Patent Publication Number: US-2023133379-A1

Title: Reducing size variations in funnel nozzles

Description:
BACKGROUND 
     This specification relates to nozzle formation in a microelectromechanical device, such as an inkjet print head. 
     Printing a high quality, high resolution image with an inkjet printer generally requires a printer that accurately ejects a desired quantity of ink at a specified location on a printing medium. Typically, a multitude of densely packed ink ejecting devices, each including a nozzle and an associated ink flow path are formed in a print head structure. The ink flow path connects an ink storage unit, such as an ink reservoir or cartridge, to the nozzle. The ink flow path includes a pumping chamber. In the pumping chamber, ink can be pressurized to flow toward a descender region that terminates in the nozzle. The ink is expelled out of an opening at the end of the nozzle and lands on a printing medium. The medium can be moved relative to the fluid ejection device. The ejection of a fluid droplet from a particular nozzle is timed with the movement of the medium to place a fluid droplet at a desired location on the medium. 
     Various processing techniques can be used to form the ink ejectors in the print head structure. These processing techniques can include layer formation, such as deposition and bonding, and layer modification, such as etching, laser ablation, punching and cutting. The techniques that are used can differ depending on desired nozzle shapes, flow path geometry, along with the materials used in the inkjet printer, for example. 
     SUMMARY 
     A funnel-shaped nozzle having a straight-walled bottom portion and a curved top portion is disclosed. The curved top portion of the funnel-shaped nozzle gradually converges toward and is smoothly joined to the straight-walled bottom portion. The funnel-shaped nozzle can have one or more side surfaces around an axis of symmetry, and cross-sections of the curved top portion and the straight-walled bottom portion in planes perpendicular to the axis of symmetry are geometrically similar. In addition, the curved top portion of the funnel-shaped nozzle encloses a substantially greater volume than the straight-walled bottom portion does, while the straight-walled bottom portion has sufficient height to maintain jetting straightness of fluid droplets ejected through the funnel-shaped nozzle. 
     To fabricate a funnel-shaped nozzle described in this specification, first, a uniform layer of photoresist is deposited on the dielectric coated surface of a semiconductor substrate. The dielectric can be thermally grown silicon dioxide and the substrate can be a silicon-on-insulator wafer. The layer of photoresist is patterned using UV exposure followed by resist development. The cross sectional shape of the smallest dimension of the nozzle can be similar to the opening in the resist, permitting oval, round, and arbitrary nozzle shapes. The opening in the resist is transferred into the dielectric using dry etching and the resist is stripped. 
     A uniform layer of photoresist is similarly patterned with an opening that has one or more sidewalls that are substantially perpendicular to the planar top surface of the semiconductor substrate and the planar top surface of the layer of photoresist. The resist opening is designed to be slightly larger, have a similar shape, and be accurately aligned to the opening in the dielectric. Then, the patterned layer of photoresist is heated in vacuum such that the photoresist material in the layer softens and reflows under the influence of surface tension of the photoresist material. As a result of the reflow, the angled corners on or between the top edge(s) of the opening become rounded and the top edge(s) transform into a single rounded edge. The radius of curvature of the rounded edge can be controlled by the reflow bake conditions. For example, the radius of curvature of the rounded edge can be equal or greater than the initial thickness of the uniform layer of photoresist deposited on the semiconductor substrate. After the desired rounded shape of the top edges is obtained, the patterned layer of photoresist is allowed to cool and re-harden, while the rounded shape of the top edges remains. After reflow, the resist layer opening at the dielectric interface remains slightly larger than the opening in the dielectric. 
     After formation of the patterned layer of photoresist that has the opening with a curved side surface gradually expanding toward and smoothly joined to an exposed top surface of the patterned layer of photoresist, the forming of a funnel-shaped recess in the semiconductor substrate can begin. 
     A straight-walled recess is etched into the semiconductor substrate through an opening defined by the dielectric layer, not an opening formed by the reflowed layer of photoresist. The straight-walled recess can be formed, for example, using a Bosch process. The high-selectivity etching of the straight-walled recess leaves the layer of photoresist substantially un-etched. The depth of the recess can be a few microns less than the final designed length of the funnel-shaped nozzle. Once the straight-walled recess is formed into the semiconductor substrate, an isotropic dry etching process is used to transform the straight-walled recess into the funnel-shaped recess. Specifically, the etchant used in the dry etching should have comparable (e.g., substantially equal) etch rates for the photoresist, the dielectric, and the material of the semiconductor substrate (e.g., a Si&lt; 100 &gt;wafer). During dry etching, the etchant gradually deepens the straight-walled recess to form a straight-walled bottom portion of the funnel-shaped recess. At the same time, dry etching expands the sidewall of the part of the bore near the dielectric layer into a curved side surface that levels off into the horizontal surface of the semiconductor substrate. This funnel converges toward and smoothly transitions into the straight-walled bottom portion of the funnel-shaped recess. The funnel-shaped recess can be opened at the bottom by removing the un-etched substrate from below. 
     In one aspect, a process for making a nozzle, the process includes forming a first opening having a first width in a top layer of a substrate, forming a patterned layer of photoresist on the top surface of the substrate, the patterned layer of photoresist including a second opening, the second opening having a second width larger than the first width. The method includes reflowing the patterned layer of photoresist to form curved side surfaces terminating on the top layer of the substrate, etching a second layer of the substrate through the first opening in the top layer of the substrate to form a straight-walled recess, the straight-walled recess having the first width, a bottom surface, and a side surface substantially perpendicular to the top surface of the semiconductor substrate. 
     After the straight-walled recess is formed, the method involves dry etching the curved side surface of the patterned layer of photoresist, the top layer of the substrate, and the second layer of the substrate, where the dry etching i) transforms the straight-walled recess into a funnel-shaped recess, the funnel-shaped recess includes a curved sidewall gradually smoothly joining a straight-walled lower portion of the recess or terminating on the bottom surface, ii) enlarges a portion of the straight-walled recess to a third width greater than the first width, and iii) enlarges the first opening in the top layer to a fourth width greater than the third width. 
     Implementations can include one or more of the following features. The second opening can be larger than the first opening by about 1 μm. A stepper can be used to accurately align the patterned layer of photoresist on the top surface of the substrate having the first opening. The first opening can be formed by etching with a thin, non-reflowed resist. The substrate can be semiconductor substrate, the first layer can be an oxide layer having a high selectivity for a Bosch etching process. A portion of the fourth width can be 40 μm larger than the first width. Reflowing the patterned layer of photoresist can include softening the patterned layer of photoresist by heat until a top edge of the second opening becomes rounded under the influence of surface tension. After the softening by heat, the patterned layer of photoresist can be re-hardened while the top edge of the second opening remains rounded. 
     The patterned layer of photoresist deposited on the top surface of the substrate can be at least 10 microns in thickness. Softening the patterned layer of photoresist by heat further can include heating the patterned layer of photoresist having the second opening formed therein in a vacuum environment until photoresist material in the patterned layer of photoresist reflows under the influence of surface tension. Heating the patterned layer of photoresist can include heating the patterned layer of photoresist to a temperature of 160-250 degrees Celsius. Re-hardening the patterned layer of photoresist can include cooling the patterned layer of photoresist while the top edge of the second opening remains rounded. A top opening of the curved top portion can be is at least four times as wide as a bottom opening of the curved top portion. Etching the top surface of the substrate to form the straight-walled recess can include etching the top surface of the semiconductor substrate through the opening in the patterned layer of photoresist using a Bosch process. 
     The dry etching to form the funnel-shaped recess can have substantially the same etch rates for the patterned layer of photoresist and the semiconductor substrate. The dry etching to form the funnel-shaped recess can include dry etching using a CF 4 /CHF 3  gas mixture. The first opening in the patterned layer of photoresist can have a circular cross-sectional shape in a plane parallel to the exposed top surface of the patterned layer of photoresist. The funnel-shaped recess can have a circular cross-sectional shape in a plane parallel to the top surface of the substrate. The plurality of nozzles can have a standard deviation in the nozzle width of less than 0.15 microns. The recess can extend all the way through the top layer. 
     Particular implementations can include none, one or more of the following advantages. 
     The funnel-shaped nozzle has a curved top portion whose volume is sufficiently large to hold several droplets (e.g., 3 or 4 droplets) of fluid. The side surface of the funnel-shaped nozzle is streamlined and free of discontinuities in the fluid ejection direction. Compared to a straight-walled nozzle (e.g., a cylindrical nozzle) of the same depth and drop size, the side surface of the funnel-shaped nozzle generates less friction on the fluid during fluid ejection, and prevents the nozzle from taking in air when the droplet breaks free from the nozzle. Reducing the fluid friction not only improves the stability and uniformity in droplet formation, but also allows higher jetting frequencies, lower driving voltages, and/or higher power efficiencies. Having a single narrow portion of the nozzle can cause the meniscus to pin in a stable location. Preventing air from entering the nozzle can help prevent trapped air bubbles from blocking the nozzle or other parts of the flow path. 
     Although a nozzle having tapered, flat sidewalls (e.g., a nozzle of an inverted pyramid shape) may also realize some advantages (e.g., reduced friction) over a cylindrical nozzle, the sharp angled edges at the bottom opening of tapered nozzle still pose more drag on the droplets than the funnel-shaped nozzle does. In addition, the angled edges and rectangular (or square) shape of the tapered nozzle opening also affect the straightness of the drop direction in an unpredictable way, leading to deterioration of printing quality. In the funnel-shaped nozzle described in this specification, the straight-walled bottom portion accounts for none or a small portion of the overall nozzle depth, thus, the straight-walled bottom portion ensures jetting straightness without causing too much friction on fluid being expelled. Thus, the funnel-shaped nozzle can help achieve better jetting straightness, higher firing frequencies, higher power efficiencies, lower driving voltages, and/or uniformity of drop shape and locations. 
     Although funnel-shaped nozzles having a curved side surface may be formed using electroforming or micro-molding techniques, such techniques are limited to metal or plastic materials and may not be workable in forming nozzles in semiconductor substrates. In addition, the electroforming or micro-molding techniques tend to have lower precision and cannot achieve the size, geometry, and pitch requirements needed for high-resolution printing. The semiconductor processing techniques can be used to produce large arrays of nozzles that are highly compact and uniform, and can meet the size, geometry, and pitch requirements needed for high-resolution printing. For example, nozzles can be as small as 5 microns, the nozzle-to-nozzle pitch accuracy can be about 0.5 microns or less (e.g. 0.25 microns), the first nozzle-to-last nozzle pitch accuracy can be about 1 micron, and the nozzle size accuracy can be at least 0.6 microns. 
     The methods and systems disclosed herein reduces variations in the diameter of the funnel bore. Reduced nozzle size variation can lessen (e.g., eliminate) print line width variation, and reduce the need to scrap nozzle plates that contain nozzles with too much variation. Since size variation is less significant in straight bore holes etched into silicon wafers using non-reflowed resist, the methods disclosed herein uses edges of an opening in an oxide layer, instead of an opening in the reflowed photoresist to define the dimensions of a Bosch-etched straight-wall recess that is a precursor of the funnel-shaped nozzle. By making the oxide opening slightly smaller than the photoresist opening, the oxide, and not the reflowed resist, allows the opening to be made with thin, non-reflowed resist, and the oxide opening is thus more precise than the reflowed resist opening. The oxide also has a high selectivity for the Bosch etch. The details of one or more embodiments of the invention are set forth in the accompanying drawings and the description below. Other features, objects, and advantages of the invention will be apparent from the description and drawings, and from the claims. 
    
    
     
       DESCRIPTION OF DRAWINGS 
         FIG.  1    shows a cross-sectional side view of an apparatus for fluid droplet ejection. 
         FIG.  2 A  is a cross-sectional side view of a print head flow path with a nozzle having a single straight sidewall (i.e., a cylindrical nozzle), and a top plan view of the nozzle. 
         FIG.  2 B  is a cross-sectional side view of a print head flow path with a nozzle having tapered, flat sidewalls, and a top plan view of the nozzle. 
         FIG.  2 C  is a cross-sectional side view of a print head flow path with a nozzle having a tapered top portion abruptly joined to a straight-walled bottom portion, and a top plan view of the nozzle. 
         FIG.  3 A  is a cross-sectional side view of a funnel-shaped nozzle having a curved top portion smoothly joined to a straight-walled bottom portion. 
         FIG.  3 B  is a top plan view of a funnel-shaped nozzle having a curved top portion smoothly joined to a straight-walled bottom portion, where the horizontal cross-sectional shapes of the nozzle are circular. 
         FIG.  3 C  is a cross-sectional side view of a print head flow path with a nozzle having a tapered top portion smoothly joined to a straight-walled bottom portion. 
         FIGS.  4 A- 4 F  illustrate the process for making a funnel-shaped nozzle having a curved top portion smoothly joined to a straight-walled bottom portion. 
         FIGS.  5 A and  5 B  show images of a funnel-shaped recess made using the process shown in  FIGS.  4 A- 4 F . 
         FIGS.  6 A and  6 B  compare the maximum, minimum, and average nozzle sizes of nozzles made using the process shown in  FIGS.  4 A- 4 F , and another process. 
         FIGS.  7 A and  7 B  compare the standard deviation for nozzles sizes of nozzles made using the process shown in  FIGS.  4 A- 4 F  and another process. 
     
    
    
     Like reference symbols in the various drawings indicate like elements. 
     DETAILED DESCRIPTION 
     Fluid drop ejection can be implemented with a substrate, for example, a microelectromechanical system (MEMS), including a fluid flow body, a membrane, and a nozzle layer. The flow path body has a fluid flow path formed therein, which can include a fluid filled passage, a fluid pumping chamber, a descender, and a nozzle having an outlet. An actuator can be located on a surface of the membrane opposite the flow path body and proximate to the fluid pumping chamber. When the actuator is actuated, the actuator imparts a pressure pulse to the fluid pumping chamber to cause ejection of a droplet of fluid through the outlet of the nozzle. Frequently, the flow path body includes multiple fluid flow paths and nozzles, such as a densely packed array of identical nozzles with their respective associated flow paths. A fluid droplet ejection system can include the substrate and a source of fluid for the substrate. A fluid reservoir can be fluidically connected to the substrate for supplying fluid for ejection. The fluid can be, for example, a chemical compound, a biological substance, or ink. 
     Referring to  FIG.  1   , a cross-sectional schematic diagram of a portion of a microelectromechanical device, such as a printhead in one implementation is shown. The printhead includes a substrate  100 . The substrate  100  includes a fluid path body  102 , a nozzle layer  104 , and a membrane  106 . The nozzle layer  104  is made of a semiconductor material, such as silicon. A fluid reservoir supplies a fluid to a fluid fill passage  108 . The fluid fill passage  108  is fluidically connected to an ascender  110 . The ascender  110  is fluidically connected to a fluid pumping chamber  112 . The fluid pumping chamber  112  is in close proximity to an actuator  114 . The actuator  114  can include a piezoelectric material, such as lead zirconium titanate (PZT), sandwiched between a drive electrode and a ground electrode. An electrical voltage can be applied between the drive electrode and the ground electrode of the actuator  114  to apply a voltage to the actuator and thereby actuate the actuator. A membrane  106  is between the actuator  114  and the fluid pumping chamber  112 . An adhesive layer (not shown) can secure the actuator  114  to the membrane  106 . 
     A nozzle layer  104  is secured to a bottom surface of the fluid path body  102  and can have a thickness between about 15 and 100 microns. A nozzle  117  having an outlet  118  is formed in an outer surface  120  of the nozzle layer  104 . The fluid pumping chamber  112  is fluidically connected to a descender  116 , which is fluidically connected to the nozzle  117 . 
     While  FIG.  1    shows various passages, such as a fluid fill passage, pumping chamber, and descender, these components may not all be in a common plane. In some implementations, two or more of the fluid path body, the nozzle layer, and the membrane may be formed as a unitary body. In addition, the relative dimensions of the components may vary, and the dimensions of some components have been exaggerated in  FIG.  1    for illustrative purposes. 
     The design of the flow path, the nozzle dimensions and shape in particular, affect printing quality, printing resolution, as well, energy efficiencies of the printing device.  FIGS.  2 A- 2 C  show a number of conventional nozzle shapes. 
     For example,  FIG.  2 A  shows a print head flow path  202  with a straight nozzle  204 . The straight nozzle  204  has a straight sidewall  206 . The top portion of  FIG.  2 A  shows a cross-sectional side view of the flow path  202  and the nozzle  204  in a plane passing through a central axis  208  of the nozzle  204 . The central axis  208  is an axis that passes through the geometric center of all the horizontal cross-sections of the nozzle  204 . In this specification, the central axis  208  of the nozzle is sometimes referred to as the axis of symmetry of the nozzle in cases where the geometric center of each horizontal cross section is also the center of symmetry of the horizontal cross section. As indicated in the top portion of  FIG.  2 A , in a plane including the central axis  208 , the profile of the sidewall  206  are straight lines parallel to the central axis  208 . In this example, the nozzle  204  is a circular right cylinder, and has a single straight sidewall. In other examples, the nozzle can be a square right cylinder, and has four straight, flat side surfaces. 
     As shown in  FIG.  2 A , the nozzle  204  is formed in a nozzle layer  210 . The nozzle  204  has the same cross-sectional shapes and sizes in planes perpendicular to the central axis  208  of the nozzle  204 . The lower portion of  FIG.  2 A  shows the top plan view of the nozzle layer  210 . In this example, the nozzle  204  has a circular cross-sectional shape in the planes perpendicular to the central axis  208  of the nozzle  204 . In various implementations, the nozzle  204  can have other cross-sectional shapes, such as oval, square, rectangular, or other regular polygonal shapes. 
     A nozzle having straight sidewall(s) is relatively easy to fabricate. The straight sidewall(s) of the nozzle can help maintain jetting straightness and making the landing positions of ink droplets ejected from the nozzle more predictable. However, to ensure a sufficient drop size, the height of the straight-walled nozzle needs to be rather large (e.g., tens of microns or more). The large vertical dimension of the straight-walled nozzle creates a significant amount of friction on the fluid inside the nozzle, when the fluid is ejected from the nozzle as a droplet. The higher flow resistance created in the straight-walled nozzle results in a lower jetting frequency, and/or a higher driving voltage, which can further lead to lower printing speed, lower resolution, lower power efficiency, and/or lower device life. 
     Another drawback of the straight-walled nozzle is that, when a droplet breaks free from the outlet (e.g., outlet  212 ) of the nozzle, air can be sucked into the nozzle from the outlet opening of the nozzle and be trapped inside the nozzle or other parts of the flow path. The air trapped inside the nozzle can block ink flow or deflect fluid droplets that are being ejected from their desired trajectory. 
       FIG.  2 B  shows a print head flow path  214  with a nozzle  216  having tapered, flat sidewalls  218 . The upper portion of  FIG.  2 B  shows a cross-sectional side view of the print head flow path  214  in a plane containing the central axis  220  of the nozzle  216 . In the plane containing the central axis  220 , the profile of the nozzle  216  are straight lines converging toward the central axis  220  going from the top opening of the nozzle  216  to the bottom opening (or outlet  212 ) of the nozzle  216 . The profile of the nozzle  216  can be formed by multiple planes that converge toward the center axis  220 . 
     The nozzle  216  is formed in a nozzle layer  224 , and the cross-sectional shapes of the nozzle  216  in planes perpendicular to the central axis  220  are squares of continuously decreasing sizes. The nozzle  216  have four flat sidewalls each slanted from an edge of the top opening of the nozzle  216  to a corresponding edge of the bottom opening of the nozzle  216 . The lower portion of  FIG.  2 B  shows a top plan view of the nozzle layer  224 . As shown in the lower portion of  FIG.  2 B , each sidewall  218  of the nozzle  216  is a flat surface that intersects with each of two adjacent flat sidewalls  218  along an edge  226 . Each edge  226  is an angled edge, rather than a rounded edge. 
     As shown in the lower portion of  FIG.  2 B , the lower opening of the nozzle  216  is a smaller square opening while the upper opening of the nozzle  216  is a larger square opening. The central axis  220  passes through the geometric centers of both the upper opening and the lower opening of the nozzle  216 . The tapered sidewalls  218  of the nozzle  216  provides reduced friction on the fluid passing through the nozzle as compared to the straight-walled nozzle  204  shown in  FIG.  2 A . The tapered shape of the nozzle  216  also reduces the amount of air intake occurring during the breakoff of droplets at the nozzle outlet  212 . 
     The tapered nozzle  216  shown in  FIG.  2 B  can be formed in a semiconductor nozzle layer  224  (e.g., a silicon nozzle layer) using KOH etching. However, the shape of the tapered nozzle  216  is dictated by the crystal planes existing in the semiconductor nozzle layer  224 . When the nozzle  216  is created by KOH etching, the side surfaces of the nozzle  216  are formed along the &lt; 111 &gt;crystal planes of the semiconductor nozzle layer  224 . Therefore, the angle between each slanted side surface  218  and the central axis  220  has a fixed value of about 35 degrees. 
     Although the tapered nozzle  216  shown in  FIG.  2 B  offers some improvement over the straight-walled nozzle  204  shown in  FIG.  2 A  in terms of lowered flow resistance and reduced air uptake, there is very little flexibility in terms of changing the shape of the nozzle opening or the angle of the tapered sidewalls. The square corners of the nozzle outlet can sometimes cause satellites (tiny secondary droplets created in addition to a main droplet during droplet ejection) to form. In addition, the sharp discontinuities between the flat sidewalls  218  and the horizontal bottom surface of the nozzle layer  224  at the edges of the nozzle outlet  212  also cause additional drag on the droplets, causing reduced jetting speed and frequency. 
       FIG.  2 C  shows another nozzle configuration that combines a tapered section as shown in  FIG.  2 B  with a straight section as shown in  FIG.  2 A . Due to the limitation posed by the KOH etching techniques, the straight bottom portion and the tapered top portion are formed by etching from two sides of the substrate. However, the two-side etching can lead to difficult alignment issues. Otherwise, specially designed steps have to be taken to form the straight bottom portion from the same side as the tapered portion, e.g., as described in U.S. Patent Publication 2011-0181664, incorporated by reference. 
     The top portion of  FIG.  2 C  shows a cross-sectional side view of a print head flow path  232  with a nozzle  234  having a tapered top portion  236  abruptly joined to a straight bottom portion  238 . The cross-sectional side view shown in  FIG.  2 C  is in a plane containing the central axis  240  of the nozzle  234 . In the plane containing the central axis  240 , the profile of the tapered top portion  236  consists of straight lines converging from the top opening of the nozzle  234  toward the intersection between the tapered top portion  236  and the straight-walled bottom portion  238 . In the plane containing the central axis  240 , the profile of the straight-walled bottom portion  238  consists of straight lines parallel to the central axis  240 . This profile can be provided by a cylinder that is co-axial with the central axis  240 . The intersection between the tapered top portion  236  and the straight-walled bottom portion  238  is not smooth and has one or more discontinuities or angled edges in the vertical direction (i.e., the fluid ejection direction in this example). 
     In this example, the cross-sectional shapes of the tapered top portion  236  in planes perpendicular to the central axis of the nozzle  234  are square, while the cross-sectional shapes of the bottom portion  238  in planes perpendicular to the central axis of the nozzle  234  are circular. Therefore, the tapered top portion  236  has four flat side surfaces  244  each slanted from an edge of the top opening of the tapered top portion  236  to a corresponding edge of the intersection between the top portion  236  and the bottom portion  238 . Although the straight bottom portion  238  shown in  FIG.  2 C  has a circular cross-section, the straight bottom portion can also have a square cross-section or cross-sections of other shapes. 
     The nozzle  234  is formed in the nozzle layer  242 . The lower portion of  FIG.  2 C  shows the top plan view of the nozzle  234 . In the top plan view, the lower opening of the straight-walled bottom portion  238  is circular, and the top opening of the tapered top portion  236  is square, and the intersection between the straight bottom portion  238  and the tapered top portion  236  is an intersection between a cylindrical hole and an inverted pyramid hole. Due to the mismatch between the cross-sectional shapes between the top and bottom portions, the edges of the intersection include curves and sharp discontinuities. These discontinuities also cause fluid friction and instability in drop formation. Even if the cross-sectional shapes of the top portion  236  and the bottom portion  238  are both square, there are still discontinuities at the intersection between the two portions in the fluid ejection direction. The square-shaped nozzle opening is also less ideal than a circular nozzle outlet for other reasons set forth with respect to  FIG.  2 B , for example. 
     In this specification, a funnel-shaped nozzle having a curved top portion smoothly joined to a straight-walled bottom portion formed in a semiconductor nozzle layer (e.g. silicon nozzle layer) is disclosed. The curved top portion of the funnel-shaped nozzle differs from a tapered top portion shown in  FIG.  2 C  in that the profile of the side surface of the curved top portion in a plane containing the central axis of the nozzle consists of curved rather than straight lines. In addition, the profile of the curved top portion converges toward the straight bottom portion and is smoothly joined to the straight-walled bottom portion, rather than bending at an abrupt angle at the intersection between the curved top portion and the straight-walled bottom portion. 
     In addition, in some implementations, the transition from the horizontal top surface of the nozzle layer to the curved side surface of the funnel-shaped nozzle is also smooth rather than abrupt. In addition, the horizontal cross-sectional shapes of the funnel-shaped nozzle in planes perpendicular to the central axis of the nozzle are geometrically similar and concentric for the entire depth of the nozzle. Therefore, there is no jagged intersection between the curved top portion and the straight-walled bottom portion of the funnel-shaped nozzle. The funnel-shaped nozzle described in this specification offer many advantages over the conventional nozzle shapes described with respect to  FIGS.  2 A- 2 C , for example. 
       FIG.  3 A  is a cross-sectional side view of a funnel-shaped nozzle  302  having a curved top portion  304  smoothly joined to a straight-walled bottom portion  306 . In the straight walled bottom portion  306 , the sides of the nozzle are parallel, and are perpendicular to the outer surface  322  of the nozzle layer. The straight-walled bottom portion  306  can be a cylindrical passage (i.e., the walls are straight up/down rather than laterally). Depending on the process parameters, the straight walled portion  306  can be avoided and the funnel portion  316  can continue to the surface  322 . The funnel-shaped nozzle  302  is a funnel-shaped through hole formed in a planar semiconductor nozzle layer  308 . The intersection between the curved top portion  304  and the straight-walled bottom portion  306 , whose location is indicated by the dotted line  320  in  FIG.  3 A , is smooth and substantially free of any discontinuities and any surfaces perpendicular to the central axis  310  of the nozzle  302 . 
     As shown in  FIG.  3 A , the height of the curved top portion  304  is substantially larger than the height of the straight-walled bottom portion  306 . However, the straight-walled bottom portion  306  can have at least some height, e.g., 10-30% of the height of the curved top portion  304 . For example, the height of the curved top portion  304  can be 40-75 microns (e.g., 40, 45, or 50 microns), while the height of the bottom portion  306  can be only 5-10 microns (e.g., 5, 7, or 10 microns). The curved top portion  304  encloses a volume much larger than the straight-walled bottom portion  306 . The larger curved top portion holds most of the fluid to be ejected. In some implementations, the volume enclosed in the curved top portion  304  is the size of several droplets (e.g., 3 or 4 droplets). Each droplet can be 3-100 picoliters. The straight bottom portion  306  has a smaller volume, such as a volume less than the size of a single droplet. 
     The height of the straight-walled portion  306  is small enough so that it does not cause a significant amount of fluid friction, and does not cause substantial air uptake during break-off of the droplets. At the same time, the height of the straight-walled portion is large enough to maintain jetting straightness. In some implementations, the height of the straight-walled portion  306  is about 10-30% of the diameter of the nozzle outlet. For example, in  FIG.  3 A , the nozzle outlet has a diameter of 35 microns, and the height of the straight-walled portion is 5-10 microns (e.g., 7 microns). In some implementations, the diameter of the nozzle outlet can be 15-45 microns. 
     Both the curved top portion  304  and the straight-walled bottom portion  306  of the nozzle  302  serve important functions in droplet formation and ejection. The curved top portion  304  is designed to hold a sufficient volume of fluid so that when a droplet is ejected from the nozzle outlet, there is little or no void created in the nozzle to form air bubbles inside the nozzle. A bottom of the funnel can hold a smaller volume of fluid. 
     The funnel-shaped nozzle  302  further differs from the nozzles shown in  FIGS.  2 B and  2 C  in that the cross-sectional shape of the funnel-shaped nozzle  302  in planes perpendicular to the central axis  310  of the nozzle  302  are circular, rather than rectangular, for the entire depth of the nozzle  302 . Thus, there is no discontinuity between the curved top portion  304  and the straight bottom portion  306  in the direction of fluid ejection. The streamlined profile of the funnel-shaped nozzle  302  provides even less fluid friction than the nozzles shown in  FIGS.  2 B  and  2 C. In addition, the side surface of the funnel-shaped nozzle  304  is completely smooth and free of any discontinuities or abrupt changes in the azimuthal direction as well. Therefore, the funnel-shaped nozzle  304  does not produce drag or instabilities to cause other drawbacks (e.g., satellite formation) present in the nozzles shown in  FIG.  2 B  and  FIG.  2 C  either. 
     It can be difficult to form a funnel-shape nozzle in silicon using conventional etching processes. Conventional etching processes, such as the Bosch process, form straight vertical walls, whereas and KOH etching which forms tapered, straight walls. Although isotropic etching can form curved features, like bowl-shaped features, it is not able to make curved walls in the opposite formation to make funnel-shaped features. 
     In addition, given the processing techniques provided in this specification, the pitch by which the curved top portion of the funnel-shaped nozzle converges from its top opening towards the straight-walled bottom portion can be varied by design, rather than fixed by the orientation of certain crystal planes. Specifically, suppose that point A is the intersection between the edge of the top opening of the curved top portion  304  and a plane containing the central axis  310 , and point B is the intersection between the edge of the bottom opening of the curved top portion  304  and the same plane containing the central axis  310 . Unlike the nozzle  234  shown in  FIG.  2 C , the angle α between a straight line joining the point A and point B and the central axis  310  is not a fixed angle (e.g., 35 degrees in  FIG.  2 C )dictated by the crystal planes of the semiconductor nozzle layer  308 . Instead, the angle α for the funnel-shaped nozzle  304  can be designed by varying the processing parameters when making the funnel-shaped nozzle  304 . In some implementations, the angle α for the funnel-shaped nozzle  304  can be between 30-40 degrees. In some implementations, the angle α for the funnel-shaped nozzle  304  can be greater than 40 degrees. 
     As is shown in  FIG.  3 A , the curved top portion  304  of the funnel-shaped nozzle  302  differ from a rounded lip resulted from a natural rounding or tapering of a recess wall created in the process of creating a cylindrical recess in a substrate. 
     First, the amount of tapering exhibited by the curved top portion  304  of the funnel-shaped recess  302  is much larger than any tapering that might be inherently present due to manufacturing imprecisions (e.g., over etching of substrate through a straight-walled photoresist mask). For example, the angle of tapering for the sidewall of a funnel-shaped nozzle is about 30 to 40 degrees. The vertical extent of the curved top portion  304  can be tens of microns (e.g., 50-75 microns). The width of the top opening of the curved top portion  304  can be 100 microns or more, and can be 3 or 4 times the width of the bottom opening of the curved top portion  304 . In contrast, the tapering or rounding present near the top opening of a cylindrical recess due to manufacturing imperfections and/or imprecisions is typically less than 1 degree. The natural tapering or rounding also has a much smaller height and width variation (e.g., in the range of nanometers or less than 1-2 microns) than those present in the funnel-shaped nozzle described in this specification. 
       FIG.  3 B  is a top plan view of a funnel-shaped nozzle (e.g., the nozzle  302  shown in  FIG.  3 A ). As shown in  FIG.  3 B , the top opening  312  and the bottom opening  314  of the funnel-shaped nozzle  302  are both circular and are concentric. There is no discontinuity at any part of the side surface  316  of the entire nozzle  302 . The width of the top opening  312  is at least 3 times the width of the bottom opening  214  of the nozzle  302 . In some implementations, the top opening  312  of the nozzle  302  is fluidically connected to a pumping chamber above the funnel-shaped nozzle  302 , and the boundary of the pumping chamber defines the boundary of the top opening  312  of the funnel-shaped nozzle  302 .  FIG.  3 C  shows a print head flow path  318  with a funnel-shaped nozzle  302 . 
     Although  FIG.  3 B  shows a funnel-shaped nozzle having a circular cross-sectional shape for its entire depth, other cross-sectional shapes are possible. The cross-sectional shape of the straight-walled bottom portion of a funnel-shaped nozzle can be oval, square, rectangular, or other polygonal shapes. The curved top portion of the funnel-shaped nozzle would have a similar cross-sectional shape as the straight-walled bottom portion. However, the corners (if any) in the cross-sectional shape of the curved top portion are gradually eliminated or smoothed out as the side surface of the curved top portion extends further away from the straight-walled bottom portion toward the top opening of the curved top portion. The exact shape of the cross-sections of the curved top portion is determined by the manufacturing steps and the materials used for creating the funnel-shaped nozzles. 
     For example, in some implementations, the funnel-shaped nozzle having a curved top portion smoothly joined to a straight-walled bottom portion can have a square horizontal cross-sectional shape. In such implementations, the center side profile of the nozzle is the same as that shown in  FIG.  3 A . However, the funnel-shaped nozzle would have four converging curved side surfaces, and the intersections between adjacent curved side surfaces are four smooth curved lines converging toward the bottom outlet of the nozzle and smoothly transition into four straight parallel lines in the straight bottom portion of the nozzle. In addition, the intersections between adjacent curved side surfaces are smoothly rounded, so that the four curved side surfaces form part of a single smooth side surface in the top portion of the funnel-shaped nozzle. 
     A print head body can be manufactured by forming features in individual layers of semiconductor material and attaching the layers together to form the body. The flow path features that lead to the nozzles, such as the pumping chamber and ink inlet, can be etched into a substrate, as described in U.S. patent application Ser. No. 10/189,947, filed Jul. 3, 2002, using conventional semiconductor processing techniques. A nozzle layer and the flow path module together form the print head body through which ink flows and from which ink is ejected. The shape of the nozzle through which the ink flows can affect the resistance to ink flow. By creating a funnel-shaped nozzle described in this application, less flow resistance, higher jetting frequencies, lower driving voltages, and/or better jetting straightness can be achieved. The processing techniques described in this specification also allow arrays of nozzles having the desired dimensions and pitches to be made with good uniformity and efficiencies. 
       FIGS.  4 A- 4 F  illustrate the process for making a funnel-shaped nozzle having a curved top portion smoothly joined to a straight-walled bottom portion, for example, the funnel-shaped nozzle shown in  FIGS.  3 A- 3 C . 
     To form the funnel-shaped nozzle, first, a patterned layer of photoresist is formed on a top surface of a semiconductor substrate, where the patterned layer of photoresist includes an opening that has a curved side surface smoothly joined to an exposed top surface of the patterned layer of photoresist. For example, an opening around a z-axis will have a side surface that curves in both the z direction and the azimuthal direction. The shape of the opening will determine the cross-sectional shapes of the funnel-shaped nozzle in planes perpendicular to the central axis of the funnel-shaped nozzle. The size of the opening is roughly the same as the bottom opening of the funnel-shaped nozzle (e.g., 35 microns). In the example shown in  FIGS.  4 A- 4 F , the opening is circular for making a funnel-shaped nozzle having circular horizontal cross-sections throughout the entire depth of the nozzle. 
     To form the patterned layer of photoresist, a resist-reflow process can be used. As shown in  FIG.  4 A , a uniform layer of photoresist  402  is applied to the planar top surface  404  of a substrate. The substrate can be a semiconductor substrate  406  (e.g., a silicon wafer). The semiconductor substrate  406  can be a substrate having one of several crystal orientations, such as a silicon&lt; 100 &gt;wafer, a silicon&lt; 110 &gt;wafer, or a silicon&lt; 111 &gt;wafer. The thickness of the layer of photoresist  402  influences the final curvature of the curved side surface of the opening in the layer of photoresist, and hence the final curvature of the curved side surface of the funnel-shaped nozzle. A thicker layer of photoresist is generally applied to obtain a larger radius of curvature for the curved side surface of the funnel-shaped nozzle. 
     In this example, the initial thickness of the uniform layer of photoresist  402  is about 10-11 microns (e.g., 11 microns). In some implementations, more than 11 microns of photoresist can be applied on the planar top surface  404  of the semiconductor substrate  406 . Some thickness of photoresist can remain on the substrate after the processing steps to make the funnel-shaped recess of a desired depth. Examples of the photoresist that can be used include AZ 9260, AZ9245, AZ4620 made by MicroChemicals® GmbH, and other positive photoresists, for example. The thickness of the semiconductor substrate  406  is equal or greater than the desired depth for the funnel-shaped nozzle to be made. For example, the substrate  406  shown in  FIG.  4 A  can be an SOI wafer having a silicon layer  403  of about 50 microns attached to a handle layer  407  via a thin oxide layer  405 . Another thin oxide layer  401  can cover the silicon layer  403 . For example, the thin oxide layer  401  can be about 1 micron. As shown in  FIG.  4 A , a first lithography and etch step can form an opening  409  having a first width  411  in the thin oxide layer  401 . The photoresist that is used to define the opening  409  can be a thin, non-reflowed resist that is more precise. The oxide in the thin oxide layer  401  can also have a high selectivity for the Bosch etch used to form the opening  409 . A selectivity between the non-reflow resist and the substrate is expected to be similar to the selectivity between the reflow resist and substrate, for example, below 100:1. In some embodiments, the first width  411  is about 1 μm smaller than the second width  413 . The uniform layer of photoresist  402  also fills the opening  409 . Alternatively, the substrate  406  can be a thin silicon layer attached to a handle layer by an adhesive layer or by Van der Waals force. 
     As shown in  FIG.  4 B , after the uniform layer of photoresist  402  is applied to the planar top surface  404  of the semiconductor substrate  406 , the uniform layer of photoresist  402  is patterned, such that an initial opening  408  having a second width of 413, and one or more vertical side walls  410  are created. The second width  413  is larger than the first width  411 . In some embodiments, the second width  413  can be about 1 μm larger than the first width  411 . A stepper can accurately align the opening  408  with the opening  409 . For example, the stepper can store information about the center of the opening  409  defined in the thin oxide layer  401  and match it with the center of the initial opening  408  during the lithography process that creates the initial opening  408 . In this example, a circular opening is created in the uniform layer of photoresist  402 , and the sidewall of the circular opening is a single curved surface that is perpendicular to the planar top surface  412  of the uniform layer of photoresist  402  and to the planar top surface  404  of the semiconductor substrate  406 . The diameter of the opening  411  determines the diameter of the bottom opening of the funnel-shaped nozzle to be made. In this example, the diameter of the initial circular opening  411  can be about 85-95 microns (e.g., 90.5 microns). The patterning of the uniform layer of photoresist  402  can include the standard UV or light exposure under a photomask and a photoresist development process to remove the portions of the photoresist layer exposed to the light. 
     After the initial opening  408  is formed in the uniform layer of photoresist  402 , the photoresist layer  402  is heated to about 160 to 250 degrees Celsius and until the photoresist material in the layer  402  is softened. When the photoresist material in the patterned layer of photoresist  402  is softened under the heat treatment, the photoresist material will start to reflow and reshape itself under the influence of surface tension of the photoresist material, particularly in regions near the top edge  414  of the opening  408 . The surface tension of the photoresist material causes the surface profile of the opening  408  to pull back and become rounded. As shown in  FIG.  4 C , the top edge  414  of the opening  408  have become rounded under the influence of surface tension. The opening in the resist  413  doesn&#39;t change substantially from reflow. 
     In some implementations, the layer of photoresist  402  is heated in a vacuum environment to achieve the reflow of the photoresist layer  402 . By heating the photoresist layer  402  in a vacuum environment, the surface of the photoresist layer  402  is smoother and without tiny air bubbles trapped inside of the photoresist material. This will lead to better surface smoothness in the final nozzle produced. 
     After the desired shape of the opening  408  is obtained, the photoresist layer  402  is cooled. The cooling can be accomplished by removing the heat source or active cooling. The cooling can also be performed in a vacuum environment to ensure better surface properties of the funnel-shaped nozzle to be made. By cooling the photoresist layer  402 , the photoresist layer  402  re-hardens, and the surface profile of the opening  408  maintains its shape during the hardening process, and the top edge  414  of the opening  408  remain rounded at the end of the re-hardening process. 
     Once the patterned layer of photoresist  402  is hardened, etching of the substrate  406  can begin. The funnel-shaped recess is created in a two-step etching process. First, a straight-walled recess is created in a first etching process. Then, the straight-walled recess is modified during a second etching process. In the second etching process, the initially formed straight-walled recess is deepened to form the straight-walled bottom portion of the funnel-shaped recess. At the same time, the second etching process expands the initially formed straight-walled recess gradually from the top to form the curved top portion of the funnel-shaped recess. 
     As shown in  FIG.  4 C , an initial straight-walled recess  416  is created through the opening  409  in a first etching process. In other words, the edge of the oxide in the thin oxide layer  401  defines the boundary of the recess  416 , not the reflowed resist  402 . The first etching process can be a Bosch process, for example. In the first etching process, a straight walled recess  416  is created and has a depth slightly smaller (e.g., 1-15 microns less) than the final desired depth of the funnel-shaped recess to be made. For example, for a funnel-shaped recess having a total depth of 50-80 microns, the straight-walled recess  416  created in the first etching process can be 49-79 microns. Although tiny scalloping patterning may be present on the side profile  418  of the straight-walled recess  416 , such small variations (e.g., 1 or 2 degrees) is small compared to the overall dimensions (e.g., 35 microns in width and 45-75 microns in depth) of the straight-walled recess  416 . 
     In the first etching process, the straight-walled recess  416  has substantially the same cross-sectional shape and size in a plane parallel to the top surface  404  of the semiconductor substrate  406  as the area enclosed by the opening  409 . As shown in  FIG.  4 D , the etchant used in the first etching process removes very little of the photoresist layer  402  as compared to the device layer  403  of the semiconductor substrate  406  exposed through the opening  409  in the thin oxide layer  401 . Therefore, the surface profile of the patterned layer of photoresist  402  remains substantially unchanged at the end of the first etching process. For example, the selectivity between the device layer  403  and the photoresist layer  402  during the first etching process can be 100:1. 
     After the initial straight-walled recess  416  is formed in the semiconductor substrate  406  through the first etching process, the second etching process can be started to transform the initial straight-walled recess  416  shown in  FIG.  4 C  into the desired funnel-shaped recess  420  shown in  FIG.  4 D . 
     As shown in  FIG.  4 D , the semiconductor substrate  406  and the patterned layer of photoresist  402  are exposed to dry etching from the vertical direction (e.g., the direction perpendicular to the planar top surface  404  of the substrate  406  in  FIG.  4 D ). The etchant used in the dry etching process can have comparable etch rates for both the photoresist and for the semiconductor substrate  406 . For example, the selectivity of the dry etching between the photoresist and the semiconductor substrate can be 1:1. In some implementations, the dry etching is performed using a CF 4 /CHF 3  and O 2  gas mixture at high platen power, e.g., greater than 400 W. 
     During the dry etching, as the etching process continues, the surface profile of the photoresist layer  402  recedes in the vertical direction under the bombardment of the etchant. Due to the curved profile  414  at the top edge of the opening  408  in the photoresist layer  402 , the surface of the thin oxide layer  401  under the thinnest portion of the photoresist layer  402  gets exposed to the etchant first, as compared to other parts of the substrate surface underneath of the photoresist layer  402 . In other words, the thin oxide layer  401  is etched. The portions of the semiconductor surface exposed to the etchant also are gradually etched away. As shown in  FIG.  4 D , the dotted lines represent the surface profiles  414  of the photoresist layer  402  and the semiconductor substrate  406  receding gradually under the bombardment of the etchant. 
     As shown in  FIG.  4 D , the regions  422  below the edge of the opening  409  in the thin oxide layer  401  are etched, and the surface of the device layer  403  are expanded in the lateral direction. An expansion of the side surface  418  of the recess  416  becomes the curved side surface  424  of the curved top portion of the funnel-shaped recess  420  formed in the semiconductor substrate  406 . 
     As dry etching continues to expand the side surface  418  of the recess  416  in the lateral direction, the dry etching also deepens the recess  416  in the vertical direction. The deepening of the recess  416  creates the straight-walled bottom portion of the funnel-shaped recess  420 . The additional amount of deepening creates a straight-walled portion that is a few microns deep. The side surface  426  of the straight-walled bottom portion is perpendicular to the planar top surface  404  of the semiconductor substrate  406 . Since the amount of lateral expansion of the side surface  424  of the recess  420  gradually decreases from top to bottom, the curved side surface  424  of the curved top portion transitions smoothly into the vertical side surface  426  of the straight-walled bottom portion. The boundary of the top opening of the funnel-shaped recess  420  is defined by the edge starting from which the photoresist meets the surface of the thin oxide layer  401 . 
     The dry etching can be timed and stopped as soon as the desired depth of the funnel-shaped recess  420  is reached. Alternatively, the dry etching is timed and stopped as soon as the desired surface profile for the curved portion of the funnel-shaped recess  420  is obtained. 
     In some implementations, if the semiconductor substrate is of the desired thickness of the nozzle layer, the dry etching can be continued until the etching goes through the entire thickness of the semiconductor substrate, and the funnel-shaped nozzle is formed completely. In some implementations, the semiconductor substrate can be etched, ground and/or polished from the backside until the funnel-shaped recess is opened from the backside to form the funnel-shaped nozzle. 
     The photoresist  402  is removed, and  FIG.  4 E  shows a completed funnel-shaped recess  428  that has been opened at the bottom. After the funnel-shaped nozzle  428  is formed, the nozzle layer  429  can be attached to other layers of a fluid ejection unit, such as a fluid ejection unit  430  shown in  FIG.  4 F . In some implementations, the funnel-shaped nozzle  428  is one of an array of identical funnel-shaped nozzles, and each of the arrays of identical funnel-shaped nozzle belongs to an independently controllable fluid ejection unit  430 . In some implementations, a fluid ejection unit includes a piezoelectric actuator assembly supported on the top surface of the semiconductor substrate  406  and including a flexible membrane sealing a pumping chamber fluidly connected to the funnel-shaped nozzle  428 . Each actuation of the flexible membrane is operable to eject a fluid droplet through the straight-walled bottom portion of the funnel-shaped nozzle  428 , and a volume enclosed by the curved top portion is three or four times a size of the fluid droplet. 
       FIGS.  5 A and  5 B  shows images of two funnel-shaped recesses (e.g., recess  502  and recess  504 ) made using the process shown in  FIGS.  4 A- 4 F . 
     The dimensions of the funnel-shaped recess may be different in different implementations. As shown in  FIG.  5 A , a bottom portion  506  of the funnel-shaped recess  502  has a depth of about 2-5 microns, while the curved top portion  508  of the funnel-shaped recess  502  has a depth of about 25-28 microns. When creating a funnel-shaped nozzle out of this funnel-shaped recess  502 , the substrate can be ground and polished from the bottom, such that the straight-walled portion  506  has the desired depth. As shown in  FIG.  5 A , the diameter of the straight-walled bottom portion  506  is roughly uniform (with a variation of less than ˜0.5 microns for a 20 micron diameter) in planes perpendicular to the central axis of the recess  502 . The bottom opening of the curved top portion  508  is smoothly joined to the top opening of the straight-walled bottom portion  506 . The diameter of the top opening of the recess  502  is in the range of 96 microns, approximately 5 times the diameter of the straight-walled bottom portion  506 . The pitch by which the curved top portion  508  expands from the bottom to the top can be defined by the width of the curved top portion  508  at half height of the curved top portion  508 . In this example, the width at half height of the curved top portion is about 27 microns. A descender  510  is positioned above the recess  502 . 
     The portion of the funnel-shaped recess  502  within the dotted rectangular box region is shown in  FIG.  5 B . The image in  FIG.  5 B  is rotated by 180°, and at higher magnification, the recess  502  actually does not have a straight-walled portion. 
       FIG.  6 A  shows plots of maximum, minimum, and average funnel nozzles sizes fabricated on two wafers using the process outlined in  FIGS.  4 A- 4 F . As a comparison,  FIG.  6 B  shows plots of maximum, minimum, and average funnel nozzles sizes fabricated on fifteen wafers using another process where the reflow photoresist has an initial opening that is smaller than an opening defined in the thin oxide layer. Using the other process, the edges of the reflow resist defines the nozzles boundary of the straight-walled recess formed during the first etching process shown in  FIG.  4 C . Plot  602  in  FIG.  6 A  shows the maximum funnel nozzle size that mostly fall between 22-23 micron. In contrast, plot  608  in  FIG.  6 B  shows a larger variation in the maximum funnel nozzle size, of between about 19 to 22.5 micron. Plot  604  in  FIG.  6 A  shows the minimum funnel nozzle size that mostly fall between 21.5-22.4 micron. In contrast, plot  610  in  FIG.  6 B  shows a significantly larger variation in the minimum funnel nozzle size, of between about 17 to 21.5 micron. Plot  606  in  FIG.  6 A  shows the average funnel nozzle size that has much less variation than plot  612  in  FIG.  6 B . 
     Based on empirical data, such as those shown in  FIGS.  6 A and  6 B , the diameter of the funnel bore varies more than the width of a KOH nozzle, such as those shown in  FIG.  2 A , where the nozzle has a straight slanted profile. A small fraction of the funnel bores can be substantially (1-3 μm) smaller than the population. Nozzle size variation can cause print line width variation, so nozzle plates with too much variation may have to be scrapped. For nozzle diameter variation specifications of ±1.5 μm, a large (e.g., 25%) die yield loss can result. As the size variation is not observed on straight bore holes etched into silicon wafers using non-reflowed resist, the processes outlined in  FIG.  4 A- 4 F  address variability that may be induced by the reflow process. The modification to the funnel nozzle process produces funnel nozzles that have reduced bore size variation, as shown in  FIG.  6 A . 
       FIG.  7 A  shows a plot  702  of the standard deviation of the width of nozzles fabricated using the processes shown in  FIGS.  4 A- 4 F . Most of the nozzles have a standard deviation of about 0.1 micron. In contrast,  FIG.  7 B  shows a plot  704  of the standard deviation of the width of nozzles fabricated using another process where the edges of the reflow resist defines the nozzles boundary of the straight-walled recess formed during the first etching process shown in  FIG.  4 C . The standard deviation in plot  704  is generally greater than 0.2 micron. 
     A number of implementations of the invention have been described. Nevertheless, it will be understood that various modifications may be made without departing from the spirit and scope of the invention. Exemplary methods of forming the aforementioned structures have been described. However, other processes can be substituted for those that are described to achieve the same or similar results. Accordingly, other embodiments are within the scope of the following claims.