MEMS resonators for biosensing applications

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Chapter 2 MEMS resonators for biosensing applications

MEMS-based biosensors are a promising new platform for the delivery of di- agnostic services close to the point of care, where issues like reliability, ease of use, and low cost are of primary importance. Moreover, the modification of standard Complementary MOS (CMOS) technologies allows the co-fabrication on the same silicon chip of MEMS components and the driving and conditioning circuitry, making the design of smart sensors possible without significant increase in cost. Resonant mass sensors (microbalances) are widely used in sensing and biosensing applications. The microbalance principle, traditionally used in the Quartz Crystal Microbalances (QCMs), has been transferred more recently to MEMS (Micro-Electro-Mechanical System) resonators, based on diﬀerent transduction mechanisms, to exploit the advantages of MEMS technology (small dimensions, batch fabrication, enhanced sensitivity).

The presented mechanical resonator is based on inductive actuation and detection, and the sensing is based on the microbalance principle. The design guidelines are discussed, focusing on the methodology to increase the sensitivity (i.e. the frequency shift to analyte concentration ratio). The sensor is fabricated with a MEMS (Micro-electro-mechanical System) post-processing method on a standard, CMOS-based VLSI technology, retaining maximum

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compatibility with the CMOS process flow. The MEMS/CMOS approach can be followed for biosensors as long as the specific problems related to the bio- activation of the sensor surface and its compatibility with on-chip MEMS and electronic components are taken into account [20]. A protocol for covalent bonding of organo-functional silanes (to be used as link sites for biomolecular probes) on the resonator surface is presented. The eﬀect on the mechanical frequency response, i.e. mass response, of the resonators undergo to three kind of test mass, is discussed. Furthermore, is presented the design of an integrated electronic oscillator, based on general purpose CMOS operational amplifiers (op-amps) and conceived to operate with the MEMS resonator fabricated on the same chip as the op-amps.

2.1 An introduction to MEMS resonators

In the biosensing word the challenge is constituted by sensor arrays for multiple simultaneous analyses. From this point of view Micro-Electro-Mechanical Systems (MEMS) are the natural response to obtain this goal[21, 22]. This is inherently due to their parallel fabrication process. Based on the gravimetric principle, Quartz Crystal Microbalances (QCMs) are widely used as resonant mass sensors for biosensing applications. The transduction principle, first investigated by Sauerbrey [23], is based on the modulation of the mechanical resonance frequency as a consequence of a change in the mass of the resonator, following the microbalance principle. The added mass is most commonly adsorbed or otherwise linked at the resonator external surface. In chemical/biochemical sensing, selectivity with respect to a specific target molecule is achieved by a specific treatment (functionalization) of the resonator surface so that only the binding of the desired species is possible. Performance improvements can be obtained by miniaturization of such a gravimetric sensor.

Moreover MEMS technology, in addition to miniaturization, allows the development of fully electrical devices, the integration of conditioning electronics on the same chip, with consequent reduction of the parasitic elements, a lower power consumption, and the possibility of integration of multiple sensors on a single chip (sensor arrays).

Several MEMS microbalances, based on diﬀerent transduction principles,

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2.1. An introduction to MEMS resonators

have been proposed. Standard cantilevers, vibrating on their flexural modes, are relatively simple to fabricate and can be integrated in a standard CMOS technology, as in [24], where electrostatic transduction is used. In [25, 26, 27]

are presented other example of full electrostatic devices. Moreover, the fabrication of piezoelectric MEMS resonant sensors is certainly possible [28, 29, 30, 31], other transduction mechanisms are accessible in the MEMS world each with advantages and drawbacks. Electroplated cantilevers, electromagnetically actuated and optically read, have also been proposed [32]. Ortiz et al. [33] developed a circular diaphragm resonator which supports two spatially independent modes of vibration with the same frequency, thus allowing the independent detection of two analytes. A similar geometry was used by Tang et al. [34], in which both driving and sensing are electrostatic. Thermal actuation is also possible even at relatively high resonance frequencies (in the MHz range). For example, [35] and [36] use thermal excitation and piezoresistive sensing with a seismic mass suspended to flexural springs, and a fabrication process based on SOI substrates. With the same sensing technique, Li et al. [37] developed magnetically actuated cantilevers. Impedenziometric one port biosensor array are also investigated [38]. In an eﬀort to improve the sensing characteristics, diamond-on-silicon resonators [39], claiming higher quality factors with respect to standard silicon MEMS approaches, have been proposed as well. Instead, by following the scaling approach, mass resolutions down to the atomic level have been demonstrated [40].

In biosensing applications, however, there are several important design goals apart from that of obtaining the highest possible mass sensitivity. Moreover, a MEMS biosensor is commonly required to operate, at least for a phase of its working cycle, in a wet environment, and is thus prone to elastocapillary collapse (i.e. stiction) [41]. The stiction problem is relaxed in case of large distances between moving parts, which reduce the eﬀect of capillary forces.

Key performance parameters of a microbalance are the quality factor, which is linked to the intrinsic noise level of the resonator and, in turn, to the minimum detectable frequency shift, and the transduction sensitivity. As most microbalance sensors are aimed at sensing the concentration of chemical or biochemical species in a gaseous or liquid sample, a reasonable measure of the sensor sensitivity is the ratio between the absolute (or relative) frequency shift

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and the analyte concentration in the sample (as opposed to the ratio between the frequency shift and the added mass on the microbalance, as often presented in the literature on MEMS microbalances).

2.2 Magnetically actuated MEMS microbalances for biosensing applications

In our biosensors, the microbalance principle is transferred to MEMS domain by use of a CMOS-compatible bulk MEMS technology, leading to the fabrication of a magnetic torsional resonator, with electrical actuation and detection [18]. The use of a CMOS-based technology allows the integration of on-chip electronics for sensor driving and signal conditioning, whereas the fully electric operation allows direct interfacing to the same electronics.

A few specific issues must be addressed in the design of a feasible MEMS resonant biosensor: the device (and its package) must withstand operation in a liquid environment (a severe requirement, for example, in capacitive MEMS resonators which are prone to stiction, i.e. elastocapillary collapse [42]; the functionalization protocol of the resonator surface must be compatible with other on-chip components (metal lines used for electric signal distribution, on-board electronics, etc.) [43]. In this work, we addressed these issues by developing a MEMS torsional resonator with magnetic driving and sensing.

The high torsional stiﬀness and large cavity under the moving parts eliminates the stiction problem, while a carefully designed silanization protocol allows for reliable operation of the sensor. In the following, after a descrip- tion of the working principle, design, MEMS fabrication and functionalization methods, we present a full electrical characterization of the resonators in terms of its frequency response.

2.3 Theory of operation

The device structure, as shown schematically in Fig. 2.1, is constituted by a rectangular silicon dioxide plate, suspended over a cavity on the silicon substrate by two beams, acting as torsional springs. Two inductors for electrical

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2.3. Theory of operation

Figure 2.1: Sketch of the sensor structure.

driving and sensing are embedded in the plate. The resonator dynamic behavior can be approximated by an equivalent, lumped parameter linear second- order model. The rotation angle of the plate ✓ obeys the ordinary diﬀerential equation:

J ¨✓(t) + D ˙✓(t) + K✓(t) = ⌧ (t) (2.1) where J, K and D correspond to the moment of inertia, spring constant and damping respectively, and ⌧(t) is an external torque. This torque can be applied on the plate through the application of an external magnetic field (B in Fig. 2.1). A sinusoidal current Id into the driving loop (red loop in Fig. 2.1) creates an oscillating torque on the structure, forcing the plate into torsional vibration. The oscillation amplitude, however, is only significant if the current frequency is close to the resonance. The plate motion creates a variation of the magnetic flux linked with the sensing loop (blue loop in Fig. 2.1), and, consequently, an induced electromotive force at its terminals.

An equivalent circuit based on the aforementioned lumped parameter ap- proximation, which is a valuable design tool, can be derived (Fig. 2.2). The central section of the circuit describes the mechanical behavior of the system [44]. Following one of the possible conventions when modeling mechanical sys-

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τ

C θ

ROUT

LOUT

Γ_OUT:1 R

L M

vOUT

EMF Γ_IN:1

LIN

RIN

vIN

τ J+δJ

θ

RS

LS

ΓS:1 D^-1

K^-1 M

EMF Γ_D:1

LD

Id RD

Vd

Is

VS

Figure 2.2: Electrical equivalent circuit of the microbalance.

tems with electrical circuits, angular velocities and torques are mapped into voltages and currents, respectively. The LCR parallel circuit implements the relationship between angular velocity and torque implied by (2.1). The two transformers model the coupling between the electrical and mechanical domain, i.e. the transduction between current and Lorentz force (at the input), the Faraday’s law (at the output). The two magneto-mechanical coupling co- eﬃcients Dand S are directly proportional to the external magnetic field B and to an equivalent loop area. The two resistors R{D,S}and inductors L{D,S}

are the resistance and inductance of the driving and sensing loops, respectively.

Finally, in order to describe the coupling between the two concentric loops, a mutual inductance M is also included.

From the equivalent circuit of the resonator it is straightforward to calculate the electrical transfer function of the device. Given the low input impedance and high output impedance of the resonator, the most descriptive input/output transfer function is its forward transimpedance H(j!), i.e. the ratio between the open circuit output voltage Vsand the input current Id:

H(j!), Vs

Id Is=0

=

j! ^{D S} K 1 !²

!²₀+ j!

Q!0

+ j!M (2.2)

where the parameters are the resonance angular frequency !0 and the quality

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2.3. Theory of operation

factor Q, which are related to the coeﬃcients in (2.1) through the relationships

!0= s

K

J and Q =

pK J

D . (2.3)

The transfer function is naturally separated in a mechanical part HM(j!)and a mutual inductance part j!M, with HM(j!) defined as

HM(j!), j! ^{D S} K 1 !²

!₀²+ j!

Q!0

=

j ! Q!0

Rf

1 !²

!²₀+ j!

Q!0

(2.4)

where Rf is the resonance transresistance, corresponding to the (real) value of HM at resonance:

Rf , H^M(j!)|!=!0 = ^{D S}

K !0Q. (2.5)

The plate surface can be functionalized to allow selective linking between the surface and the analyte of interest (see Section 2.5). The consequent increase in mass (and thus in moment of inertia) results in a lowering of the resonance frequency. From the value of the frequency shift, an information on the analyte mass linked at the surface, and thus on its concentration in the test sample, can be obtained. As the amount of analyte mass per unit area of the plate, call it µS, can be assumed to be proportional to the analyte concentration, we use as a measure of the sensor sensitivity the ratio between the relative frequency shift caused by µS and µS itself (as in [45]). Straightforward calculations give

S,

!

!0

µS ⇡ J 2 J µS =

µS

2 ⇢ tp

µS = 1 2 ⇢ tp

"

m² kg

#

(2.6)

where ⇢ and tpare the average volume mass density and thickness of the plate, respectively. In order to keep the expressions simple, we neglected the diﬀer- ence in density between aluminum (of which the metals are made) and silicon

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Table 2.1: Designed microbalances: dimensions and FEM simulated frequency resonance.

Device

Dimensions Simulated

Central plate Torsional springs frequency

W L w l resonance

[µm] [µm] [µm] [µm] [kHz]

400-M3 410 410 80 95 32.367

400-M2 410 410 80 95 28.540

200-M3 210 210 73 185 102.746

200-M3-W 284 210 73 185 76.351

200-M3-W1 376 210 73 185 57.758

200-PASS 200 200 62 190 216.773

400x200-M2 210 338 73 132 57.756

400x200-M2-W 439 338 73 132 24.412

100x140-M3 165 123 62 90 265.994

dioxide, given the small diﬀerence in densities and the minor contribution of the metals to the total plate mass.

2.4 Device design: issues and solutions

The design eﬀorts of the new generation devices were focused on improving performance in terms of voltage levels, direct magnetic feedthrough and sensitivity, with respect to the previous generation [18]. These improvements are the result of a better use of both the standard CMOS process and post-processing for structures release. Several new devices were designed. The designed chip contains, in addition to two "standard" devices, also other seven new kinds of resonators. The latter variously combine the introduced improvements. The resonators also diﬀer in the size of the central square plate. The plate sides ranging from 400 µm to 130 µm. The total area occupation of the resonators (i.e. cavity area) is comprise between 400 µm ⇥ 400 µm and 400 µm ⇥ 400 µm.

In Fig. 2.3 are showed three example of the designed microbalance layouts. The dimensions of central plate and springs are given in Table 2.1. In Fig.1.13 is shown the designed chip layout. Generally, the resonators have a single turn driving loop to minimize resistance and have an higher current Is, while several turns sensing loop to maximize the linked magnetic flux.

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2.4. Device design: issues and solutions

(a) (b) (c)

Figure 2.3: Three examples of microbalance layouts. (a) Standard 400-M3 device with enhanced loops number. (b) Thinner 400x200-M2 microbalance with decoupled loops. (c) 200-M3-W wings resonator with smaller equivalent thickness.

2.4.1 Enhancement of the output voltage level

Firstly, the design was focused to increasing the two magneto-mechanical coupling coeﬃcients D and S and thus the output voltage level. As discussed in Section 2.3 the two coeﬃcients link the electrical and mechanical domain.

The D multiplied by the input current Id(t)gives the torque ⌧(t), while the product between the angular velocity ˙✓ and S is the generated electromotive force. The two coeﬃcients are given by:

(

D= B L W

S ⇡ B A^eq. (2.7)

Dcan be increased by increasing the plate dimension, which conflicts with the requirement of a reduced area occupancy. At assigned D, the output voltage can be increased up to a maximum, which is dictated by the maximum current density allowed in the metal layer. The resonator named 200-PASS use the top metal layer (as better explained in Section 2.5), for its higher maximum density current, not as sacrificial layer but as structural layer. Consequently, this microbalance needs to be completely protected with photoresist during etching steps. Moreover, a higher thickness results, and thus a smaller sensitivity.

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As the S coeﬃcient is limited by the equivalent loop area Aeq (i.e. the product of the number of turns with its average area) it is possible to maximize

S by filling the plate area with as many turns as possible.

2.4.2 Reduction of direct magnetic feedthrough

The microbalance transfer function, as described in Section 2.3, is separated in a mechanical part HM(j!) and a mutual inductance one. The latter is an unwanted direct magnetic coupling between input and output port due to the concentric position of the driving and sensing loops. In order to minimize this contribution to the transfer function two microbalances (400x200-M2 and 400x200-M2-W) are designed with adjacent loops (Fig. 2.3(b)).

2.4.3 Enhancement of the sensitivity by thinning

An analysis of equation (2.6) gives insights helpful to increase the device sensitivity. Under the reasonable assumption that, all other things equal, the added mass is proportional to the resonator surface exposed to the sample, a general analysis shows that the sensitivity (as defined in Section 2.3) is directly proportional to the surface-to-volume ratio of the resonating mass, and also inversely proportional to the mass density of the material constituting the resonator. If the geometry of the resonator is essentially planar (as is often the case in MEMS), the sensitivity can be improved by reducing the thickness of the structural layer, and/or using the less dense material available. The plate material density is, in our case, dictated by the fabrication technology used.

Smaller thicknesses can be obtained by using fewer intermetal layers constituting the resonator structure (more detail in Section 2.5). An example of thinner microbalances layout is shown in Fig. 2.3(b). On the other hand, the plate thickness cannot be reduced below a certain value because of the need to embed the two inductors into the plate.

Another way to increase the sensitivity is to increase the active surface of the sensor by adding thinner sections to the plate. By generalizing the formula (2.6), it is not diﬃcult to show that the eﬀect of the added sections on the sensitivity is directly proportional to their moments of inertia relative to the rotation axis, and inversely proportional to their thicknesses. For these reasons,

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2.5. Fabrication process: challenges and solutions

the optimal choice is to add two lateral, thin sections (i.e. wings) on the sides of the central plate, at the furthest possible distance from the rotation axis.

The simple expression (2.6) for the sensitivity can be retained, provided that an equivalent thickness teq is used:

S = 1

2 ⇢ teq

. (2.8)

If we call tp, tw, Jp, Jw the thicknesses and moments of inertia of the central plate and one of the wings, respectively, an expression for teq is

teq= tpJp+ 2 twJw

Jp+ 2Jw

. (2.9)

With this approach, a small increase in the device dimensions results in a very large increase of the sensitivity. For example, a device with a square, 200 µm⇥ 200 µm plate and standard thicknesses (device 200-M3) has a theoretical sensitivity of 51 m²kg ¹. The addition of two, 31 µm wide wings (device 200-M3-W in Fig. 2.3(c)) results in a sensitivity of 74 m²kg ¹, with a relative increase of 45%.

During the design, the eﬀect of the wings on the resonance frequency must be taken into account as well. For the two resonators of the example, FEM simulations give resonance frequencies at 102.7 kHz and 76.4 kHz, respectively.

2.5 Fabrication process: challenges and solutions

The resonator plate is fabricated from the inter-metal dielectric layers (basi- cally silicon dioxide), while loops are fabricated using the metal interconnec- tion layers. A post-processing sequence (implementing a bulk micromachining technology), designed to be CMOS compatible, was used to release the microbalance. The used process offers three metal layers. The top metal layer is used as masking layer, to define the shape of the resonator structure, during first etch step. In order to obtain two different thicknesses, as presented in Subsection 2.4.3, two different metal layers were used as masks. The M3 option uses the metal3 as top layer, and the metal2 and metal1 for the driving

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and sensing loops, respectively (Fig. 2.4(a)). The M2 option uses metal2 as top layer, and both inductors are in metal1(Fig. 2.4(b)). In a standard IC design the metals would be embedded in the upper dielectric layers (Fig. 2.4(A)). In our case the layout rules were purposely violated and the etches used for the pad opening are exploited to remove these upper dielectrics. A sketch of the cross sections of the two structures as they are received from the foundry is shown in Fig. 2.4(B). The final thickness of the two types of microbalance, as deduced from the technology specifications, are about 4.5µm (M3) and 2.6µm (M2).

The first post-processing step is a standard photolithography (Fig. 2.4(C)) to protect the external structures as connection lines from and to the loops, pads, electronics, etc. The photolithographic process was developed to protect the chip during the two subsequent etches, oxides and top metal removal. In particular, an about 8µm thick layer of SPR 220-7.0 photoresist is used. The photoresist development and hard-bake steps were altered with respect to the standard procedure to obtain a harder layer.

As mentioned above, the structure geometry is defined by oxide removal (Fig. 2.4(D)). Initially, this step was performed in a Buﬀered-HF solution (HF(48%) : NH4F(40%) 1:6 vol.) [46]. The BHF shows the typical charac- teristic of the wet etch, the isotropicity. This results in an under-etch of the dielectric constituting the resonator structure. The problem must be considered during the design but, however, entails an higher uncertainty on the resonators mechanical characteristics. Furthermore, the partial unpredictability of the under-etch involves a low reliability of the process because of the possibility of the metal loops to be exposed and damaged by subsequent etch.

By replacing the wet isotropic etch with a dry anisotropic one it was possible to improve the reliability of the fabrication process and the fabrication yield.

Specifically, a better geometry transfer was achieved. The used dry etch is a Reactive Ion Etching (RIE), performed in a low pressure chamber where a CF4-based plasma is generated through an external RF generator. The RIE is expected to be compatible with on-board CMOS electronics because of its

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(a) M3 type (b) M2 type

Figure 2.4: Sketch of the MEMS fabrication process (not to scale). The single steps are described in the text.

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use in all CMOS process. We demonstrated that the addition of nitrogen (N2) to the CF4 plasma gives improvements in terms of selectivity (respect to the photoresist) and etch rate [47].

Once the silicon surface is reached, the top metal layer is not required any- more and is then removed (Fig. 2.4E) in a wet etch based on a orthophosphoric acid solution (H3PO4(85%) : HNO3(65%) : CH3COOH : D.I. water 16:1:1:2 vol.). The photoresist is simply removed in acetone.

The post-processing of the first generation devices [46] included an aluminum evaporation on the wafers backside acting as protection during the release phase. The silicon etch thins too much the wafers thereby aﬀecting its mechanical robustness. The evaporation step process is not necessary since the foundry did not lap the wafers at our request.

The release step is carried out in a buﬀered Tetra-Methyl-Ammonium Hy- droxide (TMAH) solution at 85 C, the silicon under the plate is anisotropically etched along (100) planes, so that the plate and springs are mechanically de- tached from the substrate. The chemistry of the TMAH solution is tuned (5%wt TMAH aqueous solution with 25 g/L of silicic acid and 7 g/L of an oxi- dizing agent, ammonium peroxodisulphate) to allow etch of the silicon while re- moving both the oxide and the metal negligibly [10]. Because of the anisotropy, a central hole is required in the plate to allow complete release of the structure (Fig. 2.4F). At this point, the resonators appear as in Fig. 2.6(a). The overall dimensions of a resonator is (depending on the specific type) in the range of a few hundreds of micrometers.

As described in Subsection 2.4.3, wings resonator are also designed. These device are fabricated with the same post-processing but diﬀer in the layer used to define structure geometry. The lower available metal layer (metal1) is used, during oxide removal, to protect the underlying dielectric layer, which will constitute the two sensitivity-enhancing wings at each side of the resonator plate. In Fig. 2.5 are sketched the main steps process for this kind of devices.

After the release a resonator with its lateral wings appears as in Fig. 2.6(b).

Once the mechanical structure of the resonators is ready, the sample is glued to the final, gold plated ceramic package (CLCC68) which will be used for electrical characterization. The input and output inductors of all the microbalances in each sample are bonded to the package contacts by means of

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Figure 2.5: Sketch of the main steps of the wings resonator fabrication process. (A) Cross sections of the structure as received from the foundry. (B) Wing resonator after oxide removal. (C) Released device.

(a) (b)

Figure 2.6: (a) Optical microscope photograph of one the fabricated resonators. The plate side length is 400 µm. The driving loop (yellow outer border) is clearly visible. The dark area corresponds to the cavity in the silicon substrate. (b) SEM image of a wings resonator after the structure release.

thin aluminum wires (Fig. 2.7). The resonators are now ready for characterization. A single sample contains two identical chip, each containing up to six resonators.

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Figure 2.7: Photograph of a sensor chip mounted in its ceramic package. Each chip contains up to six working resonators. The bonding wires connecting the chip pads to the package are also visible. The package side is 2.5 cm.

2.6 Electro-mechanical characterization

In this section the analysis of the fabricated MEMS microbalances frequency response is presented. In order to test eﬀective behavior as gravimetric sensor the resonators are loaded with gold nanoparticles NPs. The measurement before and after NP grafting allow the extraction of the microbalance sensitivity.

The sensors functionality with the probe/target interaction are validated by the measurement.

2.6.1 Analysis of the frequency response

The frequency response allows a complete characterization of the microbalances. An example of the 200-M3 resonator measured response is shown in Fig. 2.8. From the measurements is possible extract the parameters of all the resonator and thus use the equivalent circuit as design tool.

The relevant electrical and mechanical parameters are extracted by analysis of the measurement set. All the required computations were performed with custom MATLAB scripts. Most parameters were extracted by non-linear least- squares optimization based on the lsqnonlin MATLAB function.

Preliminarily, the frequency response without external magnetic field is used

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2.6. Electro-mechanical characterization

15

10

5

0

|H ( f )| [mΩ]

105 100

95 90

frequency [kHz]

(a) Magnitude

-5 0 5

Im{HM( f )} [mΩ]

15 10 5

0 Re{H_M( f )} [mΩ]

(b) Polar Figure 2.8: Typical resonator frequency response graphs (200-M3). Symbols are the

measured experimental data, lines are the fitting curves. (a) Magnitude of the full response H(f) (black line, diamonds) and of the mutual inductance contribution (green line, crosses). (b) Real part vs. imaginary part plot of the mechanical component of the response HM(f ).

to separate the eﬀect of the mechanical response HM(j!)from the contribution of the mutual inductance. In this condition the H(j!) is simply reduced to:

Vs

Id

Is=0,B=0

= j!M. (2.10)

The measured response is least-squares fitted against a linear function and from the computed slope the mutual inductance value M is determined (green hatches in Fig. 2.8(a)). The mechanical response HM(j!) is then obtained by numerically subtracting the fitted mutual inductance response from the total measured response. These corrected data could be least-squares fitted against (2.4) to obtain the values of Rf, !0, and Q, all at once, but this procedure is not numerically robust. A diﬀerent approach was then devised.

It is straightforward to show that the polar plot (real part vs. imaginary part) of HM(j!)is a circumference which is tangent to the imaginary axis and with its diameter lying on the real axis (Fig. 2.8(b)). The maximum absolute value of the response, corresponding to the resonance transresistance Rf (as defined in Section 2.3), is equal to the diameter length. Based on this fact, Rfis determined from experimental data by determining the optimum circumference in the least-squares sense, i.e. by minimizing the sum of the squared distances between the circumference and each experimental point, and by setting the estimate for Rf as the diameter of such circumference. This procedure has

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the advantage that a single parameter (Rf) can be extracted regardless of the values of !0and Q, significantly reducing the numerical convergence problems.

At this point, !0and Q are determined by least-squares fitting of the data against the function in (2.4), where the constant Rf is now already known.

The parameters influencing the electrical response are thus fully determined.

A typical result of this procedure is shown in Fig. 2.8(a).

The mechanical behavior of the system is now fully characterized. This is not suﬃcient, however, to identify the equivalent electric model of Fig. 2.2.

As far as the mechanical parameters (i.e. J, D, and K) are concerned, knowledge of one of the three, along with Q and !0, allows the calculation of the other two through the relationships (2.3). However, it can be shown [44] that one of the parameters (most commonly the mass for translational microsystems, and the moment of inertia for rotational ones) can be arbitrarily chosen. In our case, we chose to compute J based on its theoretical value computed from the dimensions and mass density of the resonator plate, and to use (2.3) to compute K and D.

As K is known at this point, the product S D can be determined using (2.5). From the point of view of the transfer function (2.2) only their product is measurable from frequency response data, but reasonable approximations for the values of the two coeﬃcients can be nonetheless determined as follows.

In our resonators, the driving inductor consists of a single loop, whereas the sensing inductor of several (of the order of a few tenths) loops. By assuming the same area (say A) for each loop, and observing that both S and D are proportional to the loop area (see Section 2.3 for details), the simple relationship S = nS Dcan be written, where nS is the number of loop in the sensing inductor. From this relationship the values of S and D can be computed.

Finally, the input and output electrical resistance components (RD, RS) were measured directly with a precision multimeter with zero external magnetic field. Given the high resistances and low frequencies involved, the inductances LSand LDcould not be measured directly. Theoretical values were determined by using a known analytical model for square planar inductors [48]. In Table 2.3 equivalent circuit parameters for a typical resonator are summarized.

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2.6. Electro-mechanical characterization Relative Intensity %

1.4

0 10 20 30 40 50 60 70 80 90 100

1.2 1.0 0.8 0.6 0.4 0.2 0.0

Depth (nm)

C_aliphatic

Si^(IV) Si^(III) N O Calcoholic/aminic Ccarboxilic

1.0 0.8 0.6 0.4 0.2 0.0

Depth(nm)

0 10 20 30 40 50 60 70 80 90 100

Relative Intensity %

0 10 20 30 40 50 60 70 80 90 100

1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0

Depth (nm)

C_aliphatic

1.0 0.8 0.6 0.4 0.2 0.0

Depth(nm)

0 10 20 30 40 50 60 70 80 90 100

(a) dip-coating Relative Intensity %

0 10 20 30 40 50 60 70 80 90 100

1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0

Depth (nm)

C_aliphatic

1.0 0.8 0.6 0.4 0.2 0.0

Depth(nm)

0 10 20 30 40 50 60 70 80 90 100

(b) drop-coating

Figure 2.9: Comparison of the in-depth distribution of the diﬀerent chemical species detected by ARXPS on the surface of silanized silicon oxide substrates.

2.6.2 Resonator response to a test mass density

Each chip can be individually functionalized to create a bio-active surface. To this purpose, organo-functional silanes are commonly used as an intermediate for the creation of a protein layer for biosensing applications. The silanization protocol used in this work was designed to suit the needs of the specific application starting from the one already presented in [43].

Whereas standard procedures to prepare bioactive surfaces, on glass or silicon substrates, normally involves dip-coating (immersion) of the sample with the required solutions, this approach may not be feasible for silicon chips containing mechanically sensitive MEMS components and electronic circuits.

Moreover, the bio-coating technique must be compatible with whatever package is used, to allow both a proper handling of the sensor and access to the electrical signals through metal wires, in the case of sensors which allow electric driving and/or readout. An alternative to this approach can be the use of single droplets of the reagents (drop-coating) [49, 50, 51].

The use of drop-coating as a substitute to immersion for the creation of bioactive surfaces on MEMS sensors is investigated. Preliminarily, a test to verify the eﬀectiveness of the functionalization protocol was performed: test silicon dioxide surfaces were cleaned in an ammonia-based hydroxylation solution, and silanized through drop-coating with an aqueous-based APTES (amino-propyl-

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(a) (b)

Figure 2.10: Fluorescence microscope images of a resonant MEMS structure exposed to a MGMT mRNA probe/FITC-marked target couple (a) in comparison with a sample exposed to the unmarked probe only (b).

triethoxysilane) solution as the preliminary step towards the deposition of a bioactive layer [52]. The surfaces were studied by means of conventional and angle resolved x-ray photoelectron spectroscopy (ARXPS). The spectroscopic characterization confirmed that the resulting surface chemical composition was not significantly diﬀerent upon the two alternative processing approaches: both the atomic percentages values and the outermost layer in-depth distribution of the functionalities are comparable for the two approaches (Fig. 2.9).

Subsequently, a sample containing several MEMS resonators underwent a similar procedure. The amino coated resonators were then exposed to a drop of solution containing an oligonucleotide specifically designed to link to a por- tion of human MGMT (methylguanine-DNA methyltransferase) mRNA [53], and subsequently to its FITC fluorescent labeled complementary target (again in drop form). A comparison between this sample and a reference sample (Fig. 2.10), not exposed to the target, shows a clear fluorescence signal, and can interpreted as the occurrence of a specific binding between probe and target. Both the XPS and fluorescence data suggest that the drop-based protocol can be successfully used for the bio-activation of MEMS-based biosensors.

The drop-based protocol to create the silane surface film was used on the measured microbalances. As mentioned before, the resonator surface needs to be terminated by hydroxyl groups, required to allow covalent bonding with the silane. To this purpose, the chip is preliminarily cleaned with a 25 µl drop of an ammonia based solution (NH4OH(25%) : H2O2(30%) : H2O 1:1:4 vol.) for

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(a) M3 type (b) M2 Wings type

Figure 2.11: Sketch of the MEMS resonator process (not to scale): (A) after release, (B) after drop-based silanization protocol and (C) after NPs grafting.

5 min, and then is rinsed twice in deionized water (DW). As a matter of fact, the most commonly used, sulfuric acid-based solutions [54] are not compatible with aluminum, which is exposed, in our samples, at the input/output pads.

Immediately after the cleaning, on the sample is deposed a 25 µl drop of an aqueous solution of amino-propyl-triethoxysilane (APTES) (0.05% vol.) for 5 min, and then rinsed again in DW. The last phase of the silanization protocol, necessary to improve the quality of silane layer and also to remove loosely bound silane clusters, is a curing step, performed by immersion in acetone for 60 min (Fig. 2.11(B)).

The silicon chips are now ready for the first frequency characterization. To

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Figure 2.12: Schematic representation of the experimental setup for electrical characterization.

provide the required external magnetic field (as exposed in Section 2.3), the sample is positioned between two permanent magnets giving a total field of around 70 mT, measured with an external Hall eﬀect sensor.

The instrumentation setup for electrical characterization is sketched in Fig. 2.12. A personal computer remotely control a waveform generator (Agi- lent 33120A) and a lock-in amplifier (EG&G 5302). The waveform generator provides the sinusoidal input current stimulus and the reference signal to the lock-in amplifier. The output voltage signal (in the range of hundreds of µV) was pre-amplified by a custom made, two-stage discrete amplifier (with a voltage amplification of approximately 500) and then sent to the lock-in amplifier.

A sweep frequency measurement is performed and the amplitude and phase response of the resonator is measured at each frequency step.

To prevent the influence of adsorbed environment moisture on frequency response measurements, the samples are heated in oven for 30 min at 120 C before each measurement session, and immediately moved to a sealed aluminum box.

Each resonator undergoes the same measurement session. A first frequency response with a 100 Hz frequency step and 20 kHz measurement window, centered at the theoretical resonance frequency obtained by FEM simulations, is performed. This response is used to extract a rough estimate of the actual resonance frequency, identified with the frequency at peak amplitude. The same measurement but without magnets (and thus with D = S = 0) is also performed, and used to extract the value of the mutual inductive coupling coeﬃcient M with a method exposed in Subsection 2.6.1.

After these preliminary measurements, three identical measurements are

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15

10

5

0

|H ( f )| [mΩ]

105 100

95 90

frequency [kHz]

Figure 2.13: Typical frequency response of a resonator, before (black diamonds) and after (red circles) NPs grafting. Actual data are indicated by the symbols, the lines are fitted curves.

performed in succession. For these measurements, the frequency step is set at 5 Hz, whereas the (500 Hz) frequency window is centered at the resonance frequency estimated in the preceding step. From the measured data, the values of the mechanical and electrical parameters in the equivalent circuit of Fig. 2.2 are extracted. For each microbalance, these values are averaged over the three measurements.

To demonstrate the functionality of the devices as gravimetric sensors and evaluate their sensitivity, the resonators are subsequently loaded with an additional mass. For ease of detection, this role is played by gold nanoparticles (NPs), which are known to bind to the exposed amino groups of the silane layer [55]. To this purpose, a 25 µl drop of a colloid of 30 nm NPs (British Biocell International) is deposed on the chip for 60 min. The sample is then rinsed in DW and dried in oven for 30 min at 120 C (Fig. 2.11(C)).

A second run of three frequency response measurements is then performed on each resonator. A typical frequency response before and after NPs deposition is presented in Fig. 2.13. A lowering of the resonance frequency, which can be attributed to the added mass, was constantly observed on each characterized resonator.

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Table 2.2: Experimentally extracted values for resonator parameters related to mass shift, for resonators with and without the sensitivity-enhancing side wings.

Sample Device f0 fD Q µS S STH

[Hz] [Hz] [-] [mg/m²] [m²/kg] [m²/kg]

MB108 400-M3 31749 31612 157 38.6 111.79 50.89 MB108 200-M3 94581 94291 286 36.7 83.73 50.89 MB108 200-M3-W 74701 74167 116 45.7 156.34 73.65 MB109 200-M3-W 75854 75354 124 37.3 176.73 73.65

To evaluate this eﬀect in a quantitative way, the microbalance surface was also investigated by Scanning Electron Microscopy (SEM). Specifically, six to eight SEM images were acquired in diﬀerent points of each resonator. The number of NPs in a sample square micrometer was determined for each image, and the values averaged over each resonator. The average density of NPs was used to calculate an estimate for the added surface mass density µS, taking into account both sides of the plate in the computation.

Typical extracted parameters from diﬀerent resonator types are summarized in Table 2.2. The MB108-400-M3 resonator is the device shown in Fig. 2.6(a);

the MB108-200-M3 resonator is a similar device, but with a smaller central plate (200 µm ⇥ 200 µm) and comparatively longer suspension springs. Finally, the resonators 200-M3-W are two identical microbalances (shown in Fig. 2.6(b)) of two diﬀerent samples.

The initial resonance frequency f0was measured immediately after silanization, and its value is aﬀected by very little error. The resonance frequency after NP exposure fD is consistently lower, as expected, than the initial frequency, and corresponds to a frequency shift of a few hundred hertz. Also, the lowering is larger than expected for all resonator. For the 200-M3 resonator, this eﬀect is reasonably close to the expected theoretical value, as can be observed by com- paring the experimental and theoretical values of the sensitivity (S and STH

of Table 2.2, respectively). For the other resonators, the measured sensitivity shows a dramatic improvement, by a factor around two, with respect to the resonator without wings. This is much more than what can be expected from the mere eﬀect of the measured added mass, as can be observed, again, by compar- ing the measured and theoretical sensitivities. A few hypotheses can be made to explain this unexpected (though beneficial, from the point of view of sensor

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performance) behavior. A non-uniform distribution of NPs on the resonator

—more specifically, a higher density of NPs on the wings, where the effect of their mass is higher, with respect to the plate— would justify this effect. No significant variation of the NP density between plate and wings was observed on the front side of the resonator. However, the back side of the resonator is also available for NP adhesion. The sensitivity values in Table 2.2 were computed with the hypothesis of equal NP density on both resonator sides, but the different nature of the surfaces might cause a difference in the NP density on the back side. Moreover, the effect of the NP adhesion on the residual (usually compressive) stresses of the plate oxide film (which are certainly present due to fabrication issues) and on the overall stiffness of the membrane (in particular in the torsional beams) were neglected in this analysis. Again, the plate and wing thicknesses used in the computation of the sensitivities are obtained from the technical specifications of the process. The resonator fabrication process, and especially the silicon etch step, Fig. 2.4(F), because of its imperfect selectivity, can cause a different thinning of the plate and wings, resulting in a smaller equivalent thickness and, in turn, in a higher sensitivity.

Noteworthy, the resonance frequency of microbalances tends to drift to higher values after a few days on ambient storage (most likely because of ad- sorption of ambient moisture), a drying step (30 min at 120 C) recovers its original value almost completely.

The frequency shifts must be compared to the measured values of the added mass density µS to obtain an estimate of the sensor sensitivity. The measured values for our resonators ranging from around 83.7 to 176.7 m²kg ¹(Table 2.2, last column). These values compare favourably to the typical values for macro- scopic QCM’s (about 1 m²kg ¹in [45]), but also to other MEMS resonant sensors: [28], for example, claims about 60 m²kg ¹. Compare also, for a review, [56].

To evaluate the eﬀectiveness of the sensitivity enhancement due to the lateral wings, data for two (nominally identical) resonators with wings (200-M3- W), and a reference resonator without wings (200-M3), are presented.

In conclusion, the operation of a magnetically actuated MEMS resonator with electrical input and output as a sensitive mass sensor was demontrated.

The measured sensitivities can be compared favourably to standard QCM’s

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and other implemented MEMS microbalances. A method to increase the sensitivity based on the addition of thin extensions of the vibrating mass, has been designed and implemented. Experimental data show a significant increase in the sensitivity with respect to the standard device. The measured increase is only partly explained by the simple, concentrated-parameter model proposed in this work. Further investigation is required to clarify this point. Moreover, a MEMS-compatible drop-based silanization protocol for the resonator active surface was developed as well. Such a silane layer can be used as a precursor to the fabrication of a bioactive layer to transform the device in a complete resonant biosensor.

2.6.3 Experimental validation of probe/target interaction

In order to verify the functionality, in a real application, of the proposed MEMS biosensors, a first experimental test was performed by using a couple of probe/target (mRNA) biomolecules. As exposed in Subsection 2.6.2, also in this case, a CMOS-compatible drop-based protocol of functionalization and hybridization was developed.

As a target/probe couple we selected the mRNA encoding for human O6- methylguanine-DNAmethyl-transferase (MGMT), a suicide enzyme involved in DNA repair [57]. To design high aﬃnity selective RNA probes to the target a predictive computational method was used [53, 58]. Following the computational selection of targets, complementary probe sequences were derived and synthesized.

During the automated synthesis some chemical modifications were introduced in order to allow the immobilization of probes on the microbalance surface. Probe molecule is a 25-mer oligonucleotide (MW ⇡ 8 kDa) with a thiolated tail that allow the immobilization on the tranducer, while the target molecule is a 835-mer RNA with a MW ⇡ 275 kDa. MGMT RNA in vitro transcribed was the target molecule and as template DNA for transcription the plasmid pG3AT835 linearised with BamHI (obtained inserting MGMT cDNA in a pGEM^r-7Zf vector cut with EcoRI) was employed.

Starting from a sample with several released resonators (Fig. 2.14(A)), the drop-based protocol, described in Subsection 2.6.2 is used to grow the silane surface film on the microbalances (Fig. 2.14(B)). The sample underwent the

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(a) M3 type (b) M2 Wings type

Figure 2.14: Sketch of the MEMS resonator process (not to scale): (A) after release, (B) after drop-based silanization protocol, (C) after functionalization and (D) after target hybridization.

functionalization by deposing a 25 µl drop of a solution of probe for 30 min, and then rinsed twice in DW (Fig. 2.14(C)).

The instrumentation setup used in previous characterization was substi-

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2.0

1.5

1.0

0.5

0.0

|Δf/f 0| ⋅ 103

0.40 0.35

0.30 0.25

0.20 0.15

0.10

1/thickness [µm^-1]

Figure 2.15: Measured relative frequency shift versus the inverse thickness of three diﬀerent resonators of the MB130 sample.

tuted by a network analyzer (Agilent E5061B) but the resonators undergoes the same measurement session. Before it, the sample was heated in oven for 30 minat 60 C instead of 120 C because of the temperature instability of the biomolecules. The fitting approach is the same of Subsection 2.6.1 and only diﬀers because of the automatic instrument point by point subtraction of the mutual inductance component of the frequency response.

The last phase, hybridization of the target molecule, was performed with a 25 µldrop of a solution of the probe for 30 min. The sample was then rinsed twice in DW (Fig. 2.14(D)).

A second run of three frequency response measurements was then performed on each resonator. In Fig. 2.15 are plotted the measured relative frequency shift due to the probe/target interaction versus the inverse thickness of three diﬀerent (in equivalent thickness) resonators. By analyzing equation 2.6 is straightforward to observe that from the slope of the first order fitting (red line in Fig. 2.15) it is possible to extract an estimation of the target molecules surface mass density. From the sensitivity definition the expression for surface

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2.7. A single chip oscillator based on the MEMS microbalance

mass density µS was deduced:

µS = 2 ⇢ tp

!

!0

"

kg m²

#

(2.11)

Experimental data give a µS = 25· 10 ⁶[kg· m ²]. This mass surface density correspond to an average distance between target molecules of about 6 nm, which is compatible with the dimension of the selected target (835 ⇥ 330 Da).

2.7 A single chip oscillator based on the MEMS microbalance

The design of an electronic oscillator based on the resonator was also carried out. The oscillator is based on general-purpose CMOS operational amplifiers (op-amps) fabricated on the resonator chip. In our design, the absence of closely facing electrodes (as in conventional capacitive MEMS) eliminates the problem of stiction, while the on-chip availability of the op-amps allows a very compact oscillator structure, potentially scalable to single-chip biosensor arrays. More- over, in the case of a CMOS-compatible MEMS technology, the fabrication of the resonator and the oscillator amplifier on the same chip gives significant advantages in terms of power, noise immunity, and parasitic eﬀects.

2.7.1 Frequency measurement for mass sensing: circuit approaches

Resonant mass sensing is a well established measurement method, widely used in the most diverse applications. Because of the high accuracy of frequency measurements, very small mass amounts can be determined. As the mass sensitivity is essentially dependent on the ratio between the added mass and the original resonator mass, a common approach to increase the mass sensitivity is down-scaling of the device. MEMS technologies come naturally into play to achieve such down-scaling.

Systems based on diﬀerent principles and techniques have been implemented during the last 25 years. The interface selection for the specific application is

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important and its limitations must be known to be conscious of its suitability, and for avoiding the possible error propagation in the interpretation of results [59]. The interface circuits currently used for sensor characterization which are based on the following principles: network or impedance analysis [60], impulse excitation or decay methods [61], oscillators [62, 24] and lock-in techniques [63, 64]. The most straightforward system to measure the resonance frequency in a resonant sensor is to use the resonator in the feedback path of an electronic oscillator.

2.7.2 Circuit design

The designed oscillator has the classic structure of a positive feedback system, with an amplifier and a bandpass filter constituting the oscillator loop (Fig. 2.16(a)). The filtering element is constituting by the MEMS microbalance, and the amplifier is based on an integrated CMOS op-amp. Both the resonator and the amplifier are integrated on the same chip. The full chip (Fig. 1.13), around 3.5 mm ⇥ 3.5 mm in size, contains several diﬀerent MEMS resonators and two identical op-amps. The resonator can be modeled by the equivalent circuit of Fig. 2.2. The parameters of the circuit can be extracted from the measurement of the resonator frequency response. These parameters, for the considered resonator (400-M3), are summarized in Table 2.3. Two uncommitted, general purpose CMOS op-amps, with input and output ports connected to bonding pads are present on the chip. The op-amp topology, similar to that reported in [65], is shown in Fig. 2.17. The first stage is a complementary folded cascode, while the output stage is a complementary common designed for class-AB operation. The op-amp bias current is derived from a reference current (IB in Fig. 2.17) equal to 10 µA, to be provided through a bonding pad. The op-amp requires a single 3.3 V power supply. The input and output range extend from ground to Vdd. The main amplifier characteristics are: 3.5 MHz gain-bandwidth product (GBW), 120 dB open-loop DC voltage gain, 2.8 mA maximum output current.

Fig. 2.16(b) shows the magnitude and phase response of the resonator, as resulting from the equivalent circuit of Fig. 2.2. The Fig. 2.16 shows the oscillator configuration, where the resonator (transfer function ) forms a loop together with the amplifier (A). The circuit oscillates at frequency f0 if the

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resonator

OUT

β

IN

A

(a)

-90 -45 0 45 90

∠β

40 35

30 25

20

frequency [kHz]

8

6

4

2

0

|β| ⋅ 103

(b)

Figure 2.16: (a) Classic scheme of an oscillator. (b) Frequency response of the used MEMS microbalance obtained by its equivalent circuit.

Figure 2.17: Schematic circuit of the two op-amps integrated on the chip.

loop gain has zero phase and magnitude greater than one at f0 (Barkhausen conditions). The peak on the magnitude diagram is favorably located around the zero crossing point of the phase diagram. However, the considerable atten- uation at resonance (7.68 · 10 ³) has to be compensated for by an amplifier gain greater than 130. This condition is not easy to be fulfilled using the available op-amps, due to the very low resonator input resistance (13 ⌦) combined with the relatively high output resistance of the op-amps (k⌦ range).

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Table 2.3: Experimentally extracted equivalent circuit parameters for the 400-M3 MEMS resonator of MB107 sample.

Electrical

RD [⌦] 13

LD [nH] 3*

RS [k⌦] 5.3

LS [µH] 1.5*

M [nH] 146

Electromechanical ^D [T · m²] 6.35· 10 ⁹

S [T · m²] 4.82· 10 ⁷

Mechanical

J [kg · m²] 2.20· 10 ¹⁷* K [kg · m²/s²] 7.92 · 10 ⁷ D [kg · m²/s] 2.65· 10 ¹⁴

f0 [kHz] 30.2

Q [-] 157

* theoretical values

In particular, a single op-amp loaded by the resonator input termination provide an open loop gain of only 1.6. This gain can be boosted to a maximum value of 4.5 by biasing the op-amp in such a way that the output DC current is around 1 mA. The reason lies in the output resistance reduction obtained by forcing one of the output MOSFETs with a current that, thanks to the class-AB architecture, can get much higher than the designed quiescent current. Clearly, even the boosted gain is widely not suﬃcient, so that two op-amps have been included into the loop, as shown in Fig. 2.18.

The circuit uses a single power supply, so that the voltage source VB = Vdd/2 is used to introduce a convenient conventional zero level for the signals. The first stage (OP1) is a non-inverting amplifier with nominal DC gain (1+R2/R1) set to 220. The actual gain at resonance is 115. The second stage drives the oscillator input ports; its output current is pre-biased at the value VB/R6, set to 1 mA to minimize the output resistance. The configuration is that of a non- inverting amplifier with nominal DC gain (1 + R4/R5) set to 3. The actual gain at the resonance frequency is 2.5. The two stage are coupled by the high pass filter C1 R3. The loop gain, simulated by cutting the loop at OP1 non inverting input, is shown in Fig. 2.19 for two diﬀerent values of capacitor C2.

Capacitor C2is used to bypass the bias resistor R6. In the case C2= 100 µF, the capacitor impedance at the resonant frequency is negligible with respect

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OP1

OP2

resonator V_d V_s

R

₆

C

₁

C

₂

V

_B

V _out

R

₁

R

₂

R

₃

R

₄

R

₅

I

_out2

R1= 1 k⌦

R2= 220 k⌦

R3= 110 k⌦

R4= 1.2 k⌦

R5= 2.4 k⌦

R6= 1.65 k⌦

C1= 100 µF C2= 220 nF

Figure 2.18: Schematic view of the simulated oscillator.

to the resonator input resistance, so that no additional phase contribution is introduced by C2. However, the corresponding phase curve crosses the zero level well out of the resonance region. This problem, due to the amplifier phase delay, was overcome by setting C2to a much smaller value (220 nF), introducing enough phase lead to restore the correct condition. The increase of C2reactance produces also a loop gain magnitude reduction. The net reduction is smaller then expected since it is partially compensated by the increase in OP2 gain following the increase in load resistance. Fig. 2.19 confirms that the loop gain magnitude is still higher than one even with the reduced C2 value.

2.7.3 Simulation results

Electrical simulations, performed using the program ELDO^TM(Mentor Graph- ics) and model provided with the process design kits, have been extensively used during the design phase, illustrated in previous section. Here we show the results of simulations performed on the circuit of Fig. 2.18 in order to (i) check

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0.01 0.1 1

|βA( f )|

33 32

31 30

29 28

27

frequency [kHz]

C₂ = 100 µF C₂ = 220 nF

-180 -90 0 90 180

∠βA( f )

33 32

31 30

29 28

27

frequency [kHz]

C₂ = 100 µF C₂ = 220 nF

Figure 2.19: Frequency response of the loop gain of the oscillator in Fig. 2.18. The curves refer to two diﬀerent values of capacitor C2.

the actual capability of sustaining free oscillations, (ii) estimate the steady state oscillation amplitude and (iii) check the design robustness against temperature and process variations.

The first two tasks have been performed by means of transient simulations.

Oscillations were triggered by a small current pulse (100 nA 10 µs) applied after 1 ms after the simulation start. The steady condition was reached after about 20 ms. Fig. 2.20(a) shows the output waveform (Vout) 25 ms after the simulation start. The output voltage reaches an amplitude of about 60 mV peak-to-peak and shows a fairly sinusoidal behavior. The output voltage at the OP2 output, not shown, is larger (around 100 mV peak-to-peak) but significantly distorted. The reason is clearly saturation of the OP2 output current due to the very low impedance of the load. Note that this current was biased at a significantly large value for the reasons exposed in Section 2.7.2. Therefore saturation at the upper limit is expected to dominate this phenomenon, which is also the self-limiting mechanism for the oscillations. Fig. 2.20(b) confirms this prediction.

Finally, in order to test the robustness of the design a series of AC sim-

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-30 -15 0 15 30

[mV]

25.20 25.15

25.10 25.05

25.00

time [ms]

(a)

-3.0 -1.5 0.0 1.5 3.0

[mA]

25.20 25.15

25.10 25.05

25.00

time [ms]

(b)

Figure 2.20: Transient simulation of relevant waveforms in steady conditions.

ulations of the loop gain have been performed in a wide range of conditions.

For each case, the oscillation frequency was calculated by finding the points of zero phase. The tests were performed varying the temperature and model corners. The results, summarized in Fig. 2.21, indicate that the variation of the oscillation frequency deviation from the nominal case is less than 0.1% over the 0÷100 C interval for typical process parameters. Taking into account also process corners the total oscillation frequency variability is only slightly wider (0.16%). For the whole set of simulations, the loop gain magnitude varied from 1.47to 1.84, remaining reliably over the minimum value (one) for the onset of oscillations.

The electrical simulations demonstrate the feasibility of a single chip MEMS oscillator based on the elements integrated on the sensor chip described in Sec- tion 2.7.2. In particular, the tests performed by varying the process corners and temperature of the amplifiers produced frequency deviations well below the typical process spread and temperature drift of the resonance frequency

MEMS resonators for biosensing applications

Chapter 2