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In this chapter we present experiments performed on piezoresistive micro- cantilevers embedded in microfluidics. The fabrication procedure for microfluidic embedded devices was discussed in section 3.1.5. A typical device is shown in Fig. 7.2.A. The microfluidic valves are operated using a voltage controlled pressure switch purchased from Fluidigm, Inc. This allowed an adjustable pressure (a pressure of between 21-24 PSI was used) to be applied to the control valves. The valves could be opened using a computer controlled voltage to the Fluidigm controller. In the case of fluidic drive, an oscillating voltage of square wave form was supplied to the Fludigm controller via an Agilent 33250A function generator, allowing the valve of interest (generally the output valve, although other valves also worked for this technique) to be opened and closed at known frequency.

7.2.1 Cantilevers with Silicon Piezoresistive Elements

We consider first a silicon piezoresistive cantilever under fluidics drive. In Fig. 7.2.B we show the measured resistance change of the device for a fluid drive at 1.1 and 1.3 Hz. The cantilever is positioned in the outflow via, i.e., when the valve is opened the cantilever is deflected downward under forward flow, and when the valve is closed the cantilever deflects upward due to the back flow. The direction of resistance change is consistent with these directions of deflection. These measurements were performed on a device of length =23µm, width w=5µm, leg length _leg =5µm, leg width wleg =2µm, and thickness t=100nm. The custom preamplifier described in section 4.2.1 was used, followed by the Stanford SR560 low noise preamplifier set to gain 5 with 6dB filtering

Fig. 7.2.A Piezoresistive device embedded in microfluidics

The microfluidic channels are comprised of three layers, a lower layer fabricated from PDMS containing all of the control valves and fluidic inlets and outlets, a DRIE etched channel through the silicon wafer, and a topside channel connectiong the DRIE etched vias fabricated from SU-8 resist patterned on a glass side. (See section 3.1.5). The entire assembled chip is shown in (a). A backside view of the control valves is shown in (b).

(a)

(b)

low pass 0.03 Hz and high pass 30Hz. The signal was then collected with the Hewlett Packard Infinium oscilloscope, AC coupled on 1MΩ input.

The piezoresistively-detected signal from fluid drive (Fig. 7.2.B) was input into a Stanford SR830 lock-in amplifier. A bridge circuit was used with a bias resistor of 81.5kΩ and 1.3V applied across both the device and bias resistor. A SR560 preamplifier was used with a gain of 1000. A time constant of 1s was used for the lock-in detection. The RMS signal from pulsatory fluidic drive was analyzed as the flow pressure was changed. The pressure of the fluid in the flow channels is directly related to the flow rate and consequently the force applied to cantilever. We begin with an estimate of the flow rates and forces which can be achieved with this means of excitation. The microfluidic channel is comprised of three paths: the PDMS flow path, flow through the silicon fluidic vias, and the topside fluidic path (through the flow channel defined by SU-8 and the glass coverslip). Of these the PDMS flow path is by far the longest and dominates the fluidic resistance. The flow channels are typically 70µm wide. They are 10µm high at the center of the channel. We model this geometry using an ellipse of equivalent cross- sectional area and use the width of the channel for the length of the major axis of the ellipse. The volumetric flow rate, Q, for pressure driven laminar flow through a tube of elliptical cross-section (with semi-axes a and b) is given by:

3 3 2 2 4 G a b Q a b π µ = + 1

where µ is the dynamic or shear viscosity and G= ∆p l/ is the pressure gradient.2 The mean flow rate is then given by u Q A= / where A is the cross-sectional area of the flow.

the PDMS channels. However, our cantilevers are located within the silicon vias for which the cross-sectional area of 75µm x 75µm is noticeably greater. We estimate the flow rate in the vias to be _{via PDMS}

via

PDMS A

u u

A

= . For our devices we obtain

via ~ 0.55mm/s/PSI

u . As a judge of the role geometry plays in this estimation, if we instead assume a circular cross-section of the same cross-sectional area, we obtain

via ~ 2 mm/s/PSI

u . Direct measurements to estimate the flow rate of beads confirms a flow rate on the order of a few mm/s.3 _{Only a rough estimate was obtained directly in}

these experiments because the camera used on the microscope was not fast enough to accurately measure these flow rates. An alternative is to measure the flow rate in the tubing used at the inlet to the fluidics. Due to the larger cross-section the flow rate there is much slower and therefore easier to measure. Based on the above flow rates and the inner diameter of the tubing (0.01” ), at a pressure of 7PSI the fluid should flow through 1m of tubing in ~36 min. This is roughly consistent with what we observe. We obtain a rough estimate of the force exerted on the cantilever by the flow by considering the Stokes formula for the force exerted on a sphere of radius, a: F=6πηau.4 We approximate

/

c

a= A π where A_c is the area of the lower surface of the cantilever. For our device this gives Ftip=αF =120pN at 7PSI. Where we used the parameter α introduced in sections 2.2.2 and 2.3.2.

In Fig. 7.2.C we show the pressure dependent device response. The flow rates used in Fig. 7.2.C (b) were calculated in the manner of the preceeding paragraph. The resistance of this device is 75kΩ. The force scale was calculated from the measured

resistance change using the calculated values _{/ 1x10}8_Ω/m

d

R x

∂ ∂ = (section 2.3.4) and

K=13mN/m (section 2.3.1). At 7PSI, a resistance change of 211ppm was measured. This corresponds to a force of 2.5nN. Using the calculations above we can thereby estimate a flow rate of 88mm/s at the location of the cantilever. The linearity with pressure and reproducibility is shown in Fig. 7.2.C (b). This data suggests a possible application of these devices for measuring flow rates within microfluidic channels.

This variance in the data of Fig. 7.2.C (a) provides a measure of the sensitivity for our experiments. The standard deviation in the response at 7PSI was 0.94ppm or 41pN, over a 1Hz bandwidth for a sensitivity of 41pN/ Hz.