Scholarly article on topic 'A novel inductive technique for microcantilever displacement detection'

A novel inductive technique for microcantilever displacement detection Academic research paper on "Materials engineering"

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{inductance / "magnetic field" / "coupling coefficient"}

Abstract of research paper on Materials engineering, author of scientific article — Madhu Santosh K. Mutyala, Hai-Feng Ji, Ji Fang, Kody Varahramyan

Abstract A novel inductive technique for the detection of microcantilever displacement for sensing applications was presented. We highlight the basic structure and evaluate its characteristics with the aid of modeling and simulation. Results generated by numerical simulations using ANSOFT are compared with those obtained from an equivalent circuit model using PSPICE. There are indications that the sensitivity of the inductive cantilever is about one order of magnitude higher as compared to piezoresistive silicon cantilevers of the same dimension under the same cantilever bending.

Academic research paper on topic "A novel inductive technique for microcantilever displacement detection"

THEORETICAL & APPLIED MECHANICS LETTERS 1, 031006 (2011)

A novel inductive technique for microcantilever displacement detection

Madhu Santosh K Mutyala,1 Hai-Feng Ji,2, a) JiFang,1 and Kody Varahramyan3

^ Institute for Micro-manufacturing, Louisiana Tech University, Ruston, LA 71272, USA ^Department of Chemistry, Drexel University, Philadelphia, PA 19104, USA 3)Indiana University - Purdue University Indianapolis, Indianapolis, IN 46202, USA

(Received 10 December 2010; accepted 26 March 2011; published online 10 May 2011)

Abstract A novel inductive technique for the detection of microcantilever displacement for sensing applications was presented. We highlight the basic structure and evaluate its characteristics with the aid of modeling and simulation. Results generated by numerical simulations using ANSOFT are compared with those obtained from an equivalent circuit model using PSPICE. There are indications that the sensitivity of the inductive cantilever is about one order of magnitude higher as compared to piezoresistive silicon cantilevers of the same dimension under the same cantilever bending. © 2011 The Chinese Society of Theoretical and Applied Mechanics. [doi:10.1063/2.1103106]

Keywords inductance, magnetic field, coupling coefficient

Microcantilevers have come a long way in the field of sensors. These advancements in microcantilevers have opened the doors for ultrasensitive sensors. Several methods, like optical,1 capacitive,2'3 piezoresistive,4'5 and piezoelectric,6 have been used for the detection of cantilever bending motion. Compared with others, optical method is considered to be sensitive and accurate, but expensive and bulky. Other methods like capacitive, piezoelectric and piezoresistive are less complex, but have relatively lower sensitivity. A new detection method of the cantilever motion based on inductive effect is proposed here.

In general, two sides of a microcantilever are covered by different materials and either side of the micro-cantilever can be modified with molecular recognition agents to make it chemically specific. The unique characteristic of microcantilevers is that the device can be made to undergo bending due to molecular adsorption by confining the adsorption to one side of the cantilever. By monitoring changes in the bending response of a cantilever, changes in surface stress induced by adsorption or molecular recognition can be precisely and accurately recorded.

In our design, the microcantilever beam is surrounded by a fixed collar (unmovable) as shown in Fig. 1. The metal line on the fixed collar forms the primary coil and the metal line on the cantilever beam forms the secondary coil. The primary and secondary coils are separated by an air gap of 5 ^m. Although larger coupling effect between the primary and secondary metal lines is expected when the gap is smaller, the gap distance is limited by the resolution of the traditional UV lithography technology. A 5 ^m gap is selected in the experiments because it can be readily achieved in a standard microfabrication facility. When a sinusoidal voltage is applied on the primary coil, a magnetic field created around it will induce a voltage on the secondary coil through the inductive effect. When

a)Corresponding author. Email: hj56@drexel.edu.

the cantilever bends due to the change in surface stress caused by the adsorption of analyte on the cantilever, the coupling coefficient between the two coils decreases. The difference in the induced voltage before and after bending can be used to measure the concentration of the analyte.

Firstly we have used ANSOFT for the simulation of the inductive cantilevers. In this simulation, the air gap between the primary and secondary coils was varied, representing the cantilever bending due to analyte deposition on the coated cantilever surface. As the air gap increased, the voltage induced on the secondary coil decreased. Three designs were simulated at an input voltage of 2 V with an original air gap of 5 ^m representing a gap before cantilever bending and 5.1 ^m representing a gap after bending, as shown in Fig. 2. The 100 nm distance change between the two metal lines is a result of bending of the microcantilever.

In Fig. 2, Port1-Port2 forms the primary metal line and Port3-Port4 forms the secondary metal line. Gold line was assumed for the simulations. The space between the two metal lines represented the air gap. Designs (a)-(c) consisted of metal lines with different shapes. In all the designs the cantilever width was 50 ^m and the length was 250 ^m. For the metal line (a, b, c), the thickness and the width of lines are 0.1 ^m and 1 ^m, respectively. The distance between the edges of coils is 5 ^m. Since voltage supply cannot be applied to the physical structure directly for simulation, the physical design layout was converted to a circuit design layout as shown in Fig. 3. All the designs were simulated under the same conditions of frequency (01 GHz) and voltage (2 V).

The simulation results (Fig. 4) indicated that design (c) had the highest induced voltage difference (AV) and sensitivity (AV/V) to the cantilever bending. The lower induced voltage for design (a) and (b) is due to the offset of the magnetic field that does not exist in design (c) as shown in Fig. 5. The magnetic field offset causes negative inductance effect, and thus lesser voltage is induced on the secondary line.

Primary

Porti Port!

3~ " " " " -

(a) Before bending (b) After bending

Fig. 1. Scheme of an inductive cantilever (a) before and (b) after bending.

Portit/t/tW

poidr^ö^zrzr^T^ (b)

Portl Port3~~

Port4_ Port2

Output voltage

Fig. 2. Various inductive cantilever metal line designs. Fig. 3. Circuit design layout for the ANSOFT simulation.

0.16-1 0.14-

0.12 0.10 0.08 0.06 0.04 0.02 0.00

0.0 0.2 0.4 0.6 0.8 1.0 1.2 Frequency / GHz

0.014 0.012 0.010

^ 0.008 <1

0.006 0.004 0.002

^ ^ ▼ ▼——t—▼—

-•- Design (a) a Design(b) -T- Design(c)

o........0........o........0.......0.......0.......0.......o

o'.o 0.2 0.4 0.6 0.8 1.0 1.2

Frequency / GHz (b)

Fig. 4. The voltage difference (Ay, in the unit of mV) and sensitivity (AV/V) of designs (a, b, c) vs. frequency. AV is the difference between the induced voltage before and after cantilever bending. V is the initial voltage that is induced before bending.

Fig. 5. Magnetic field offset observed in designs (a) and (b) causes negative inductance effect.

0.06 0.05 0.04

0.0 0.1 0.2 0.3 0.4 0.5 0.6 Deflection / |im

0.0 0.1 0.2 0.3 0.4 0.5 0.6 Deflection / |im

Fig. 6. AV/V (a) and inductance change (b) as a function of cantilever deflection.

2 3 4 Width /|im

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Thickness / |im

Fig. 7. AV and AV/V of the cantilever with respect to (a) width and (b) thickness of the metal lines.

Figure 6 (a) shows that although the inductance decreased as the deflection of cantilevers increased due to larger distance between the two wires, the AV/V change increased as the deflection of the cantilevers increased. The effects of thickness and width of the metal lines on the sensitivity in design (c) were simulated for the optimized design. As shown in Fig. 7 (a), AV increased as the width of metal lines increased due to larger inductance as a result of less metal resistance according to the following equation.

The basic formula for inductance L is

¡io N 2 A uqN2 p

where ¡i0 is the permittivity of free space, N is the number of turns, p is the resistivity of the material, l is the length of the line, and A is the area of the line. It reached a plateau after approximately 5 ^m. The AV/V, however, decreased as the width of metal lines increased. From Fig. 7(a), we concluded that although a 3 ^m line width was an optimized width to obtain a balanced AV and AV/V, a 1 ^m line width could be used to obtain higher AV/V. When the line width is 1 ^m, the AV/V is approximately 0.013, which is approximately 10-fold higher than that of 0.001 sensitiv-

ity (AR/R) of piezoresistive silicon cantilevers of the same dimension under the same cantilever bending.7 Figure 7(b) shows AV increased as the thickness of metal lines increased, which is also due to larger inductance as a result of less metal resistance. It reached a plateau after approximately 0.4 ^m. The AV/V decreased as the thickness of metal lines increased.

The gap between two lines at their nearest edges was 5 ^m before bending and 5.1 ^m after bending. The above simulated results showed that AV was larger when the lines were wider and thicker.

We built an equivalent circuit model to compare with the simulated results obtained above. The dimensions of the gold lines are 0.1 ^m in thickness, 3 ^m in width, and 5 ^m in the gap between the two gold lines. We calculated the self-inductance of each coil and the mutual inductance and the coupling coefficient between the primary and secondary coils by the formulas and procedure discussed below.

As shown in Fig. 8 (a), the physical structure considers for the inductive cantilevers consist of metal lines formed on silicon substrate separated by insulating layer of silicon dioxide. The lumped model, illustrated in Fig. 8 (b), consists of a voltage source, a resistor (Ri and an inductor L1 representing the metal line). Since

Table 1. Parameters considered for the mathematical model

Parameler Formula applied Symbol definition Unlue

Series resistance of Metal lines (gold for primary, secondary) fis = ^ wt p (resistivity) = 2.4 x 10~8 Qm 11 (primaryline) = 560 |im 12 (secondaryline) = 550 |m Ri = 44.8 Q (primary coil) R2 = 40.0 Q (secondary coil)

Oxide capacitance Substrate resistance (considering substrate area right below the metal layer only) Cox = tW^ tox psubl Rs = - wt w (width) = 3 |m t (thickness) = 0.1 |m constant = 3.9 e tox (thickness of oxide layer) =0.5 |m eox = 8.85 x 10-12 F/m psub (substrate resistivity) = 0.02 Qm t=2|m w=3|m Ci = 0.115 pF (primary coil) C2 = 0.113 pF (secondary coil) Rsi = 18.6 kQ (primary coil) Rs2 = 18.3 kQ (secondary coil)

the combined metal line-oxide layer-doped silicon structure acts as a capacitor, there should be a capacitance effect between the metal line and the substrate Cox. The overall impedance of the silicon substrate is represented by a substrate resistance Rsi. The substrate was grounded to avoid any parasitic effects. The value of each parameter can be obtained by using basic electrical formulas provided in Table 1. Using PSPICE, the inductance of each metal line, the mutual inductance and the coupling coefficient between the two lines are needed to calculate the induced voltage. These parameters were obtained from the equations provided below.

The self inductance of the primary and secondary metal lines is obtained from Eq. (2).8

M0l L l L l2

+ 4 1 +

i GMD,

where l is the overall length of the metal line (primary line li = 560 ^m, secondary line l2 = 550 ^m), is the permeability of vacuum (4^x10~7 F/m), GMDseif is geometric mean distance between many metal filaments in cross section (the metal strip can be treated as many filaments in a cross section for calculating self inductance8), which can be calculated from Eq. (3).8

ln GMDself = ln (Vw2 + t2) -

— • tan~x ( —) + — • tan-1 f t \w) w \tJ

- -, (3)

12 ' ( )

where w and t are the width and thickness of the metal lines, respectively.

From Eq. (3), we obtained GMDself = 0.69 ^m. Thus, from Eq. (2) we obtained L1 = 7.16x10~10 H (self inductance of primary coil), L2= 7.01 x10~10 H (self inductance of secondary coil).

The mutual inductance, M, between the primary and secondary metal lines can be obtained from Eq. (4)

l +1/1 +

M = ^ 2n

1 + GMD^ut + GMDmut

where GMDmut is the geometric mean distance between the primary and secondary metal lines obtained from Eq. (5)

ln GMDr

= -x +

2 2wawb

_ Wa _ Wb y 2 2

2 inf d - Wa - Wb) +

' wb 2 ) +

d + ^ + wb) in id + ^ + ^ -wb 2 2 2

d _ w + w )2 in(d - w +

d - ^ + H)2 in (d - ^ + ?

where wa and wb are the width of primary and secondary metal lines, respectively (3 ^m in this case), and d (8 ^m) is the distance between the centre of primary to the centre of secondary metal lines.8 From Eq. (5), we obtained GMDmut = 7.904 ^m. Thus from Eq. (4) we obtained M = 4.44x10~10 H. The coupling coefficient k between the primary and secondary metal lines was 0.626 7, according to

%/ L1L2

When the distance between two lines is 5.1 ^m (constant throughout the length), which roughly corresponds to 2 ^m cantilever deflection at the end, we obtained a GMDmut of 8.005 ^m, a mutual inductance

Fig. 8.

(a) (b)

(a) Physical structure and (b) lumped model of inductive cantilevers considered for mathematical model.

(a) Equivalent circuit (PSPICE model)for the inductive cantilever sensor

Frequency / GHz (b) A V versus frequency as determined by models used in PSPICE and ANSOFT

Fig. 9.

of 4.43x10 10 H. The coupling coefficient decreases to 0.625 2.

The equivalent circuit for our model is shown in Fig. 9. In the circuit, the left hand side represents the input voltage source and the primary metal line on the fixed collar surrounding the cantilever beam, and the right hand side represents the secondary metal line on the cantilever beam and the output voltage measuring device.

By using the PSPICE circuit model in Fig. 9 in conjunction with the above obtained parameters, we obtained the voltage difference AV as a function of frequency for an input voltage of 2V. The AV vs. frequency result obtained by the ANSOFT circuit model (shown in Fig. 3) for design (c) in Fig. 2 with metal (gold) lines having width 3 ^m and thickness 0.1 ^m is also presented in Fig. 9 right for comparison. The two results closely match with each other at lower frequencies. At higher frequencies (about 1 GHz), there was still a 60 % difference between the two results.

This resultant difference is attributed to the difference in the algorithm used by the two softwares. AN-SOFT is a finite element analysis software that uses the method of moments (MoM) algorithm to solve a physical system, whereas, PSPICE is a circuit simulator which does not consider all the parameters as the ANSOFT does. It is most likely that the ANSOFT results are more accurate, experimental results will be needed to confirm these in the future. In our design, a 2 V input voltage was applied to the primary metal

line. Therefore the heat dissipated from the metal line in a period of 900 s is given as

Q = R = 82 J,

where V is input voltage, R is the primary metal line resistance (44.8 O), t is time. This dissipated heat is too low to affect the inductance and is negligible.

The basic structure and key features of a new inductive technique for the detection of microcantilever deflection have been discussed with the aid of modeling and simulation. Results generated by numerical simulation using ANSOFT compare well with those obtained from an equivalent circuit model using PSPICE. The sensitivity of the inductive cantilever was estimated to be about one order of magnitude higher as compared to piezoresistive silicon cantilevers of the same dimension under the same cantilever bending. The results obtained will guide for the development of inductive cantilevers for sensing applications.

Each previous sensing mechanism has its own advantages and drawbacks. The inductive method seems to be able to overcome the disadvantages in these methods, and may eventually be applied in industry for cost-effective and sensitive detection of target molecules. From fabrication point of view, apparently it takes least efforts to fabricate plain cantilevers for the optical method. It is most sophisticated to fabricate piezoelectric cantilevers because of multiple layers involved, including the sensing materials, the driving materials, and the circuit wires. It is also a challenge to fabricate

capacitive cantilevers since there is a need for uniform distance between the cantilever tip and the bottom electrode. The piezoresistive and inductive cantilevers are relatively easier to fabricate, as it just requires a few fabrication steps to deposite metal wires on the cantilever. Being more sensitive, the inductive method has a more clear advantage than the piezoresistive method.

This work was supported by the Institute for Microman-ufacturing at Louisiana Tech University, a Louisiana Board of Regents Industrial Ties grant, the National Institutes of Health (1R01NS057366) and the National Natural Science Foundation of China (20728506B05).

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