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arxiv: 2604.20694 · v1 · submitted 2026-04-22 · ⚛️ physics.app-ph

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Gradient Residual Stress in Transferred Thin-Film Lithium Niobate and Its Compenstation Using Periodically Poled Piezoelectric Bilayers

Byeongjin Kim , Ian Anderson , Tzu-Hsuan Hsu , Ruochen Lu
Authors on Pith no claims yet

Pith reviewed 2026-05-09 22:28 UTC · model grok-4.3

classification ⚛️ physics.app-ph
keywords thin-film lithium niobateresidual stress gradientcantilever curvaturebilayer compensationMEMSperiodically poled piezoelectricTFLNpiezoelectric bilayer
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The pith

Transferred thin-film lithium niobate films carry a residual stress gradient that varies with crystal orientation and thickness and can be partially cancelled by bilayers of opposite orientation.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper measures the through-thickness residual stress gradient in transferred 128-degree Y-cut lithium niobate films 100 to 460 nanometers thick by observing how test cantilevers bend. The gradient strength changes with both the film's rotation angle and thickness, and certain orientations produce almost no net gradient in thicker films. Stacking two layers with opposing crystal orientations forms a periodically poled structure that cancels a large fraction of the stress, leaving much less bending. Finite-element models match the observed shapes, confirming the gradient is orientation-dependent. This shows a practical route to flatter and more scalable mechanical devices built from these films.

Core claim

In 128 deg Y-cut transferred TFLN the normalized gradient stress sigma1 reaches 3.4 MPa/nm in 100 nm films and falls with thickness, with near-zero-gradient orientations near 55 and 125 degrees for 220-460 nm films but shifting to 20 and 160 degrees for 100 nm films. Finite element simulations confirm the gradient arises from orientation-dependent residual stress. A 90/110 nm bilayer with opposite orientations reduces the effective gradient to -0.4 to -0.04 MPa/nm and markedly lowers cantilever deformation.

What carries the argument

Cantilever curvature measurement used to extract the normalized residual stress gradient sigma1, together with periodically poled piezoelectric film (P3F) bilayers formed from two TFLN layers of opposite crystallographic orientation that partially cancel the gradient.

Load-bearing premise

Cantilever curvature directly and exclusively reflects the film's internal through-thickness stress gradient without significant contributions from bonding interfaces or transfer artifacts.

What would settle it

Depth-resolved stress mapping, for example by x-ray diffraction or Raman spectroscopy through the film thickness on the same low-curvature samples, would show whether the extracted gradient is truly near zero.

Figures

Figures reproduced from arXiv: 2604.20694 by Byeongjin Kim, Ian Anderson, Ruochen Lu, Tzu-Hsuan Hsu.

Figure 2
Figure 2. Figure 2: Residual stress components in a TFLN cantilever: (a) decomposition [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: TFLN cantilever array and film structure: (a) schematic of single-layer films (100, 220, and 460 nm) with crystallographic orientations; (b) optical image of cantilever array with θ = 0°–160° in 20° steps; (c) SEM image of released cantilevers; (d) fabrication process flow [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 6
Figure 6. Figure 6: Bilayer TFLN cantilever array and structure: [PITH_FULL_IMAGE:figures/full_fig_p004_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Beam tip height and normalized σ₁ versus in [PITH_FULL_IMAGE:figures/full_fig_p005_7.png] view at source ↗
read the original abstract

In this work, we experimentally investigate the gradient stress (sigma1) in 128 deg Y-cut transferred thin film lithium niobate (TFLN) films with thicknesses from 100 to 460 nm using cantilever curvature analysis. The results reveal a strong dependence of sigma1 on both crystallographic orientation and film thickness, with stress-free orientations at approximately 55 deg and 125 deg for 220-460 nm films, shifting to approximately 20 deg and 160 deg for 100 nm films. The extracted normalized sigma1 ranges from -0.1 to 3.4 MPa/nm (100 nm), -0.8 to 0.34 MPa/nm (220 nm), and -0.12 to 0.08 MPa/nm (460 nm), indicating a pronounced thickness-dependent through-thickness stress gradient. Finite element simulations show excellent agreement with the measurements, validating the curvature-based extraction method and confirming that sigma1 originates from an orientation-dependent residual stress gradient. To mitigate this effect, a bilayer TFLN structure with opposite crystallographic orientations, forming a periodically poled piezoelectric film (P3F), is investigated, enabling partial cancellation of sigma1. A 90/110 nm P3F bilayer reduces the equivalent normalized sigma1 to -0.4 to -0.04 MPa/nm, resulting in significantly reduced deformation. These results establish gradient stress engineering through orientation, thickness, and bilayer design as an effective strategy for achieving mechanically stable and scalable TFLN microelectromechanical systems (MEMS) devices.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript experimentally investigates the through-thickness residual stress gradient (σ₁) in transferred 128° Y-cut TFLN films (100–460 nm thick) via cantilever curvature analysis, reporting strong dependence on crystallographic orientation and thickness with stress-free angles shifting from ~55°/125° (thicker films) to ~20°/160° (100 nm films). Normalized σ₁ values decrease with increasing thickness, finite-element simulations show agreement with measurements, and a periodically poled piezoelectric bilayer (P3F) with opposite orientations is shown to reduce effective σ₁ (e.g., 90/110 nm bilayer yields –0.4 to –0.04 MPa/nm).

Significance. If the curvature-to-stress mapping is validated, the results demonstrate a viable engineering approach for mitigating deformation in TFLN MEMS through orientation, thickness, and bilayer design, supporting scalability. The experimental-simulation agreement is a strength, though its value depends on model completeness and experimental controls.

major comments (2)
  1. [Methods] Methods (curvature analysis description): The extraction of normalized σ₁ from cantilever curvature assumes observed deflection reports exclusively the intrinsic through-thickness stress gradient. No controls, subtraction procedures, or discussion address possible contributions from interface bonding, transfer-process artifacts, or interfacial compliance, which directly undermines the reported orientation dependence, thickness scaling, and bilayer cancellation efficacy.
  2. [Abstract/Results] Abstract and Results (reported stress values): Specific normalized σ₁ ranges (e.g., –0.1 to 3.4 MPa/nm for 100 nm films) and claims of 'excellent agreement' with FE simulations are given without error bars, sample statistics, reproducibility details, or data-exclusion criteria, preventing assessment of whether measurements robustly support the central claims on gradient engineering.
minor comments (1)
  1. [Abstract] The abstract states the bilayer 'results in significantly reduced deformation' but provides no quantitative comparison of curvature or deflection before/after compensation.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed review of our manuscript on gradient residual stress in transferred thin-film lithium niobate. The comments highlight important aspects of methodological transparency and statistical reporting that we will address in revision. Below we respond point by point to the major comments.

read point-by-point responses

  1. Referee: [Methods] Methods (curvature analysis description): The extraction of normalized σ₁ from cantilever curvature assumes observed deflection reports exclusively the intrinsic through-thickness stress gradient. No controls, subtraction procedures, or discussion address possible contributions from interface bonding, transfer-process artifacts, or interfacial compliance, which directly undermines the reported orientation dependence, thickness scaling, and bilayer cancellation efficacy.

    Authors: We agree that the curvature analysis relies on the assumption that deflection is dominated by the film's intrinsic stress gradient, and that explicit discussion of potential interface contributions was insufficient. The orientation dependence and thickness scaling we observe are difficult to attribute to isotropic interface or transfer artifacts, as these would not produce the systematic shifts in stress-free angles or the specific bilayer cancellation we demonstrate. The finite-element simulations, which model only the film stress gradient, also match the data closely. In the revised manuscript we will expand the Methods and/or Discussion sections with a dedicated paragraph on possible confounding factors (interface bonding, transfer artifacts, interfacial compliance), explaining why they are unlikely to dominate based on the crystallographic specificity of the results and the bilayer behavior. We cannot retroactively add new experimental controls or subtraction procedures, but the added discussion will make the assumptions and supporting evidence more transparent. revision: partial

  2. Referee: [Abstract/Results] Abstract and Results (reported stress values): Specific normalized σ₁ ranges (e.g., –0.1 to 3.4 MPa/nm for 100 nm films) and claims of 'excellent agreement' with FE simulations are given without error bars, sample statistics, reproducibility details, or data-exclusion criteria, preventing assessment of whether measurements robustly support the central claims on gradient engineering.

    Authors: We appreciate this point on statistical transparency. The reported ranges reflect the variation across crystallographic orientations for each thickness, obtained from repeated cantilever measurements. In the revised manuscript we will update the Abstract and Results to include error bars (standard deviation or standard error) on the normalized σ₁ values, state the number of independent samples per condition, and add a short description of reproducibility and data-exclusion criteria (e.g., exclusion of visibly damaged cantilevers). The agreement with finite-element simulations will be quantified (for example via RMS deviation between measured and simulated curvatures) rather than described only qualitatively. These changes will allow readers to evaluate the robustness of the gradient-engineering claims more directly. revision: yes

Circularity Check

0 steps flagged

No significant circularity; experimental extraction and FE validation remain independent

full rationale

The paper's core chain consists of direct cantilever curvature measurements on transferred TFLN films of varying thickness and orientation, followed by extraction of normalized residual stress gradient σ₁ using standard curvature-to-stress relations. Finite-element simulations are then used to confirm consistency with the measured curvatures under the same physical assumptions, but this does not constitute a fitted-input prediction loop because the FE model incorporates the independently measured geometry, material properties, and orientation dependence rather than re-using the extracted σ₁ values as the sole input to reproduce the identical data set. Bilayer compensation is likewise shown by direct fabrication and re-measurement of reduced curvature, not by algebraic rearrangement of the original extraction equations. No self-citations, ansatzes, or uniqueness theorems are invoked to close the derivation; the results are therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim depends on the validity of curvature-to-stress conversion and the assumption that bilayer orientation reversal produces the modeled cancellation. No explicit free parameters are introduced beyond the extracted stress values.

axioms (2)
  • domain assumption Cantilever curvature analysis via established thin-film formulas accurately isolates the through-thickness stress gradient sigma1
    Invoked to convert measured bending into the reported normalized sigma1 values for each thickness and orientation.
  • domain assumption Finite element model of the bilayer correctly predicts stress cancellation without unmodeled interface or fabrication effects
    Used to confirm that the 90/110 nm P3F structure reduces deformation as observed.

pith-pipeline@v0.9.0 · 5602 in / 1333 out tokens · 44176 ms · 2026-05-09T22:28:42.683871+00:00 · methodology

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Works this paper leans on

47 extracted references · 40 canonical work pages

  1. [1]

    Mechanical behaviour of metallic thin films on polymeric substrates and the effect of ion beam assistance on crack propagation,

    M. George, C. Coupeau, J. Colin, and J. Grilhé, “Mechanical behaviour of metallic thin films on polymeric substrates and the effect of ion beam assistance on crack propagation,” Acta Mater., vol. 53, no. 2, pp. 411 – 417, 2005

    2005

  2. [2]

    Materials issues in microelectromechanical devices: science, engineering, manufacturability and reliability,

    A. D. Romig, M. T. Dugger, and P. J. McWhorter, “Materials issues in microelectromechanical devices: science, engineering, manufacturability and reliability,” Acta Mater. , vol. 51, no. 19, pp. 5837–5866, Nov. 2003, doi: 10.1016/S1359-6454(03)00440-3

    work page doi:10.1016/s1359-6454(03)00440-3 2003

  3. [3]

    How soft substrates affect the buckling delamination of thin films through crack front sink - in,

    R. Boijoux, G. Parry, J.-Y. Faou, and C. Coupeau, “How soft substrates affect the buckling delamination of thin films through crack front sink - in,” Appl. Phys. Lett. , vol. 110, no. 14, p. 141602, Apr. 2017, doi: 10.1063/1.4979614

    work page doi:10.1063/1.4979614 2017

  4. [4]

    From telephone cords to branched buckles: A phase diagram,

    J.-Y. Faou, S. Grachev, E. Barthel, and G. Parry, “From telephone cords to branched buckles: A phase diagram,” Acta Mater., vol. 125, pp. 524– 531, Feb. 2017, doi: 10.1016/j.actamat.2016.12.025

    work page doi:10.1016/j.actamat.2016.12.025 2017

  5. [5]

    Post buckling of micromachined beams,

    W. Fang and J. A. Wickert, “Post buckling of micromachined beams,” J. Micromechanics Microengineering , vol. 4, no. 3, p. 116, Sep. 1994, doi: 10.1088/0960-1317/4/3/004

    work page doi:10.1088/0960-1317/4/3/004 1994

  6. [6]

    Comparative study of the mechanical properties of nanostructured thin films on stretchable substrates,

    S. Djaziri et al. , “Comparative study of the mechanical properties of nanostructured thin films on stretchable substrates,” J. Appl. Phys., vol. 116, no. 9, p. 093504, Sep. 2014, doi: 10.1063/1.4894616

    work page doi:10.1063/1.4894616 2014

  7. [7]

    A methodology for determining mechanical properties of freestanding thin films and MEMS materials,

    H. D. Espinosa, B. C. Prorok, and M. Fischer, “A methodology for determining mechanical properties of freestanding thin films and MEMS materials,” J. Mech. Phys. Solids, vol. 51, no. 1, pp. 47 –67, Jan. 2003, doi: 10.1016/S0022-5096(02)00062-5

    work page doi:10.1016/s0022-5096(02)00062-5 2003

  8. [8]

    Enhanced Proton Conductivity in Y -Doped BaZrO3 via Strain Engineering,

    A. Fluri et al., “Enhanced Proton Conductivity in Y -Doped BaZrO3 via Strain Engineering,” Adv. Sci. , vol. 4, no. 12, p. 1700467, 2017, doi: 10.1002/advs.201700467

    work page doi:10.1002/advs.201700467 2017

  9. [9]

    Growth stress induced tunability of dielectric permittivity in thin films,

    K. V. L. V. Narayanachari et al., “Growth stress induced tunability of dielectric permittivity in thin films,” J. Appl. Phys. , vol. 119, no. 1, p. 014106, Jan. 2016, doi: 10.1063/1.4939466

    work page doi:10.1063/1.4939466 2016

  10. [10]

    Stress Engineering of Perovskite Ceramics for Enhanced Piezoelectricity and Temperature Stability toward Energy Harvesting,

    X. Yu, Y. Hou, M. Zheng, and M. Zhu, “Stress Engineering of Perovskite Ceramics for Enhanced Piezoelectricity and Temperature Stability toward Energy Harvesting,” ACS Appl. Electron. Mater. , vol. 4, no. 3, pp. 1359–1366, Mar. 2022, doi: 10.1021/acsaelm.2c00135

    work page doi:10.1021/acsaelm.2c00135 2022

  11. [11]

    The correlation between mechanical stress and magnetic anisotropy in ultrathin films,

    D. Sander, “The correlation between mechanical stress and magnetic anisotropy in ultrathin films,” Rep. Prog. Phys. , vol. 62, no. 5, p. 809, May 1999, doi: 10.1088/0034-4885/62/5/204

    work page doi:10.1088/0034-4885/62/5/204 1999

  12. [12]

    On the geometry design of AlN Lamb wave resonators with predefined shallow release cavities,

    T.-H. Hsu et al. , “On the geometry design of AlN Lamb wave resonators with predefined shallow release cavities,” in Proc. Solid - State Sensor, Actuator, Microsyst. Workshop (Hilton Head) , 2022, pp. 1–62. Accessed: Nov. 10, 2025. foundation.org/technical_digests/HiltonHead_2022/hh2022_0210.pdf

    2022

  13. [13]

    5 Ghz lithium niobate MEMS resonators with high FoM of 153,

    Y. Yang, A. Gao, R. Lu, and S. Gong, “5 Ghz lithium niobate MEMS resonators with high FoM of 153,” in 2017 IEEE 30th International Conference on Micro Electro Mechanical Systems (MEMS) , Jan. 2017, pp. 942–945. doi: 10.1109/MEMSYS.2017.7863565

    work page doi:10.1109/memsys.2017.7863565 2017

  14. [14]

    Recent advances in high-performance millimeter-Wave acoustic resonators and filters using thin -film lithium niobate,

    R. Lu, “Recent advances in high-performance millimeter-Wave acoustic resonators and filters using thin -film lithium niobate,” Prog. Quantum Electron., vol. 100 –101, p. 100565, 2025, doi: https://doi.org/10.1016/j.pquantelec.2025.100565

    work page doi:10.1016/j.pquantelec.2025.100565 2025

  15. [15]

    Applications of thin -film lithium niobate in nonlinear integrated photonics,

    M. G. Vazimali and S. Fathpour, “Applications of thin -film lithium niobate in nonlinear integrated photonics,” Adv. Photonics, vol. 4, no. 3, pp. 034001–034001, 2022

    2022

  16. [16]

    Optical nonlinearity of thin film lithium niobate: devices and recent progress,

    L. Wang, H. Du, X. Zhang, and F. Chen, “Optical nonlinearity of thin film lithium niobate: devices and recent progress,” J. Phys. Appl. Phys., vol. 58, no. 2, p. 023001, Oct. 2024, doi: 10.1088/1361-6463/ad7ff7

    work page doi:10.1088/1361-6463/ad7ff7 2024

  17. [17]

    Dual -Axis MEMS Resonant Scanner Using 128∘Y Lithium Niobate Thin -Film,

    Y. Lu, K. Liu, and T. Wu, “Dual -Axis MEMS Resonant Scanner Using 128∘Y Lithium Niobate Thin -Film,” Acoustics, vol. 4, no. 2, pp. 313 – 328, Apr. 2022, doi: 10.3390/acoustics4020019

    work page doi:10.3390/acoustics4020019 2022

  18. [18]

    High-Performance Piezoelectric-Type MEMS Vibration Sensor Based on LiNbO3 Single -Crystal Cantilever Beams,

    H. Wei et al., “High-Performance Piezoelectric-Type MEMS Vibration Sensor Based on LiNbO3 Single -Crystal Cantilever Beams,” Micromachines, vol. 13, no. 2, p. 329, Feb. 2022, doi: 10.3390/mi13020329

    work page doi:10.3390/mi13020329 2022

  19. [19]

    LiNbO3 films – A low -cost alternative lead -free piezoelectric material for vibrational energy harvesters,

    G. Clementi et al. , “LiNbO3 films – A low -cost alternative lead -free piezoelectric material for vibrational energy harvesters,” Mech. Syst. Signal Process. , vol. 149, p. 107171, Feb. 2021, doi: 10.1016/j.ymssp.2020.107171

    work page doi:10.1016/j.ymssp.2020.107171 2021

  20. [20]

    Nanophotonic waveguide chip -to-world beam scanning,

    M. Saha et al. , “Nanophotonic waveguide chip -to-world beam scanning,” Nature, vol. 651, no. 8105, pp. 356–363, 2026

    2026

  21. [21]

    Thickness dependent stresses and thermal expansion of epitaxial LiNbO3 thin films on C-sapphire,

    A. Bartasyte et al. , “Thickness dependent stresses and thermal expansion of epitaxial LiNbO3 thin films on C-sapphire,” Mater. Chem. Phys., vol. 149 –150, pp. 622 –631, Jan. 2015, doi: 10.1016/j.matchemphys.2014.11.018

    work page doi:10.1016/j.matchemphys.2014.11.018 2015

  22. [22]

    Residual Stress in Lithium Niobate Film Layer of LNOI/Si Hybrid Wafer Fabricated Using Low-Temperature Bonding Method,

    R. Takigawa, T. Tomimatsu, E. Higurashi, and T. Asano, “Residual Stress in Lithium Niobate Film Layer of LNOI/Si Hybrid Wafer Fabricated Using Low-Temperature Bonding Method,” Micromachines, vol. 10, no. 2, p. 136, Feb. 2019, doi: 10.3390/mi10020136

    work page doi:10.3390/mi10020136 2019

  23. [23]

    Stress reduction and wafer bow accommodation for the fabrication of thin film lithium niobate on oxidized silicon,

    K. Prabhakar, R. J. Patton, and R. M. Reano, “Stress reduction and wafer bow accommodation for the fabrication of thin film lithium niobate on oxidized silicon,” J. Vac. Sci. Technol. B Nanotechnol. Microelectron. Mater. Process. Meas. Phenom. , vol. 39, no. 6, p. 062208, Dec. 2021, doi: 10.1116/6.0001283

    work page doi:10.1116/6.0001283 2021

  24. [24]

    Residual Stress Anisotropy in Thin -Film Lithium Niobate for Stress -Managed Mems,

    B. Kim et al. , “Residual Stress Anisotropy in Thin -Film Lithium Niobate for Stress -Managed Mems,” in 2026 IEEE 39th International Conference on Micro Electro Mechanical Systems (MEMS) , Jan. 2026, pp. 1352–1355. doi: 10.1109/MEMS64181.2026.11419544

    work page doi:10.1109/mems64181.2026.11419544 2026

  25. [25]

    3 8-GHz acoustic filter in periodically poled piezoelectric film lithium niobate with 1.52 - L an F ,

    S. Cho et al. , “23.8 -GHz Acoustic Filter in Periodically Poled Piezoelectric Film Lithium Niobate With 1.52-dB IL and 19.4% FBW,” IEEE Microw. Wirel. Technol. Lett. , vol. 34, no. 4, pp. 391 –394, Apr. 2024, doi: 10.1109/LMWT.2024.3368354

    work page doi:10.1109/lmwt.2024.3368354 2024

  26. [26]

    Periodically Poled Piezoelectric Single -Layered and Multilayered Lithium Niobate for Thickened High-Order Lamb Wave Acoustic Devices,

    J. Zheng, Z. Ren, J. Xu, X. Liu, F. Qian, and Y. Yang, “Periodically Poled Piezoelectric Single -Layered and Multilayered Lithium Niobate for Thickened High-Order Lamb Wave Acoustic Devices,” IEEE Trans. Microw. Theory Tech. , vol. 73, no. 10, pp. 7069 –7079, Oct. 2025, doi: 10.1109/TMTT.2025.3567329

    work page doi:10.1109/tmtt.2025.3567329 2025

  27. [27]

    Determining mean and gradient residual stresses in thin films using micromachined cantilevers,

    W. Fang and J. A. Wickert, “Determining mean and gradient residual stresses in thin films using micromachined cantilevers,” J. Micromechanics Microengineering , vol. 6, no. 3, pp. 301 –309, Sep. 1996, doi: 10.1088/0960-1317/6/3/002

    work page doi:10.1088/0960-1317/6/3/002 1996

  28. [28]

    L. B. Freund and S. Suresh, Thin film materials: stress, defect formation and surface evolution . Cambridge university press, 2004. Accessed: Mar. 23, 2026

    2004

  29. [29]

    On the thermal expansion coefficients of thin films,

    W. Fang and C. -Y. Lo, “On the thermal expansion coefficients of thin films,” Sens. Actuators Phys. , vol. 84, no. 3, pp. 310 –314, Sep. 2000, doi: 10.1016/S0924-4247(00)00311-3

    work page doi:10.1016/s0924-4247(00)00311-3 2000

  30. [30]

    Review Article: Stress in thin films and coatings: Current status, challenges, and prospects,

    G. Abadias et al. , “Review Article: Stress in thin films and coatings: Current status, challenges, and prospects,” J. Vac. Sci. Technol. A , vol. 36, no. 2, p. 020801, Mar. 2018, doi: 10.1116/1.5011790

    work page doi:10.1116/1.5011790 2018

  31. [31]

    High resolution determination of local residual stress gradients in single- and multilayer thin film systems,

    R. Treml et al., “High resolution determination of local residual stress gradients in single- and multilayer thin film systems,” Acta Mater., vol. 103, pp. 616–623, Jan. 2016, doi: 10.1016/j.actamat.2015.10.044

    work page doi:10.1016/j.actamat.2015.10.044 2016

  32. [32]

    Anisotropic thermal expansion of stoichiometric lithium niobate crystals grown along the normal direction of facets,

    X. Xu, T. -C. Chong, S. Solanki, X. Liang, and S. Yuan, “Anisotropic thermal expansion of stoichiometric lithium niobate crystals grown along the normal direction of facets,” Opt. Mater. , vol. 26, no. 4, pp. 489–494, Sep. 2004, doi: 10.1016/j.optmat.2003.12.027

    work page doi:10.1016/j.optmat.2003.12.027 2004

  33. [33]

    Residual stresses and clamped thermal expansion in LiNbO3 and LiTaO3 thin films,

    A. Bartasyte et al., “Residual stresses and clamped thermal expansion in LiNbO3 and LiTaO3 thin films,” Appl. Phys. Lett. , vol. 101, no. 12, p. 122902, Sep. 2012, doi: 10.1063/1.4752448

    work page doi:10.1063/1.4752448 2012

  34. [34]

    Theory of plates and shells,

    S. Timoshenko and S. Woinowsky -Krieger, “Theory of plates and shells,” 1959, Accessed: Mar. 23, 2026

    1959

  35. [35]

    Computer -program description. Transformation of tensor constants of anisotropic materials due to 8 rotations of the co-ordinate axes,

    A. H. Fahmy and E. L. Adler, “Computer -program description. Transformation of tensor constants of anisotropic materials due to 8 rotations of the co-ordinate axes,” Proc. Inst. Electr. Eng., vol. 122, no. 5, pp. 591–592, May 1975, doi: 10.1049/piee.1975.0163

    work page doi:10.1049/piee.1975.0163 1975

  36. [36]

    Anisotropic elasticity of silicon and its application to the modelling of X-ray optics,

    L. Zhang, R. Barrett, P. Cloetens, C. Detlefs, and M. Sanchez del Rio, “Anisotropic elasticity of silicon and its application to the modelling of X-ray optics,” J. Synchrotron Radiat., vol. 21, no. 3, pp. 507 –517, May 2014, doi: 10.1107/S1600577514004962

    work page doi:10.1107/s1600577514004962 2014

  37. [37]

    X-ray analysis of residual stress gradients in TiN coatings by a Laplace space approach and cross -sectional nanodiffraction: a critical comparison,

    M. Stefenelli et al., “X-ray analysis of residual stress gradients in TiN coatings by a Laplace space approach and cross -sectional nanodiffraction: a critical comparison,” J. Appl. Crystallogr. , vol. 46, no. 5, pp. 1378–1385, Oct. 2013, doi: 10.1107/S0021889813019535

    work page doi:10.1107/s0021889813019535 2013

  38. [38]

    In -situ Observation of Cross -Sectional Microstructural Changes and Stress Distributions in Fracturing TiN Thin Film during Nanoindentation,

    A. Zeilinger et al. , “In -situ Observation of Cross -Sectional Microstructural Changes and Stress Distributions in Fracturing TiN Thin Film during Nanoindentation,” Sci. Rep., vol. 6, no. 1, p. 22670, Mar. 2016, doi: 10.1038/srep22670

    work page doi:10.1038/srep22670 2016

  39. [39]

    Residual stress evaluation at the micrometer scale: Analysis of thin coatings by FIB milling and digital image correlation,

    A. M. Korsunsky, M. Sebastiani, and E. Bemporad, “Residual stress evaluation at the micrometer scale: Analysis of thin coatings by FIB milling and digital image correlation,” Surf. Coat. Technol. , vol. 205, no. 7, pp. 2393–2403, Dec. 2010, doi: 10.1016/j.surfcoat.2010.09.033

    work page doi:10.1016/j.surfcoat.2010.09.033 2010

  40. [40]

    Review Paper: Residual Stresses in Deposited Thin -Film Material Layers for Micro - and Nano -Systems Manufacturing,

    M. Huff, “Review Paper: Residual Stresses in Deposited Thin -Film Material Layers for Micro - and Nano -Systems Manufacturing,” Micromachines, vol. 13, no. 12, p. 2084, Nov. 2022, doi: 10.3390/mi13122084

    work page doi:10.3390/mi13122084 2084

  41. [41]

    A Generalized Acoustic Framework for Multilayer Piezoelectric Platforms,

    J. Kramer and R. Lu, “A Generalized Acoustic Framework for Multilayer Piezoelectric Platforms,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control , vol. 72, no. 9, pp. 1302 –1311, Sep. 2025, doi: 10.1109/TUFFC.2025.3595433

    work page doi:10.1109/tuffc.2025.3595433 2025

  42. [42]

    Enabling Higher Order Lamb Wave Acoustic Devices With Complementarily Oriented Piezoelectric Thin Films,

    R. Lu, Y. Yang, S. Link, and S. Gong, “Enabling Higher Order Lamb Wave Acoustic Devices With Complementarily Oriented Piezoelectric Thin Films,” J. Microelectromechanical Syst., vol. 29, no. 5, pp. 1332 – 1346, Oct. 2020, doi: 10.1109/JMEMS.2020.3007590

    work page doi:10.1109/jmems.2020.3007590 2020

  43. [43]

    Twist piezoelectricity: giant electromechanical coupling in magic-angle twisted bilayer LiNbO3,

    H. Yao et al., “Twist piezoelectricity: giant electromechanical coupling in magic-angle twisted bilayer LiNbO3,” Nat. Commun., vol. 15, no. 1, p. 5002, Jun. 2024, doi: 10.1038/s41467-024-49321-x

    work page doi:10.1038/s41467-024-49321-x 2024

  44. [44]

    Double -layer LiNbO3 longitudinally excited shear wave resonators with ultra -large electromechanical coupling coefficient and spurious-free performance,

    Z.-H. Qin et al. , “Double -layer LiNbO3 longitudinally excited shear wave resonators with ultra -large electromechanical coupling coefficient and spurious-free performance,” Appl. Phys. Lett., vol. 126, no. 19, May 2025, doi: 10.1063/5.0250773

    work page doi:10.1063/5.0250773 2025

  45. [45]

    Thermal expansion of lithium tantalate an lithium niobate single crystals,

    Y. S. Kim and R. T. Smith, “Thermal Expansion of Lithium Tantalate and Lithium Niobate Single Crystals,” J. Appl. Phys. , vol. 40, no. 11, pp. 4637–4641, Oct. 1969, doi: 10.1063/1.1657244

    work page doi:10.1063/1.1657244 1969

  46. [46]

    Yim \ and\ author R

    W. M. Yim and R. J. Paff, “Thermal expansion of AlN, sapphire, and silicon,” J. Appl. Phys. , vol. 45, no. 3, pp. 1456 –1457, Mar. 1974, doi: 10.1063/1.1663432. BYEONGJIN KIM (Student Member, IEEE) received the B.S. degree in applied physics from Korea Military Academy, Seoul, South Korea , in 2019 . He is currently pursuing the M.S. degree in Electrical ...

    work page doi:10.1063/1.1663432 1974

  47. [47]

    His research focuses on the development of advanced piezoelectric RF acoustic devices targeting the next generation wireless signal processing . He received the Scholarship Pilot Program to Cultivate Outstanding Doctoral Students from Ministry of Science and Technology of Taiwan in 2020 , the CTCI Foundation Science and Technology Research Scholarship in ...

    2020