Abstract
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.
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References
W.H. Brattain, J. Bardeen, Surface properties of germanium. Bell Syst. Tech. J. 32(1), 1–41 (1953)
T. Seiyama et al., A new detector for gaseous components using semiconductive thin films. Anal. Chem. 34(11), 1502–1503 (1962)
P.J. Shaver, Activated tungsten oxide gas detectors. Appl. Phys. Lett. 11(8), 255–257 (1967)
N. Taguchi, Gas-detecting device. U.S Patent 3,631,436, 28 Dec 1971
K. Kalantar-Zadeh et al., Intestinal gas capsules: A proof-of-concept demonstration. Gastroenterology 150(1), 37–39 (2016)
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)
M. Ortel et al., Spray pyrolysis of ZnO–TFTs utilizing a perfume atomizer. Solid State Electron. 86, 22–26 (2013)
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)
D.D. Lee et al., Environmental gas sensors. IEEE Sensors J. 1(3), 214–224 (2001)
MarketsandMarkets, Gas Sensors Market worth 1,297.6 Million USD by 2023, 2018. [Online]. https://www.marketsandmarkets.com/PressReleases/gas-sensor.asp. Accessed Jul 2018
World Health Organization, 9 out of 10 people worldwide breathe polluted air, but more countries are taking action, 2018. [Online]. http://www.who.int/news-room/detail/02-05-2018-9-out-of-10-people-worldwide-breathe-polluted-air-but-more-countries-are-taking-action. Accessed Jul 2018
Hemming Fire, Looking to the future of gas sensing—a new galaxy of possibilities, Hemming Group Ltd, 08 April 2010. [Online]. http://www.hemmingfire.com/news/fullstory.php/aid/844/Looking_to_the_future_of_gas_sensing__96_a_new_galaxy_of_possibilities__.html. Accessed May 2018
J. Riegel et al., Exhaust gas sensors for automotive emission control. Solid State Ionics 152, 783–800 (2002)
G.F. Fine et al., Metal oxide semi-conductor gas sensors in environmental monitoring. Sensors 10(6), 5469–5502 (2010)
E. Kanazawa et al., Metal oxide semiconductor N2O sensor for medical use. Sensors Actuators B Chem. 77(1–2), 72–77 (2001)
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)
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)
S.Z. Ali et al., Nanowire hydrogen gas sensor employing CMOS micro-hotplate, in Proceedings of IEEE Sensors 2009 Conference, (2009)
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)
D.-D. Lee et al., Low power micro gas sensor, in Solid-State Sensors and Actuators and Eurosensors IX.. Transducers’ 95, IEEE, (1995)
I. Simon et al., Micromachined metal oxide gas sensors: Opportunities to improve sensor performance. Sensors Actuators B Chem. 73(1), 1–26 (2001)
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)
K. Zhang et al., Fabrication, modeling and testing of a thin film Au/Ti microheater. Int. J. Therm. Sci. 46(6), 580–588 (2007)
L. Xu et al., Development of a reliable micro-hotplate with low power consumption. IEEE Sensors J. 11(4), 913–919 (2011)
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)
U. Dibbern, A substrate for thin-film gas sensors in microelectronic technology. Sensors Actuators B Chem. 2(1), 63–70 (1990)
I. Haneef et al., Thermal characterization of SOI CMOS micro hot-plate gas sensors, in Thermal Investigations of ICs and Systems (THERMINIC), IEEE, (2010)
S.Z. Ali et al., Tungsten-based SOI microhotplates for smart gas sensors. IEEE J. Microelectromech. Syst. 17(6), 1408–1417 (2008)
W. Yan et al., Nickel membrane temperature sensor in micro-flow measurement. J. Alloys Compd. 449(1–2), 210–213 (2008)
D. Monika et al., Design and simulation of MEMS based microhotplate as gas sensor. Int. J. Adv. Eng. Res. Technol. 2, 2487–2492 (2013)
L. Mele et al., A molybdenum MEMS microhotplate for high-temperature operation. Sensors Actuators A Phys. 188, 173–180 (2012)
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)
J.F. Creemer et al., Microhotplates with TiN heaters. Sensors Actuators A Phys. 148(2), 416–421 (2008)
G. Benn, Design of a Silicon Carbide Micro-Hotplate Geometry for High Temperature Chemical Sensing, M.S. thesis (MIT, Cambridge, 2001)
J. Spannhake et al., High-temperature MEMS heater platforms: Long-term performance of metal and semiconductor heater materials. Sensors 6(4), 405–419 (2006)
S.Z. Ali et al., A low-power, low-cost infra-red emitter in CMOS technology. IEEE Sensors J. 15(12), 6775–6782 (2015)
A. Lahlalia et al., Electro-thermal simulation & characterization of a microheater for SMO gas sensors. J. Microelectromech. Syst. 27(3), 529–537 (2018)
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)
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)
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)
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)
F. Udrea et al., Design and simulations of SOI CMOS micro-hotplate gas sensors. Sensors Actuators B Chem. 78(1–3), 180–190 (2001)
Y. Çengel et al., Fundamentals of Thermal-Fluid Sciences (McGraw-Hill, New York, 2001)
C. DĂ¼csö et al., Porous silicon bulk micromachining for thermally isolated membrane formation. Sensors Actuators A Phys. 60(1–3), 235–239 (1997)
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)
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)
M. Aslam et al., Polyimide membrane for micro-heated gas sensor array. Sensors Actuators B Chem. 103(1–2), 153–157 (2004)
T. Taliercio et al., Realization of porous silicon membranes for gas sensor applications. Thin Solid Films 255(1–2), 310–312 (1995)
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)
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)
T. Zhang et al., Electrochemically functionalized single-walled carbon nanotube gas sensor. Electroanalysis 18(12), 1153–1158 (2006)
J. Li et al., A gas sensor array using carbon nanotubes and microfabrication technology. Electrochem. Solid-State Lett. 8(11), H100–H102 (2005)
K.D. Mitzner et al., Development of a micromachined hazardous gas sensor array. Sensors Actuators B Chem. 93(1–3), 92–99 (2003)
V. Guarnieri et al., Platinum metallization for MEMS application: Focus on coating adhesion for biomedical applications. Biomatter 4(1), e28822 (2014)
Q. Zhou et al., Fast response integrated MEMS microheaters for ultra low power gas detection. Sensors Actuators A 223, 67–75 (2015)
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)
D.G. Cahill, Analysis of heat flow in layered structures for time-domain thermoreflectance. Rev. Sci. Instrum. 75(12), 5119 (2004)
F. Claro, Theory of resonant modes in particulate matter. Phys. Rev. B 30(9), 4989–4999 (1984)
S. Gomès et al., Scanning thermal microscopy: A review. Phys. Status Solidi A 212(3), 477–494 (2015)
V. Szekely, Identification of RC networks by deconvolution: Chances and limits. IEEE Trans. Circ. Syst. Fund. Theor. Appl. 45(3), 244–258 (1998)
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)
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)
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)
M. Flik et al., Heat transfer regimes in microstructures. J. Heat Transf. 114(3), 666–674 (1992)
G. Chen, Nonlocal and nonequilibrium heat conduction in the vicinity of nanoparticles. J. Heat Transf. 118(3), 539–545 (1996)
J.Å. Schweitz, Mechanical characterization of thin films by micromechanical techniques. MRS Bull. 17(7), 34–45 (1992)
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)
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)
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)
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)
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)
N. Sabaté et al., FIB-based technique for stress characterization on thin films for reliability purposes. Microelectron. Eng. 84, 1783–1787 (2007)
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)
G. Moser et al., Sample preparation by metallography and focused ion beam for nanomechanical testing. Pract. Metallogr. 49(6), 343–355 (2012)
D. Kiener et al., Source truncation and exhaustion: Insights from quantitative in situ TEM tensile testing. Nano Lett. 11(9), 3816–3820 (2011)
D. Kiener et al., Strength, hardening, and failure observed by in situ tem tensile testing. Adv. Eng. Mater. 14(11), 960–967 (2012)
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)
P. Chaudhari, Grain growth and stress relief in thin films. J. Vac. Sci. Technol. 9(1), 520–522 (1972)
R.W. Hoffman, Stresses in thin films: The relevance of grain boundaries and impurities. Thin Solid Films 34, 185–190 (1976)
E. Klokholm et al., Intinsic stress in evaporated metal films. J. Electrochem. Soc. 115(8), 823–826 (1968)
B.W. Sheldon et al., Intinsic compressive stress in polycrystalline films with negligible grain boundary diffusion. J. Appl. Phys. 94(2), 948–957 (2003)
E. Chason et al., Origin of compressive residual stress in polycrystalline thin films. Phys. Rev. Lett. 88(15), 156103 (2002)
K. Cholevas, Misfit dislocation patterning in thin films. Phys. Status Solidi B 209(10), 295–304 (1998)
L.B. Freund et al., Thin Film Materials: Stress, Defect Formation and Surface Evolution (Cambridge University Press, Cambridge, 2003)
P. Tsilingiris, Thermal conductivity of air under different humidity conditions. Energy Convers. Manag. 49, 1098–1110 (2008)
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)
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)
R. Machunze et al., Stress and strain in titanium nitride thin films. Thin Solid Films 517, 5888–5893 (2009)
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)
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)
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)
J. Keckes et al., X-ray nanodiffraction reveals strain and microstructure evolution in nanocrystalline thin films. Scr. Mater. 67, 748–751 (2012)
C. Genzel, X-ray residual stress analysis in thin films under grazing incidence–basic aspects and applications. Mater. Sci. Technol. 21, 10–18 (2005)
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)
M. Stefenelli et al., X-ray nanodiffraction reveals stress distribution across an indented multilayered CrN–Cr thin film. Acta Mater. 85, 24–31 (2015)
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)
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)
T.L. Anderson, Fracture Mechanics: Fundamentals and Applications (CRC, Boca Raton, 2017)
M. Kuna, Finite Elements in Fracture Mechanics: Theory—Numerics—Applications. Solid Mechanics and Its Applications (Springer, Dordrecht, 2015)
O. Kolednik, Fracture Mechanics, Wiley Encyclopedia of Composites (Wiley, New York, 2011)
X.K. Zhu et al., Review of fracture toughness (G, K, J, CTOD, CTOA) testing and standardization. Eng. Fract. Mech. 85, 1–46 (2012)
G. Irwin, Analysis of stresses and strains near the end of a crack traversing a plate. J. Appl. Mech. 24(3), 361–364 (1957)
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)
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)
N.K. Simha et al., J-integral and crack driving force in elastic-plastic materials. J. Mech. Phys. Solids 56(9), 2876–2895 (2008)
O. Kolednik et al., A new view on J-integrals inelastic–plastic materials. Int. J. Fract. 187(1), 77–107 (2014)
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)
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)
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)
O. Kolednik et al., Improvement of fatigue life by compliant and soft interlayers. Scr. Mater. 113, 1–5 (2016)
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)
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)
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)
N.K. Simha et al., Material force models for cracks—influences of eigenstrains, thermal strains & residual stresses, in 11th International Conference on Fracture, (2005)
J.D. Eshelby, Energy Relations and the Energy-Momentum Tensor in Continuum Mechanics BT (Springer, Berlin, 1999)
M.E. Gurtin, Configurational Forces as Basic Concepts of Continuum Physics (Springer, New York, 2000)
G.A. Maugin, Configurational Forces: Thermodynamics, Physics, Mathematics, and Numerics (CRC, Boca Raton, 2010)
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)
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)
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)
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)
D. Kozic et al., Extracting flow curves from nano-sized metal layers in thin film systems. Scr. Mater. 130, 143–417 (2017)
G. Klemes, Thermal Conductivity: Metallic Elements and Alloys (Plenum, New York, 1970)
J. Hostetler et al., Thin-film thermal conductivity and thickness measurements using picosecond ultrasonics. Microsc. Thermophys. Eng. 1(3), 237–244 (1997)
L. Xiang, Thermal conductivity modeling of copper and tungsten damascene structures. J. Appl. Phys. 105(9), 094301 (2009)
T.L. Bergman et al., Fundamentals of Heat and Mass Transfer (Wiley, New York, 2011)
H.A. Schafft et al., Thermal conductivity measurements of thin-film silicon dioxide in microelectronic test structures, in Microelectronic Test Structures (ICMTS), IEEE, (1989)
X. Zhang et al., Thermal conductivity and diffusivity of free-standing silicon nitride thin films. Rev. Sci. Instrum. 66(2), 1115–1120 (1995)
Texas Instruments, Thermal conductivity and thermal diffusivity, Report (2014)
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)
S. Andersson, Thermal conductivity and heat capacity of amorphous SiO2: pressure and volume dependence. J. Phys. Condens. Matter 4(29), 6209 (1992)
A.S. Grove, Physics and Technology of Semiconductor Devices (Wiley, New York, 1967)
T. Ohmura et al., Specific heat measurement of high temperature thermal insulations by drop calorimeter method. Int. J. Thermophys. 24(2), 559–575 (2003)
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)
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)
J. Harrigill et al., Method for Measuring Static Young’s Modulus of Tungsten to 1900 K (1972)
J.W. Davis et al., ITER material properties handbook. J. Nucl. Mater. 233, 1593–1596 (1996)
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)
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)
S. Krimpalis et al., Comparative study of the mechanical properties of different tungsten materials for fusion applications. Phys. Scripta 2017(T170), 014068 (2017)
F.F. Schmidt et al., The Engineering Properties of Tungsten and Tungsten Alloys, No. DMIC191 (Battelle Memorial Institute, Defense Metals Information Center, Columbus, 1963)
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)
O. Morozov et al., Mechanical strength study of SiO2 isolation blocks merged in silicon substrate. J. Micromech. Microeng. 25(1), 015014 (2014)
W.N. Sharpe et al., Strain measurements of silicon dioxide microspecimens by digital imaging processing. Exp. Mech. 47(5), 649–658 (2007)
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)
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)
E. SĂ¡nchez-GonzĂ¡lez et al., Effect of temperature on the pre-creep mechanical properties of silicon nitride. J. Eur. Ceram. Soc. 29(12), 2635–2641 (2009)
aZo Materials, Sintered Silicon Nitride (Si3N4), [Online]. https://www.azom.com/properties.aspx?ArticleID=260
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)
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)
A. Khan et al., Young’s modulus of silicon nitride used in scanning force microscope cantilevers. J. Appl. Phys. 95(4), 1667–1672 (2004)
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)
Acknowledgements
Financial support by the Austrian Federal Government (in particular from Bundesministerium fĂ¼r Verkehr, Innovation und Technologie and Bundesministerium fĂ¼r Wissenschaft, Forschung und Wirtschaft) represented by Ă–sterreichische 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.
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Appendix: Thermo-Mechanical Properties of W, SiO2, and Si3N4
Appendix: Thermo-Mechanical Properties of W, SiO2, and Si3N4
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Coppeta, R. et al. (2020). Electro-Thermal-Mechanical Modeling of Gas Sensor Hotplates. In: van Driel, W., Pyper, O., Schumann, C. (eds) Sensor Systems Simulations. Springer, Cham. https://doi.org/10.1007/978-3-030-16577-2_2
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