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arxiv: 2606.28195 · v1 · pith:SI4M6TEVnew · submitted 2026-06-26 · ❄️ cond-mat.mes-hall · quant-ph

Role of the Casimir force in the capacitive radio-frequency microelectromechanical switches

G. L. Klimchitskaya , A. S. Korotkov , V. V. Loboda , V. M. Mostepanenko This is my paper

Pith reviewed 2026-06-29 02:30 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall quant-ph
keywords Casimir forceMEMS switchescapacitive microelectromechanical systemssurface roughnessreal material propertiespull-in instabilityradio-frequency switchesmembrane thickness
0
0 comments X

The pith

Casimir force can exceed electric force at contact in MEMS switches, determining needed membrane thickness for stable operation.

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

The paper computes the Casimir force between a cylindrical membrane and bottom electrode in capacitive radio-frequency microelectromechanical switches, using real material properties and surface roughness. It shows that at the shortest separations where the membrane contacts the transmission line, this force can surpass the electric force depending on operating voltage. A sympathetic reader would care because the results indicate how to choose membrane thickness so the restoring elastic force prevents pull-in and supports reliable cycling. Ideal-metal smooth-surface models produce incorrect force values, making the real-property calculation essential.

Core claim

The Casimir force between the switch membrane and electrode, calculated with real material properties and roughness, may exceed the electric force at contact separations; its magnitude then sets the membrane thickness that produces the required elastic restoring force for stable cyclic operation without pull-in.

What carries the argument

Computation of the Casimir force that incorporates real dielectric responses of membrane and electrode materials together with surface-roughness corrections.

If this is right

  • Switch design must include the Casimir contribution when selecting membrane thickness to avoid pull-in.
  • Ideal-metal approximations cannot be used for force estimates at the relevant separations.
  • Membrane thickness depends on the chosen operating voltage to balance all three forces.
  • Real-material and roughness corrections are required for any quantitative prediction of switch stability.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same force-balance approach could be applied to other MEMS structures that reach nanometer-scale gaps.
  • Voltage-dependent Casimir dominance might set a practical lower limit on reliable operating voltage for a given geometry.
  • Direct force measurements at contact separations in fabricated switches would test whether the computed values guide thickness correctly.

Load-bearing premise

The calculated Casimir-force values with real materials and roughness correctly predict the actual forces present in the operating device.

What would settle it

Measure the actual force or observe pull-in behavior in switches built with the membrane thicknesses predicted from the Casimir calculation at given voltages; mismatch would show the values are not usable for design.

Figures

Figures reproduced from arXiv: 2606.28195 by A. S. Korotkov, G. L. Klimchitskaya, V. M. Mostepanenko, V. V. Loboda.

Figure 1
Figure 1. Figure 1: FIG. 1: Schematic of the geometrical configuration of MEMS ca [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: The magnitudes of the Casimir and electric forces act [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: The magnitudes of the Casimir and electric forces act [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: The magnitudes of the Casimir and electric forces act [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
read the original abstract

We determine the role of the fluctuation-induced Casimir force acting between a membrane of cylindrical shape and a bottom electrode in microelectromechanical capacitive switches. For this purpose, the Casimir force is computed taking into account the real properties of both a membrane and a bottom electrode materials with account of surface roughness. The obtained results are compared with those found for the smooth surfaces using the idealization of ideal metal. It is shown that an account of both the real material properties and surface roughness is crucial for obtaining the correct values of the Casimir force. According to our results, at the shortest separations, when the switch membrane is in contact with the transmission line, the magnitudes of the Casimir force may exceed the magnitudes of the electric one depending on the value of the operating voltage. The obtained values of the Casimir force can be used for determining the thickness of the switch membrane, which ensures the necessary magnitude of the restoring elastic force required for a stable cyclic functioning of the micromechanical switch with no pull-in.

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 / 2 minor

Summary. The manuscript computes the Casimir force between a cylindrical membrane and bottom electrode in capacitive RF MEMS switches, incorporating real material dielectric properties and surface roughness via the Lifshitz formalism. Results are contrasted with the ideal-metal, smooth-surface case. The central claim is that at contact separations the Casimir force magnitude can exceed the electric force (depending on operating voltage) and that the computed Casimir values can be used to select membrane thickness so that the restoring elastic force ensures stable cyclic operation without pull-in.

Significance. If the numerical values are quantitatively reliable, the work supplies concrete guidance for MEMS switch design at the scale where fluctuation forces become comparable to electrostatic forces, directly addressing pull-in instability.

major comments (2)
  1. [Computational method and Results sections] The load-bearing claim that the obtained Casimir values can be used to determine membrane thickness for stable operation (final paragraph) presupposes that the computed forces are accurate to within the precision needed to set thickness. No comparison to known analytic limits (e.g., proximity-force approximation for cylinder-plane geometry), no convergence tests with respect to Matsubara frequencies or wave-vector cutoff, and no uncertainty quantification are supplied.
  2. [Results section (contact-separation data)] The roughness correction is stated to be included, yet the manuscript does not demonstrate that the model remains valid when the mean separation approaches the rms roughness amplitude (the regime of the strongest claim). This directly affects the quantitative comparison between Casimir and electric forces at contact.
minor comments (2)
  1. [Figures] Figure captions and axis labels should explicitly state the membrane radius, material pair, and roughness parameters used for each curve.
  2. [Computational method] The dielectric functions or tabulated optical data for the membrane and electrode materials should be referenced or reproduced so that the calculation can be reproduced.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. We address the major comments point by point below.

read point-by-point responses

  1. Referee: [Computational method and Results sections] The load-bearing claim that the obtained Casimir values can be used to determine membrane thickness for stable operation (final paragraph) presupposes that the computed forces are accurate to within the precision needed to set thickness. No comparison to known analytic limits (e.g., proximity-force approximation for cylinder-plane geometry), no convergence tests with respect to Matsubara frequencies or wave-vector cutoff, and no uncertainty quantification are supplied.

    Authors: We agree that explicit validation strengthens the quantitative claim regarding membrane thickness selection. In the revised manuscript we will add a comparison of the ideal-metal results to the proximity-force approximation for cylinder-plane geometry, convergence tests for the number of Matsubara frequencies and wave-vector cutoff, and an uncertainty estimate derived from variations in the tabulated dielectric functions. These additions will support the use of the computed forces for design guidance. revision: yes

  2. Referee: [Results section (contact-separation data)] The roughness correction is stated to be included, yet the manuscript does not demonstrate that the model remains valid when the mean separation approaches the rms roughness amplitude (the regime of the strongest claim). This directly affects the quantitative comparison between Casimir and electric forces at contact.

    Authors: The roughness correction follows the standard perturbative treatment within the Lifshitz formalism. We acknowledge that the regime where mean separation approaches rms roughness requires explicit discussion of model validity. In the revision we will add a paragraph on the applicability limits of the roughness model and its implications for the contact-separation comparison. revision: yes

Circularity Check

0 steps flagged

Casimir force computation uses external material data and standard formalism; no reduction to fitted inputs or self-definitions

full rationale

The paper computes Casimir forces via the Lifshitz formula (or equivalent scattering approach) incorporating tabulated dielectric functions for real materials plus a roughness correction, then contrasts the results against the ideal-metal smooth-surface limit. The abstract and reader's summary contain no equations or statements indicating that any output quantity (e.g., force magnitude at contact) is obtained by fitting a parameter to the same quantity, by redefining a variable in terms of itself, or by a load-bearing self-citation whose validity is presupposed. The claim that Casimir force may exceed the electric force at shortest separations follows directly from these independent numerical evaluations rather than from any internal re-labeling or tautological construction. Consequently the derivation chain is self-contained against external benchmarks and receives the default non-circularity score.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract supplies no information on free parameters, background axioms, or new postulated entities; ledger left empty.

pith-pipeline@v0.9.1-grok · 5729 in / 1089 out tokens · 52680 ms · 2026-06-29T02:30:01.127798+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

93 extracted references

  1. [1]

    J. J. Allen, ``Micro Electro Mechanical System Design,'' (CRC Press, New York, 2005)

    2005

  2. [2]

    \ A.\ Parsegian, ``Van der Waals Forces: A Handbook for Biologists, Chemists, Engineers, and Physicists,'' (Cambridge University Press, Cambridge, 2005)

    V. \ A.\ Parsegian, ``Van der Waals Forces: A Handbook for Biologists, Chemists, Engineers, and Physicists,'' (Cambridge University Press, Cambridge, 2005)

    2005

  3. [3]

    Bordag, G

    M. Bordag, G. L. Klimchitskaya, U.\ Mohideen, and V.\ M.\ Mostepanenko, ``Advances in the Casimir Effect,'' (Oxford University Press, Oxford, 2015)

    2015

  4. [4]

    G. L. Klimchitskaya, V. M. Mostepanenko, V. M. Petrov, and T. Tschudi, ``Optical chopper driven by the Casimir force,'' Phys. Rev. Applied 10 , 014010 (2018)

    2018

  5. [5]

    Esquivel-Sirvent, A

    R. Esquivel-Sirvent, A. Gusso, S. Castillo-L\' o pez, and F. S\' a nchez-Ochoa, ``Casimir forces: from Au to time crystals,'' Riv. Nuovo Cim. 49 , 137 (2026)

    2026

  6. [6]

    R. H. French, V. A. Parsegian, R. Podgornik, et al., ``Long range interactions in nanoscale science,'' Rev. Mod. Phys. 82 , 1887 (2010)

    2010

  7. [7]

    Sarabadani, A

    J. Sarabadani, A. Naji, R. Asgari, and R. Podgornik, ``Many-body effects in the van der Waals–Casimir interaction between graphene layers,'' Phys. Rev. B 84 , 155407 (2011)

    2011

  8. [8]

    L. M. Woods, D. A. R. Dalvit, A. Tkatchenko, P.\ Rodriguez-Lopez, A.\ W.\ Rodriguez, and R.\ Podgornik, ``Materials perspective on Casimir and van der Waals interactions,'' Rev. Mod. Phys. 88 , 045003 (2016)

    2016

  9. [9]

    Drosdoff, I

    D. Drosdoff, I. V. Bondarev, A. Widom, R. Podgornik, and L. M. Woods, ``Charge-induced fluctuation forces in graphitic nanostructures,'' Phys. Rev. X 6 011004 (2016)

    2016

  10. [10]

    P. D. Grant, M. W. Denhoff, and R. R. Mansour, ``A Comparison between RF MEMS Switches and Semiconductor Switches,'' in 2004 International Conference on MEMS, NANO and Smart Systems (ICMENS'04) , (Banff, Canada, 2004), pp. 515-521

    2004

  11. [11]

    M. A. Llamas, E. Pausas, L. Pradell, D. Girbau, S. Aouba, C. Villeneuve, V. Puyal, P. Pons, R. Plana, S. Colpo, and F. Giacomozzi, ``Capacitive and resistive RF-MEMS switches 2.5D & 3D electromagnetic and circuit modelling,'' in 7th Spanish Conference on Electron Devices CDE-2009 (Santiago de Compostela, Spain, 2009), pp. 451-454,

    2009

  12. [12]

    B. Shao, C. Lu , Y. Xiang, F. Li, and M. Song, ``Comprehensive review of RF MEMS switches in satellite communications,'' Sensors 24 , 3135 (2024)

    2024

  13. [13]

    Lin and Y.-P

    W.-H. Lin and Y.-P. Zhao, ``Casimir effect on the pull-in parameters of nanometer switches,'' Microsyst. Technol. 11 , 80 (2005)

    2005

  14. [14]

    Lin and Y.-P

    W.-H. Lin and Y.-P. Zhao, ``Nonlinear behavior for nanoscale electrostatic actuators with Casimir force,'' Chaos, Solit. Fract. 23 , 1777 (2005)

    2005

  15. [15]

    Palasantzas and J

    G. Palasantzas and J. Th. M. De Hosson, ``Pull-in characteristics of electromechanical switches in the presence of Casimir forces: Influence of self-affine surface roughness,'' Phys. Rev. B 72 , 115426 (2005)

    2005

  16. [16]

    Palasantzas and J

    G. Palasantzas and J. Th. M. De Hosson, ``Phase maps of microelectromechanical switches in the presence of electrostatic and Casimir forces,'' Phys. Rev. B 72 , 121409(R) (2005)

    2005

  17. [17]

    Ramezani, A

    A. Ramezani, A. Alasty, and J. Akbari, ``Pull-in parameters of cantilever type nanomechanical switches in presence of Casimir force,'' Nonlin. Anal.: Hybrid Syst. 1 , 364 (2007)

    2007

  18. [18]

    G.\ Palasantzas, ``Contact angle influence on the pull-in voltage of microswitches in the presence of capillary and quantum vacuum effects,'' J. Appl. Phys. 101 , 053512 (2007)

    2007

  19. [19]

    G.\ Palasantzas, ``Pull-in voltage of microswitch rough plates in the presence of electromagnetic and acoustic Casimir forces,'' J. Appl. Phys. 101 , 063548 (2007)

    2007

  20. [20]

    L. Wu, V. Rochus, L. Noels, and J. C. Golinval, ``Influence of adhesive rough surface contact on microswitches,'' J. Appl. Phys. 106 , 113502 (2009)

    2009

  21. [21]

    X. L. Jia, J. Yang, and S. Kitipornchai, ``Characterization of FGM micro-switches under electrostatic and Casimir forces,'' IOP Conf. Series: Mater. Sci. Engineer. 10 , 012178 (2010)

    2010

  22. [22]

    E. S. Reich, ``Casimir effect put to work as a nano-switch,'' New Sci. 207 , 19 (2010)

    2010

  23. [23]

    X. L. Jia, J. Yang, and S. Kitipornchai, ``Pull-in instability of geometrically nonlinear micro-switches under electrostatic and Casimir forces,'' Acta Mech. 218 , 161 (2011)

    2011

  24. [24]

    J. B. Ma, S. F. Asokanthan, and L. Jiang, ``Surface effects considerations for the design of Casimir actuated nanoswitches,'' Appl. Mech. Mater. 110-116 , 1036 (2011)

    2011

  25. [25]

    Yang, G.-F

    F. Yang, G.-F. Wang, J.-M. Long, and B.-L. Wang, ``Influence of surface energy on the pull-in instability of electrostatic nano-switches,'' J. Comput. Theor. Nanosci. 10 , 1273 (2013)

    2013

  26. [26]

    S. A. A. Ghorbanpour Arani, A. Jalilvand, M. Ghaffari, M. Talebi Mazraehshahi, R. Kolahchi, M. A. Roudbari, and S. Amir, ``Nonlinear pull-in instability of boron nitride nano-switches considering electrostatic and Casimir forces,'' Scientia Iranica F 21 , 1183 (2014)

    2014

  27. [27]

    Di Maida and G

    P. Di Maida and G. Bianchi, ``Numerical investigation of pull-In instability in a micro-switch MEMS device through the pseudo-spectral method,'' Model. Simul. Eng. 2016 , 8543616 (2016)

    2016

  28. [28]

    X.-f. Liu, Y. Li, and H. Jing, ``Casimir switch: steering optical transparency with vacuum forces,'' Sci. Reports 6 , 27102 (2016)

    2016

  29. [29]

    Inui, ``Optical switching of a graphene mechanical switch using the Casimir effect,'' J

    N. Inui, ``Optical switching of a graphene mechanical switch using the Casimir effect,'' J. Appl. Phys. 122 , 104501 (2017)

    2017

  30. [30]

    R. Yang, J. Qian, and P. X.-L. Feng, ``Electrodynamic force, Casimir effect, and stiction mitigation in silicon carbide nanoelectromechanical switches,'' Small 16 , 2005594 (2020)

    2020

  31. [31]

    \" O zmen and I

    R. \" O zmen and I. Esen, ``The Casimir, Van der Waals, and electrostatic forces’ effects on the response of magneto-electro-elastic nanosensor/switch beams under thermal environment,'' Mech. Based Des. Struct. Mach. 52 , 2318615 (2024)

    2024

  32. [32]

    G. L. Klimchitskaya, A. S. Korotkov, V. V. Loboda, and V. M. Mostepanenko, ``Pull-in features of nanoswitches in the Casimir regime with account of contact repulsion,'' EPL 148 , 16002 (2024)

    2024

  33. [33]

    G. L. Klimchitskaya, A. S. Korotkov, V. V. Loboda, and V. M. Mostepanenko, ``Contact separation in nanoswitches with regard to the Casimir force and exchange repulsion: Role of surface roughness and transmitted signal,'' EPL 150 , 46003 (2025)

    2025

  34. [34]

    Molaei and B

    S. Molaei and B. A. Ganji, ``Design and simulation of a novel RF MEMS shunt capacitive switch with low actuation voltage and high isolation,'' Microsyst. Technol. 23 , 1907 (2017)

    1907

  35. [35]

    Mulloni, B., Margesin, P

    V. Mulloni, B., Margesin, P. Farinelli, R. Marcelli, A. Lucibello, and G. De Angelis, ``Cycling reliability of RF-MEMS switches with gold-platinum multilayers as contact material,'' Microsyst. Technol. 23 , 3843 (2017)

    2017

  36. [36]

    H. Wei, Z. Deng, X. Guo, Y. Wang, and H. Yang, ``High on/off capacitance ratio RF MEMS capacitive switches,'' J. Micromech. Microeng. 27 , 055002 (2017)

    2017

  37. [37]

    K. Han, H. Guo, S. Smith, Z. Deng, and W. Li, ``Novel high-capacitance-ratio mems switch: design, analysis and performance verification,'' Micromachines 9 , 390 (2018)

    2018

  38. [38]

    B. Jmai, P. Anacleto, P. Mendes, A. Gharsallah, ``Modeling, design, and simulation of a radio frequency microelectromechanical system capacitive shunt switch,'' Numerical Modelling 31 , e2266 (2018)

    2018

  39. [39]

    Pertin and K

    O. Pertin and K. R. Kurmendra, ``Pull-in-voltage and RF analysis of MEMS based high performance capacitive shunt switch,'' Microelectron. J. 77 , 5 (2018)

    2018

  40. [40]

    A. K. Ravirala, L. K. Bethapudi, J. Kommareddy, B. S. Thommandru, S. Jasti, P. R. Gorantla, P. Ashok, G. S. Karumuri, and S. R. Karumuri, ``Design and performance analysis of uniform meander structured RF MEMS capacitive shunt switch along with perforations.'' Microsyst. Technol. 24 , 901 (2018)

    2018

  41. [41]

    Zhang, Z

    N. Zhang, Z. Yan, R. Song, C. Wang, Q. Guo, and J. Yang, ``Design and performance of a J band MEMS switch,'' Micromachines 10 , 467 (2019)

    2019

  42. [42]

    Deshmukh and M

    D. Deshmukh and M. Angira, ``Investigation on switching structure material selection for RF-MEMS shunt capacitive switches using Ashby, TOPSIS and VIKOR,'' Trans. Electr. Electron. Mater. 20 , 181 (2019)

    2019

  43. [43]

    K. R. Kurmendra and R. Kumar, ``Design and analysis of MEMS shunt capacitive switch with Si _3 N _4 dielectric and Au beam material to improve actuation voltage and RF performance in consideration with and without circular perforations,'' Trans. Electr. Electron. Mater. 20 , 299 (2019)

    2019

  44. [44]

    H. Wei, S. Jia, F. Zhao, L. Dang, G. Liang, Y. Xu, and Z. Deng, ``A new RF MEMS capacitive switch for K-band application,'' Progress Electromagn. Res. 93 , 253 (2019)

    2019

  45. [45]

    Angira, D

    M. Angira, D. Bansal, P. Kumar, K. Mehta, and K. Rangra, ``A novel capacitive RF-MEMS switch for multi-frequency operation,'' Superlatt. Microstruct. 133 , 106204 (2019)

    2019

  46. [46]

    Nawaz, M

    H. Nawaz, M. U. Masooda, M. M. Saleema, J. Iqbal, and M. Zubair, ``Surface roughness effects on electromechanical performance of RF-MEMS capacitive switches,'' Microelectronics Reliability 104 , 113544 (2020)

    2020

  47. [47]

    K. G. Sravani, K. Guha, and A. Elsinawi, ``Design and optimisation of a novel structure capacitive RF MEMS switch to integrate with an antenna to improve its performance parameters,'' IET Circuits, Devices & Systems 14 , 261 (2020)

    2020

  48. [48]

    K. R. Kurmendra and R. Kumar, ``Novel capacitance evaluation model for microelectromechanical switch considering fringe and effect of holes in pull-up and pull-down conditions,'' Microsyst. Technol. 26 , 873 (2020)

    2020

  49. [49]

    L. N. Thalluri, K. Guha, K. S. Rao, G. V. H. Prasad, K. G. Sravani, K. S. R. Sastry, A. R. Kanakala, and P. B. Babu, ``Perforated serpentine membrane with AlN as dielectric material shunt capacitive RF MEMS switch fabrication and characterization,'' Microsyst. Technol. 26 , 2029 (2020)

    2029

  50. [50]

    R. Qin, B. Zhang, C. Lei, Y. Xu, J. Qin, C. Fan, B. Mi, Y. Y. Wang, and J. Duan, ``A novel switch beam design method with extending switching radiofrequency bandwidth,'' Microsyst. Technol. 27 , 315 (2021)

    2021

  51. [51]

    K. S. Rao, P. A. Kumar, K. Guha, B. V. S. Sailaja, K. V. Vineetha, K. L. Baishnab, and K. G. Sravani, ``Design and simulation of fixed–fixed flexure type RF MEMS switch for reconfigurable antenna,'' Microsyst. Technol. 27 , 455 (2021)

    2021

  52. [52]

    K. G. Sravani, T. L. Narayana, K. Guha, and K. S. Rao, ``Role of dielectric layer and beam membrane in improving the performance of capacitive RF MEMS switches for Ka-band applications,'' Microsyst. Technol. 27 , 493 (2021)

    2021

  53. [53]

    K. R. Kurmendra and R. Kumar, ``A review on RF micro-electro-mechanical systems (MEMS) switch for radio frequency applications,'' Microsyst. Technol. 27 , 2525 (2021)

    2021

  54. [54]

    K. R. Kurmendra and R. Kumar, ``Investigations on beam membrane and dielectric materials using Ashby’s methodology and their impact on the performance of a MEMS capacitive switch,'' Microsyst. Technol. 27 , 4269 (2021)

    2021

  55. [55]

    H. Feng, J. Zhao, C. Zhou, and M. Song, ``Design and analysis of the capacitive RF MEMS switches with support pillars,'' Sensors 22 , 8864 (2022)

    2022

  56. [56]

    Z. Deng, Y. Wang, K. Deng, C. Lai, and J. Zhou, ``Novel high isolation and high capacitance ratio RF MEMS switch: Design, analysis and performance verification,'' Micromachines 13 , 646 (2022)

    2022

  57. [57]

    Z. Deng, C. Lai, J. Zhou, and Y. Wang, ``Design and analysis of a novel low RF MEMS switch with low pull-in voltage and high capacitance ratio,'' Microsyst. Technol. 29 , 809 (2023)

    2023

  58. [58]

    Bajpai, K

    A. Bajpai, K. Rangra, and D. Bansal, ``Fabrication process improvement of high isolation of RF MEMS switch for 5G applications,'' Sens. Actuat. A: Phys. 376 , 115582 (2024)

    2024

  59. [59]

    Karthick and S.P.K

    R. Karthick and S.P.K. Babu, ``Electromechanical modelling and analysis of RF MEMS switch for mm-wave application,'' SSRG Int. J. Electron. Commun. Eng. 11 , 89 (2024)

    2024

  60. [60]

    Michalas, G

    L. Michalas, G. Stavrinidis, K. Tsagaraki, A. Stavrinidis, and G. Konstantinidis, ``An experimental study of the pull-in voltage in RF MEMS switches fabricated by Au electroplating and standard wet release: Considering the bridge geometry,'' Sensors 25 , 1877 (2025)

    2025

  61. [61]

    Anusha, K

    Y. Anusha, K. Guha, K. Mummaneni, and J. Thati, ``Low-voltage U-shaped RF MEMS shunt switch integration for K-band phased array beam steering,'' Sci. Rep., 16 , 11585 (2026)

    2026

  62. [62]

    Kundu, S

    A. Kundu, S. Sethi, N.C. Mondal, B. Gupta, S.K. Lahiri, and H. Saha, ``Analysis and optimization of two movable plates RF MEMS switch for simultaneous improvement in actuation voltage and switching time,'' Microelectron. J. 41 , 257 (2010)

    2010

  63. [63]

    W. M. van Spengen, ``Capacitive RF MEMS switch dielectric charging and reliability: a critical review with recommendations,'' J. Micromech. Microeng. 22 , 074001 (2012)

    2012

  64. [64]

    K. N. Bhadri Narayanan, and M. R. Baiju, ``Electromagnetic analysis of RF MEMS switch,'' Int. J. Engin. Res. Technol. 3 , 1197 (2014)

    2014

  65. [65]

    T. Emig, R. L. Jaffe, M. Kardar, and A. Scardicchio, ``Casimir Interaction between a Plate and a Cylinder,'' Phys. Rev. Lett. 96 , 080403 (2006)

    2006

  66. [66]

    Bordag, ``Casimir effect for a sphere and a cylinder in front of a plane and corrections to the proximity force theorem,'' Phys

    M. Bordag, ``Casimir effect for a sphere and a cylinder in front of a plane and corrections to the proximity force theorem,'' Phys. Rev. D 73 , 125018 (2006)

    2006

  67. [67]

    F. C. Lombardo, F. D. Mazzitelli, and P. I. Villar, ``Numerical evaluation of the Casimir interaction between cylinders,'' Phys. Rev. D 78 , 085009 (2008)

    2008

  68. [68]

    E. M. Lifshitz and L. P. Pitaevskii, ``Statistical Physics,'' Pt II, (Pergamon Press, Oxford, 1984)

    1984

  69. [69]

    R. S. Decca, E. Fischbach, G. L. Klimchitskaya, D. E. Krause, D. L\' o pez, and V. M. Mostepanenko, ``Possibility of measuring the thermal Casimir interaction between a plate and a cylinder attached to a micromachined oscillator,'' Phys. Rev. A 82 , 052515 (2010)

    2010

  70. [70]

    Gradshteyn and I.M

    I.S. Gradshteyn and I.M. Ryzhik, ``Table of Integrals, Series, and Products,'' (Elsevier, New York, 2007)

    2007

  71. [71]

    A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev, ``Integrals and Series: Elementary Functions,'' (Gordon and Breach, New York, 1986)

    1986

  72. [72]

    Revisiting the divergent multipole expansion of atom-surface interactions: Hydrogen and positronium, -quartz, and physisorption

    G. L. Klimchitskaya, ``Comment on "Revisiting the divergent multipole expansion of atom-surface interactions: Hydrogen and positronium, -quartz, and physisorption",'' Phys. Rev. A 111 , 016801 (2025)

    2025

  73. [73]

    V. M. Mostepanenko, ``A few remarks concerning application of the Lifshitz theory to calculation of the Casimir–Polder interaction,'' Int. J. Mod. Phys. A 40 , 2543001 (2025)

    2025

  74. [74]

    Frenkel and B

    D. Frenkel and B. Smit, ``Understanding Molecular Simulation From Algorithms to Applications,'' (Academic Press, San Diego, 2023)

    2023

  75. [75]

    Yu. N. Moiseev, V. M. Mostepanenko, V. I. Panov, and I. Yu. Sokolov, ``Force dependences for the definition of the atomic force microscopy spatial resolution,'' Phys. Lett. A 132 , 354 (1988)

    1988

  76. [76]

    S. I. Zanette, A. O. Caride, V. B. Nunes, G. L. Klimchitskaya, F. L. Freire Jr., and R. Prioli, ``Theoretical and experimental investigation of the force-distance relation for an atomic force microscope with a pyramidal tip,'' Surf. Sci. 453 , 75 (2000)

    2000

  77. [77]

    Tabor and R

    D. Tabor and R. H. S. Winterton, ``The direct measurement of normal and retarded van der Waals forces,'' Proc. Roy. Soc. Lond. A 312 , 435 (1969)

    1969

  78. [78]

    J. N. Israelachvili and D. Tabor, ``The measurement of van der Waals dispersion forces in the range 1.5 to 130 nm,'' Proc. Roy. Soc. Lond. A 331 , 19 (1972)

    1972

  79. [79]

    Bordag, G

    M. Bordag, G. L. Klimchitskaya, and V. M. Mostepanenko, ``The Casimir force between plates with small deviations from plane parallel geometry,'' Int. J. Mod. Phys. A 10 , 2661 (1995)

    1995

  80. [80]

    Connelly and T.-J

    D. Connelly and T.-J. King Liu, ``Modeling nanoelectromechanical switches with random surface roughness,'' IEEE Trans. Electron Devices 64 , 2409 (2017)

    2017

Showing first 80 references.