties in terms of crystalline structure, microstructure and ferroelectricity. Finally, we review the last developments in two areas of interest for the applications of BaTiO3 films on silicon, namely integrated photonics, which benefits from the large Pockels effect of BaTiO3, and low power logic devices, which may benefit from the negative capacitance of the ferroelectric.
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Affiliation(s)
- Lucie Mazet
- Institut des Nanotechnologies de Lyon, CNRS, Ecole Centrale de Lyon, Université de Lyon, 69134 Ecully, France
| | - Sang Mo Yang
- Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA
| | - Sergei V Kalinin
- Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA
| | | | - Catherine Dubourdieu
- Institut des Nanotechnologies de Lyon, CNRS, Ecole Centrale de Lyon, Université de Lyon, 69134 Ecully, France
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10
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Krug H. Focus on materials challenges for protection - environment and health. SCIENCE AND TECHNOLOGY OF ADVANCED MATERIALS 2015; 16:030301. [PMID: 27877781 PMCID: PMC5099818 DOI: 10.1088/1468-6996/16/3/030301] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/24/2014] [Revised: 03/13/2015] [Accepted: 03/16/2015] [Indexed: 06/05/2023]
Affiliation(s)
- Harald Krug
- Swiss Federal Laboratories for Materials Science and Technology (Empa), Switzerland
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11
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Koczorowski W, Grzela T, Radny MW, Schofield SR, Capellini G, Czajka R, Schroeder T, Curson NJ. Ba termination of Ge(001) studied with STM. NANOTECHNOLOGY 2015; 26:155701. [PMID: 25797886 DOI: 10.1088/0957-4484/26/15/155701] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
We use controlled annealing to tune the interfacial properties of a sub-monolayer and monolayer coverages of Ba atoms deposited on Ge(001), enabling the generation of either of two fundamentally distinct interfacial phases, as revealed by scanning tunneling microscopy. Firstly we identify the two key structural phases associated with this adsorption system, namely on-top adsorption and surface alloy formation, by performing a deposition and annealing experiment at a coverage low enough (∼0.15 ML) that isolated Ba-related features can be individually resolved. Subsequently we investigate the monolayer coverage case, of interest for passivation schemes of future Ge based devices, for which we find that the thermal evaporation of Ba onto a Ge(001) surface at room temperature results in on-top adsorption. This separation (lack of intermixing) between Ba and Ge layers is retained through successive annealing steps to temperatures of 470, 570, 670 and 770 K although a gradual ordering of the Ba layer is observed at 570 K and above, accompanied by a decrease in Ba layer density. Annealing above 770 K produces the 2D surface alloy phase accompanied by strain relief through monolayer height trench formation. An annealing temperature of 1070 K sees a further change in surface morphology but retention of the 2D surface alloy characteristic. These results are discussed in view of their possible implications for future semiconductor integrated circuit technology.
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Affiliation(s)
- W Koczorowski
- London Centre for Nanotechnology, University College London, 17-19 Gordon Street, London, UK. Institute of Physics, Poznan University of Technology, ul. Piotrowo 3, 60-965 Poznan, Poland
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Integration of lead-free ferroelectric on HfO2/Si (100) for high performance non-volatile memory applications. Sci Rep 2015; 5:8494. [PMID: 25683062 PMCID: PMC4329549 DOI: 10.1038/srep08494] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/07/2014] [Accepted: 01/20/2015] [Indexed: 11/08/2022] Open
Abstract
We introduce a novel lead-free ferroelectric thin film (1-x)BaTiO3-xBa(Cu1/3Nb2/3)O3 (x = 0.025) (BT-BCN) integrated on to HfO2 buffered Si for non-volatile memory (NVM) applications. Piezoelectric force microscopy (PFM), x-ray diffraction, and high resolution transmission electron microscopy were employed to establish the ferroelectricity in BT-BCN thin films. PFM study reveals that the domains reversal occurs with 180° phase change by applying external voltage, demonstrating its effectiveness for NVM device applications. X-ray photoelectron microscopy was used to investigate the band alignments between atomic layer deposited HfO2 and pulsed laser deposited BT-BCN films. Programming and erasing operations were explained on the basis of band-alignments. The structure offers large memory window, low leakage current, and high and low capacitance values that were easily distinguishable even after ~106 s, indicating strong charge storage potential. This study explains a new approach towards the realization of ferroelectric based memory devices integrated on Si platform and also opens up a new possibility to embed the system within current complementary metal-oxide-semiconductor processing technology.
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Hu X, Cueff S, Romeo PR, Orobtchouk R. Modeling the anisotropic electro-optic interaction in hybrid silicon-ferroelectric optical modulator. OPTICS EXPRESS 2015; 23:1699-1714. [PMID: 25835926 DOI: 10.1364/oe.23.001699] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
We present a numerical method to accurately model the electro-optic interaction in anisotropic materials. Specifically, we combine a full-vectorial finite-difference optical mode solver with a radio-frequency solver to analyze the overlap between optical modes and applied electric field. This technique enables a comprehensive understanding on how electro-optic effects modify individual elements in the permittivity tensor of a material. We demonstrate the interest of this approach by designing a modulator that leverages the Pockels effect in a hybrid silicon-BaTiO3 slot waveguide. Optimized optical confinement in the active BaTiO3 layer as well as design of travelling-wave index-matched electrodes is presented. Most importantly, we show that the overall electro-optic modulation is largely governed by off-diagonal elements in the permittivity tensor. As most of active electro-optic materials are anisotropic, this method paves the way to better understand the physics of electro-optic effects and to improve optical modulators.
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