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Materials Science

ELSEVIER Procedia Materials Science 5 (2014) 1308 - 1313

www.elsevier.com/locate/procedia

International Conference on Advances in Manufacturing and Materials Engineering,

AMME 2014

Piezoresistivity and its Applications in Nanomechanical Sensors

M.Z. Ansari3'*, B.S. Gangadharab

aPDPM-Indian Institute of Information Technology, Design and Manufacturing-Jabalpur, Khamaria, Jabalpur 482 005, MP, India bVergenta Systems India, Lab#120, Materials Research Center, Indian Institute of Science, Bangalore 560 012, Karnataka, India

CrossMar]

Abstract

Piezoresistivity is continuing to find novel applications in modern sensors technology. In this study, we discuss the applications and design requirements of a piezoresistive microcantilever for use in AFM and biosensor. The cantilevers are made of silicon with p-doped piezoresistor inside. Three cantilever designs for each application are analyzed using finite element analysis software. Tip force and bi-axial tensile force are used to simulate the AFM and biosensor behavior, respectively. Results showed that the design principles for AFM and biosensor are fundamentally different and that the sensitivity of AFM increases with cantilever length but that of biosensor is relatively unaffected. ©2014ElsevierLtd.Thisisanopenaccessarticleunder the CC BY-NC-ND license (http://creativecommons.Org/licenses/by-nc-nd/3.0/).

Selection and peer-review under responsibility of Organizing Committee of AMME 2014

Keywords: Piezoresistivity; microcantilever; atomic force microscopy; biosensor; surface stress; self-heating; finite element analysis.

1. Introduction

Piezoresistivity is a material property that changes the bulk electrical resistivity of a material when compressed. Most materials show some level of piezoresistivity, but it is much prominent in doped semiconductors. Though discovered more than a century ago, piezoresistivity continues to be an invaluable and efficient means in view of its many diverse sensing applications. Its first application as a mechanical strain sensor for structures has now evolved into numerous novel sensing applications like pressure sensor, flow sensor, force sensor, temperature sensor, chemical/biochemical sensor and biosensor. The developments in silicon microfabrication technologies for IC and VLSI chips associated with electronics industry have greatly helped the innovation and application of modern

* Corresponding author. Tel.: +91-761-2632273; fax: +91-761-2632524. E-mail address: zahid@iiitdmj.ac.in

2211-8128 © 2014 Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/).

Selection and peer-review under responsibility of Organizing Committee of AMME 2014 doi: 10.1016/j.mspro.2014.07.447

piezoresistive sensors. A detailed study on applications of piezoresistive sensors is available in Barlian et al. (2009). The present study discusses the design requirements of a piezoresistive cantilever used in two very important nanomechanical applications of piezoresistivity as a force sensor in AFM and surface-stress sensor for biosensor.

AFM is used to study the surface topology by means of detecting the atomic force between the AFM cantilever tip and the work by means of measuring the cantilever tip deflection. AFM force sensor with piezoresistive readout was first proposed by Tortonese et al. (1993). Later, it was improved upon by Chui et al. (1998) and Thaysen et al. (2000). Rasmussen et al. (2003), Mukhopadhyay et al. (2005) and Zhou et al. (2009) used piezoresistive microcantilever biosensor to study analyte-receptor type interactions. The variation in surface-stress distribution on the active cantilever surface because of the interaction produces normal stress in the cantilever. The deflection and normal stress is determined by measuring the voltage change across the terminals of the piezoresistor. Thus, the integrated readout ability of piezoresistive microcantilever sensors makes these devices compact, robust and low-power. Fig. 1 shows the schematic deign of a piezoresistive silicon microcantilever commonly used in AFM (tip not shown) and biosensor application. The piezoresistor layout in u-shape created by p-type doping is also indicated.

Fig. 1. Schematic of a piezoresistive microcantilever sensor with u-shape piezoresistor.

In this work, finite element analysis software AN SYS is used to find the design parameters of the piezoresistor for application in AFM and biosensor. A silicon microcantilever with p-doped piezoresistor is studied. Three cantilever models for each application were studied. The cantilever and piezoresistor lengths varied as 200 цm and 400 ^m. The results for maximum tip deflection and average longitudinal stress induced in the piezoresistor were obtained. Finally, the sensitivity result for each design was determined.

2. Theory and Finite Element Analysis

The normal stress in a piezoresistor is related to its resistance change as AR/R — o\, where it\ is the coefficient of piezoresistivity and o\ is normal stress induced in the piezoresistor because of deflection. Fig. 2(a) and (b) show the schematic principle of operation of AFM and biosensor. The piezoresistor is indicated as a black layer near to the top cantilever surface. In AFM, the atomic attraction force between the cantilever tip and the sample atoms produces a downward deflection; whereas, the change in surface-stress distribution results in a downward deflection in case of biosensor. Although the cantilever is deflected downward in both cases, the fundamental bending mechanics is different. AFM bends with non-uniform bending moment, but biosensor with uniform one (Fig. 2 (c)).

Fig. 2. Schematic of mechanical model of (a) AFM and (b) biosensor; and (c) their lengthwise bending moment distribution.

In AFM, the cantilever tip deflection (¿afm) is related to the atomic attraction force (F) as: AFl3

= ^ d)

where, E is elastic modulus, L is length, b is width and t is thickness of cantilever. Here, E = 210 GPa, v = 0.23, b = 100 prn and t =1 p,m. The relation between tip deflection (¿Bio.) and surface stress (y) for a biosensor can be given as (Stoney (1909)):

4(1 -v)bl2

where, v is Poisson's ratio. Comparing (1) and (2), we get the relationship between tip force and its equivalent surface-stress required for producing the same amount of tip deflection in the cantilever as:

w bt (1 ~V) rn F =---7 (3)

In the numerical analysis, a commercial FEA software ANSY was used to apply tip force (in AFM) and surface stress on the top surface (in biosensor) of the cantilevers and determine the tip deflection and normal stress inside their piezoresistor. Three models for each case were studied: I = /p= 200 prn in Model#l, I = 2/p = 400 prn in Model#2 and I = /p = 400 prn in Model#3. The piezoresistor width and thickness was 20 prn and 0.1 prn, respectively. A typical value of surface stress of about 0.052 N/m and its equivalent tip force of about 20 nN was used as load. In AFM, the tip force is applied downward to the free end of cantilever; whereas, in case of biosensor, the surface stress is applied as bi-directional tensile force acting on the top cantilever surface. The results for maximum tip deflections and average normal stress inside their piezoresistor are obtained.

3. Results and Discussion

Table 1 presents the tip deflection, average longitudinal stress and sensitivity results for different cantilever models when used in AFM and biosensor. The deflection results for Model#l are about same when used in AFM and biosensor because of eq. (3). Changing Model#l to Model#2 increased the deflection in AFM and biosensor, as suggested by eq. (1) and eq. (2). The deflection results for Model#2 and Model#3 are same because the two models are identical in mechanics view, i.e. same material and size. k\ = 72 x 10"11 m2/N for p-doped piezoresistor. The sensitivity results for AFM show a maximum when the piezoresistor size is half the cantilever size. This suggests the sensitivity of AFM can be improved by increasing the cantilever length and keeping the piezoresistor length about half the cantilever length. The sensitivity results for biosensor are unaffected by the cantilever model.

Table 1. Deflection, stress and sensitivity results for different cantilever models used in AFM and biosensor.

Application Model S (prn) oi (MPa) AR/R (%)

Model#l 0.029 0.063 0.005

AFM Model#2 0.315 0.241 0.017

Model#3 0.315 0.156 0.011

Model#l 0.028 0.153 0.011

Biosensor Model#2 0.128 0.164 0.012

Model#3 0.128 0.163 0.012

Fig. 3. Deflection distribution in different AFM (left column) and biosensor (right column) piezoresistive microcantilever designs (^m).

Fig. 3 presents the deflection distribution in different cantilevers designs when used in AFM and biosensor applications. The distribution is one-dimensional in AFM, but two-dimensional in biosensor. Thus, the fundamental deflection behaviour of AFM and biosensor are different. Fig. 4 shows the average longitudinal stress distribution inside the piezoresistor element of different cantilever models when used in AFM and biosensor. The models show similar behaviour for each application. But, the stress distribution in AFM and biosensor is different. In AFM, the stress values increase continuously from the cantilever tip to its fixed-end where a maximum occurs; whereas, in biosensor, the stress values show significant variation only towards the fixed-end and are almost constant for most portion of the cantilever. In other words, the stress distribution is highly non-uniform in AFM, but is relatively uniform in case of biosensor. In addition, the average stress values in AFM show significant variation with

cantilever models. However, the stress values for biosensor are almost constant for the three models. Thus, changing the cantilever model is helpful only to AFM and not to biosensor performance.

Fig. 4. Longitudinal stress distribution in piezoresistor of different AFM (left column) and biosensor (right column) piezoresistive

microcantilever designs (MPa).

Self-heating or Joule heating is a major source of noise in piezoresistive microcantilever sensors. The temperatures produced depend on many parameters including the piezoresistor size, its total resistance, the bias voltage, cantilever size and operating environment (Ansari and Cho (2010), (2011), (2012)). It has been shown that piezoresistive cantilevers with short and narrow piezoresistor are helpful in reducing the adverse effects of self-heating in piezoresistive microcantilever. In addition, the higher the cantilever-to-piezoresistor volume ratio the

lower the maximum temperature produced will be. In other words, a long cantilever with short piezoresistor is better design from self-heating criterion. Therefore, we can conclude that Model#2 is the best design for AFM because it not only increases the sensitivity by more than three times, but also has the highest cantilever-to-piezoresistor volume ratio. Similarly, Model#2 is also the best design for biosensor not because of its improved sensitivity but because of its highest cantilever-to-piezoresistor volume ratio.

4. Conclusions

This study investigated the design requirements of a piezoresistive microcantilever with a u-shaped piezoresistor to be used in AFM and biosensor applications using FEA. We proposed three cantilever models and compared their sensitivities when used in AFM and biosensor by applying atomic force and surface stress load, respectively. Results showed that the effect of tip force on deflection in AFM can be approximated by an equivalent surface stress in case of biosensor. We found that increase is cantilever length is beneficial to sensitivity of AFM, but not to biosensor. In addition, the piezoresistor length should be about half the cantilever length for optimum AFM performance. The biosensor sensitivity was relatively unaffected by change in cantilever or piezoresistor length. Finally, Model#2 was found to be the best design for both AFM and biosensor applications. Piezoresistive microcantilevers with short piezoresistor should be selected for reducing the adverse effects of self-heating on its performance.

Acknowledgements

This study was supported by PDPM-IIITDMJ. References

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