A new bimaterial microcantilever with tunable thermomechanical response

Microelectronic Engineering 96 (2012) 18–23

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A new bimaterial microcantilever with tunable thermomechanical response A. Najafi Sohi a,b,⇑, P. Nieva a,b, A. Khajepour a a b

Department of Mechanical and Mechatronics Engineering, University of Waterloo, Waterloo, ON, Canada Waterloo Institute for Nanotechnology, University of Waterloo, ON, Canada

a r t i c l e

i n f o

Article history: Received 31 October 2011 Received in revised form 10 February 2012 Accepted 1 March 2012 Available online 19 March 2012 Keywords: Bimaterial microcantilever Sensitivity to temperature Tunable thermomechanical response

a b s t r a c t In this paper, a new structural design is proposed which allows the tuning of the thermomechanical response of a bimaterial microcantilever. Through altering its cross section, it is shown that the bimaterial microcantilever can be tailored to either bend up or down when temperature increases, with tunable thermomechanical response. To prove the new design concept, various gold–polysilicon test specimens with capacitance readout system were fabricated using the PolyMUMPsÒ foundry process. Thermal loading experiments performed on these devices show good agreement with analytical modeling and finite element simulations. The new design concept is then used to show how the problem of sensitivity to temperature in gold–polysilicon bimaterial microcantilevers can be minimized for temperatures up to 100 °C. Ó 2012 Elsevier B.V. All rights reserved.

1. Introduction Microcantilevers have always attracted considerable attention because of their potential as a platform for the development of highly sensitive sensors in chemical, biological and physical sensing areas [1–11]. In many of these sensing applications, bimaterial microcantilevers respond to surface stress changes due to different stimuli [12]. A very typical sensing scheme measures these surface stress changes by determining the static deflection of the microcantilever [13]. Using transduction techniques such as optical beam deflection [4], piezoresistivity [14], and capacitance measurement [11], this static deflection can be measured with very high precision [15]. However, in order to design an accurate bimaterial microcantilever-based sensor effectively and efficiently, the side effects of undesired parameters on its performance should be minimized. Sensors often operate in complex environments where various parameters change simultaneously. In such cases, one of the major problems is the sensor’s sensitivity to parameters different from the desired measurand. For example, in bimaterial microcantilevers-based sensors, sensitivity to temperature which originates from the difference in the coefficient of thermal expansion (CTE) between the two materials is an important source of error and/or noise [12,16], and could significantly affect the readout of the sensor [17–20]. Three methods have been proposed and widely used to minimize sensitivity to temperature in bimaterial microcantileverbased sensors. In the first method, the ambient temperature around the microcantilever is strictly controlled, thus the influence ⇑ Corresponding author at: Department of Mechanical and Mechatronics Engineering, University of Waterloo, Waterloo, ON, Canada. E-mail address: alinajafi[email protected] (A. Najafi Sohi). 0167-9317/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.mee.2012.03.002

of change of temperature is minimized [17,21]. This method has been effectively used in research environments, but it requires precise temperature controlling equipment [21], so its implementation in real field applications has not been effectively proven. The second method involves incorporating an additional sensor for measuring the ambient temperature and then employing signal processing to cancel out its effect [4,22]. However, added cost and complexity due to the addition of the new sensor, its corresponding readout mechanism, and the additional signal processing are the main downsides that have hindered ubiquitous implementation of this method. It is worth mentioning here that an alternative adaptation of the second method has been developed which associates a reference microcantilever whose response is later subtracted from that of the measurement microcantilever [4,23–27]. In this case, the measurement microcantilever responds to changes of both desired and undesired parameters. But, the reference microcantilever only responds to changes of the undesired parameter (this is usually achieved by passivation of its surface to that measurand [23–26]). As a result, the measured differential bending corresponds to the desired parameter. This alternative method has been used in many sensing applications, such as detection of proteins [25], and measuring pH of solutions [28]. However, it suffers from an inherent downside which limits its effectiveness, and that is the difference between the mechanical properties of the reference and the measurement microcantilevers [29]. A third method, usually utilized to minimize the sensitivity to ambient temperature change of bimaterial microcantilever-based thermal detectors, is based on using multi-folded bimaterial supporting legs [30,31]. In this method, a serial combination of an even number of bimaterial legs, in a serpentine manner, results in them cancelling out each others thermomechanical response. As a result, the effect of ambient temperature change on the thermomechanical response

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of the device is minimized. The added length of supporting legs; however, can adversely affect the performance of the device by for example, lowering its resonance frequency. This also increases the thermal vibrational noise which is undesirable in chemical and biological microcantilever-based sensing applications [32]. In this paper, a new method for tuning the thermomechanical response and minimizing the sensitivity to temperature of bimaterial microcantilevers is proposed. The new method employs geometrical alterations to the cross section of the bimaterial microcantilever to modify its thermomechanical response. It allows controlling the direction and the amplitude of the out-ofplane deflection of the bimaterial structure when a certain temperature change happens. Using the new design concept, various bimaterial gold–polysilicon test microcantilevers were fabricated using the commercially available foundry process PolyMUMPsÒ [33]. Thermal loading experiments were carried out using a temperature-controlled ceramic heater. Thermomechanical responses of the test specimens were quantified using a capacitance measurement technique. Experiments show good agreement with numerical simulations of the controllable deflection of the bimaterial microcantilevers. 2. Design concept The thermomechanical response of a bimaterial microcantilever subjected to a temperature change is related to the thermomechanical stresses generated in its structure. In a bimaterial microcantilever with rectangular cross section (Fig. 1(a)) subjected to a temperature increase DT, the CTE mismatch between the two layers bends the structure in such a way that the material with the higher CTE lies on the convex side of the deformed body (Fig. 1(b)). A gold–polysilicon bimaterial microcantilever is a typical example of such structures. The interactions of the two materials can be represented by axial forces P1 and P2, and bending moments M1 and M2. As a result of the equilibrium condition

P1 ¼ P2 ;

M1 ¼

P1 t1 ; 2

M2 ¼

P2 t2 : 2

ð1Þ

The radius of thermally induced curvature of the structure can be expressed as [34]

q¼

   1 h 2ðE1 I1 þ E2 I2 Þ 1 1 ; þ þ h E1 t1 E2 t2 DaDT 2

ð2Þ

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ments of inertia, and Da is the difference between the CTEs of the two materials. The distance between the centers of area (centroids) of the two materials is represented by h (Fig. 1(a)) and is equal to (t1 + t2)/2. Taking into account the total length of the bimaterial microcantilever L, the corresponding deflection of the tip can be approximated as Dy = L2/2q [15]. Similarly, for small displacements, the lateral deflection at any point along the length of the beam can be approximated as

DyðzÞ ¼ z2 =2q:

ð3Þ

Accordingly, the capacitance between the thermally deformed bimaterial microcantilever and the fixed electrode underneath is expressed as

C¼

Z

eWdz g þ DyðzÞ

¼

Z

eWdz ; g  z2 =2q

ð4Þ

where e is the permittivity of air, W is the width of the microcantilever, and g is the initial gap between the microcantilever and the bottom electrode (Fig. 1). In this analytical model, all the material properties are assumed temperature-independent and the beam is considered narrow widthwise, i.e. @y=@x ¼ 0. From Eqs. (3) and (4), it is inferred that the sensitivity to temperature, which manifests itself in the form of lateral deflection yðzÞ, can be minimized by maximizing the radius of curvature q (which according to Eq. (2) is a function of temperature change DT). This can be achieved by doing either h ? 1 or h ? 0 in Eq. (2). Since h is the distance between the centers of area of the two materials, h ? 0 stands out as the only physically viable option. This suggests that in order to minimize the sensitivity to temperature, the cross section of the bimaterial microcantilever should be modified in such a way that the centers of area of the two materials get as close to each other as possible, and ideally coincide. Based on the previous analysis, Fig. 2(a) proposes a new bimaterial microcantilever with a corrugated cross section (Fig. 2(b)) that enables tuning of its thermomechanical response. Although in this analysis the device is designed in accordance with the PolyMUMPs process design rules [33], the concept can be customized to any fabrication process or combination of materials. In this particular design, through a selective combination of etching steps and sacrificial layers, a corrugated silicon base layer is obtained with a centroid that can be positioned at a desired height. By changing the geometrical parameters of the cross

where t1 and t2 are the thicknesses of the two layers, E1 and E2 are the Young’s modulus of the two materials, I1 and I2 are the area mo-

Fig. 1. Bimaterial microcantilever; (a) cross-section; (b) concave down deflection due to temperature increase when material #1 exhibits more thermal expansion than material #2.

Fig. 2. New bimaterial microcantilever; (a) 3D schematic and (b) cross section.

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section, the centroid can be shifted vertically, so that it can be below (h > 0 in Eq. (2)), above (h < 0 in Eq. (2)), or at the same height as that of the gold layer (h = 0 in Eq. (2)). If t1 and t2 represent the thicknesses of the gold and polysilicon layers in the new bimaterial microcantilever, respectively, the distance between the centers of area of the two materials in the cross section of Fig. 2(b) is calculated to be

G  y Si ¼ t1 =2  h¼y

Z

  ydA =A Si

¼ t1 =2  ½2W 1 ðg 1  g 3  t 2 =2Þ þ 2W 2 ðg 2  g 3  t 2 =2Þ  t 2 ðW G þ 2W 3 Þ=2 þ 2t 2 ðg 3  g 1 Þ þ ðg 21 þ 2g 22 þ g 23  2g 1 g 2  2g 1 g 3 Þ =½2W 1 þ 2W 2 þ 2W 3 þ W G þ 2ðg 1  g 3 Þ



ð5Þ

G and y Si are the y-coordinates of the two centroids, and A is where y the cross section area. The origin of the x–y coordinate system in Fig. 2 is located on the bearing surface of the two layers and the whole structure is symmetric with respect to the y-axis. The geometrical parameters g1, g2, g3, W1, W2, W3, WG and L are introduced in Fig. 2. Note that by setting g1 = g2 = g3, Eq. (5) reduces to h = (t1 + t2)/2 which is the case for the rectangular cross section shown in Fig. 1(a). In the new cross section, the two sides whose width is W1 are called the ‘‘side wings’’ and are responsible for shifting the center of area of the silicon base layer vertically. The wider the side wings are, the higher the corresponding center of area will be. For a given thickness of the gold layer, we can thus find the W1 which results in h = 0 in Eq. (5) and q = 1 in Eq. (2). This specific width is referred to as the critical width and is represented by W1,cr hereafter. In next sections, Eq. (5) is used to calculate the critical width for a given set of geometrical parameters and the results are then verified by finite element simulations and thermal loading experiments. 3. Modeling The fact that each layer can be individually patterned in the PolyMUMPsÒ fabrication process makes it possible to fabricate the corrugated cross section of Fig. 2(b). This fabrication process offers two polysilicon structural layers (2 lm and 1.5 lm in thickness), two silicon oxide sacrificial layers (2 lm and 0.75 lm in thickness), and one metal layer on top (0.52 lm in thickness) [33]. Using this process, various devices with the proposed new cross section design were fabricated. The nominal design parameters common in all the fabricated devices are t1 = 0.52 lm, t2 = 1.5 lm, g1 = 4 lm, g2 = 2 lm, g3 = 1.25 lm, W2 = 7 lm, W3 = 3 lm, WG = 60 lm and L = 320 lm. As mentioned before, by changing W1 we can manipulate the centroid of the silicon base layer. Using the nominal design parameters, and based on the analysis provided in the previous section, Fig. 3 shows how the y-coordinates of the two centroids change with W1 (bold solid lines labeled as ‘‘Silicon’’ and ‘‘Gold’’). According to Fig. 3, we can determine a critical side wing width, W1,cr, of approximately 25.5 lm that causes the two centroids to coincide, and thus corresponds to h = 0 in Eq. (5) and q = 1 in Eq. (2). The effect of deviation of thicknesses of various layers from their nominal values, i.e. fabrication tolerances, is also incorporated in Si; min , y Si;max , y G;min , and y G;max . Fig. 3 by the dotted lines labeled as y According to the PolyMUMPsÒ Design Handbook [33], these fabrication tolerances are: ±0.15 lm for the first polysilicon (Poly 1), ±0.10 lm for the second polysilicon (Poly 2), ±0.25 lm for the first silicon oxide (Oxide 1), ±0.08 lm for the second silicon oxide (Oxide 2), and ±0.06 lm for the top metal layer. Accordingly, the area beSi;min and y Si;max in Fig. 3 represents the postween the dotted lines y sible y-coordinate of the centroid of the silicon layer when all the corresponding dimensional tolerances are taken into account. SimG;min and y G;max represents ilarly, the area between the dotted lines y

Fig. 3. Change of height of the centers of area with W1; () symbol marks the W1 values used in the fabricated devices.

the possible y-coordinate of the centroid of the gold layer. Based on Eq. (5) and Fig. 3, and regardless of the fabrication tolerances, if W1 < 18.5 lm, then the centroid of the silicon layer is below that Si < y G zone) and h > 0 in Eq. (2) and as a result of the gold layer (y the whole structure bends down when temperature increases, similar to Fig. 1(b). Alternatively, if W1 > 36.5 lm, then the centroid of Si > y G zone) and the silicon layer is above that of the gold layer (y the bimaterial microcantilever bends up when temperature increases (h < 0 in Eq. (2)). Because of the unpredictability of the fabrication tolerances of the PolyMUMPsÒ process, the exact determination of the critical width W1,cr is a tedious task. Consequently, in order to prove the design concept, in the following we focus more on proving the occurrence of the two opposite thermomechanical responses mentioned above, corresponding to Si < y G and y Si > y G zones in Fig. 3. the y The analytical model presented above is based on the assumption that the beam is narrow in width and no change of slope happens along the width, i.e. @y=@x ¼ 0. However, this assumption is questionable when the width of the beam is much bigger than its thickness. To address this concern and to predict the thermomechanical response of the bimaterial microcantilevers precisely, numerical simulations have also been carried out using the finite element software ANSYSÒ. To reduce the processing time, the inherent symmetry of the new design is used and one-half solid models are constructed. SOLID-186 and SOLID-122 elements, which are three-dimensional 20-Node brick elements, are used to mesh the models for thermomechanical and electrostatic analysis, respectively. In addition, all the materials are assumed linear elastic (no plastic deformation occurs) and their properties are assumed temperature-independent. The material properties used in the simulations are ESi = 160 GPa, mSi = 0.22, aSi = 2.9  106/°C, EAu = 78 GPa, mAu = 0.44, and aAu = 14.2  106/°C, where m represents the Poisson’s ratio of the corresponding material; however, since Eq. (5) is solely based on geometrical parameters, the design concept can be easily extended to any combination of materials. Microfabrication processes often introduce residual stress to microstructures. In our bimaterial microcantilevers, this residual stress manifests itself in the form of structural deformations like warping or curling. In the PolyMUMPsÒ process, the Poly 2 polysilicon and the gold layers (refer to Fig. 4) have on average 10 MPa compressive and 50 MPa tensile residual stresses, respectively [33]. The ANSYSÒ simulations incorporate these residual stresses as initial stresses. Additionally, during the PolyMUMPs process, the deposition of the gold layer is carried out at 110 °C and then the samples are cooled down to room temperature, without any further annealing step [33]. In order to incorporate the effect of this temperature change (from deposition temperature down to room

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the instrumentation used, the precision of temperature setting was determined as ±0.5 °C for 27 °C and 40 °C, ±1.0 °C for 60 °C, and ±2.5 °C for 80 °C and 100 °C.

5. Results and discussion

Fig. 4. Fabrication process flow; (a) fixed electrode and Oxide 1 deposited and patterned, (b) Poly 1 spacer deposited and patterned, (c) Oxide 2, Poly 2 base layer and gold deposited and patterned, (d) device released and spacers removed.

temperature), the initial reference temperature in our finite element simulations was set to 110 °C and the final temperature (before applying thermal loading) was set to 27 °C. In other words, an initial temperature difference of 83 °C is applied to the finite element models before the main thermal loading step is performed. After the thermomechanical analysis is completed, the electrostatic analysis is performed to calculate the capacitance between the microcantilever and the underneath fixed electrode (Fig. 2). The medium used between the two electrodes is air with a permittivity of 8.854  1012 F/m. 4. Fabrication and experiment The PolyMUMPsÒ foundry process begins with a silicon wafer, on top of which a silicon nitride (SiN) layer is deposited as electrical isolating layer. The first polysilicon layer (Poly 0) is then deposited and patterned to form the fixed bottom electrode. This is followed by the deposition and reactive ion etching of the first oxide layer (Oxide 1, Fig. 4(a)). Next, the second polysilicon layer (Poly 1) is deposited and patterned (Fig. 4(b)) to form the spacer which is used to create corrugation in the microcantilever base silicon layer. Then, the second sacrificial oxide layer (Oxide 2) is deposited, followed by the deposition and patterning of the third polysilicon (Poly 2) and the top metal layers (Fig. 4(c)). The next step is HF releasing of the device followed by supercritical CO2 drying. Once the device is completely released and dried, the Poly 1 spacers are removed (Fig. 4(d)). For experimental verification, various specimens with different widths of side wing were fabricated. Results shown in this paper correspond to two of these side wing sizes, i.e. W1 = 18 lm (bending-down behavior with a temperature increase) and W1 = 38 lm (bending-up behavior with a temperature increase). Fig. 5 shows the scanning electron microscope (SEM) micrograph of the specimen with W1 = 38 lm. To test the fabricated devices in real conditions, thermal loading experiments were carried out at our facilities. The test setup for the thermal loading experiments is shown in Fig. 6 and includes an ULTRAMICÒ ceramic heater from WATLOW (AlN ceramic, Tmax = 400 °C, including type K thermocouple), a M-150 probe station from Cascade Microtech, and a precision 20 Hz – 2 MHz LCR meter from Agilent (Model: E4980A). The microcantilever and the fixed electrode (Fig. 2(a)) are each connected to a 100  100 lm2 gold pad which is used for probing and capacitance measurement. The sensing signal was set to a voltage of 10 mV and a frequency of 1 MHz. During the experiments, the silicon substrate and all other polysilicon devices on the chip were grounded to minimize parasitic capacitance. The measurements were performed at 27 °C (room temperature), 40, 60, 80, and 100 °C. To investigate the repeatability of the measurements, each device was subjected to two complete cycles of heating up and cooling down. For

Experimental results are presented in Fig. 7, in which each data point corresponds to the average of two measurements during the heating up and cooling down steps. Fig. 7 also includes the results of finite element simulations, using the nominal thicknesses provided by the PolyMUMPsÒ design manual. For the device with W1 = 18 lm, the experiment shows a capacitance increase of approximately 6.5 fF when temperature increases from 27 to 100 °C. This clearly corresponds to a bendingdown deflection due to temperature increase and therefore, a decrease in the gap between the microcantilever and the fixed electrode. For the device with W2 = 38 lm, the opposite behavior is observed. A capacitance decrease of approximately 6.3 fF is measured as the temperature increases from 27 to 100 °C, which corresponds to a bending-up deflection. The experimental results shown in Fig. 7 suggest that the thermomechanical performance of the microcantilevers is repeatable over the temperature range of 27– 100 °C. Moreover, it clearly exhibits the two predicted opposite thermomechanical responses of the bimaterial microcantilevers, i.e. bending up and bending down behavior with temperature increase. This proves that the thermomechanical response in the new bimaterial microcantilevers can be manipulated easily within the same chip and without any need for change of fabrication process. Fig. 8 shows the results of further finite element simulations for different values of W1 between 18 and 38 lm. In this figure, the change of capacitance versus temperature is shown for a range in temperature between 27 and 100 °C. The marked data points are the result of finite element simulations and the solid lines correspond to cubic polynomial fits. As suggested previously through analytical modeling, for a given thickness of the gold layer, a W1,cr can be found which minimizes the temperature-dependence of thermomechanical response. In other words, the capacitive readout of the bimaterial microcantilever will display a minimum sensitivity to temperature (which is defined as dC/dT) for a critical width equal to W1,cr. Using the nominal design parameters of the PolyMUMPsÒ process, Eq. (5) predicted W1,cr to be approximately 25.5 lm (Fig. 3) for the given dimensions. On the other hand, the results of finite element simulations shown in Fig. 8 suggest that the sensitivity can have different values depending on W1 and the temperature range of operation. For example, the curve corresponding to W1 = 33 lm, shows a sensitivity less than 0.01 fF/°C between 85 °C and 97 °C (marked in Fig. 8). The difference between the results of finite element simulations (Fig. 8) and the simple analytical model of Eq. (5) (see Fig. 3) can be mainly attributed to the effect of the assumption we made earlier that the microcantilever performs like a narrow beam. For the two fabricated devices with W1 = 18 lm and W1 = 38 lm, the sensitivity to temperature was measured to be equal to 0.089 fF/°C and 0.086 fF/°C, respectively, for a temperature range between 27 and 100 °C. Fairly good agreement can therefore be observed between experimental results and FEM simulations. Table 1 summarizes the results of sensitivity analysis of the various devices analyzed in Fig. 8 with 23 lm < W1 < 33 lm, and shows the temperature range of operation in which the sensitivity to temperature could be less than 0.01 fF/°C. In this paper, a sensitivity to temperature equal to 0.01 fF/°C is assumed to be small enough to consider the corresponding device’s thermomechanical behavior near temperature-independent for a certain operating temperature range. However, depending on the application and

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Fig. 5. SEM micrograph of gold–polysilicon bimaterial microcantilever with W1 = 38 lm. The removed Poly 1 spacer can be seen next to the microcantilever.

Fig. 6. Test setup for thermal loading experiment; inset shows the test chip on ceramic heater and three probe tips for measurements and grounding of the substrate.

Fig. 8. Change of capacitance with temperature for different values of W1.

Fig. 7. Experimental change of capacitance with temperature; (s) and (h) symbols correspond to results of the first and the second loading cycles, respectively (hollow symbols correspond to W1 = 18 lm and filled symbols correspond to W1 = 38 lm); (J) and (I) symbols characterize the finite element simulation results for W1 = 18 lm and W1 = 38 lm, respectively.

operating conditions, lower sensitivities could be obtained for smaller temperature ranges. The results of the finite element simulations shown in Table 1 suggest that we can find W1 values which result in a thermomechanical response with sensitivity to temperature less than 0.01 fF/°C for temperature ranges as wide as 20 °C. Furthermore, according to Fig. 8, by considering narrower temperature ranges, it is possible to achieve bimaterial microcantilevers with temperature sensitivities as small as 0.001 fF/°C. For instance, for the

A. Najafi Sohi et al. / Microelectronic Engineering 96 (2012) 18–23 Table 1 Temperature range of operation of the microcantilevers studied in Fig. 8 for temperature sensitivity less than0.01 fF/°C. Device

W1 (lm)

Temperature range associated with dC/dT < 0.01 fF/°C

1 2 3 4 5 6 7

23 25 27 28 29 31 33

27–44 °C 44–62 °C 51–69 °C 54–74 °C 72–84 °C 75–93 °C 85–97 °C

bimaterial microcantilever with W1 = 33 lm, the sensitivity to temperature is calculated to be less than 0.001 fF/°C in the temperature range of 91–94 °C (Fig. 8).

6. Summary In summary, a new design for bimaterial microcantilevers was proposed which enables tailoring of their thermomechanical response. Using this new design concept, bimaterial microcantilever specimens were fabricated and it was demonstrated that their thermomechanical behavior could be reversed within the same wafer and without changing processing parameters or order of deposition of the thin film materials. Experiments performed on two fabricated devices using PolyMUMPsÒ process with W1 = 18 lm and W1 = 38 lm show a sensitivity to temperature equal to 0.089 fF/°C and 0.086 fF/°C, respectively, for a temperature range between 27 and 100 °C. These results agree fairly well with FEM simulations and show the flexibility and the potential of this design to tune the thermomechanical response of bimaterial microcantilevers. An important industrial application of this new design concept is the potential for fabrication of bimaterial microcantilever-based sensors with intrinsic minimized sensitivity to ambient temperature change, which drastically alleviates the need for sophisticated temperature compensation schemes/systems. Finally, although our experimental results were obtained using a capacitive measurement method, the proposed design concept can easily be extended to bimaterial microcantilever-based sensors with other readout systems.

Acknowledgement The authors would like to acknowledge funding provided by the Ontario Centres of Excellence (OCE) and the National Science and Engineering Research Council of Canada (NSERC). They would also like to acknowledge the products and services provided by CMC Microsystems (www.cmc.ca) that facilitated this research. A. Najafi Sohi also thanks the Waterloo Institute of Nanotechnology (WIN) for their financial support through the WIN Nanotechnology Graduate Student Scholarship.

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