On the micromechanics of micro-cantilever sensors: Property analysis and eigenstrain modeling

Sensors and Actuators A 139 (2007) 70–77

On the micromechanics of micro-cantilever sensors: Property analysis and eigenstrain modeling Alexander M. Korsunsky a,∗ , Suman Cherian b , Roberto Raiteri b , R¨udiger Berger c a

Department of Engineering Science, University of Oxford, Parks Road, Oxford OX1 3PJ, United Kingdom b Department of Biophysical and Electronic Engineering, University of Genova, Via Opera Pia 11a, Genova 16145, Italy c Max Planck Institute for Polymer Research, Ackermannweg 10, Mainz 55128, Germany Received 16 August 2006; received in revised form 1 March 2007; accepted 2 March 2007 Available online 14 March 2007

Abstract Micro-cantilevers can be utilized as sensors primarily due to their low stiffness/high flexibility and high resonance frequency. The cantilever system is therefore very sensitive to small changes of properties that can be detected either as change of deflection, or of resonance frequency. The development of small forces in the near-surface layers results in significant property changes of micro-cantilevers allowing their use for the detection of very small effects, e.g. associated with the adsorption of biological or chemical substances on the cantilever surfaces. While many experiments providing proof of principle deformation have been reported in the literature, quantitative analysis of the cantilever transduction effect requires precise characterization of the device deflection in response to known forces, i.e. detector calibration. The present paper addresses two aspects of this issue: property evaluation of micro-cantilever components, particularly the coating layer, and the use of analytical and numerical models of cantilever deformation using the concept of eigenstrain, a term that is used in residual stress theory to describe inelastic deformation. The analytical model proposed here accounts for the presence of surface tension and thermal mismatch effects, and predicts the resulting cantilever curvature. The numerical model presented is developed within the framework of finite element analysis, and allows the prediction of effects of cantilever attachment to the chip on complete cantilever deflection. Comparisons of model predictions with the experimental data on cantilever deflection due to changes in temperature obtained using optical interferometry show good agreement. © 2007 Elsevier B.V. All rights reserved. Keywords: Micro-cantilever; Bio-sensor; Eigenstrain modeling; Finite element modeling; Residual stress

1. Introduction Micro-cantilevers have the potential to deliver highly sensitive, flexible and reliable sensor technology for physical, chemical, biological and mechanical systems [1,2]. The central principle of micro-cantilever sensing concerns the ability of the sensor to respond to perturbations. These may be externally applied loads or pressures, temperature changes, or adsorption of biological or chemical species. They result in the development of additional surface tension and/or an increase in the cantilever mass. The consequence is either to a change in cantilever

∗

Corresponding author. Tel.: +44 1865 273043; fax: +44 1865 273010. E-mail address: [email protected] (A.M. Korsunsky).

0924-4247/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.sna.2007.03.007

deflection (static mode), or a shift in its resonance frequency (dynamic mode), or both [2,3]. In order to provide sufficient sensitivity for bio-sensing in the static mode, cantilevers of small thickness (≤l ␮m) are made on the basis of silicon chips using micro-fabrication techniques. Micro-cantilever sensors are usually produced in the form of arrays, as illustrated in Fig. 1, allowing simultaneous multiple sensing through the use of differently functionalized surfaces of individual cantilevers. The detection of cantilever deflection is tantamount to the measurement of surface tension change induced by adsorption or film expansion, provided (a) the cantilever stiffness (or flexibility) is known, (b) the cantilever stiffness remains unchanged in time and is the same for each individual cantilever, and (c) the initial, reference deflected shape of the cantilever is known. In practice these requirements are not easy to fulfill, since the

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2. Experimental 2.1. Thermally induced deflection

Fig. 1. SEM image of an array of micro-cantilever sensors on a silicon chip.

cantilevers are designed and produced to have exceedingly low stiffness, so that they readily deflect in response to any variation in the fabrication process. Many publications devoted to micro-cantilever sensors found in the literature are devoted to ‘demonstration of principle’ type of experiments that show the ability of these systems to detect very small effects of surface modification due to chemi-sorption and adsorption [4–7]. However, in order for these sensor systems to become widely accepted as practical research tools and industrial instruments, precise quantitative calibration of their performance is crucial, including validation of reliability and repeatability. Eigenstrain modeling is an advanced technique for the analysis of residual stresses induced by inelastic deformations and is based on the assumption that self-equilibrated internal stresses arise are in response to the inhomogeneity of deformation (misfit) introduced into the object by thermal, mismatch, growth strains [8], phase transformation strains, or plastic deformation [9,10]. According to continuum solid mechanics, total strains within the object must obey equations of compatibility, which results in the development of accommodating elastic strains and residual stresses. Change of temperature also produces misfitting inelastic strains, but only if either the temperature field is non-uniform, or the thermal expansion coefficient varies across the body. This analogy between inhomogeneous thermal expansion and generic misfit eigenstrain provides the basis for model development, including eigenstrain finite element simulations. In this paper, we focus on the calibration of cantilever stiffness using a set of experimental measurements of deflected shapes of bimaterial gold-coated cantilevers [11] over a range of temperatures spanning 30 ◦ C. The curvature variation with temperature is found to be linear, and the curvature-temperature coefficient for the micro-cantilever system is evaluated. Understanding cantilever response requires the knowledge of mechanical properties of cantilever constituent materials. The results of nanoindentation experiments for the determination of the properties (stiffness, hardness) of the gold layer are briefly presented. Hardness interpretation of thin coatings presents a particular challenge, and is discussed here on the basis of the work-ofindentation approach [12,13]. Thermally induced cantilever curvature change is predicted using two separate modeling approaches, one relying on an analytical description of the system response to thermal misfit strain, and another using finite element simulation. The agreement between the models and experiments is discussed in the light of quantitative interpretation of micro-cantilever signals.

Micro-cantilevers investigated in this study consisted of single crystal silicon substrates thinned down to about l ␮m thickness with a 5 nm TiW interlayer sputter coated with about 30 nm of gold (Protiveris Inc., Rockville, MD, USA). Dimensions and mechanical properties of layers are specified in Table 1. Experimental measurements of micro-cantilever profiles were carried out using phase-shifting optical interferometry. This technique allows accurate estimation of vertical displacement of cantilever surface in the range of several nanometers to microns [14]. Fig. 2 shows the micro-cantilever deflected profiles obtained at three different temperatures (10, 25 and 40 ◦ C). Data from the region lying close to the point of attachment of the microcantilever to the silicon chip were excluded from further consideration, since the deflected profile in this region is sensitive to the detailed geometry of the object produced by etching that is difficult to control and to quantify precisely. Cantilever deflection on the remaining ‘free’ extent of the cantilever is approximated by a parabolic fit of the form. m2 x2 (1) + m1 x + m 3 , 2 where y denotes the cantilever deflection, x denotes position along the cantilever, and fit parameters ml , m3 and m2 denote cantilever slope, reference deflection and curvature, respectively. It will become apparent from the discussion of cantilever modeling that the curvature parameter m2 , y=

d2 y , (2) dx2 plays a particularly important role in the analysis of residual and ‘live’ stresses in cantilevers, since it provides a key measure of surface effects. Parameters m1 , m3 are less convenient, since their values are sensitive to the choice of reference, initial alignment, etc. Parameter m2 is measured in units of inverse length, e.g. m−1 . m2 =

Table 1 Dimensional and mechanical properties of constituent materials of microcantilevers Parameter

Value

Width, b (␮m) Length, l (␮m) Thickness, d (␮m) Poisson’s ratio Young’s modulus, E (GPa) Coefficient of thermal expansion (CTE) (K−1 ) Interlayer thickness, t (␮m) Interlayer Poisson’s ratio Interlayer modulus, E (GPa) Interlayer CTE (K−1 ) Gold layer thickness, t (␮m) Gold layer Poisson’s ratio Gold layer modulus, E (GPa) Gold layer CTE (K−1 )

150 500 1 0.28 112.4 2.5 × 10−6 0.005 0.3 160 3.5 × 10−6 0.03 0.42 77.2 14.4 × 10−6

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Fig. 2. Micro-cantilever profiles at different temperatures determined using optical profilometry, shown together with parabolic fits to the profiles for the purpose of curvature determination.

Significant changes in curvature are apparent, with the cantilever profile changing from concave at 10 ◦ C to convex at 40 ◦ C. The profiles shown in Fig. 2 are representative of the data collected from many measurements. It was found that in all cases the deflected shape was well described by the parabolic fit in Eq. (1). Cantilever curvature variation with the test temperature was found to be linear, with the curvature-temperature coefficient (curvature change per degree) of 2.16 m−1 K−1 (Fig. 3). Interestingly, a linear dependence on temperature was also found in our experiments for cantilever deflection y(x0 ) and cantilever slope y’(x0 ) at a particular point x0 along its length.

Fig. 3. Illustration of the linear nature of temperature-induced changes in cantilever curvature.

However, the values of these parameters depend on the choice of reference position on the chip, and of the position where measurements are made. The values are also affected by horizontal and vertical variation in chip position, and so repeatable interpretation is practically difficult, or impossible to achieve, particularly in cases when cantilevers need to be removed and re-installed within the measurement device in the course of an experiment. In contrast, the curvature parameter m2 is insensitive to these effects. In order to investigate the reversibility of thermally induced curvature changes, thermal cycling experiments were undertaken in the range of 17–41 ◦ C. It was found that, within the bounds of experimental errors, deflected cantilever profile at a given temperature was preserved under these conditions. This suggests that the deformation process was linearly thermoelastic, i.e. no inelastic permanent deformation took place, since stress and temperature were insufficient to cause any plastic deformation or creep. It follows from the above discussion that during thermal cycling, the yield conditions were not exceeded. Estimating the conditions when plastic flow might occur within the thin coating layer requires the knowledge of coating yield stress (hardness). Furthermore, plastic flow may also be affected by the presence of residual stress in the coating. Experimental arrangements allowing the investigation of these parameters are discussed below. 2.2. Nanoindentation While the mechanical properties of silicon are well known and stable, hardness and stiffness of the thin (30 nm) sputtered gold layers may vary significantly, since they depend strongly on the deposition conditions and the resulting microstructure, most notably the grain size. In practice these properties need to be determined in situ. An experimental technique offering appropriate displacement resolution is nanoindentation, a method involving continuous recording of load and displacement while a threesided diamond pyramidal Berkovich indenter is driven into the surface of the specimen. One of the serious obstacles in the application of this technique to hardness analysis of ultra-thin coatings lies in the fact that for indentation depths exceeding about l/10th of the coating thickness the system response represents a convolution of substrate and coating properties. If, on the other hand, the indentation depth is kept to only a few nanometers, then the results are prone to systematic errors arising from indentation size effects that arise from such phenomena as tip rounding and strain gradient hardening effects. A significant amount of effort has therefore been expended by various researchers on the development of suitable testing methods using which the coating-only properties can be backed out [11]. This usually requires the analysis of nanoindentation experiments performed to different depths. An attractive approach to the problem has been developed using a generalized definition of hardness based on the work-of-indentation concept [12]. Fig. 4 illustrates the load-displacement curve obtained during 32 nm deep nanoindentation of the 30 nm gold layer on a 5 nm

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2.3. Residual stress measurement in micro-components

Fig. 4. Nanoindentation load-displacement trace obtained from 32 nm deep indentation in the gold coating layer on silicon substrate.

TiW interlayer and massive Si substrate. Note that the maximum indentation depth is close to the total (Au + TiW) layer thickness of 35 nm. This depth is significantly larger than the rule-of-thumb 1/10th of the layer thickness indentation depth that would elicit coating-only response [12]. In this case that depth amounts to only 3–4 nm, leading to practical difficulty, since presently no indenter tip can be manufactured to be sharp on that length scale, i.e. with the tip radius of the order of 1 nm. Consequently, sophisticated interpretation procedures must be developed in order to extract such coating-only properties as hardness and modulus from indentation data. This is a topic of great current interest in the contact mechanics of coated systems, and is likely to provide improved insight into mechanical behaviour of thin films in the future. The work-of-indentation approach is one of the very few techniques that allow an estimation of composite (layer + substrate) hardness, using the following formula [12]. H=

2 κPm , 9W 3

(3)

where κ = 0.0408 for the Berkovich pyramidal indenter, Pm is the maximum load, and W denotes the work-of-indentation. This latter parameter may be defined as total work (area under the upper, loading curve in Fig. 4), or dissipated energy (area between the loading and unloading curves in Fig. 4). The application of Eq. (3) to data shown in Fig. 4 results in the hardness value of approximately 6.25 GPa. This value is significantly lower than the hardness in excess of 12 GPa reported for Si indented along the (1 1 1) plane normal [15]. On the other hand, even if extreme grain size hardening arising from the nano-structured nature of the gold layer is taken into account, this value is still much greater than gold layer hardness of about 1 GPa estimated on the basis of uniaxial tensile experiments on sub-micron thick Au films [16]. Given current state-of-the-art of nanoindentation interpretation, one must conclude that a composite value of hardness is obtained, and further measurements at lower indentation depths are required, in combination with detailed modeling of deformation, in order to back out inherent gold layer properties.

Residual stress measurement in micro- and nano-scale components presents a significant challenge to traditional methods applied at the macroscopic scale, such as X-ray diffraction, hole drilling and layer removal. Laboratory X-ray diffraction relies on accurate measurement of Bragg scattering angles of relatively low energy (a few keV) photons in reflection mode. A collimated beam of nearmonochromatic X-rays impinges on the sample surface within an area occupying fractions of mm2 . The penetration depth of the X-rays into the sample amounts to a few microns, and thus offers an excellent method of near-surface stress evaluation in macroscopic engineering components. However, this technique is clearly not suitable for extremely thin layers, such as the 30 nm thick layer of gold on silicon, since most of the X-ray flux penetrates the layer without scattering, producing very weak signal. The situation can be improved through the use of grazing incident or scattering angles of a few degrees, although this means that conventional sin2 ψ analysis technique has to be modified to extract stress values. Material removal and relaxation techniques, such as hole drilling and layer removal, rely on the modification of sample geometry by some minimally disturbing technique, such as chemical etching or electro-discharge machining. This results in a change of residual stress and residual strain distributions within the body. The latter is detected using sensors, such as strain gauges, or optical and interferometric methods. For example, the conventional blind hole drilling technique involves drill bits having diameters of about 1 mm, and a strain gauge rosette providing simultaneous measurement of changes in three strain components. The application of material removal and relaxation techniques to the analysis of micro- and nano-scale components requires the introduction of several modifications in terms of scale and measurement techniques. The use of focused ion beam is a particularly attractive experimental technique, since it combines the capabilities for material removal in the nanometer range, and surface imaging at sub-nanometer resolution. The latter imaging ability, in combination with the application of suitable markers (or the use of natural surface roughness as reference) allows strain measurement to be carried out. Fig. 5 shows a focused ion beam images of milled patterns in the 30 nm gold layer on Si substrate. The pattern shown in Fig. 5(a) follows the traditional pattern used in hole drilling application, with the central circular hole used for creating strain pattern change, and arrays of markers for strain evaluation. However, it appears that more successful interpretation can be achieved using the pattern illustrated in Fig. 5(b) in the form of a thin (about 200 nm wide) single slot milled in the coating layer causing strain change in the surrounding material that is similar to the effect relaxation around a crack. In this case the strain change pattern must be computed using digital image correlation (DIC) techniques [17] that rely on detecting small (sub-pixel) displacements of light and dark (‘speckle’) patterns generated by the natural roughness of the coating surface.

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Fig. 6. Residual stress distribution within the multilayer cantilever calculated using the eigenstrain model.

Fig. 5. Illustration of focused ion beam (FIB) milling and imaging of the 30 nm gold layer on Si substrate, (a) in a pattern imitating hole drilling arrangement, and (b) slotting. FIB milling and imaging were carried out for the purpose of residual stress estimation using material removal and digital image correlation (DIC) strain change measurement.

The application of grazing incident angle laboratory X-ray diffraction and FIB slot milling/imaging and digital image correlation analysis suggested that in the system studied in this paper residual stress levels in the gold layer at room temperature did not exceed 20 MPa. Indeed, consideration of Fig. 3 reveals that cantilever curvature becomes zero at temperatures between 22 and 23 ◦ C. This finding is in agreement with the result of eigenstrain analysis presented in the next section. 3. Modeling 3.1. Analytical eigenstrain modeling The eigenstrain modeling approach has been developed as a flexible and versatile technique of residual stress analysis in engineering components [9,10]. The approach has been applied primarily to study the effects of prior inelastic deformation by plasticity and creep mechanisms that take place during material processing (rolling, forging, forming, etc.).

In the present study, eigenstrain modeling has been used in order to analyse the deformation of micro-cantilever sensors due to temperature change, or, equivalently, due to the adsorption of layers inducing surface tension and attendant deflection. The principal equations of eigenstrain modeling of cantilever beam bending due to eigenstrains or thermal mismatch strains are given in the Appendix A. Formulae (12) and (13) provide explicit expressions for beam curvature as a function of system parameters and eigenstrain. In the present case eigenstrain is thought to be associated with thermal expansion coefficient mismatch between the coating(s) and the silicon substrate. If the temperature change of 1◦ is specified, the resulting value of b = m2 has the meaning of the cantilever curvature-temperature coefficient. Fig. 6 illustrates the predicted stress distribution across the thickness of the cantilever due to 1◦ temperature change, calculated using the analytical expressions derived using the eigenstrain approach. Note that the TiW interlayer appears virtually unstressed, explaining why it may have been chosen to improve the adhesion of gold layer to the silicon substrate. 3.2. Finite element eigenstrain modeling Eigenstrain-based finite element modeling of cantilever deformation due to temperature change was carried out both in 2D and 3D formulation for the purposes of comparison (Fig. 7). While 3D formulations are potentially more accurate, they also require greater computational effort, so the use of 2D approximations is preferable, provided it can be shown that sufficient accuracy can be achieved. It was found in the present study that for the simple geometry of cantilever beams, the difference between the results of a 2D plane strain approximation and a fully three-dimensional simulation was negligible. The variation of initial slope of cantilever (at its attachment to the chip) with temperature requires further investigation. The precise geometry of the device obtained during etching, particularly near the point of attachment of the cantilever to the chip, is difficult to image or measure, but would exert

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Fig. 7. Illustrative output from an ABAQUS finite element model.

considerable influence over the effective initial slope of the cantilever. The effective initial slope would also change with temperature due to the presence of the dissimilar gold layer. Accurate modeling of this effect using eigenstrain-based finite element modeling was found to be viable, but accurate quantitative prediction of this effect would require unrealistically detailed knowledge of the underside shape of each individual cantilever. Cantilever curvature, on the other hand, displays reliable linear correlation with test temperature. The two modeling approaches used in this study were based on the use of eigenstrain to represent misfit between components. Both analytical and finite element eigenstrain approaches led to the same predicted value of the curvature-temperature coefficient of the cantilever (curvature change per degree) of 2.25 m−1 K−1 . This value is within about 4% of the experimental result of 2.16 m−1 K−1 . This difference in cantilever flexibility between model and experiment can be caused by the silicon cantilever thickness differing from the nominal value of 1 ␮m by a small fraction of only about 14 nm. 4. Results and discussion Both eigenstrain-based modeling approaches used in the study led to the predicted value of the curvature-temperature coefficient of the cantilever (curvature change per degree) of 2.25 m−1 K−1 . This value is within about 4% of the experimental result of 2.16 m−1 K−1 . This variation in cantilever flexibility can be caused by the variation of gold layer parameters (Young’s modulus, or thickness) of 4%, or by the variation of the silicon substrate thickness of only 1.4%, i.e. about 14 nm. This degree of control over the cantilever geometry is difficult to achieve during micro-fabrication. Additionally, mechanical properties of the gold layer may vary significantly with deposition conditions. It appears, therefore, that calibration of individual cantilever flexibility prior to their utilization may be a necessary prerequisite for the use of this method for quantitative analysis of surface tension/film expansion. Thermally induced deflection of the cantilevers with optical phase-shifting interferometry

readout clearly offers a viable option for precise and reliable measurement of cantilever curvature. Eigenstrain-based modeling of cantilever deformation offers an efficient numerical technique for the calibration of flexibility, since it can be readily implemented in the form of a simple spreadsheet, or incorporated into cantilever readout software package in the form of calibration algorithm. Eigenstrain-based FEA approach offers a flexible framework likely to be useful for analysis of residual stress effects, e.g. in combination with focused ion beam milling. The analysis of temperature-induced cantilever deflection provides a convenient method of flexibility calibration. Surface tension and film expansion effects can be studied quantitatively, once a numerical model of cantilever(s) has been calibrated on this basis. Acknowledgements Discussions with Robert Cain (Protiveris Inc., Rockville, MD, USA) and the provision of micro-cantilever arrays are gratefully acknowledged. The contributions of Jonathan Belnoue and Sebastien Jegou (ENSICAEN, Caen, France) are acknowledged to eigenstrain FE analysis of micro-cantilevers, and FIB milling and digital image correlation, respectively. The support of Dr. Yizhong Huang (Oxford Materials) has been invaluable for focused ion beam work. Appendix A Within the framework of beam bending theory the total strain, ε, is given by the sum of the elastic, e, and inelastic, ε* , components, ε = e + ε∗ .

(4)

Furthermore, the Kirchhof hypothesis of straight normals then requires that the total strain varies linearly across the crosssection of the coated cantilever, i.e. ε = a + by.

(5)

Note that the coefficient a refers to the component of strain that is uniform across the section and corresponds to the tensile

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or compressive deformation of the cantilever. The coefficient b describes the slope of the strain-position relationship, and is related to the radius of curvature of the cantilever, R, by the simple expression b=

1 = y = m2 . R

(6)

Assuming R to correspond to the radius of curvature of the neutral axis, the total strain difference between a layer spanning an angle θ at radius R + y, and a layer lying at the neutral axis at R is given by (R + y)θ − Rθ y = , Rθ R

ε − εc =

(7)

and alternatively, in accordance with Eq. (5), ε − εc = a + by − a = by.

(8)

Elastic part alone of total strain gives rise to stress in layer i, σi = Ei ei = Ei (ε − ε∗i ) = Ei (a + by − ε∗i ),

(9)

Ei

denotes the proportionality coefficient between where longitudinal components of strain and stress in the cantilever. Simple analysis shows that in the case considered the appropriate choice of this parameter is the plane strain modulus given by Ei = Ei /(1 − νi2 ), where νi2 is Poisson’s ratio. Schematic at the bottom of Fig. 6 illustrates the structure of the cantilever considered here, with material 1 (silicon substrate) occupying the region between y0 and yl , material 2 (TiW interlayer) occupying the region between yl and y2 , and material 3 (Au top layer) occupying the region between y2 and y3 . The above equations provide the basis for developing a thermo-mechanical deformation model and the determination of parameters a and b, and hence the prediction of cantilever curvature and its change with temperature. The eigenstrain model is constructed as follows. The conditions of equilibrium for the coated cantilever system are expressed in terms of the resultant force and moment per unit width of the cantilever,  y3 F = σ(y) dy y0

 =

y1

y0



+  M=

y3

y2 y3

y0

 =

y1

y0



+





E1 (a + by) dy +

y2

y1



E2 (a + by − ε∗2 ) dy



E3 (a + by − ε∗3 ) dy = 0.

(10)

σ(y) ydy E1 (a + by) ydy + y3

y2



y2

y1

E2 (a + by − ε∗2 ) ydy

E3 (a + by − ε∗3 ) ydy = 0.

(11)

Of particular interest is the solution for parameter b (and hence the radius of curvature, R) in the form b=

2BN , where BD

BN = [E1 (y1 − y0 ) + E2 (y2 − y1 ) + E3 (y3 − y2 )] × [E2 ε∗2 (y22 − y12 ) + E3 ε∗3 (y32 − y22 )] − [E1 (y12 − y02 ) + E2 (y22 − y12 ) + E3 (y32 − y22 )] × [E2 ε∗2 (y2 − y1 ) + E3 ε∗3 (y3 − y2 )]

(12)

BD = [E1 (y12 − y02 ) + E2 (y22 − y12 )   4 2 [E1 (y1 − y0 ) + E3 (y32 − y22 ) ] − 3 + E2 (y2 − y1 ) + E3 (y3 − y2 )] × [E1 (y13 − y03 ) + E2 (y23 − y13 ) + E3 (y33 − y23 )]

(13)

and the eigenstrain due to temperature change was assumed to be equal to ε∗2 = (α2 − α1 ) T,

ε∗3 = (α3 − α1 ) T

(14)

in materials 2 and 3, respectively. Solution for parameter a can be written out similarly. From the dependence of b on eigenstrains ε∗2 and ε∗3 , and Eq. (12) it is apparent that curvature b scales linearly with the temperature change T. References [1] R. Raiteri, H.-J. Butt, D. Beyer, S. Jonas, Phys. Chem.-Chem. Phys. 1 (1999) 4881. [2] R. Berger, Ch. Gerber, H.P. Lang, J.K. Gimzewski, Microelectron. Eng. 35 (1997) 373. [3] R. Raiteri, M. Grattarola, H.-J. Butt, P. Skladal, Sens. Actuators B-Chem. 79 (2001) 115. [4] M. Yue, H. Lin, D.E. Dedrick, S. Satyanarayana, A. Majumdar, A.S. Bedekar, J.W. Jenkins, S. Sundaram, J. Microelectromech. Syst. 13 (2004) 290. [5] L. Fadel, F. Lochon, I. Dufour, O. Franc¸ais, J. Micromech. Microeng. 14 (2004) S23–S30. [6] K.M. Hansen, T. Thundat, Methods 37 (2005) 57–64. [7] P. Fortina, L.J. Kricka, S. Surrey, P. Grodzinski, Trends Biotechnol. 23 (2005) 168–173. [8] Y. Wang, R. Ballarini, H. Kahn, A.H. Heuer, J. MEMS 14 (2005) 160– 166. [9] A.M. Korsunsky, J. Strain Anal. 40 (2005) 817. [10] A.M. Korsunsky, J. Strain Anal. 41 (2006) 113. [11] R. Berger, Ch. Gerber, J.K. Gimzewski, E. Meyer, H.-J. G¨untherodt, Appl. Phys. Lett. 69 (1996) 40–42. [12] A.M. Korsunsky, M.R. McGurk, S.J. Bull, T.F. Page, Surf. Coat. Technol. 99 (1998) 171–183. [13] J.R. Tuck, A.M. Korsunsky, S.J. Bull, R.I. Davidson, Surf. Coat. Technol. 137 (2001) 217. [14] M. Helm, J.J. Servant, F. Saurenbach, R. Berger, Appl. Phys. Lett. 87 (2005) 64101. [15] S.E. Grillo, M. Ducarroir, M. Nadal, E. Tournie, J.-P. Faurie, J. Phys. D: Appl. Phys. 36 (2003) L5–L9.

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Biographies Alexander M. Korsunsky is Professor of Engineering Science and Dean at Trinity College, University of Oxford. He received BSc and MSc in Theoretical Physics (Landau-Lifschitz course) from Moscow Institute of Physics and Technology, and DPhil from Merton College, Oxford. He pursues research into mechanical properties and deformation behaviour of engineering components and structures across the range of scales, from large assemblies, such as aeroengines (much of it in collaboration with Rolls-Royce plc) to micro- and nano-mechanical objects, such as electronics devices and thin layers and coatings. His work on eigenstrain aims to provide a uniform basis for the analysis and modeling of residual stress states. Suman Cherian received her PhD in Chemistry in 1998 from Portland State University, USA. From 1998–1999, she worked as a Post Doctoral Research Scientist at Arizona State University where she worked on photon-induced chemical switching in spiropyrans for the control of surface charges. In 2000, she joined the Life Science division of Oak Ridge National Laboratory, TN, as Post Doctoral Research Scientist where she started her research work on micro-cantilever sensors. Since 2004, she has been working as a Researcher at the University of Genova, Italy, on studies on micro-cantilever array sensors for various appli-

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cations. Her research interests include development of micro-cantilever sensors for monitoring biomolecular interactions and photon controlled processes for different applications. Roberto Raiteri is Assistant Professor of Bioengineering at the Department of Biophysical and Electronic Engineering, University of Genova, Italy. He received his BSc and MSc (“Laurea” degree) in Electronic Engineering from University of Genova in 1993 and the DPhil in Electronic Engineering from University of Trento, Italy, in 1997. His current research interests include the development of Scanning Probe Microscopy-based methods to characterize biomolecules, living cells and biological tissues at the nanometer scale, and the development of micro/nano mechanical bio-sensors. ¨ Rudiger Berger studied Physics at the Friedrich-Alexander University of Erlangen-N¨urnberg. He got his diploma in Physics in 1994 in the field of high Tc-superconductors where he worked on imaging and manipulation methods using Scanning Probe Microscopy. Then he moved to Switzerland where he made his PhD thesis and a PostDoc in the field of micromechanical sensors at the IBM Zurich Research Laboratory. In 1998, he joined the Analysis Laboratory at the IBM Deutschland Speichersysteme GmbH (Mainz). Here, he worked on the automation of test systems, in situ flight height control and the investigation of ion beam structuring of magnetic materials. Since October 2002, R¨udiger Berger is working at the MPI for Polymer Research where he is investigating micromechanical sensor techniques to explore nano-mechanical properties of polymer materials.