Design and realization of an electrostatic micropump used in a linear mode

Olivier FRANÇAIS, Samir BENDIB Group ESIEE Cité Descartes , BP 99 93162 Noisy le Grand Cedex France Tel : +33 1 45 92 65 86 Fax :+33 1 45 92 66 99 [email protected] , [email protected]

Abstract modeling a fluidic device [2] and used it This paper is focused on the to extract the resonant frequency of a modeling and realization of an micropump. Here, due to the use of a electrostatic micropump composed of polarization voltage, the electrostatic passive valves without mechanical part. actuator is modeled and used in a linear The electrostatic actuator is used here in mode (equivalent to a pneumatic a linear mode by using a polarization pressure). (DC voltage) and activating the actuator around this polarization (ac voltage). The 2. Micropump description micropump modeling is based on The working of the micropump is electrical analogies. By this way, the based on electrostatic pressure to deflect a implementation of the micropump under a membrane. The deflection of the Pspice simulator allows to define its membrane modifies the chamber volume resonant frequency from the flow and generates a pressure variation, which behavior versus frequency of actuation. A activates the fluid displacement. By the realization is associated to the modeling. use of passive microvalves [3], the fluid Three different wafers are needed to moves throughout the micropump in a obtain the complete structure (by DRIE direction imposed by them. technique) and five steps of Connection photolithography are sufficient to obtain Valve the micropump. Membrane Si Wafer 1. Introduction SOI Wafer The developments of microfluidic Glass Wafer devices have enabled a lot of new kind of Electrostatic excitation applications in a lot of analysis device Fig. 1 : view of the valveless electrostatic [1]. Micropump has a great part for micropump controlling microfluidic transmission. For optimizing such a microsystem, using an The micropump structure is depicted in FEM software is too heavy because of the figure 1. It’s composed of three different coupling effect between mechanic, wafers : fluidic, and electric phenomena. This - A Pyrex wafer to obtain the electrostatic paper recalled the electric analogy for actuator. - A SOI wafer to obtain both membrane Table 1. Electric equivalence of and valves (Fig. 4). fluidic parameters - A Si wafer to close the micropump and Fluidic parameters Electric equivalence define the access. Pressure (P) Voltage V Û P Flow (f) Current I Û f 3. Micropump modeling Inertia of fluid : Inductance l In order to estimate the micropump density (r) in a channel L = r (length l and hydraulic S performances, we have to model the H section S ) electrostatic actuator and the fluid H Loss Pressure in a Resistance behavior versus pressure. 32hl channel : R = D2 .S 3.1 Electrostatic actuator (length l, dynamic H viscosity h and hydraulic The pressure generated by an diameter DH) electrostatic actuator can be expressed by Compliance Capacitance the formula : dVol 3p R6 Cm = Cm = 2 dP 16E h3 e0 (UDC + u ac ) (Silicon circular membrane: Pe = 2 (1) 2(e - WDC - w ac ) Radius R, thickness h and By supposing that the AC voltage young’s modulus E) The mechanical resonant (u ) is smallest than the DC voltage ac frequency is not taken into account here (U ) and that the position variation w DC ac but can be implemented if needed. around static position WDC doesn’t influence the electrostatic pressure, the 3.3 Particular fluidic component equation 1 can be decomposed in a DC For the valve behavior, the part and in an AC part : modeling must take into account the flow 2 e 0U DC e 0U DC evolution with the pressure [3]. In this Pe = 2 + 2 u ac (2) 2(e - WDC ) (e - WDC ) case, we use a current source driven by a It means that by using a voltage that corresponds to the differential potential of the current polarization UDC, the variation of the electrostatic pressure can be considered source. The flow is than implemented as a linear pressure (first term in equ. 2) analytically in the current source I. To and becomes directly proportional to the simplify, two current sources are used for AC voltage (second term in equ. 2). The each microvalve, one for the direct flow electrostatic pressure can then be viewed and a second for the reverse flow: as a pneumatic pressure and be modeled · Direct flow (DU>0) : by a simple voltage source. Id=[Fd(DU)/ DU]*(abs(DU)+ DU)/2 Note : Id=0 if DU<0 3.2 Fluidic behavior · Reverse flow (DU<0) : The electric analogy [2] can be Ir=[Fr(DU)/ DU]*(abs(DU)- DU)/2 applied to a micropump structure, by this Note : I =0 if DU>0 way a Pspice simulator can be used to r simulate the micropump behavior. The Fd is the analytic approximated equivalence is based on the used of relation of the flow versus pressure in the simple electric components such as R, L direct mode and Fr in the reverse mode. It or C. The analogy is depicted in table 1 : means that the valve behaviors are not linear but depends on the pressure. DU represents the pressure applied on the 1 2 fo = (3) valve. This analytic relation can be 2p LC deduced from numeric simulation or (with L and C defined in table 1 and measurement. Here nozzle-diffuser [3] represented in figure 2) (fig. 4) and Tesla diode (fig. 4) are used in the realization. (nl/s) 10 4. Implementation and simulation results 1 A very classical software can be used to simulate the micropump (Pspice). 0.1 The result of implementation is depicted in figure 2 with all the electric analogy defined in table 1.

0.01 (Hz) 10 100 1k 10k Fig. 3 : Frequency behavior of the micropump

To optimize the working of the micropump, the ac voltage of the electrostatic actuator will be used at this frequency. The variation of the flow will be obtain by controlling the ac amplitude. The average values of parameters used Fig. 2: Electric representation of a volumetric for the simulation correspond to micropump membrane in silicon with a radius of The circuit obtained is very close 1400µm and a thickness of 16µm (Equivalent capacitor value of 6.25e-15). to a RLC circuit with two RL branches The channels have an average section of (the input and output channel) connected 500µ*150µm with a length of 2350µm to a capacitor (the chamber). A (Equivalence Resistor of 3.4e10 and simulation of the micropump flow versus inductance of 6e7). The fluid used is frequency has been achieved by several supposed to be water (h =1e -3Pa.s ). The transient analysis. A resonant frequency occurs and reflects the second order average expected fluidic resonant comportment of every fluidic system frequency is 370 Hz. (Fig. 3). A comparison with electronic linear circuit (RLC type “second order” 5. Realization of a prototype and RC type “first order”) is added to the The micropump realization is figure 3. centered on the used on a SOI wafer to The micropump behavior is very obtain both the membrane and the valve. closed to a capacitor connected to two RL The depth of the valve and channel is circuits. We can than expressed the equal to the thickness of the top SOI resonant frequency (fo) of the micropump wafer (500µm for our wafers), the as : thickness of the membrane is equal to the SOI (here 16µm are used). For the silicon wafer, a complete etch of the wafer is done by DRIE technique (Fig. 7.1). A 4000 angstrom layer of Al is used to protect the wafer during all the etch. Then a complete cleaning is done to obtain the cap (Fig. 7.2). Finally, we do first an anodic bonding between the SOI wafer and the Fig. 4: Top view of the etched SOI wafer Pyrex wafer (380°, 450V) (Fig. 8.1). (Nozzle-Diffuser and Tesla valve) Then a direct silicon/silicon bonding is achieved with the Si wafer (Fig. 8.2) to For the SOI process, a first DRIE obtain the complete structure. etching is done on the SOI (Fig. 5.1) for preparing an access window. Than the top side is etched until the SiO2 layer is reached (Fig. 5.2). A complete cleaning is done to remove the SiO2 (Fig. 5.3), the membrane and the valve are then obtained. For the electrostatic actuator, a Pyrex wafer is used. The Pyrex process starts with a HF10% etching (with chrome protecting layer) of 5 µm to obtain the Fig. 7 : Silicon process Fig. 8 :Bonding step electrode localization (Fig. 6.1). Than a step of Aluminum sputtering enable to 6. Conclusion design the shape of the electrode. (Fig. From the development of electric 6.2) A last step of PECVD for Si3N4 analogies applied to an electrostatic deposition enables to protect the electrode micropump, a micropump simulator which activate the membrane. This step (implemented under Pspice) has been can be shortened, it’s a protection achieved. From the simulation results and between the electrode and the membrane comparison to classical RLC circuit, a in case of short cut. This protective layer formula of the resonant frequency is is etched by RIE technique (Fig. 6.3) for presented from the electric equivalent the external connections. parameters. Then, the realization of a prototype is depicted. The process is based on DRIE technique and used a double bonding step for the micropump assembly.

7. References [1] N. Giordano, J-T Cheng, “Microfluid mechanics : progress and opportunities”, Journal of Physics Condensated Matter, Vol 13 (2001) pp 271 295. [2] BOUROUINA T., GRANDCHAMP J.P., "Modeling micropumps with electrical equivalent networks", Journal of Micromechanics and Microengineering, vol.6 (1996) pp. 398-404. [3] A. Olsson, G. Stemme and E. Stemme, "Numerical and experimental studies of flat-walled diffuser elements for valve-less micropumps", Sensors and Actuators A, 84 Fig. 5 SOI process Fig. 6 Pyrex process (2000) pp. 165-175.