Electro-Thermal-Mechanical Modeling of Gas Sensor Hotplates

  • Raffaele CoppetaEmail author
  • Ayoub Lahlalia
  • Darjan Kozic
  • René Hammer
  • Johann Riedler
  • Gregor Toschkoff
  • Anderson Singulani
  • Zeeshan Ali
  • Martin Sagmeister
  • Sara Carniello
  • Siegfried Selberherr
  • Lado Filipovic


Before fabrication, sensors are often designed, simulated, and optimized using the Technology Computer Aided Design (TCAD) tools to reduce the manufacturing costs and the prototype development cycle. In this chapter, the electro-thermo-mechanical behavior of gas sensor hotplates is simulated by means of the finite element method (FEM). In particular, FEM is primarily used to study the mechanical stability of the membrane, the temperature uniformity over the active area, and the power consumption of the sensor. Furthermore, the chapter deals with the appropriate choice of the initial and boundary conditions of the problem, which are necessary to obtain accurate numerical solutions.


FEM Hotplate Joule effect Temperature Power dissipation Membrane bending Crack 



Financial support by the Austrian Federal Government (in particular from Bundesministerium für Verkehr, Innovation und Technologie and Bundesministerium für Wissenschaft, Forschung und Wirtschaft) represented by Österreichische Forschungsförderungsgesellschaft mbH and the Styrian and the Tyrolean Provincial Government, represented by Steirische Wirtschaftsförderungsgesellschaft mbH and Standortagentur Tirol, within the framework of the COMET Funding Programme is gratefully acknowledged.


  1. 1.
    W.H. Brattain, J. Bardeen, Surface properties of germanium. Bell Syst. Tech. J. 32(1), 1–41 (1953)Google Scholar
  2. 2.
    T. Seiyama et al., A new detector for gaseous components using semiconductive thin films. Anal. Chem. 34(11), 1502–1503 (1962)Google Scholar
  3. 3.
    P.J. Shaver, Activated tungsten oxide gas detectors. Appl. Phys. Lett. 11(8), 255–257 (1967)Google Scholar
  4. 4.
    N. Taguchi, Gas-detecting device. U.S Patent 3,631,436, 28 Dec 1971Google Scholar
  5. 5.
    K. Kalantar-Zadeh et al., Intestinal gas capsules: A proof-of-concept demonstration. Gastroenterology 150(1), 37–39 (2016)Google Scholar
  6. 6.
    E. Abad et al., Flexible tag microlab development: Gas sensors integration in RFID flexible tags for food logistic. Sensors Actuators B Chem. 127(1), 2–7 (2007)Google Scholar
  7. 7.
    M. Ortel et al., Spray pyrolysis of ZnO–TFTs utilizing a perfume atomizer. Solid State Electron. 86, 22–26 (2013)Google Scholar
  8. 8.
    M. Prasad et al., Design and fabrication of Sidiaphragm, ZnO piezoelectric film-based MEMS acoustic sensor using SOI wafers. IEEE Trans. Semicond. Manuf. 26(2), 233–241 (2013)Google Scholar
  9. 9.
    D.D. Lee et al., Environmental gas sensors. IEEE Sensors J. 1(3), 214–224 (2001)Google Scholar
  10. 10.
    MarketsandMarkets, Gas Sensors Market worth 1,297.6 Million USD by 2023, 2018. [Online]. Accessed Jul 2018
  11. 11.
    World Health Organization, 9 out of 10 people worldwide breathe polluted air, but more countries are taking action, 2018. [Online]. Accessed Jul 2018
  12. 12.
    Hemming Fire, Looking to the future of gas sensing—a new galaxy of possibilities, Hemming Group Ltd, 08 April 2010. [Online]. Accessed May 2018
  13. 13.
    J. Riegel et al., Exhaust gas sensors for automotive emission control. Solid State Ionics 152, 783–800 (2002)Google Scholar
  14. 14.
    G.F. Fine et al., Metal oxide semi-conductor gas sensors in environmental monitoring. Sensors 10(6), 5469–5502 (2010)Google Scholar
  15. 15.
    E. Kanazawa et al., Metal oxide semiconductor N2O sensor for medical use. Sensors Actuators B Chem. 77(1–2), 72–77 (2001)Google Scholar
  16. 16.
    T. Konduru et al., A customized metal oxide semiconductor-based gas sensor array for onion quality evaluation: System development and characterization. Sensors 15(1), 1252–1273 (2015)Google Scholar
  17. 17.
    A. Lahlalia et al., Modeling and simulation of novel semiconducting metal oxide gas sensors for wearable devices. IEEE Sensors J. 18(5), 1960–1970 (2018)Google Scholar
  18. 18.
    S.Z. Ali et al., Nanowire hydrogen gas sensor employing CMOS micro-hotplate, in Proceedings of IEEE Sensors 2009 Conference, (2009)Google Scholar
  19. 19.
    H.M. Low et al., Thermal induced stress on the membrane in integrated gas sensor with micro-heater, in Proceedings of the 1998 IEEE Electron Devices Meeting, Hong Kong, (1998)Google Scholar
  20. 20.
    D.-D. Lee et al., Low power micro gas sensor, in Solid-State Sensors and Actuators and Eurosensors IX.. Transducers’ 95, IEEE, (1995)Google Scholar
  21. 21.
    I. Simon et al., Micromachined metal oxide gas sensors: Opportunities to improve sensor performance. Sensors Actuators B Chem. 73(1), 1–26 (2001)Google Scholar
  22. 22.
    R. Phatthanakun et al., Fabrication and control of thin-film aluminum microheater and nickel temperature Sensor, in Electrical Engineering/Electronics, Computer, Telecommunications and Information Technology (ECTI-CON), IEEE, (2011)Google Scholar
  23. 23.
    K. Zhang et al., Fabrication, modeling and testing of a thin film Au/Ti microheater. Int. J. Therm. Sci. 46(6), 580–588 (2007)Google Scholar
  24. 24.
    L. Xu et al., Development of a reliable micro-hotplate with low power consumption. IEEE Sensors J. 11(4), 913–919 (2011)Google Scholar
  25. 25.
    P. Bhattacharyya et al., A low power MEMS gas sensor based on nanocrystalline ZnO thin films for sensing methane. Microelectron. Reliab. 48(11), 1772–1779 (2008)Google Scholar
  26. 26.
    U. Dibbern, A substrate for thin-film gas sensors in microelectronic technology. Sensors Actuators B Chem. 2(1), 63–70 (1990)Google Scholar
  27. 27.
    I. Haneef et al., Thermal characterization of SOI CMOS micro hot-plate gas sensors, in Thermal Investigations of ICs and Systems (THERMINIC), IEEE, (2010)Google Scholar
  28. 28.
    S.Z. Ali et al., Tungsten-based SOI microhotplates for smart gas sensors. IEEE J. Microelectromech. Syst. 17(6), 1408–1417 (2008)Google Scholar
  29. 29.
    W. Yan et al., Nickel membrane temperature sensor in micro-flow measurement. J. Alloys Compd. 449(1–2), 210–213 (2008)Google Scholar
  30. 30.
    D. Monika et al., Design and simulation of MEMS based microhotplate as gas sensor. Int. J. Adv. Eng. Res. Technol. 2, 2487–2492 (2013)Google Scholar
  31. 31.
    L. Mele et al., A molybdenum MEMS microhotplate for high-temperature operation. Sensors Actuators A Phys. 188, 173–180 (2012)Google Scholar
  32. 32.
    V. Balakrishnan et al., Steady-state analytical model of suspended p-type 3C–SiC bridges under consideration of Joule heating. J. Micromech. Microeng. 27(7), 075008 (2017)Google Scholar
  33. 33.
    J.F. Creemer et al., Microhotplates with TiN heaters. Sensors Actuators A Phys. 148(2), 416–421 (2008)Google Scholar
  34. 34.
    G. Benn, Design of a Silicon Carbide Micro-Hotplate Geometry for High Temperature Chemical Sensing, M.S. thesis (MIT, Cambridge, 2001)Google Scholar
  35. 35.
    J. Spannhake et al., High-temperature MEMS heater platforms: Long-term performance of metal and semiconductor heater materials. Sensors 6(4), 405–419 (2006)Google Scholar
  36. 36.
    S.Z. Ali et al., A low-power, low-cost infra-red emitter in CMOS technology. IEEE Sensors J. 15(12), 6775–6782 (2015)Google Scholar
  37. 37.
    A. Lahlalia et al., Electro-thermal simulation & characterization of a microheater for SMO gas sensors. J. Microelectromech. Syst. 27(3), 529–537 (2018)Google Scholar
  38. 38.
    I. Elmi et al., Development of ultra-low-power consumption MOX sensors with ppb-level VOC detection capabilities for emerging applications. Sensors Actuators B Chem. 135(1), 342–351 (2008)Google Scholar
  39. 39.
    J.C. Belmonte et al., High-temperature low-power performing micromachined suspended micro-hotplate for gas sensing applications. Sensors Actuators B Chem. 114(2), 826–835 (2006)Google Scholar
  40. 40.
    J. Li et al., Dynamic characteristics of transient boiling on a square platinum microheater under millisecond pulsed heating. Int. J. Heat Mass Transf. 51(1/2), 273–282 (2008)zbMATHGoogle Scholar
  41. 41.
    S.M. Lee et al., Design and optimisation of a high-temperature silicon micro-hotplate for nanoporous palladium pellistors. Microelectron. J. 34(2), 115–126 (2003)Google Scholar
  42. 42.
    F. Udrea et al., Design and simulations of SOI CMOS micro-hotplate gas sensors. Sensors Actuators B Chem. 78(1–3), 180–190 (2001)Google Scholar
  43. 43.
    Y. Çengel et al., Fundamentals of Thermal-Fluid Sciences (McGraw-Hill, New York, 2001)Google Scholar
  44. 44.
    C. Dücsö et al., Porous silicon bulk micromachining for thermally isolated membrane formation. Sensors Actuators A Phys. 60(1–3), 235–239 (1997)Google Scholar
  45. 45.
    A.I. Uddin et al., Low temperature acetylene gas sensor based on Ag nanoparticles-loaded ZnO-reduced graphene oxide hybrid. Sensors Actuators B Chem. 207, 362–369 (2015)Google Scholar
  46. 46.
    R. Artzi-Gerlitz et al., Fabrication and gas sensing performance of parallel assemblies of metal oxide nanotubes supported by porous aluminum oxide membranes. Sensors Actuators B Chem. 136(1), 257–264 (2009)Google Scholar
  47. 47.
    M. Aslam et al., Polyimide membrane for micro-heated gas sensor array. Sensors Actuators B Chem. 103(1–2), 153–157 (2004)Google Scholar
  48. 48.
    T. Taliercio et al., Realization of porous silicon membranes for gas sensor applications. Thin Solid Films 255(1–2), 310–312 (1995)Google Scholar
  49. 49.
    S. Astié et al., Design of a low power SnO2 gas sensor integrated on silicon oxynitride membrane. Sensors Actuators B Chem. 67(1–2), 84–88 (2000)Google Scholar
  50. 50.
    G. Wiche et al., Thermal analysis of silicon carbide based micro hotplates for metal oxide gas sensors. Sensors Actuators A Phys. 123, 12–17 (2005)Google Scholar
  51. 51.
    T. Zhang et al., Electrochemically functionalized single-walled carbon nanotube gas sensor. Electroanalysis 18(12), 1153–1158 (2006)Google Scholar
  52. 52.
    J. Li et al., A gas sensor array using carbon nanotubes and microfabrication technology. Electrochem. Solid-State Lett. 8(11), H100–H102 (2005)Google Scholar
  53. 53.
    K.D. Mitzner et al., Development of a micromachined hazardous gas sensor array. Sensors Actuators B Chem. 93(1–3), 92–99 (2003)Google Scholar
  54. 54.
    V. Guarnieri et al., Platinum metallization for MEMS application: Focus on coating adhesion for biomedical applications. Biomatter 4(1), e28822 (2014)Google Scholar
  55. 55.
    Q. Zhou et al., Fast response integrated MEMS microheaters for ultra low power gas detection. Sensors Actuators A 223, 67–75 (2015)Google Scholar
  56. 56.
    D.G. Cahill et al., Thermometry and thermal transport in micro/nanoscale solid-state devices and structures. J. Heat Transf. 124(2), 223–241 (2002)Google Scholar
  57. 57.
    D.G. Cahill, Analysis of heat flow in layered structures for time-domain thermoreflectance. Rev. Sci. Instrum. 75(12), 5119 (2004)Google Scholar
  58. 58.
    F. Claro, Theory of resonant modes in particulate matter. Phys. Rev. B 30(9), 4989–4999 (1984)Google Scholar
  59. 59.
    S. Gomès et al., Scanning thermal microscopy: A review. Phys. Status Solidi A 212(3), 477–494 (2015)MathSciNetGoogle Scholar
  60. 60.
    V. Szekely, Identification of RC networks by deconvolution: Chances and limits. IEEE Trans. Circ. Syst. Fund. Theor. Appl. 45(3), 244–258 (1998)MathSciNetGoogle Scholar
  61. 61.
    L. Mitterhuber et al., Validation methodology to analyze the temperature-dependent heat path of a 4-chip LED module using a finite volume simulation. Microelectron. Reliab. 79, 462–472 (2017)Google Scholar
  62. 62.
    A.J. Schmidt et al., Pulse accumulation, radial heat conduction, and anisotropic thermal conductivity in pump-probe transient thermoreflectance. Rev. Sci. Instrum. 79, 114902(9) (2008)Google Scholar
  63. 63.
    P.B. Allen et al., Diffusons, locons and propagons: Character of atomie yibrations in amorphous si. Philos. Mag. B 79(11–12), 1715–1731 (1999)Google Scholar
  64. 64.
    M. Flik et al., Heat transfer regimes in microstructures. J. Heat Transf. 114(3), 666–674 (1992)Google Scholar
  65. 65.
    G. Chen, Nonlocal and nonequilibrium heat conduction in the vicinity of nanoparticles. J. Heat Transf. 118(3), 539–545 (1996)MathSciNetGoogle Scholar
  66. 66.
    J.Å. Schweitz, Mechanical characterization of thin films by micromechanical techniques. MRS Bull. 17(7), 34–45 (1992)Google Scholar
  67. 67.
    V.M. Paviot et al., Measuring the mechanical properties of thin metal films by means of bulge testing of micromachined windows. MRS Online Proc. Libr. Arch. 356, 579–584 (1994)Google Scholar
  68. 68.
    S. Mahabunphachai et al., Investigation of size effects on material behavior of thin sheet metals using hydraulic bulge testing at micro/meso-scales. Int. J. Mach. Tools Manuf. 48(9), 1014–1029 (2008)Google Scholar
  69. 69.
    T.P. Weihs et al., Mechanical deflection of cantilever microbeams: A new technique for testing the mechanical properties of thin films. J. Mater. Res. 3(5), 931–942 (1988)Google Scholar
  70. 70.
    X. Song et al., Residual stress measurement in thin films at sub-micron scale using focused ion beam milling and imaging. Thin Solid Films 520(6), 2073–2076 (2012)Google Scholar
  71. 71.
    M. Krottenthaler et al., A simple method for residual stress measurements in thin films by means of focused ion beam milling and digital image correlation. Surf. Coat. Technol. 215, 247–252 (2013)Google Scholar
  72. 72.
    N. Sabaté et al., FIB-based technique for stress characterization on thin films for reliability purposes. Microelectron. Eng. 84, 1783–1787 (2007)Google Scholar
  73. 73.
    S. Massl et al., A direct method of determining complex depth profiles of residual stresses in thin films on a nanoscale. Acta Mater. 55, 4835–4844 (2007)Google Scholar
  74. 74.
    G. Moser et al., Sample preparation by metallography and focused ion beam for nanomechanical testing. Pract. Metallogr. 49(6), 343–355 (2012)Google Scholar
  75. 75.
    D. Kiener et al., Source truncation and exhaustion: Insights from quantitative in situ TEM tensile testing. Nano Lett. 11(9), 3816–3820 (2011)Google Scholar
  76. 76.
    D. Kiener et al., Strength, hardening, and failure observed by in situ tem tensile testing. Adv. Eng. Mater. 14(11), 960–967 (2012)Google Scholar
  77. 77.
    M.F. Dorner et al., Stresses and deformation processes in thin films on substrates. CRC Crit. Rev. Solid State Mater. Sci. 14(3), 225–267 (1988)MathSciNetGoogle Scholar
  78. 78.
    P. Chaudhari, Grain growth and stress relief in thin films. J. Vac. Sci. Technol. 9(1), 520–522 (1972)Google Scholar
  79. 79.
    R.W. Hoffman, Stresses in thin films: The relevance of grain boundaries and impurities. Thin Solid Films 34, 185–190 (1976)Google Scholar
  80. 80.
    E. Klokholm et al., Intinsic stress in evaporated metal films. J. Electrochem. Soc. 115(8), 823–826 (1968)Google Scholar
  81. 81.
    B.W. Sheldon et al., Intinsic compressive stress in polycrystalline films with negligible grain boundary diffusion. J. Appl. Phys. 94(2), 948–957 (2003)Google Scholar
  82. 82.
    E. Chason et al., Origin of compressive residual stress in polycrystalline thin films. Phys. Rev. Lett. 88(15), 156103 (2002)Google Scholar
  83. 83.
    K. Cholevas, Misfit dislocation patterning in thin films. Phys. Status Solidi B 209(10), 295–304 (1998)Google Scholar
  84. 84.
    L.B. Freund et al., Thin Film Materials: Stress, Defect Formation and Surface Evolution (Cambridge University Press, Cambridge, 2003)zbMATHGoogle Scholar
  85. 85.
    P. Tsilingiris, Thermal conductivity of air under different humidity conditions. Energy Convers. Manag. 49, 1098–1110 (2008)Google Scholar
  86. 86.
    A. Moridi et al., Residual stresses in thin film systems:Effects of lattice mismatch, thermal mismatch and interface dislocations. Int. J. Solids Struct. 50(22–23), 3562–3569 (2013)Google Scholar
  87. 87.
    H. Köstenbauer et al., Annealing of intrinsic stresses in sputtered TiN films: The role of thickness-dependent gradients of point defect density. Surf. Coat. Technol. 201, 4777–4780 (2007)Google Scholar
  88. 88.
    R. Machunze et al., Stress and strain in titanium nitride thin films. Thin Solid Films 517, 5888–5893 (2009)Google Scholar
  89. 89.
    R. Treml et al., High resolution determination of local residual stress gradients in single- and multilayer thin film systems. Acta Mater. 103, 616–623 (2016)Google Scholar
  90. 90.
    R. Hammer et al., High resolution residual stress gradient characterization in W/TiN-stack on Si(100): Correlating in-plane stress and grain size distributions in W sublayer. Mater. Des. 132, 72–78 (2017)Google Scholar
  91. 91.
    R. Konetschnik et al., Micro-mechanical in situ measurements in thin film systems regarding the determination of residual stress, fracture properties and Interface toughness. Microsc. Microanal. 23, 750–751 (2017)Google Scholar
  92. 92.
    J. Keckes et al., X-ray nanodiffraction reveals strain and microstructure evolution in nanocrystalline thin films. Scr. Mater. 67, 748–751 (2012)Google Scholar
  93. 93.
    C. Genzel, X-ray residual stress analysis in thin films under grazing incidence–basic aspects and applications. Mater. Sci. Technol. 21, 10–18 (2005)Google Scholar
  94. 94.
    J. Todt et al., X-ray nanodiffraction analysis of stress oscillations in a W thin film on through-silicon via. J. Appl. Crystallogr. 49, 182–187 (2016)Google Scholar
  95. 95.
    M. Stefenelli et al., X-ray nanodiffraction reveals stress distribution across an indented multilayered CrN–Cr thin film. Acta Mater. 85, 24–31 (2015)Google Scholar
  96. 96.
    R. Schöngrundner et al., Critical assessment of the determination of residual stress profiles in thin films by means of the ion beamlayer removal method. Thin Solid Films 564, 321–330 (2014)Google Scholar
  97. 97.
    M. Sebastiani et al., Depth-resolved residual stress analysis of thin coatings by a new FIB–DIC method. Mater. Sci. Eng. A 528, 7901–7908 (2011)Google Scholar
  98. 98.
    T.L. Anderson, Fracture Mechanics: Fundamentals and Applications (CRC, Boca Raton, 2017)zbMATHGoogle Scholar
  99. 99.
    M. Kuna, Finite Elements in Fracture Mechanics: Theory—Numerics—Applications. Solid Mechanics and Its Applications (Springer, Dordrecht, 2015)Google Scholar
  100. 100.
    O. Kolednik, Fracture Mechanics, Wiley Encyclopedia of Composites (Wiley, New York, 2011)Google Scholar
  101. 101.
    X.K. Zhu et al., Review of fracture toughness (G, K, J, CTOD, CTOA) testing and standardization. Eng. Fract. Mech. 85, 1–46 (2012)Google Scholar
  102. 102.
    G. Irwin, Analysis of stresses and strains near the end of a crack traversing a plate. J. Appl. Mech. 24(3), 361–364 (1957)Google Scholar
  103. 103.
    A.A. Griffith, The phenomena of rupture and flow in solids. Philos. Trans. R. Soc. A Math. Phys. Eng. Sci. 221(582–593), 163–198 (1921)Google Scholar
  104. 104.
    J.R. Rice, A path independent integral and the approximate analysis of strain concentration by notches and cracks. J. Appl. Mech. 35(2), 379–386 (1968)Google Scholar
  105. 105.
    N.K. Simha et al., J-integral and crack driving force in elastic-plastic materials. J. Mech. Phys. Solids 56(9), 2876–2895 (2008)MathSciNetzbMATHGoogle Scholar
  106. 106.
    O. Kolednik et al., A new view on J-integrals inelastic–plastic materials. Int. J. Fract. 187(1), 77–107 (2014)Google Scholar
  107. 107.
    R.O. Ritchie, Mechanisms of fatigue crack propagation in metals, ceramics and composites: Role of crack tip shielding. Mater. Sci. Eng. 103(1), 15–28 (1988)Google Scholar
  108. 108.
    N.K. Simha et al., Inhomogeneity effects on the crack driving force in elastic and elastic-plastic materials. J. Mech. Phys. Solids 51(1), 209–240 (2003)MathSciNetzbMATHGoogle Scholar
  109. 109.
    R.O. Ritchie et al., Fatigue crack propagation in ARALL® LAMINATES: Measurement of the effect of crack-tip shielding from crack bridging. Eng. Fract. Mech. 32(3), 361–377 (1989)Google Scholar
  110. 110.
    O. Kolednik et al., Improvement of fatigue life by compliant and soft interlayers. Scr. Mater. 113, 1–5 (2016)Google Scholar
  111. 111.
    Y. Sugimura et al., Fracture normal to a biomaterial interface: Effects of plasticity on crack-tip shielding and amplification. Acta Metall. Mater. 43(3), 1157–1169 (1995)Google Scholar
  112. 112.
    J. Predan et al., On the local variation of the crack driving force in a double mismatched weld. Eng. Fract. Mech. 74(11), 1739–1757 (2007)Google Scholar
  113. 113.
    O. Kolednik et al., Modeling fatigue crack growth in a bimaterial specimen with the configurational forces concept. Mater. Sci. Eng. A 519(1–2), 172–183 (2009)Google Scholar
  114. 114.
    N.K. Simha et al., Material force models for cracks—influences of eigenstrains, thermal strains & residual stresses, in 11th International Conference on Fracture, (2005)Google Scholar
  115. 115.
    J.D. Eshelby, Energy Relations and the Energy-Momentum Tensor in Continuum Mechanics BT (Springer, Berlin, 1999)Google Scholar
  116. 116.
    M.E. Gurtin, Configurational Forces as Basic Concepts of Continuum Physics (Springer, New York, 2000)zbMATHGoogle Scholar
  117. 117.
    G.A. Maugin, Configurational Forces: Thermodynamics, Physics, Mathematics, and Numerics (CRC, Boca Raton, 2010)Google Scholar
  118. 118.
    N.K. Simha et al., Crack tip shielding or anti-shielding due to smooth and discontinuous material inhomogeneities. Int. J. Fract. 135(1), 73–93 (2005)zbMATHGoogle Scholar
  119. 119.
    R. Treml et al., Miniaturized fracture experiments to determine the toughness of individual films in a multilayer system. Extreme Mech. Lett. 8, 235–244 (2016)Google Scholar
  120. 120.
    B. Merle et al., Fracture toughness of silicon nitride thin films of different thicknesses as measured by bulge tests. Acta Mater. 59, 1772–1779 (2011)Google Scholar
  121. 121.
    E. Harry et al., Mechanical properties of W and W(C) thin films: Young’s modulus, fracture toughness and adhesion. Thin Solid Films 332, 195–201 (1998)Google Scholar
  122. 122.
    D. Kozic et al., Extracting flow curves from nano-sized metal layers in thin film systems. Scr. Mater. 130, 143–417 (2017)Google Scholar
  123. 123.
    G. Klemes, Thermal Conductivity: Metallic Elements and Alloys (Plenum, New York, 1970)Google Scholar
  124. 124.
    J. Hostetler et al., Thin-film thermal conductivity and thickness measurements using picosecond ultrasonics. Microsc. Thermophys. Eng. 1(3), 237–244 (1997)Google Scholar
  125. 125.
    L. Xiang, Thermal conductivity modeling of copper and tungsten damascene structures. J. Appl. Phys. 105(9), 094301 (2009)Google Scholar
  126. 126.
    T.L. Bergman et al., Fundamentals of Heat and Mass Transfer (Wiley, New York, 2011)Google Scholar
  127. 127.
    H.A. Schafft et al., Thermal conductivity measurements of thin-film silicon dioxide in microelectronic test structures, in Microelectronic Test Structures (ICMTS), IEEE, (1989)Google Scholar
  128. 128.
    X. Zhang et al., Thermal conductivity and diffusivity of free-standing silicon nitride thin films. Rev. Sci. Instrum. 66(2), 1115–1120 (1995)Google Scholar
  129. 129.
    Texas Instruments, Thermal conductivity and thermal diffusivity, Report (2014)Google Scholar
  130. 130.
    P.I. Dorogokupets et al., Optimization of experimental data on the heat capacity, volume, and bulk moduli of minerals. Petrology 7(6), 574–591 (1999)Google Scholar
  131. 131.
    S. Andersson, Thermal conductivity and heat capacity of amorphous SiO2: pressure and volume dependence. J. Phys. Condens. Matter 4(29), 6209 (1992)Google Scholar
  132. 132.
    A.S. Grove, Physics and Technology of Semiconductor Devices (Wiley, New York, 1967)Google Scholar
  133. 133.
    T. Ohmura et al., Specific heat measurement of high temperature thermal insulations by drop calorimeter method. Int. J. Thermophys. 24(2), 559–575 (2003)Google Scholar
  134. 134.
    C.H. Mastrangelo et al., Thermophysical properties of low-residual stress, silicon-rich, LPCVD silicon nitride films. Sensors Actuators A Phys. 23(1–3), 856–860 (1990)Google Scholar
  135. 135.
    A. Jain et al., Measurement of the thermal conductivity and heat capacity of freestanding shape memory thin films using the 3ω method. J. Heat Transf. 130(10), 102402 (2008)Google Scholar
  136. 136.
    J. Harrigill et al., Method for Measuring Static Young’s Modulus of Tungsten to 1900 K (1972)Google Scholar
  137. 137.
    J.W. Davis et al., ITER material properties handbook. J. Nucl. Mater. 233, 1593–1596 (1996)Google Scholar
  138. 138.
    G.P. Škoro et al., Dynamic Young’s moduli of tungsten and tantalum at high temperature and stress. J. Nucl. Mater. 409(1), 40–46 (2011)Google Scholar
  139. 139.
    D. Makwana et al., Review of miniature specimen tensile test method of tungsten at elevated temperature. Int. J. Eng. Dev. Res. 4(4), 132–139 (2016)Google Scholar
  140. 140.
    S. Krimpalis et al., Comparative study of the mechanical properties of different tungsten materials for fusion applications. Phys. Scripta 2017(T170), 014068 (2017)Google Scholar
  141. 141.
    F.F. Schmidt et al., The Engineering Properties of Tungsten and Tungsten Alloys, No. DMIC191 (Battelle Memorial Institute, Defense Metals Information Center, Columbus, 1963)Google Scholar
  142. 142.
    T. Shinoda et al., Young’s modulus of RF-sputtered amorphous thin films in the SiO2-Y2O3 system at high temperature. Thin Solid Films 293(1–2), 144–148 (1997)Google Scholar
  143. 143.
    O. Morozov et al., Mechanical strength study of SiO2 isolation blocks merged in silicon substrate. J. Micromech. Microeng. 25(1), 015014 (2014)Google Scholar
  144. 144.
    W.N. Sharpe et al., Strain measurements of silicon dioxide microspecimens by digital imaging processing. Exp. Mech. 47(5), 649–658 (2007)Google Scholar
  145. 145.
    T. Tsuchiya et al., Tensile testing of insulating thin films; humidity effect on tensile strength of SiO2 films. Sensors Actuators A Phys. 82(1–3), 286–290 (2000)Google Scholar
  146. 146.
    J.-H. Zhao et al., Measurement of elastic modulus, Poisson ratio, and coefficient of thermal expansion of on-wafer submicron films. J. Appl. Phys. 85(9), 6421–6424 (1999)Google Scholar
  147. 147.
    E. Sánchez-González et al., Effect of temperature on the pre-creep mechanical properties of silicon nitride. J. Eur. Ceram. Soc. 29(12), 2635–2641 (2009)Google Scholar
  148. 148.
    aZo Materials, Sintered Silicon Nitride (Si3N4), [Online].
  149. 149.
    R.J. Bruls et al., The temperature dependence of the Young’s modulus of MgSiN2, AlN and Si3N4. J. Eur. Ceram. Soc. 21(3), 263–268 (2001)Google Scholar
  150. 150.
    A.E. Kaloyeros et al., Silicon nitride and silicon nitride-rich thin film technologies: Trends in deposition techniques and related applications. ECS J. Solid State Sci. Technol. 6(10), 691–714 (2017)Google Scholar
  151. 151.
    A. Khan et al., Young’s modulus of silicon nitride used in scanning force microscope cantilevers. J. Appl. Phys. 95(4), 1667–1672 (2004)Google Scholar
  152. 152.
    G.F. Cardinale et al., Fracture strength and biaxial modulus measurement of plasma silicon nitride films. Thin Solid Films 207(1–2), 126–130 (1992)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Raffaele Coppeta
    • 1
    Email author
  • Ayoub Lahlalia
    • 2
  • Darjan Kozic
    • 3
  • René Hammer
    • 3
  • Johann Riedler
    • 3
  • Gregor Toschkoff
    • 1
  • Anderson Singulani
    • 1
  • Zeeshan Ali
    • 1
  • Martin Sagmeister
    • 1
  • Sara Carniello
    • 1
  • Siegfried Selberherr
    • 2
  • Lado Filipovic
    • 2
  1. 1.ams AGPremstaettenAustria
  2. 2.Institute for Microelectronics, TU WienViennaAustria
  3. 3.Materials Center Leoben Forschung GmbHLeobenAustria

Personalised recommendations