An analytic model of thermal drift in piezoresistive microcantilever sensors

A closed-form semiempirical model has been developed to understand the physical origins of thermal drift in piezoresistive microcantilever sensors. The two-component model describes both the effects of temperature-related bending and heat dissipation on the piezoresistance. The temperature-related bending component is based on the Euler–Bernoulli theory of elastic deformation applied to a multilayer cantilever. The heat dissipation component is based on energy conservation per unit time for a piezoresistive cantilever in a Wheatstone bridge circuit, representing a balance between electrical power input and heat dissipation into the environment. Conduction and convection are found to be the primary mechanisms of heat transfer, and the dependence of these effects on the thermal conductivity, temperature, and flow rate of the gaseous environment is described. The thermal boundary layer value that defines the length scale of the heat dissipation phenomenon is treated as an empirical fitting parameter. Using t...

[1]  Songlin Feng,et al.  Detection of trace organophosphorus vapor with a self-assembled bilayer functionalized SiO2 microcantilever piezoresistive sensor. , 2006, Analytica chimica acta.

[2]  B. Yalçin,et al.  Flexible nanofiber-reinforced aerogel (xerogel) synthesis, manufacture, and characterization. , 2009, ACS applied materials & interfaces.

[3]  M. Maeda,et al.  Stress evaluation of radio-frequency-biased plasma-enhanced chemical vapor deposited silicon nitride films , 1998 .

[4]  Robert Gardon,et al.  The Emissivity of Transparent Materials , 1956 .

[5]  Anthony O'Neill,et al.  Three-dimensional finite-element investigation of current crowding and peak temperatures in VLSI multilevel interconnections , 1993 .

[6]  William Paul King,et al.  Thermal conduction between a heated microcantilever and a surrounding air environment , 2009 .

[7]  N F de Rooij,et al.  Advanced temperature compensation for piezoresistive sensors based on crystallographic orientation. , 2007, The Review of scientific instruments.

[8]  Xinxin Li,et al.  A single-sided micromachined piezoresistive SiO2 cantilever sensor for ultra-sensitive detection of gaseous chemicals , 2006 .

[9]  W. M. Haynes.  CRC Handbook of Chemistry and Physics , 1990 .

[10]  Wen-li Wu,et al.  Thermal Expansion of Supported Thin Polymer Films: A Direct Comparison of Free Surface vs Total Confinement , 2001 .

[11]  F. Barlage.  An Analysis of Current Crowding at 180° Bends in Film Resistors , 1973 .

[12]  P. Tsilingiris.  Thermophysical and transport properties of humid air at temperature range between 0 and 100 °C , 2008 .

[13]  Bryan D. Vogt,et al.  Elastic Moduli of Ultrathin Amorphous Polymer Films , 2006 .

[14]  M. Esashi,et al.  Ultrathin single-crystalline-silicon cantilever resonators: Fabrication technology and significant specimen size effect on Young’s modulus , 2003 .

[15]  Characterizations of Elastic Behaviors of Silicon Nitride Thin Films with Varying Thicknesses , 2007 .

[16]  R. Pease,et al.  Thermal conductivity measurements of thin-film resist , 2001 .

[17]  C. Sotiriou-Leventis,et al.  Nanoengineering Strong Silica Aerogels , 2002 .

[18]  R. A. McGill,et al.  A sensitive, handheld vapor sensor based on microcantilevers , 2004 .

[19]  M. Yovanovich,et al.  Laminar forced convection modeling of isothermal rectangular plates , 2001 .

[20]  L.A. Pinnaduwage,et al.  Moore's law in homeland defense: an integrated sensor platform based on silicon microcantilevers , 2005, IEEE Sensors Journal.

[21]  F. Völklein,et al.  Thermal conductivity and diffusivity of a thin film SiO2Si3N4 sandwich system , 1990 .

[22]  J. Goudriaan,et al.  Modelling diurnal patterns of air temperature, radiation wind speed and relative humidity by equations from daily characteristics , 1996 .

[23]  Yozo Kanda,et al.  Piezoresistance effect of silicon , 1991 .

[24]  Teodor Gotszalk,et al.  Chemical recognition based on micromachined silicon cantilever array , 2003 .

[25]  William Paul King,et al.  Microcantilever hotplates with temperature-compensated piezoresistive strain sensors , 2008 .

[26]  Daniel C. Harris,et al.  Durable 3-5 μm transmitting infrared window materials , 1998 .

[27]  Adam H Love,et al.  Chemical vapor discrimination using a compact and low-power array of piezoresistive microcantilevers. , 2008, The Analyst.

[28]  F. Hua,et al.  Electromigration in flip chip solder joints having a thick Cu column bump and a shallow solder interconnect , 2006 .

[29]  Y. Jaluria,et al.  An Introduction to Heat Transfer , 1950 .

[30]  T. Porter,et al.  A solid-state sensor platform for the detection of hydrogen cyanide gas , 2007 .

[31]  O. Hansen,et al.  Atomic force microscopy probe with piezoresistive read-out and a highly symmetrical Wheatstone bridge arrangement , 2000 .

[32]  Michael P. Eastman,et al.  Sensor based on piezoresistive microcantilever technology , 2001 .

[33]  A new method for measuring thermal conductivity of thin films , 1997 .

[34]  M. Sepaniak,et al.  Cantilever transducers as a platform for chemical and biological sensors , 2004 .

[35]  U. Deiters.  Calculation of densities from cubic equations of state , 2002 .

[36]  O. Hansen,et al.  Optimization of sensitivity and noise in piezoresistive cantilevers , 2002 .

[37]  W. G. Delinger,et al.  Gas sensing using embedded piezoresistive microcantilever sensors , 2004 .

[38]  Nicolae Lobontiu,et al.  Induced-strain multimorphs for microscale sensory actuation design , 2004 .

[39]  Songlin Feng,et al.  Dual-SAM functionalization on integrated cantilevers for specific trace-explosive sensing and non-specific adsorption suppression , 2007 .