High-k materials based on SrHfO3 and BaHfO3: A Hybrid Density Functional Theory Study

High-k materials based on SrHfO3 and BaHfO3: A Hybrid Density Functional Theory Study | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article High-k materials based on SrHfO3 and BaHfO3: A Hybrid Density Functional Theory Study Abdul Hannan Yeo, Wei Wu, Kwang-Leong Choy This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-1765020/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 5 You are reading this latest preprint version Abstract High-dielectric-constant (high- k ) materials are important as dielectric layers for computer processors to prevent unnecessary electrical current leakages. There is a fast-growing demand in the semiconductor industry for the exploration and integration of alternative high- k materials with the electronic device because the conventional dielectric material such as it gradually becomes difficult for SiO 2 to satisfy the industrial need. There are many promising candidates for the high- k materials such as BaTiO 3 and HfO 2 . Among these, ternary oxides (consisting of three elements and usually having perovskite crystal structure) can offer much better electrical properties than SiO 2 , thus providing potentially better solutions for the current-leakage problem. The previous experiments on the band structure and dielectric properties of SrHfO 3 and BaHfO 3 have shown their good potential for high- k materials. However, the theoretical understanding of these materials is still rare. In this paper, we have computed the electronic structure, optical and static dielectric constants of SrHfO 3 and BaHfO 3 by using hybrid-exchange density-functional theory. This work aims to provide a better understanding through accurate computational calculations of ternary oxides to prove its compatibility and superior material qualities for the future integration into semiconductor devices. A larger band gap (~ 10 eV) with comparable static dielectric constant with HfO 2 (another good candidate for high- k dielectrics) has been suggested by our calculations for SrHfO 3 and BaHfO 3 . The computed static dielectric constants for both materials are in agreement with the experimental results reported previously. Our calculations will provide a solid theoretical foundation for using Hf-bearing ternary oxides to tackle the future need of high- k materials. Figures Figure 1 Figure 2 Figure 3 Figure 4 Introduction The Moore’s law implies that the size of the transistor decreases by half over approximately every two-year period. For the moment, Intel has developed the 6nm technology for integrated circuits 1 . A semiconductor roadmap in the industry 2 is a guiding tool to foresee the transistors scale in the future. There are, however, some limitations to the Moore's law, such as the electrical current leakage due to the thin oxide layer, thus it would not be possible for it to be valid forever. In recent times, the most pressing challenge in logic circuits is the field-effect transistors gate stack, formed by the gate electrode, the dielectric layer and the silicon substrate 3 . The current thickness of the silicon-dioxide layer is so thin (within a few nanometers) that the gate leakage current can easily occur through the direct tunneling of electrons into the silicon-dioxide layer. This results in significant energy dissipations, which are unacceptable for improving the performance of these logic chips. It turns out 4 that the solution to this problem with electrical current leakage is to replace the current widely used silicon dioxide layer with a thicker layer of a new material which should also possess a higher dielectric constant k . With these changes, the tunneling current would decrease and maintain the same level of capacity for the oxide layer, according to \(C= \frac{\epsilon A}{t}\) , where C is the capacitance, \(\epsilon\) the relative permittivity/dielectric constant, and t the thickness 4 . These new oxides with higher dielectric constant can be classified as so-called high- k oxides. The general requirement for the high- k materials is that the dielectric constant should be above 12 and preferably between 25–30 for long-term integrations into the fabrication processes 5 . There are also a few additional requirements of a high- k oxide 3 : The k -value should be sufficiently large for several years of scaling. The material must be thermodynamically stable when integrated with the silicon substrate. Kinetically stable and compatible to up to 1000°C based on fabrication processes. Good electrical interface with silicon. Few electrically active defects in the bulk. Another important parameter for a suitable dielectric material would be the band gap. The high- k material must function as a good insulator with a wide band gap, which will ensure the prevention of thermally activated electrical currents. The typical high- k materials with a large band gap are ZrO 2 and HfO 2 . 6 , 7 Several studies have shown that preferably the band gap for a high- k material should be above ~ 5 eV. Below this value, valence band may be offset and can result in a narrower bandgap. The static dielectric tensor \({ϵ}_{\alpha \beta }^{0}\) , which is a key parameter for the dielectric properties, can be computed from first principles essentially in two parts. First of all, we can compute the optical dielectric constant \({ϵ}_{\infty }\) (or high-frequency dielectric constant) by using coupled perturbed Kohn-Sham (CPKS) methods 8 , where \({ϵ}_{\infty }\) can be deduced through the polarizability computed from first principles such as the perturbation theory based on density-functional theory. The second part, originating from the lattice vibrations, plays a much more important role, which reads 9 , \({ϵ}_{\alpha \beta }^{0}={ϵ}_{\alpha \beta }^{\infty }+\frac{4\pi }{{\Omega }}\sum _{m}\frac{{Z}_{m\alpha }^{*}{Z}_{m\beta }^{*}}{{\omega }_{m}^{2}}\) . Here \(\alpha\) and \(\beta\) run over x , y and z . \({ϵ}_{\alpha \beta }^{0}\) is the static dielectric tensor, \({ϵ}_{\alpha \beta }^{\infty }\) the optical dielectric tensor computed using CPKS, \({\Omega }\) the unit cell volume, \({\omega }_{m}\) is the frequency of the m th vibrational mode, and \({Z}_{m\alpha }^{*}\) the Born effective charge for the m th vibrational mode at the \(\alpha\) direction. Extensive experimental and theoretical studies have been carried out on the Hf-based binary oxides for high- k materials. 10 However, perovskite structured ternary oxides have received much less attention due to the complex crystal structure with many phases at different experimental conditions such as temperatures and pressures 11 , which will lead to phase transitions. It could be very promising to design the Hf-based materials for many applications such as gate dielectrics 12 . SrHfO 3 has shown a dielectric constant value of ~ 25 experimentally, which, in combination with its large bandgap (~ 6 eV), are the main motivations for this study 11 . In contrast to HfO 2 , the perovskite ABX 3 materials can offer much higher bandgap with comparable dielectric constant 7 – 13 , thus improving the figure of merit of the high- k materials significantly. In this paper, we have used hybrid-exchange density-functional theory, CPKS and the follow-on phonon calculations to compute the static dielectric constants for SrHfO 3 and BaHfO 3 . Our calculations are in good agreements with the previous experimental results, pointing to enhancing the dielectric properties by theoretical materials design. Our remaining discussion falls into three sections. In the section 2, we introduce our computational details. In the section 3, we present and discuss the calculation results. In the section 4, we draw some general conclusions. Computational Methods All the density-functional-theory (DFT) calculations were performed using CRYSTAL14 code 19 . We have employed the hybrid-exchange functional B3LYP 20 . The CPKS method 20 has been used to compute the high-frequency dielectric constant, while the static dielectric constant has been obtained by computing the vibrational modes of the lattice 20 , which contributes most of the dielectric properties of the material. The crystal structure of SrHfO 3 was taken from the inorganic crystal structure database 15 . The symmetry group for SrHfO3 is Pbnm ; for the lattice parameters, a = 5.752 Å, b = 5.765 Å, c = 8.134 Å, and a = b = g = 90°. 21 The symmetry group for BaHfO 3 is Pnma ; for the lattice parameters, a = 5.809 Å, b = 8.195 Å, c = 5.802 Å, and a = b = g = 90°. 22 The DFT calculations have been accelerated by a mixing factor of 30% of the density matrices. The Monkhorst-Pack sampling of reciprocal space is carried out by choosing a grid of shrinking factor equal to eight. 23 The basis sets for Sr 24 , Ba 25 , Hf 26 , and O 27 have been chosen from the CRYSTAL basis set database. Results And Discussion As shown in Table 1 , we have computed the static dielectric constant by using CPHF and phonon spectrum analysis. The computed static dielectric constant for SrHfO 3 is 25.56, which is in agreement with the previous experimental work for the dielectric property for SrHfO 3 nanoparticles (~ 17) 16 , but much smaller than that computed using HSE06 previously 9 , as illustrated in Fig. 2 . The reason for this difference could be the functionals used. The static dielectric constant for BaHfO 3 is slightly smaller than that for SrHfO 3 , which is 17.40. Table 1 The computed dielectric constants and bandgaps for SrHfO 3 and BaHfO 3 . Parameter BaHfO 3 SrHfO 3 Static Dielectric constant 17.40 25.56 Top of Valence (Hartree) -0.108 -0.152 Bottom of Valence (Hartree) 0.115 0.072 Band gap (eV) 6.1 6.1 The computed band structures of SrHfO 3 and BaHfO 3 are displayed in Fig. 3 . These calculations show that the band gaps for SrHfO 3 and BaHfO 3 are ~ 6 eV and indirect, which suggests that both of them are good material candidates for high-k materials, in combination with the relatively high dielectric constant. In Fig. 4 we have also compared the infrared (IR) intensities (both the transverse and longitudinal phonon spectra) for SrHfO 3 and BaHfO 3 . We can see that they show similar patterns, which is consistent with the closeness between their dielectric constants. The low-frequency modes (< 5 THz) are responsible for the high dielectric constants. Comparing the two materials, BaHfO 3 is more responsive to the frequencies below 5 THz. Between 5 and 10 THz, both materials show similar IR spectra. Between 10 and 15 (15 and 20) THz, BaHfO 3 has stronger (weaker) IR absorption than SrHfO 3 . Conclusions In summary, we have calculated the static dielectric constants and the electronic structures for SrHfO 3 and BaHfO 3 using the B3LYP hybrid-exchange density-functional theory, based on CPHF and phonon-mode calculations. The computed static dielectric constant for SrHfO 3 was found to be substantially better than the previous theoretical work, which shows that our current work is more consistent with the previous experimental data. 8 For BaHfO 3 , our calculations need to be validated by the further experiments. This work has demonstrated that SrHfO 3 and BaHfO 3 are appropriate dielectric materials for the semiconducting devices. The wide band gaps for both materials (> 5 eV) are also advantageous for many applications, such as random-access memory and logic gates. Our calculations suggest that the Hf-bearing perovskite materials have great potential to be integrated into semiconductor devices as dielectric layers. However, further theoretical studies are needed to consider the finite thickness of the materials and the effects of the interface between the dielectric layers and silicon. In addition, the experimental study on the practical aspect of this calculation such as thermal stabilities should be carried out to determine the theoretical feasibility for lab-scale integration and production. Declarations Data Availability All the data that support the findings of this study are available from the corresponding author upon reasonable request. Acknowledgements We thank UCL research computing team for their technical support. W. W. would like to acknowledge the funding support from EU Marketplace Project 545083. Competing Interests The authors declare no competing interests. References Burg, D.; Ausubel, J. H. 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Dovesi, R.; Orlando, R.; Erba, A.; Zicovich-Wilson, C. M.; Civalleri, B.; Casassa, S.; Maschio, L.; Ferrabone, M.; De La Pierre, M.; D’Arco, P.; Noël, Y.; Causà, M.; Rérat, M.; Kirtman, B. C RYSTAL14: A Program for the Ab Initio Investigation of Crystalline Solids. Int. J. Quantum Chem. 2014 , 114 (19), 1287–1317. https://doi.org/10.1002/qua.24658. Becke, A. D. Density-Functional Thermochemistry. III. The Role of Exact Exchange. J. Chem. Phys. 1993 , 98 (7), 5648–5652. https://doi.org/10.1063/1.464913. Kennedy, B. J.; Howard, C. J.; Chakoumakos, B. C. High-Temperature Phase Transitions in <span Class. Phys. Rev. B 1999 , 60 (5), 2972. https://doi.org/10.1103/PhysRevB.60.2972. Li, L.; Kennedy, B. J.; Kubota, Y.; Kato, K.; Garrett, R. F. Structures and Phase Transitions in Sr1−xBaxHfO3 Perovskites. J. Mater. Chem. 2004 , 14 (2), 263–273. https://doi.org/10.1039/B308258J. Monkhorst, H. J.; Pack, J. D. Special Points for Brillonin-Zone Integrations*. NUMBER 1976 , 13 . 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Cite Share Download PDF Status: Under Review Version 1 posted Reviewers agreed at journal 09 Jul, 2022 Reviewers invited by journal 08 Jul, 2022 Editor invited by journal 05 Jul, 2022 Editor assigned by journal 20 Jun, 2022 First submitted to journal 16 Jun, 2022 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-1765020","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":119620277,"identity":"ff1c3cac-21bf-4c93-b352-80fe4a3ca649","order_by":0,"name":"Abdul Hannan Yeo","email":"","orcid":"","institution":"University College London","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Abdul","middleName":"Hannan","lastName":"Yeo","suffix":""},{"id":119620278,"identity":"3550f31a-7391-4e4c-acba-6c3198e526a1","order_by":1,"name":"Wei Wu","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAt0lEQVRIiWNgGAWjYFACxgYgYcPAwA7hGhCrJY2BgZl4LWBwmAQtBsebG5h5284n9jczMH74wXDYmLCWMwdBWm4nzjjMwCzZw3DYjKAWsxuJDcy5QC0bgA6TBrrQhrCW+w9BWs6BtDD/Jk7LDUaQlgMgLWwgWwg7zP5MYsPhP+eSjWccZmyz7DFIJ+x9yfbjDx/OKLOT7W9vPnzjR4W1YQNBPUBwAEKB4pToiBwFo2AUjIJRgBcAAMSIOIDFsOCgAAAAAElFTkSuQmCC","orcid":"https://orcid.org/0000-0003-2843-5113","institution":"University College London","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"Wei","middleName":"","lastName":"Wu","suffix":""},{"id":119620279,"identity":"305551dc-79a2-4d7b-bf41-ae4b8a6c6861","order_by":2,"name":"Kwang-Leong Choy","email":"","orcid":"","institution":"University College London","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Kwang-Leong","middleName":"","lastName":"Choy","suffix":""}],"badges":[],"createdAt":"2022-06-16 12:39:19","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-1765020/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-1765020/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":23997360,"identity":"f43def50-4e43-4112-a22d-9d637929aae7","added_by":"auto","created_at":"2022-07-18 17:15:25","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":171534,"visible":true,"origin":"","legend":"\u003cp\u003eThe crystal structure of perovskite SrHfO\u003csub\u003e3\u003c/sub\u003e and BaHfO\u003csub\u003e3\u003c/sub\u003e. Both possess the same symmetry \u003cem\u003ePbnm\u003c/em\u003e (\u003cem\u003ePnma\u003c/em\u003e). Here A: Strontium/Barium (Sr/Ba), B: Hafnium (Hf) and X: Oxygen (O).\u003c/p\u003e\u003cp\u003e\u003cbr\u003e\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-1765020/v1/e96bea32495cf418702b44e5.png"},{"id":23997361,"identity":"1dc35633-39c1-498c-94aa-4fbe7e6ca1a4","added_by":"auto","created_at":"2022-07-18 17:15:25","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":150384,"visible":true,"origin":"","legend":"\u003cp\u003eA comparison of the static dielectric constants of SrHfO\u003csub\u003e3\u003c/sub\u003e with the previously reported literatures, which suggests our calculation of the dielectric constant based on B3LYP functional provides better consistency with the experiments than the calculation performed by Yim, et. al.\u003csup\u003e8\u003c/sup\u003e\u003c/p\u003e\u003cp\u003e\u003cbr\u003e\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-1765020/v1/4d48b8ce04dee580ad2c5972.png"},{"id":23997359,"identity":"21b83360-7c82-47a7-a3eb-7b6ec6f324ab","added_by":"auto","created_at":"2022-07-18 17:15:25","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":140804,"visible":true,"origin":"","legend":"\u003cp\u003eThe band structures of SrHfO\u003csub\u003e3\u003c/sub\u003e (a) and BaHfO\u003csub\u003e3\u003c/sub\u003e (b). The Fermi energy (labeled in red) is zero here.\u003c/p\u003e\u003cp\u003e\u003cbr\u003e\u003c/p\u003e\u003cp\u003e\u003cbr\u003e\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-1765020/v1/980ba4eb8734b8e5edff9d7c.png"},{"id":23997362,"identity":"5e3ea1cf-7914-44ad-9c8f-b2d3c006992b","added_by":"auto","created_at":"2022-07-18 17:15:25","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":111270,"visible":true,"origin":"","legend":"\u003cp\u003eThe longitudinal (red) and transverse (blue) modes are shown for: (a) SrHfO\u003csub\u003e3\u003c/sub\u003e and (b) BaHfO\u003csub\u003e3\u003c/sub\u003e.\u003c/p\u003e\u003cp\u003e\u003cbr\u003e\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-1765020/v1/5df1cc4b7934ce92a3063f7f.png"},{"id":23997363,"identity":"8f6e371e-9500-45a2-8087-f7267ed1e775","added_by":"auto","created_at":"2022-07-18 17:15:28","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":458324,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-1765020/v1/ff7033f4-5789-4a5f-bd7e-c8ccf515bf01.pdf"}],"financialInterests":"","formattedTitle":"High-k materials based on SrHfO3 and BaHfO3: A Hybrid Density Functional Theory Study","fulltext":[{"header":"Introduction","content":"\u003cp\u003eThe Moore\u0026rsquo;s law implies that the size of the transistor decreases by half over approximately every two-year period. For the moment, Intel has developed the 6nm technology for integrated circuits\u003csup\u003e\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003e. A semiconductor roadmap in the industry\u003csup\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003e is a guiding tool to foresee the transistors scale in the future. There are, however, some limitations to the Moore's law, such as the electrical current leakage due to the thin oxide layer, thus it would not be possible for it to be valid forever. In recent times, the most pressing challenge in logic circuits is the field-effect transistors gate stack, formed by the gate electrode, the dielectric layer and the silicon substrate\u003csup\u003e\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e\u003c/sup\u003e. The current thickness of the silicon-dioxide layer is so thin (within a few nanometers) that the gate leakage current can easily occur through the direct tunneling of electrons into the silicon-dioxide layer. This results in significant energy dissipations, which are unacceptable for improving the performance of these logic chips. It turns out\u003csup\u003e\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u003c/sup\u003e that the solution to this problem with electrical current leakage is to replace the current widely used silicon dioxide layer with a thicker layer of a new material which should also possess a higher dielectric constant \u003cem\u003ek\u003c/em\u003e. With these changes, the tunneling current would decrease and maintain the same level of capacity for the oxide layer, according to \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(C= \\frac{\\epsilon A}{t}\\)\u003c/span\u003e\u003c/span\u003e, where \u003cem\u003eC\u003c/em\u003e is the capacitance, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\epsilon\\)\u003c/span\u003e\u003c/span\u003e the relative permittivity/dielectric constant, and \u003cem\u003et\u003c/em\u003e the thickness\u003csup\u003e\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u003c/sup\u003e. These new oxides with higher dielectric constant can be classified as so-called high-\u003cem\u003ek\u003c/em\u003e oxides. The general requirement for the high-\u003cem\u003ek\u003c/em\u003e materials is that the dielectric constant should be above 12 and preferably between 25\u0026ndash;30 for long-term integrations into the fabrication processes\u003csup\u003e\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e\u003c/sup\u003e. There are also a few additional requirements of a high-\u003cem\u003ek\u003c/em\u003e oxide\u003csup\u003e\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e\u003c/sup\u003e:\u003c/p\u003e \u003cp\u003e \u003col\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eThe \u003cem\u003ek\u003c/em\u003e-value should be sufficiently large for several years of scaling.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eThe material must be thermodynamically stable when integrated with the silicon substrate.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eKinetically stable and compatible to up to 1000\u0026deg;C based on fabrication processes.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eGood electrical interface with silicon.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eFew electrically active defects in the bulk.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003c/ol\u003e \u003c/p\u003e \u003cp\u003eAnother important parameter for a suitable dielectric material would be the band gap. The high-\u003cem\u003ek\u003c/em\u003e material must function as a good insulator with a wide band gap, which will ensure the prevention of thermally activated electrical currents. The typical high-\u003cem\u003ek\u003c/em\u003e materials with a large band gap are ZrO\u003csub\u003e2\u003c/sub\u003e and HfO\u003csub\u003e2\u003c/sub\u003e.\u003csup\u003e\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e,\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e\u003c/sup\u003e Several studies have shown that preferably the band gap for a high-\u003cem\u003ek\u003c/em\u003e material should be above ~\u0026thinsp;5 eV. Below this value, valence band may be offset and can result in a narrower bandgap.\u003c/p\u003e \u003cp\u003eThe static dielectric tensor \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({ϵ}_{\\alpha \\beta }^{0}\\)\u003c/span\u003e\u003c/span\u003e, which is a key parameter for the dielectric properties, can be computed from first principles essentially in two parts. First of all, we can compute the optical dielectric constant \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({ϵ}_{\\infty }\\)\u003c/span\u003e\u003c/span\u003e (or high-frequency dielectric constant) by using coupled perturbed Kohn-Sham (CPKS) methods\u003csup\u003e\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e\u003c/sup\u003e, where \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({ϵ}_{\\infty }\\)\u003c/span\u003e\u003c/span\u003e can be deduced through the polarizability computed from first principles such as the perturbation theory based on density-functional theory. The second part, originating from the lattice vibrations, plays a much more important role, which reads\u003csup\u003e\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e\u003c/sup\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({ϵ}_{\\alpha \\beta }^{0}={ϵ}_{\\alpha \\beta }^{\\infty }+\\frac{4\\pi }{{\\Omega }}\\sum _{m}\\frac{{Z}_{m\\alpha }^{*}{Z}_{m\\beta }^{*}}{{\\omega }_{m}^{2}}\\)\u003c/span\u003e\u003c/span\u003e. Here \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\alpha\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\beta\\)\u003c/span\u003e\u003c/span\u003e run over \u003cem\u003ex\u003c/em\u003e, \u003cem\u003ey\u003c/em\u003e and \u003cem\u003ez\u003c/em\u003e. \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({ϵ}_{\\alpha \\beta }^{0}\\)\u003c/span\u003e\u003c/span\u003eis the static dielectric tensor, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({ϵ}_{\\alpha \\beta }^{\\infty }\\)\u003c/span\u003e\u003c/span\u003e the optical dielectric tensor computed using CPKS, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\Omega }\\)\u003c/span\u003e\u003c/span\u003e the unit cell volume, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\omega }_{m}\\)\u003c/span\u003e\u003c/span\u003e is the frequency of the \u003cem\u003em\u003c/em\u003eth vibrational mode, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({Z}_{m\\alpha }^{*}\\)\u003c/span\u003e\u003c/span\u003e the Born effective charge for the \u003cem\u003em\u003c/em\u003eth vibrational mode at the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\alpha\\)\u003c/span\u003e\u003c/span\u003e direction.\u003c/p\u003e \u003cp\u003eExtensive experimental and theoretical studies have been carried out on the Hf-based binary oxides for high-\u003cem\u003ek\u003c/em\u003e materials.\u003csup\u003e\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e\u003c/sup\u003e However, perovskite structured ternary oxides have received much less attention due to the complex crystal structure with many phases at different experimental conditions such as temperatures and pressures\u003csup\u003e\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e\u003c/sup\u003e, which will lead to phase transitions. It could be very promising to design the Hf-based materials for many applications such as gate dielectrics\u003csup\u003e\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u003c/sup\u003e. SrHfO\u003csub\u003e3\u003c/sub\u003e has shown a dielectric constant value of ~\u0026thinsp;25 experimentally, which, in combination with its large bandgap (~\u0026thinsp;6 eV), are the main motivations for this study\u003csup\u003e\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e\u003c/sup\u003e. In contrast to HfO\u003csub\u003e2\u003c/sub\u003e, the perovskite ABX\u003csub\u003e3\u003c/sub\u003e materials can offer much higher bandgap with comparable dielectric constant\u003csup\u003e\u003cspan additionalcitationids=\"CR8 CR9 CR10 CR11 CR12\" citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e\u003c/sup\u003e, thus improving the figure of merit of the high-\u003cem\u003ek\u003c/em\u003e materials significantly. In this paper, we have used hybrid-exchange density-functional theory, CPKS and the follow-on phonon calculations to compute the static dielectric constants for SrHfO\u003csub\u003e3\u003c/sub\u003e and BaHfO\u003csub\u003e3\u003c/sub\u003e. Our calculations are in good agreements with the previous experimental results, pointing to enhancing the dielectric properties by theoretical materials design. Our remaining discussion falls into three sections. In the section 2, we introduce our computational details. In the section 3, we present and discuss the calculation results. In the section 4, we draw some general conclusions.\u003c/p\u003e"},{"header":"Computational Methods","content":"\u003cp\u003eAll the density-functional-theory (DFT) calculations were performed using CRYSTAL14 code\u003csup\u003e\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e\u003c/sup\u003e. We have employed the hybrid-exchange functional B3LYP\u003csup\u003e\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e\u003c/sup\u003e. The CPKS method\u003csup\u003e\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e\u003c/sup\u003e has been used to compute the high-frequency dielectric constant, while the static dielectric constant has been obtained by computing the vibrational modes of the lattice\u003csup\u003e\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e\u003c/sup\u003e, which contributes most of the dielectric properties of the material. The crystal structure of SrHfO\u003csub\u003e3\u003c/sub\u003e was taken from the inorganic crystal structure database\u003csup\u003e\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e\u003c/sup\u003e. The symmetry group for SrHfO3 is \u003cem\u003ePbnm\u003c/em\u003e; for the lattice parameters, \u003cem\u003ea\u003c/em\u003e\u0026thinsp;=\u0026thinsp;5.752 \u0026Aring;, \u003cem\u003eb\u003c/em\u003e\u0026thinsp;=\u0026thinsp;5.765 \u0026Aring;, \u003cem\u003ec\u003c/em\u003e\u0026thinsp;=\u0026thinsp;8.134 \u0026Aring;, and \u003cem\u003ea\u003c/em\u003e\u0026thinsp;=\u0026thinsp;\u003cem\u003eb\u003c/em\u003e\u0026thinsp;=\u0026thinsp;\u003cem\u003eg\u003c/em\u003e\u0026thinsp;=\u0026thinsp;90\u0026deg;.\u003csup\u003e21\u003c/sup\u003e The symmetry group for BaHfO\u003csub\u003e3\u003c/sub\u003e is \u003cem\u003ePnma\u003c/em\u003e; for the lattice parameters, \u003cem\u003ea\u003c/em\u003e\u0026thinsp;=\u0026thinsp;5.809 \u0026Aring;, \u003cem\u003eb\u003c/em\u003e\u0026thinsp;=\u0026thinsp;8.195 \u0026Aring;, \u003cem\u003ec\u003c/em\u003e\u0026thinsp;=\u0026thinsp;5.802 \u0026Aring;, and \u003cem\u003ea\u003c/em\u003e\u0026thinsp;=\u0026thinsp;\u003cem\u003eb\u003c/em\u003e\u0026thinsp;=\u0026thinsp;\u003cem\u003eg\u003c/em\u003e\u0026thinsp;=\u0026thinsp;90\u0026deg;.\u003csup\u003e22\u003c/sup\u003e The DFT calculations have been accelerated by a mixing factor of 30% of the density matrices. The Monkhorst-Pack sampling of reciprocal space is carried out by choosing a grid of shrinking factor equal to eight.\u003csup\u003e\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e\u003c/sup\u003e The basis sets for Sr\u003csup\u003e\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e\u003c/sup\u003e, Ba\u003csup\u003e\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e\u003c/sup\u003e, Hf\u003csup\u003e\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e\u003c/sup\u003e, and O\u003csup\u003e\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e\u003c/sup\u003e have been chosen from the CRYSTAL basis set database.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"Results And Discussion","content":"\u003cp\u003eAs shown in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, we have computed the static dielectric constant by using CPHF and phonon spectrum analysis. The computed static dielectric constant for SrHfO\u003csub\u003e3\u003c/sub\u003e is 25.56, which is in agreement with the previous experimental work for the dielectric property for SrHfO\u003csub\u003e3\u003c/sub\u003e nanoparticles (~\u0026thinsp;17)\u003csup\u003e\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e\u003c/sup\u003e, but much smaller than that computed using HSE06 previously\u003csup\u003e\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e\u003c/sup\u003e, as illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. The reason for this difference could be the functionals used. The static dielectric constant for BaHfO\u003csub\u003e3\u003c/sub\u003e is slightly smaller than that for SrHfO\u003csub\u003e3\u003c/sub\u003e, which is 17.40.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eThe computed dielectric constants and bandgaps for SrHfO\u003csub\u003e3\u003c/sub\u003e and BaHfO\u003csub\u003e3\u003c/sub\u003e.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eParameter\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eBaHfO\u003csub\u003e3\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eSrHfO\u003csub\u003e3\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eStatic Dielectric constant\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e17.40\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e25.56\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTop of Valence (Hartree)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e-0.108\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e-0.152\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBottom of Valence (Hartree)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.115\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.072\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBand gap (eV)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e6.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e6.1\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe computed band structures of SrHfO\u003csub\u003e3\u003c/sub\u003e and BaHfO\u003csub\u003e3\u003c/sub\u003e are displayed in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. These calculations show that the band gaps for SrHfO\u003csub\u003e3\u003c/sub\u003e and BaHfO\u003csub\u003e3\u003c/sub\u003e are ~\u0026thinsp;6 eV and indirect, which suggests that both of them are good material candidates for high-k materials, in combination with the relatively high dielectric constant. In Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e we have also compared the infrared (IR) intensities (both the transverse and longitudinal phonon spectra) for SrHfO\u003csub\u003e3\u003c/sub\u003e and BaHfO\u003csub\u003e3\u003c/sub\u003e. We can see that they show similar patterns, which is consistent with the closeness between their dielectric constants. The low-frequency modes (\u0026lt;\u0026thinsp;5 THz) are responsible for the high dielectric constants. Comparing the two materials, BaHfO\u003csub\u003e3\u003c/sub\u003e is more responsive to the frequencies below 5 THz. Between 5 and 10 THz, both materials show similar IR spectra. Between 10 and 15 (15 and 20) THz, BaHfO\u003csub\u003e3\u003c/sub\u003e has stronger (weaker) IR absorption than SrHfO\u003csub\u003e3\u003c/sub\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"Conclusions","content":"\u003cp\u003eIn summary, we have calculated the static dielectric constants and the electronic structures for SrHfO\u003csub\u003e3\u003c/sub\u003e and BaHfO\u003csub\u003e3\u003c/sub\u003e using the B3LYP hybrid-exchange density-functional theory, based on CPHF and phonon-mode calculations. The computed static dielectric constant for SrHfO\u003csub\u003e3\u003c/sub\u003e was found to be substantially better than the previous theoretical work, which shows that our current work is more consistent with the previous experimental data.\u003csup\u003e\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e\u003c/sup\u003e For BaHfO\u003csub\u003e3\u003c/sub\u003e, our calculations need to be validated by the further experiments. This work has demonstrated that SrHfO\u003csub\u003e3\u003c/sub\u003e and BaHfO\u003csub\u003e3\u003c/sub\u003e are appropriate dielectric materials for the semiconducting devices. The wide band gaps for both materials (\u0026gt;\u0026thinsp;5 eV) are also advantageous for many applications, such as random-access memory and logic gates. Our calculations suggest that the Hf-bearing perovskite materials have great potential to be integrated into semiconductor devices as dielectric layers. However, further theoretical studies are needed to consider the finite thickness of the materials and the effects of the interface between the dielectric layers and silicon. In addition, the experimental study on the practical aspect of this calculation such as thermal stabilities should be carried out to determine the theoretical feasibility for lab-scale integration and production.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eData Availability\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eAll the data that support the findings of this study are available from the corresponding author upon reasonable request.\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAcknowledgements\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eWe thank UCL research computing team for their technical support. W. W. would like to acknowledge the funding support from EU Marketplace Project 545083.\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting Interests\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare no competing interests.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eBurg, D.; Ausubel, J. H. Moore\u0026rsquo;s Law Revisited through Intel Chip Density. \u003cem\u003ePLoS One\u003c/em\u003e \u003cstrong\u003e2021\u003c/strong\u003e, \u003cem\u003e16\u003c/em\u003e (8), e0256245. https://doi.org/10.1371/journal.pone.0256245.\u003c/li\u003e\n\u003cli\u003eGargini, P. The International Technology for Semiconductors (ITRS): \u0026ldquo;Past, Present and Future.\u0026rdquo; \u003cem\u003eTech. Dig. - GaAs IC Symp. (Gallium Arsenide Integr. 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B\u003c/em\u003e \u003cstrong\u003e1994\u003c/strong\u003e, \u003cem\u003e50\u003c/em\u003e (8), 5041\u0026ndash;5054. https://doi.org/10.1103/PHYSREVB.50.5041.\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":true,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"journal-of-computational-electronics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"jcel","sideBox":"Learn more about [Journal of Computational Electronics](https://www.springer.com/journal/10825)","snPcode":"10825","submissionUrl":"https://submission.nature.com/new-submission/10825/3","title":"Journal of Computational Electronics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-1765020/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-1765020/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003e High-dielectric-constant (high-\u003cem\u003ek\u003c/em\u003e) materials are important as dielectric layers for computer processors to prevent unnecessary electrical current leakages. There is a fast-growing demand in the semiconductor industry for the exploration and integration of alternative high-\u003cem\u003ek\u003c/em\u003e materials with the electronic device because the conventional dielectric material such as it gradually becomes difficult for SiO\u003csub\u003e2\u003c/sub\u003e to satisfy the industrial need. There are many promising candidates for the high-\u003cem\u003ek\u003c/em\u003e materials such as BaTiO\u003csub\u003e3\u003c/sub\u003e and HfO\u003csub\u003e2\u003c/sub\u003e. Among these, ternary oxides (consisting of three elements and usually having perovskite crystal structure) can offer much better electrical properties than SiO\u003csub\u003e2\u003c/sub\u003e, thus providing potentially better solutions for the current-leakage problem. The previous experiments on the band structure and dielectric properties of SrHfO\u003csub\u003e3\u003c/sub\u003e and BaHfO\u003csub\u003e3\u003c/sub\u003e have shown their good potential for high-\u003cem\u003ek\u003c/em\u003e materials. However, the theoretical understanding of these materials is still rare. In this paper, we have computed the electronic structure, optical and static dielectric constants of SrHfO\u003csub\u003e3\u003c/sub\u003e and BaHfO\u003csub\u003e3\u003c/sub\u003e by using hybrid-exchange density-functional theory. This work aims to provide a better understanding through accurate computational calculations of ternary oxides to prove its compatibility and superior material qualities for the future integration into semiconductor devices. A larger band gap (~\u0026thinsp;10 eV) with comparable static dielectric constant with HfO\u003csub\u003e2\u003c/sub\u003e (another good candidate for high-\u003cem\u003ek\u003c/em\u003e dielectrics) has been suggested by our calculations for SrHfO\u003csub\u003e3\u003c/sub\u003e and BaHfO\u003csub\u003e3\u003c/sub\u003e. The computed static dielectric constants for both materials are in agreement with the experimental results reported previously. Our calculations will provide a solid theoretical foundation for using Hf-bearing ternary oxides to tackle the future need of high-\u003cem\u003ek\u003c/em\u003e materials.\u003c/p\u003e","manuscriptTitle":"High-k materials based on SrHfO3 and BaHfO3: A Hybrid Density Functional Theory Study","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2022-07-18 17:15:23","doi":"10.21203/rs.3.rs-1765020/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"reviewerAgreed","content":"","date":"2022-07-09T12:53:04+00:00","index":0,"fulltext":""},{"type":"reviewersInvited","content":"","date":"2022-07-08T13:16:39+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"Journal of Computational Electronics","date":"2022-07-06T00:04:19+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2022-06-20T12:07:23+00:00","index":"","fulltext":""},{"type":"submitted","content":"Journal of Computational Electronics","date":"2022-06-16T08:37:42+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"journal-of-computational-electronics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"jcel","sideBox":"Learn more about [Journal of Computational Electronics](https://www.springer.com/journal/10825)","snPcode":"10825","submissionUrl":"https://submission.nature.com/new-submission/10825/3","title":"Journal of Computational Electronics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"558c7857-652b-4001-8543-9f581e346376","owner":[],"postedDate":"July 18th, 2022","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2023-09-12T21:52:13+00:00","versionOfRecord":[],"versionCreatedAt":"2022-07-18 17:15:23","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-1765020","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-1765020","identity":"rs-1765020","version":["v1"]},"buildId":"rHA-KDH7Qsr4HCuvH75dn","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}