Patent Publication Number: US-9427961-B2

Title: Microfluidic jetting device with piezoelectric actuator and method for making the same

Description:
BACKGROUND 
     1. Technical Field 
     The present disclosure generally relates to a piezoelectrically actuated microfluidic jetting device. 
     2. Description of the Related Art 
     Piezoelectric materials are useful for actuating electromechanical devices. Piezoelectric materials are those that exhibit both a piezoelectric effect and a reverse piezoelectric effect. The piezoelectric effect is the generation of a voltage across opposite faces of a piezoelectric material in response to applying pressure to the piezoelectric material. The reverse piezoelectric effect is the contraction, expansion, or otherwise deformation of a piezoelectric material in response to applying an electric field across the piezoelectric material. Some approaches to jetting ink utilize the reverse piezoelectric effect for actuation. 
     U.S. Pat. No. 6,294,860 (hereinafter &#39;860 patent) describes an ink jet recording device equipped with a piezoelectric film element. The recording device includes a vibrating plate with a piezoelectric film placed over an ink reservoir formed in a first substrate. The vibrating plate creates pressure within the ink reservoir causing ink to eject from the ink reservoir. The ink reservoir is formed by entirely removing a portion of the first substrate located beneath the piezoelectric film. Ink is ejected from the ink reservoir through an ink jetting nozzle formed in a second substrate that is bonded to a lower surface of the first substrate so that the nozzle jets ink in a direction that is away from the piezoelectric film. 
     Japanese publication JP2003133604 describes an ink jet recording device that is similar to &#39;860 patent with the exception that a nozzle is formed in a plate that is thinner than the second substrate of the &#39;860 patent, however, similar to the &#39;860 patent the thin plate is bonded to the bottom of the first substrate. 
     The existing approaches appear to be limited to jetting ink in a direction that is away from the piezoelectric element out of an ink reservoir that extends completely through a substrate. 
     BRIEF SUMMARY 
     The techniques of the herein disclosed embodiments of the invention are directed towards a microfluidic jetting device having a cavity formed in but not completely through a substrate. The jetting device also has a piezoelectrically displaceable membrane through which an inlet port opening and an outlet port opening are formed. The displaceable membrane is a composition of dielectrics, a composition of monocrystalline silicon (“monosilicon”) and dielectrics, a composition of epitaxially grown polysilicon (“epipoly”) and dielectrics, a uniform piece of monosilicon, or a uniform layer of epipoly according to several embodiments of the invention. Piezoelectric displacement of the membrane pressurizes liquid contained in the cavity, causing a portion of the liquid to eject from the cavity through the outlet port opening. Piezoelectric displacement of the membrane also creates suction in the cavity, causing liquid to be drawn into the cavity through the inlet port opening. 
     Advantageously, positioning the inlet port opening and the outlet port opening in the membrane results in a less costly jetting device because both the inlet port opening and the outlet port opening are openable using the same manufacturing process step. Additionally, utilizing a cavity that does not pass entirely through the substrate eliminates the several process steps needed to protect the active side of a wafer for a back side etched used to make a cavity that passes entirely through a substrate. Furthermore, the presently disclosed embodiments of the invention enable orienting the piezoelectric actuator in the same direction of liquid ejection, which cannot be done with the approaches of the prior art. 
    
    
     
       BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS 
       In the drawings, identical reference numbers identify similar elements or acts. The sizes and relative positions of elements in the drawings are not necessarily drawn to scale. For example, the shapes of various elements and angles, and some of the elements are enlarged and positioned to improve understanding of the inventive features 
         FIG. 1  is a schematic cross-sectional view of an actuated microfluidic jetting device, according to an embodiment of the invention. 
         FIG. 2  is a top plan view illustrating the application of an etch to form channels in a substrate as part of forming the microfluidic jetting device of  FIG. 1 , according to an embodiment of the invention. 
         FIG. 3  is a schematic cross-sectional view of the microfluidic jetting device of  FIG. 2 , according to an embodiment of the invention. 
         FIG. 4  is a schematic cross-sectional view illustrating the application of an isotropic etch to the microfluidic jetting device of  FIG. 2  to form a cavity, according to an embodiment of the invention. 
         FIG. 5  is a schematic cross-sectional view illustrating the deposition of a dielectric layer to form a membrane of the microfluidic jetting device of  FIG. 4 , according to an embodiment of the invention. 
         FIG. 6  is a schematic cross-sectional view illustrating the addition of piezoelectric element above the membrane of the microfluidic device of  FIG. 5 , according to one embodiment of the invention. 
         FIG. 7  is a schematic cross-sectional view of the addition of a fluid reservoir to the microfluidic jetting device of  FIG. 6 , according to one embodiment of the invention. 
         FIG. 8  is a schematic cross-sectional view illustrating the application of an anisotropic etch to the microfluidic jetting device of  FIG. 3 , according to another embodiment of the invention. 
         FIG. 9  is a schematic cross-sectional view of the application of an isotropic etch to form a cavity of the microfluidic jetting device of  FIG. 8 , according to an embodiment of the invention. 
         FIG. 10  is a schematic cross-sectional view illustrating the growth of epitaxial monosilicon to enclose the cavity of the microfluidic jetting device of  FIG. 9  with a membrane, according to an embodiment of the invention. 
         FIG. 11  is a schematic cross-sectional view illustrating the addition of a piezoelectric element to the microfluidic jetting device of  FIG. 10 , according to an embodiment of the invention. 
         FIG. 12  is a schematic cross-sectional view illustrating the growth of silicon nitride around silicon dioxide to enclose the cavity of the microfluidic jetting device of  FIG. 9  with a membrane, according to an embodiment of the invention. 
         FIG. 13  is a schematic cross-sectional view illustrating the growth of epitaxial monosilicon to enclose the cavity of the microfluidic jetting device of  FIG. 9  with a membrane, according to an embodiment of the invention. 
         FIG. 14  is a top plan view of a printer having a plurality of microfluidic jetting devices actuated with an electrical pulse, according to an embodiment of the invention. 
     
    
    
     DETAILED DESCRIPTION 
     In the description provided herewith, certain specific details are set forth in order to provide a thorough understanding of various disclosed embodiments. However, one skilled in the relevant art will recognize that embodiments may be practiced without one or more of these specific details, or with other methods, components, etc. In some instances, well-known structures or processes associated with fabrication of MEMS have not been shown or described in detail to avoid unnecessarily obscuring descriptions of the inventive embodiments. 
     Unless the context requires otherwise, throughout the specification and claims that follow, the words “comprise” and “include” and variations thereof, such as “comprises,” “comprising,” and “including,” are to be construed in an open, inclusive sense, that is, as meaning “including, but not limited to.” 
     Reference throughout this specification to “one embodiment” or “an embodiment” means that a particular feature, structure or characteristic described in connection with the embodiment is included in at least one embodiment. Thus, the appearances of the phrases “in one embodiment” or “in an embodiment” in various places throughout this specification are not necessarily all referring to the same embodiment. Furthermore, the particular features, structures, or characteristics may be combined in any suitable manner in one or more embodiments. 
     As used in this specification and the appended claims, the singular forms “a,” “an,” and “the” include plural referents unless the content clearly dictates otherwise. It should also be noted that the term “or” is generally employed in its sense including “and/or” unless the content clearly dictates otherwise. 
     As used in the specification and appended claims, the use of “correspond,” “corresponds,” and “corresponding” is intended to describe a ratio of or a similarity between referenced objects. The use of “correspond” or one of its forms should not be construed to mean the exact shape or size. 
       FIG. 1  is a schematic cross-section illustrating a microfluidic jetting device  20 , according to one embodiment of the invention. The microfluidic jetting device  20  includes a membrane  22 , a piezoelectric element  24 , a bottom electrode  26 , and a top electrode  28 , which together constitute an actuator  30 . The microfluidic jetting device  20  also includes a substrate  32 , a cavity  34 , an inlet port  36 , and an outlet port  38 . 
     The membrane  22  is positioned above the cavity  34  and is configured to express, namely to expel, displace, or eject a volume of liquid from the cavity  34 , according to one embodiment of the invention. The membrane  22  may be formed using one of various techniques that will be described in detail in connection with  FIGS. 2-15 . According to one embodiment, the membrane  22  includes a plurality of silicon dioxide fingers surrounded by silicon nitride. According to another embodiment, the membrane  22  also includes a layer of polycrystalline silicon (“polysilicon”). According to another embodiment, the membrane  22  is shaped and grown from monocrystalline silicon (“monosilicon”). 
     The piezoelectric element  24  is positioned above the membrane  22  and is configured to displace the membrane  22  through a counter or reverse piezoelectric effect, according to one embodiment. Piezoelectric materials generate charge when subject to pressure or stress. Such materials are commonly used in applications for weight or pressure measurements as well as for spark or fire ignition. The piezoelectric effect is a reversible process, so under the reverse piezoelectric effect, piezoelectric materials tend to constrict, expand, or deflect when subject to an external electric field. An example of a piezoelectric material is PZT (lead zirconate titante). PZT is a ceramic perovskite material. Other examples of piezoelectric materials include crystals such as gallium orthophosphate and ceramics such as barium titanate, lead titanate, and lithium niobate. According to one embodiment, the piezoelectric element  24  is PZT. According to other embodiments, the piezoelectric element  24  is one of gallium orthophosphate, barium titanate, lead titanate, lithium niobate, and the like. 
     A lower electrode  26  and an upper electrode  28  are disposed below and above the piezoelectric element  24 , respectively. The lower and upper electrodes  26 ,  28  are conductive films or layers electrically coupled to receive electrical signals and generate an electric field E z  across a thickness d of the piezoelectric element  24 . The strength of the electric field E z  applied to the piezoelectric element  24  is directly proportional to the voltage of the signal applied and indirectly proportional to the thickness d of the piezoelectric element  24 . The applied electric field is expressed as E z =V/d, according to one embodiment of the invention. 
     The inlet port  36  extends through the membrane  22  on a side of the piezoelectric element  24  that is opposite to the outlet port  38 , according to one embodiment of the invention. The inlet port  36  is an aperture that is opened through the membrane  22  adjacent to the piezoelectric element  24  and is configured as a fluidic constrictor. According to one embodiment, the inlet port  36  is a polygonal-shaped aperture. According to another embodiment, the inlet port  36  is a henagonal-shaped aperture. The inlet port  36  unidirectionally permits fluid to flow into the cavity  34  while substantially preventing fluid from flowing out of the cavity  34 . The cavity  34  is filled with liquid through the inlet port  36  by capillary force or other fluidic forces such as suction, according to one embodiment of the invention. 
     The outlet port  38  extends through the membrane  22  on a side of the piezoelectric element  24  that is opposite to the inlet port  36 , according to one embodiment of the invention. The outlet port  38  is an aperture that is opened through the membrane  22  adjacent to the piezoelectric element  24  and is configured as a nozzle or orifice to expel a volume of fluid from the cavity  34 . The shape and size of the perimeter of the outlet port  38  enable the selective and unidirectional expression of fluid from the cavity  34 . As a result of the shape and size of the outlet port  38 , a surface tension of the liquid prevents the liquid held in the cavity  34  from undesirably discharging through the outlet port  38 . According to one embodiment, the outlet port  38  is a polygonal-shaped aperture. According to another embodiment, the outlet port  38  is a henagonal-shaped aperture. The outlet port  38  is an opening having a smaller area than the opening of the inlet port  36  according to one embodiment of the invention. 
     The inlet port  36  is opened in one of several locations in the membrane  22  with reference to the outlet port  38 , according to several embodiments of the invention. The inlet port  36  is opened on the same side of the piezoelectric element  24  as the outlet port  38 , according to one embodiment. The inlet port  36  is opened on a side of the piezoelectric element  24  that is adjacent to the side of the piezoelectric element  24  next to which the outlet port  38  is opened, according to another embodiment. The inlet port  36  is opened proximate to a first corner of the piezoelectric element  24  and the outlet port  38  is opened proximate to a second corner of the piezoelectric element  24  that is different from the first corner, according to another embodiment. The piezoelectric element  24  is henagonal and the inlet port  36  is positioned from 90 degrees to 180 degrees away from the outlet port  38  around a perimeter of the piezoelectric element  24 , according to another embodiment. 
     The actuator  30 , the inlet port  36 , and the outlet port  38  are manufactured above the cavity  34 , according to one embodiment of the invention. The cavity  34  is formed in a substrate  32  that is monosilicon. As will be discussed in further detail below, the cavity  34  is opened by isotropically etching silicon away from the area below the actuator  30 . According to another embodiment, the illustrated substrate  32  is polysilicon that has been deposited above one or more circuits manufactured using semiconductor processes. 
     In operation, the actuator  30  displaces by deflecting into and out of the cavity  34  in response to electrical signals, such as voltages, being applied across the lower and upper electrodes  26 ,  28 . According to another embodiment, the actuator  30  undulates or moves with a wavelike motion into and out of the cavity  34  in response to electrical signals being applied across the lower and upper electrodes  26 ,  28 , and the undulations and wavelike motions are tuned and controlled by altering the amplitude, shape, and or duration of the electrical signals being applied. Initially, the actuator  30  is at a resting position such that the membrane  22  is substantially parallel to a bottom surface  40  of the cavity  34  and is substantially coplanar to an upper surface  42 . In response to the application of the electric field E z  across the thickness d of the piezoelectric element  24  from the upper electrode  28  to the lower electrode  26 , the piezoelectric element  24  mechanically contracts. The mechanical contraction of the piezoelectric element  24  results in a deflection of membrane  22  in the direction of the cavity  34 . The mechanical contraction and deflection produce a displacement Δz of the actuator  30  from the resting position toward the cavity  34 . The membrane  22  has an initial length L, measured from one side of the cavity  34  to another. The mechanical contraction and deflection also produces a variation ΔL of the length L of the membrane so that the total length of the membrane  22  is L+ΔL from one side of the cavity to another while displacing a quantity of the volume of the cavity  34 . 
     The volume of liquid expressed from the cavity  34  through the outlet port  38  is determined by the variation ΔL of the length L of the membrane  22 . The variation ΔL is expressed as:
 
Δ L=α×ΔL   f  
 
     where: 
     ΔL f =d 31 ×E z , is the length variation of a free standing and unclamped piezoelectric layer of length L, 
     α is a proportionality coefficient that takes into account the mechanical constraints of the clamped membrane, 
     d 31  is the transverse direct piezoelectric coefficient of the piezoelectric element  24 , and
 
 E   z   =V/d,  
 
     where: 
     V is the amplitude of the electric pulse applied between the lower and upper electrodes  26 ,  28 , and 
     d is the thickness of the piezoelectric element  24 . 
     Accordingly, the variation ΔL is proportional to the transverse direct piezoelectric coefficient d 31  multiplied by the transverse electric field E z . According to one embodiment, the variation ΔL causes the membrane  22  to deflect or displace by a distance Δz from the resting position of the actuator  30 . The distance Δz of displacement of the actuator  30  is a few tens of nanometers to a few hundreds of nanometers, according to one embodiment. 
     The displacement Δz multiplied by the area of the membrane  22  that is above the cavity  34  is approximately equal to the volume of the cavity  34  that is displaced or suctioned in when the actuator  30  is powered. 
     The volume of liquid expressed from the cavity  34  is adjustable by varying the amplitude V of the electric pulse applied to the actuator  30 , according to one embodiment of the invention. Generally, the distance Δz of displacement of the actuator  30  is a function of the amplitude V of the electric pulse. Accordingly, increasing and decreasing the amplitude V of the electric pulse will correspondingly increase and decrease the extension ΔL of the membrane  22 . According to one embodiment, the amplitude V of the electric pulse ranges between a few tens of volts to a few volts. As discussed above, the volume of liquid displaced from the cavity  24  is proportional to the extension ΔL, according to one embodiment. 
     The volume of liquid expressed from the cavity  34  is adjustable by varying the rate at which the amplitude V of the electric pulse is applied to the actuator  30 , according to another embodiment of the invention. As discussed above, the volume of liquid contained within the cavity  34  is prevented from undesirably discharging from the outlet port  38  by the surface tension of the liquid at the outlet port  38 . According to one embodiment, increasing the rate at which the membrane  22  displaces a volume of the liquid in the cavity  34  decreases the cohesion of the fluid molecules of the surface of the fluid at the outlet port  38 , enabling a greater volume of fluid to be expressed from the cavity  34  than when the membrane  22  is displaced at a lower rate. Accordingly, the volume of liquid expressed from the cavity  34  is adjustable at a given amplitude V of the electric pulse by altering the rate at which the amplitude V of the electric pulse is applied to the actuator  30 . 
     According to one embodiment, the shape of the electric pulse applied to the actuator  30  is trapezoidal (see  FIG. 14 ). The trapezoidal electric pulse includes a rate of increasing voltage, a steady-state, and a rate of decreasing voltage. According to one embodiment the rate of decreasing voltage is much higher or faster than the rate of increasing voltage in order to cause the membrane  22  to mechanically overshoot its resting position as the electric field E z  is removed from across the piezoelectric element  24 . By causing the membrane  22  to mechanically overshoot its resting position, the actuator  30  creates a suction force at the inlet port  36 , introducing additional liquid into the cavity  34 . According to another embodiment, the trapezoidal electric pulse is symmetric so that the rate of increasing voltage is the negative of the rate of decreasing voltage. The first symmetric trapezoidal electric pulse is followed by a second symmetric trapezoidal electric pulse having a polarity that is opposite to the first symmetric trapezoidal electric pulse. By applying a positive electric pulse followed by a negative electric pulse to the actuator  30 , the contraction or deformation of the piezoelectric element  24  causes a deflection or displacement of the membrane  22  in a direction away from the cavity  34 , creating a suction force at the inlet port  36  that facilitates the flow of liquid into the cavity  34  to replace the volume of liquid expressed or jetted from the outlet port  38 . 
     The displacement of the membrane  22  is tuned by sizing the area of the lower electrode  26  and the area of the upper electrode  28  to control the mechanical contraction of the piezoelectric element  24 , according to one embodiment of the invention. The lower electrode  26  spans a portion of the base of the piezoelectric element  24  so that the upper electrode  28  has a greater surface area than the lower electrode  26 . According to another embodiment, the lower electrode  26 ′ is at least as wide as the width of the base of the piezoelectric element  24 , and the lower electrode  26 ′ has a greater surface area than the upper electrode  28 . 
     Advantageously, the inlet port  36  and the outlet port  38  are opened through the membrane  22  which is displaced to force liquid in the inlet port  36  and out of the outlet port  38 . Having both the inlet port  36  and the outlet port  38  opened through the membrane  22  simplifies the manufacturing process by allowing the ports  36 ,  38  to be opened during the same manufacturing process step, according to one embodiment. Additionally, opening the outlet port  38  through the membrane  22  provides the advantage of enabling the actuator to be oriented in the same direction as liquid ejection from the outlet port  38 . 
     In general, a mechanical fluid actuator, such as the one described in  FIG. 1  and subsequent Figures, is easier to operate and adjust to the type of fluid being ejected from the outlet port  38 , than thermally operated jetting devices. For example, a thermally operated jetting device must take into account coefficients of thermal expansion and contraction of the liquid being ejected. Furthermore, the thermally operated jetting device must include circuitry to measure and adjust the temperature of the liquid in order to compensate for changes in ambient temperatures of surrounding circuits and systems. In contrast, a mechanical fluid actuator is relatively robust to temperature changes occurring in the liquid being ejected due to increases in ambient or surrounding temperatures caused by operation of a system of which the mechanical fluid actuator is a part. 
       FIGS. 2-7  illustrate various stages in a method of manufacturing a microfluidic jetting device in accordance with several embodiments of the invention. 
       FIG. 2  is a top plan view of a microfluidic jetting device  20  illustrating the formation of a plurality of channels  44  in the substrate  32 , during the manufacturing process. The plurality of channels  44  are formed by first depositing a layer of photoresist, patterning and developing the layer of photoresist, removing the developed portions of the layer of photoresist, and etching through a hard mask  46  that has been deposited over the substrate  32 . Subsequently, the layer of photoresist is removed and an etch that is selective to silicon is applied, resulting in each of the plurality of channels  44  will having a width W C  and a length L C . The formation of the plurality of channels  44  also results in the formation of a plurality of fingers  48 . Each of the plurality of fingers  48  includes a length L F  and a width W F . The length L C  of the plurality of channels  44  and the length L F  of the plurality of fingers  48  is a few tens to a few hundreds of micrometers, according to one embodiment. The channels can also be in the submicron range, for example, in the range of 100-400 nanometers if desired. According to another embodiment, the widths W C  of the plurality of channels  44  is substantially narrower than the widths W F  of the plurality of fingers  48 . 
       FIG. 3  is a cross-sectional view along line  3 - 3  of the microfluidic jetting device  20  illustrated in  FIG. 2 , during the manufacturing process. As illustrated, the hard mask  46  includes an oxide layer  50  grown or deposited over the substrate  32  and includes a dielectric layer  52  deposited over the oxide layer  50 . The dielectric layer  52  is silicon nitride deposited via chemical vapor deposition (CVD), according to one embodiment. As will be discussed in more detail below, the height H F  of each of the plurality of fingers  48  at least partially determines an overall thickness of the membrane  22 , according to one embodiment. 
       FIG. 4  is a cross-sectional view of the microfluidic jetting device  20  of  FIG. 3  and illustrates the formation of the cavity  34 , during the manufacturing process. An isotropic etch is applied through the pattern defined by the hard mask  46  to the microfluidic jetting device  20 . The isotropic etch removes portions of the substrate  32  that are beneath the plurality of fingers  48  of the hard mask  46  to define a depth D cavity  of the cavity  34 . The depth D cavity  of the cavity  34  is determined, in part, by the duration of the isotropic etch an in part by the depth D c  of the plurality of channels  44 . The depth D cavity  of the cavity  34  is a few tens of micrometers to a few hundreds of micrometers, according to one embodiment. The isotropic etch also undercuts perimeter portions  54  of the oxide layer  50  by a length L UC , so that a portion of the oxide layer  50  is suspended over the cavity  34 . The width W F  of each of the plurality of fingers ranges from hundreds of nanometers to tens of micrometers, according to one embodiment. The thickness of the oxide layer  50  is tens of nanometers to hundreds of nanometers, according to another embodiment. 
       FIG. 5  is a cross-sectional view of the microfluidic jetting device  20  of  FIG. 4  and illustrates the formation of the membrane  22 , during the manufacturing process. Initially, the dielectric layer  52  of the hard mask  46  is removed from the surface of the oxide layer  50 , for example, by an anisotropic etch. Then a layer  56 , such as silicon nitride, is deposited to surround the plurality of fingers  48  of the oxide layer  50 . The layer  56  may be a dielectric layer, such as a silicon nitride, or it can be a layer of very high resistivity, such as intrinsic polysilicon, which is so resistive as to be considered an insulator in the undoped state The layer  56  is deposited by a CVD process which is continued until spaces between the plurality of fingers  48  are filled with silicon nitride. As illustrated, the deposition of the layer  56  results in both the top, bottoms, and sides of the plurality of fingers  48  being enclosed with the layer  56 , so that the membrane  22  has continuous length L (shown in  FIG. 1 ) across the cavity  34 . Optionally, the membrane  22  includes a layer of polysilicon  58  deposited over a dielectric layer  56 . 
     During the layer  56  deposition, the layer  56  also covers surfaces of the substrate  32  are defined by the walls  60  and the bottom  40  of the cavity  34 . Because monosilicon and some dielectrics, such as silicon nitride, have poor interface properties, a layer of thermal oxide is grown on the walls  60  and bottom  40  of the cavity  34  to improve the adhesion of the layer  56  that is deposited within the cavity  34 . The resulting membrane  22  is hundreds of nanometers to a few micrometers thick and hundreds of micrometers to a few millimeters long. 
       FIG. 6  is a cross-sectional view of the microfluidic jetting device  20  of  FIG. 5  and illustrates the formation of the remainder of the actuator  30 , according to one embodiment. As discussed above in connection with  FIG. 1 , the actuator  30  includes the membrane  22 , the lower electrode  26 , the piezoelectric element  24 , and the upper electrode  28 . 
     The lower electrode  26  and the upper electrode  28  are deposited as thin film layers. Upon completion of the formation of the membrane  22 , one or more layers of resist are used to pattern or define the shape of the lower electrode  26 . The lower electrode  26  is deposited using CVD and is a silicide layer that is titanium silicide, tungsten silicide, or the like, according to one embodiment. While the use of a silicide is specified, it is within the scope of embodiments of the invention to use other thin-film conductive layers, such as platinum, tungsten, or other metal for the lower electrode  26  and the upper electrode  28 . 
     The piezoelectric element  24  is deposited above the lower electrode  26 . The piezoelectric element  24  is a piezoelectric ceramic layer, such as PZT (lead zirconate titanate). The piezoelectric element  24  is deposited with a sol-gel spin coat, sputtering, CVD, or the like. After the deposition of the piezoelectric element  24 , thermal treatments are applied to the microfluidic jetting device  20  to produce a perovskite ceramic characteristic of the piezoelectric element  24  to enhance the piezoelectric effects of the actuator  30 . 
     The upper electrode  28  is deposited in a manner described above for the lower electrode  26  after the formation of the piezoelectric element  24 , according to one embodiment of the invention. 
     The inlet port  36  and the outlet port  38  are opened in the membrane  22  after the deposition of the upper electrode  28 , according to one embodiment of the invention. According to another embodiment, the inlet port  36  and the outlet port  38  are opened in the membrane  22  before the deposition of the lower electrode  26 . The inlet and outlet ports  36 ,  38  are opened using techniques known to those of ordinary skill in the art. For example, the inlet and outlet ports  36 ,  38  are opened by depositing a layer of photoresist, developing the photoresist to the approximate shape and size of the inlet and outlet ports  36 ,  38 , and then applying an anisotropic etch to the openings in the photoresist to open the inlet and outlet ports  36 ,  38  through the membrane  22 . 
       FIG. 7  is a cross-sectional view of the microfluidic jetting device  20  of  FIG. 6  illustrated with the addition of a reservoir  62 . The reservoir  62  is communicatively coupled to the inlet port  36  to supply a quantity of liquid into the cavity  34 . The reservoir  62  is disposed at least partially over the membrane  22 . The reservoir  62  is formed using techniques similar to those described above in connection with the formation of the membrane  22 , according to one embodiment of the invention. According to another embodiment, the inlet port  36  is opened under the surface  64  and is communicatively coupled to the cavity  34  through a channel  66 , so that neither the inlet port  36  nor the reservoir  62  inhibit the operation of the actuator  30 . 
       FIGS. 8-11  illustrate various stages in a method of manufacturing a microfluidic jetting device  70  in accordance with several embodiments of the invention. 
       FIG. 8  is a cross-sectional view of the microfluidic jetting device  70  that is based on the cross-sectional view of the microfluidic jetting device of  FIG. 3 , during the manufacturing process. After a plurality of channels  45  and the plurality of fingers of monosilicon  49  are formed a dielectric layer  72  is deposited over at the plurality of fingers of monosilicon  49  and in the plurality of channels  45 . An anisotropic etch is performed to increase the depth of the plurality of channels  45  to a depth D C ′. During the anisotropic etch portions of the dielectric layer  72  are removed so that the dielectric layer  72  lines the side walls  74  of the plurality of channels  45  and a dielectric layer  76  remains above the oxide layer  50 . According to one embodiment, the dielectric layer  72  and the dielectric layer  76  are silicon nitride. 
       FIG. 9  is a cross-sectional view of the microfluidic jetting device  70  of  FIG. 8  and illustrates the formation of a cavity  78 , during the manufacturing process. The cavity  78  is formed by applying an isotropic etch for a duration of time sufficient to remove the silicon from below the plurality of fingers of monosilicon  49 . An oxide layer  80  is grown or deposited on the exposed silicon in preparation for the process steps illustrated in  FIG. 10 . Accordingly, the thickness H F  of the plurality of fingers of monosilicon  49  that was defined while etching the plurality of channels  45  determines a minimal thickness of the subsequently formed membrane. 
       FIG. 10  is a cross-sectional view of the microfluidic jetting device  70  of  FIG. 9  further illustrating the growth of an epitaxial layer, during the manufacturing process. Initially, the dielectric layers  72 ,  76  are removed with a selective etch to expose sidewalls  82  and the side walls  74  of the plurality of fingers of monosilicon  49 . Next, an epitaxial layer  84  is grown to fill the plurality of spaces  45  that are between the plurality of fingers of monosilicon  49 . Accordingly the top of the cavity  78  is enclosed by a membrane  86  which includes the plurality of fingers  49  laterally connected with the epitaxial layer  84 . The oxide layer  80  that was grown or deposited within the cavity  78  inhibits the growth of epitaxial layer  84  on the walls and the floor of the cavity  78  and thus preserves the dimensions of the cavity  78  during the growth of the epitaxial layer  84 . 
       FIG. 11  is a cross-sectional view of the microfluidic jetting device  70  of  FIG. 10  and illustrates the formation of a piezoelectric element  88 . After formation of the membrane  86 , a conformal layer  90  is optionally deposited over the membrane  86  to provide a surface adequate to receive subsequent layers, according to one embodiment. According to another embodiment, an upper surface  92  of the membrane  86  is polished smooth, using a process such as a chemical mechanical polish in preparation for the deposition of subsequent layers. The piezoelectric element  88 , a lower electrode  94 , and an upper electrode  96  are each deposited using techniques described above in accordance with  FIG. 6 . 
     An inlet port  98  and an outlet port  100  are opened through the membrane  86  using the techniques described above, according to several embodiments of the invention. With respect to the inside of the cavity  78 , the inlet port  98  is shaped as divergent nozzle, and liquid supplied to the cavity  78  through the inlet port  98  is pressurized. With respect to the inside of the cavity  78 , the outlet port  100  is shaped as a convergent nozzle to increase the pressure of the volume of liquid to be ejected from the cavity  78  through the outlet port  100 . 
       FIG. 12  is a cross-sectional view of a microfluidic jetting device  102  manufactured in accordance with another embodiment of the invention. The microfluidic jetting device  102  includes an actuator  104 , a cavity  106 , an inlet port  108 , and an outlet port  110 . 
     The actuator  104  includes a membrane  112 , a piezoelectric element  114 , a lower electrode  116 , and an upper electrode  118 . The membrane  112  includes a plurality of fingers of monosilicon  49 . The plurality of fingers of monosilicon  49  are surrounded or enclosed by a first dielectric layer  120 . The first dielectric layer  120  is thermally grown or is deposited, according to various embodiments of the invention. The first dielectric layer  120  is also grown on walls  122  and a bottom  124  of the cavity  106 . A second dielectric layer  126  is subsequently formed over the first dielectric layer  120 . The second dielectric layer  126  is deposited until each of the plurality of fingers of monosilicon  49  are laterally joined together as a single composite structure of the membrane  112 . According to one embodiment, the first dielectric layer  120  is an oxide layer that is thermally grown or deposited with a manufacturing process such as CVD. According to another embodiment, the second dielectric layer  126  is a silicon nitride layer that is deposited using CVD, sputtering, or the like. 
     The actuator  104  includes the piezoelectric element  114 , the lower electrode  116 , and the upper electrode  118  deposited above the membrane  112  using techniques described above in connection with previously disclosed Figures, according to several embodiments of the invention. 
     The cavity  106 , the inlet port  108 , and the output port  110  are opened using techniques described above in connection with previously disclosed Figures, according to several embodiments of the invention. 
       FIG. 13  is a cross-sectional view of a microfluidic jetting device  128  manufactured in accordance with another embodiment of the invention. The microfluidic jetting device  128  includes an actuator  130 , a cavity  132 , an inlet port  134 , and an outlet port  136 . 
     The actuator  130  includes a membrane  138 . The membrane  138  is formed by growing an epitaxial layer  140  around the plurality of fingers  49  of monosilicon. The epitaxial layer  140  is grown until the plurality of fingers  49  of monosilicon are joined together, making the membrane  138  a single structure expanding across the length L (shown in  FIG. 1 ) of the cavity  132 . The actuator  130  also includes a piezoelectric member  142  disposed between the lower electrode  144  and an upper electrode  146  according to the techniques described above. 
     The cavity  132 , the inlet port  134 , and the outlet port  136  are opened using techniques described above in connection with previously disclosed Figures, according to several embodiments of the invention. 
       FIG. 14  is a top plan view of a plurality of microfluidic jetting devices that are part of a printer  148 . The printer  148  includes a housing  152 , a plurality of input rollers  150 , a power supply  154 , one or more output rollers  156 , an output tray  158 , an ink reservoir  159 , and a plurality of microfluidic jetting devices  160 . 
     The plurality of microfluidic jetting devices  160  are represented by individual microfluidic jetting devices  160   a ,  160   b ,  160   c . The plurality of microfluidic jetting devices  160  include tens, hundreds, or thousands of devices similar to the illustrated microfluidic jetting devices  160   a ,  160   b ,  160   c , according to several embodiments of the invention. Each of the plurality of microfluidic jetting devices  160  is manufactured according to one or more of the embodiments disclosed herein in connection with  FIGS. 1-13 . 
     The plurality of microfluidic jetting devices  160  are electrically coupled or connected together with a conductive member  162 . The conductive member  162  is a trace that connects an electrode  164  of each of the actuators  166  to an electric signal generator  168 . The electric signal generator  168  is configured to generate a plurality of pulses  176  or sinusoidal signals that cause each of the plurality of actuators  166  to suction ink, e.g., from the ink reservoir  159 , into a plurality of input ports  170  and eject ink from a plurality of output ports  172 . As described in connection with  FIG. 1 , each of the plurality of pulses  176  is trapezoidal having a rate of increasing amplitude  178 , at least one steady-state amplitude  180 , and a rate of decreasing amplitude  182 , according to one embodiment. The rate of increasing amplitude  178  is slower than the rate of decreasing amplitude  182  in order to precisely control the ejection of liquid from the outlet port  172 . The rate of decreasing amplitude  182  faster or steeper than the rate of increasing amplitude to allow the membranes of the plurality of actuators  166  to whip past and overshoot a resting position of the membranes in order to create suction within the cavities of the jetting devices  160  at the plurality of inlet ports  170 . 
     The printer  148  operates by receiving one or more pieces of paper  174  through the plurality of input rollers  150 . The input rollers, or some other intermediate mechanism, causes the paper  174  to pass proximate to the plurality of microfluidic jetting devices  160 . The plurality of microfluidic jetting devices  160  eject ink from the plurality of outlet ports  172  on to the paper  174 , in response to the plurality of pulses  176  generated by the signal generator  168 , which are generated to cause the plurality of actuators  166  to displace the ink carried within the plurality of microfluidic jetting devices  160 . The paper  174  is subsequently guided to the one or more output rollers  156 , which propel(s) the paper  174  on to the output tray  158 . 
     The above description of illustrated embodiments, including what is described in the Abstract, is not intended to be exhaustive or to limit the embodiments to the precise forms disclosed. Although specific embodiments and examples are described herein for illustrative purposes, various equivalent modifications can be made without departing from the spirit and scope of the disclosure, as will be recognized by those skilled in the relevant art. 
     These and other changes can be made to the embodiments in light of the above-detailed description. In general, in the following claims, the terms used should not be construed to limit the claims to the specific embodiments disclosed in the specification and the claims, but should be construed to include all possible embodiments along with the full scope of equivalents to which such claims are entitled. Accordingly, the claims are not limited by the disclosure. 
     The various embodiments described above can be combined to provide further embodiments. All of the U.S. patents, U.S. patent application publications, U.S. patent applications, foreign patents, foreign patent applications and non-patent publications referred to in this specification and/or listed in the Application Data Sheet are incorporated herein by reference, in their entirety, including: U.S. Pat. Nos. 6,294,860; 6,673,593; 6,693,039; 6,770,471; 7,678,600; 7,705,416; 7,754,578; and 7,811,848 in addition to foreign publications JP2003133604 and JPH10287468. Aspects of the embodiments can be modified, if necessary to employ concepts of the various patents, applications and publications to provide yet further embodiments.