Abstract:
A method of ejecting a drop of liquid through a nozzle having a plurality of lobes. Liquid or ink is ejected through a plurality of lobes such that the liquid or ink passing through the lobes collapses into a single drop before the liquid or ink reaches a receiving substrate. A central region of the ejected drop is pinched by the lobes of the nozzle. The method is preferably implemented in an inkjet printer by providing a plurality of multi-lobed nozzles formed in a printhead of the printer.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
       [0001]    Reference is made to commonly assigned, co-pending U.S. patent applications:
   Ser. No. by Yonglin Xie (Docket 95278) filed of even date herewith entitled “Drop Ejector Having Multi-Lobed Nozzle”; and   Ser. No. by Yonglin Xie (Docket 95807) filed of even date herewith entitled “Method Of Making A Multi-Lobed Nozzle”; the disclosures of which are incorporated herein by reference in their entireties.   
 
     
    
     FIELD OF THE INVENTION 
       [0004]    This invention relates generally to the field of printing devices, and more particularly to the shape of a nozzle for drop ejector, for example for an inkjet printing device. 
       BACKGROUND OF THE INVENTION 
       [0005]    Many types of printing systems include one or more printheads that have arrays of dot forming elements that are controlled to make marks of particular sizes, colors, or densities in particular locations on the recording medium in order to print the desired image. In some types of printing systems the array(s) of dot forming elements extends across the width of the page, and the image can be printed one line at a time, as the recording medium is moved relative to the printhead. Alternatively, in a carriage printing system (whether for desktop printers, large area plotters, etc.) the printhead or printheads are mounted on a carriage that is moved past the recording medium in a carriage scan direction as the dot forming elements are actuated to make a swath of dots. At the end of the swath, the carriage is stopped, printing is temporarily halted and the recording medium is advanced. Then another swath is printed, so that the image is formed swath by swath. 
         [0006]    In an inkjet printer, the dot forming elements are also called drop ejectors. A drop ejector includes a nozzle and a drop forming mechanism (such as a resistive heater for thermal inkjet, or a piezoelectric device for piezoelectric inkjet) in order to generate pressure within an ink-filled chamber and eject ink from the nozzle. In page-width inkjet printers as well as in carriage inkjet printers, the printhead and the recording medium are moved relative to one another as drops are ejected in order to form the image. When drops are ejected from the nozzle toward the recording medium, a major portion of the ink is contained at the head of the drop, i.e. the leading portion of the drop. A lesser portion of the ink is contained in the tail of the drop, which initially takes the form of a narrower column of ink trailing the head of the drop. As the drop continues to fly toward the recording medium, the head typically moves at higher velocity and breaks off from the tail to form a main drop. The tail typically breaks up to form one or more smaller satellite drops that hit the recording medium after the main drop, because they are slower than the main drop. Because the recording medium is being moved with respect to the printhead, the slower satellite drops land at a different position than the main drop. In addition, there can be an angular difference in the trajectories of the main drop and the satellite drops, leading to further displacement, which can be additive to or subtractive from the velocity-dependent separation, depending on relative motion direction of printhead and recording medium. In a bi-directional print mode in a carriage printer, the satellite drops can land on one side of the main drop during a right-to-left printing pass, and on the other side of the main drop during a left-to-right printing pass. Thus satellite spots can cause printing defects including broadened vertical line width, fuzzy vertical line edges, and apparent jaggedness between portions of a vertical line that are printed by successive swaths printed in different directions. 
         [0007]    In the prior art attempts have been made to reduce print defects due to satellites by reducing print speed, changing ink formulation to modify properties such as surface tension, or refining pulse optimization. Other attempts have included using an asymmetric nozzle to steer satellite drops so that they tend to land closer to the main drop, when printing in a preferred direction. However, with such a nozzle geometry, satellite caused defects are compounded when printing in the opposite direction. 
         [0008]    What is needed is an improved inkjet printing device that is capable of printing at full speed, is compatible with a wide range of inks and driving conditions. In addition, what is needed for carriage printers having bi-directional print modes is an inkjet printing device that reduces satellite printing defects for both left-to-right and right-to-left printing swaths. 
       SUMMARY OF THE INVENTION 
       [0009]    A preferred embodiment of the present invention includes a method of ejecting a drop of liquid through a nozzle having a plurality of lobes. The lobes are narrower near the center of the nozzle and increase in width further from the center. A drop ejecting mechanism is actuated to eject a drop of the liquid such that a central region of the drop is pinched by the constricting central region of the nozzle. This provides advantages such as shortening a tail length of the drop, and other advantages as described herein. 
         [0010]    Another preferred embodiment of the invention is implementing the method in an inkjet printer by providing a plurality of multi-lobed nozzles formed in a printhead of the printer wherein ink ejected through each of the multi-lobed nozzles itself forms lobes that collapse together into a single drop before striking a receiving substrate such as printer paper or other media. 
         [0011]    These, and other, aspects and objects of the present invention will be better appreciated and understood when considered in conjunction with the following description and the accompanying drawings. It should be understood, however, that the following description, while indicating preferred embodiments of the present invention and numerous specific details thereof, is given by way of illustration and not of limitation. Many changes and modifications may be made within the scope of the present invention without departing from the spirit thereof, and the invention includes all such modifications. The figures below are not intended to be drawn to any precise scale with respect to size, angular relationship, or relative position. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0012]      FIG. 1  is a schematic representation of an inkjet printer system; 
           [0013]      FIG. 2  is a schematic layout of a printhead die including two nozzle arrays plus associated electronics; 
           [0014]      FIG. 3  is a cross sectional view of two drop ejectors together with ejected drops at two different times for circular nozzles; 
           [0015]      FIG. 4  is a perspective view of a portion of a printhead chassis; 
           [0016]      FIG. 5  is a perspective view of a portion of a carriage printer; 
           [0017]      FIGS. 6A-6G  are top views of embodiments of multi-lobed nozzles; 
           [0018]      FIGS. 7A-7D  show geometries of triangles and overlapping triangles; 
           [0019]      FIG. 8  is a cross-sectional view of two drop ejectors together with ejected drops at two different times for an embodiment of multi-lobed nozzles; 
           [0020]      FIG. 9  is a cross-sectional view of two drop ejectors as ink is being extruded through a multi-lobed nozzle; 
           [0021]      FIG. 10  is a printhead die having an array of multi-lobed nozzles; 
           [0022]      FIGS. 11A and 11B  are perspective views respectively of two-lobed and four-lobed nozzles; and 
           [0023]      FIGS. 12A to 12I  show a process for forming drop ejectors with multi-lobed nozzles. 
       
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       [0024]    Referring to  FIG. 1 , a schematic representation of an inkjet printer system  10  is shown, for its usefulness with the present invention and is fully described in U.S. Pat. No. 7,350,902, which is incorporated by reference herein in its entirety. Inkjet printer system  10  includes an image data source  12 , which provides data signals that are interpreted by a controller  14  as being commands to eject drops. Controller  14  includes an image processing unit  15  for rendering images for printing, and outputs signals to an electrical pulse source  16  of electrical energy pulses that are inputted to an inkjet printhead  100 , which includes at least one inkjet printhead die  110 . 
         [0025]    In the example shown in  FIG. 1 , there are two nozzle arrays  120  and  130  in the printhead that are each disposed along an array direction  254 . Nozzles in the two nozzle arrays  120  and  130  are shown as circular in the generic example  FIG. 1 . Circular nozzles will serve as a comparative example for the multi-lobed shaped embodiments of the present invention described below. 
         [0026]    In the example of  FIG. 1 , nozzles  121  in the first nozzle array  120  have a larger opening area than nozzles  131  in the second nozzle array  130 . In this example, each of the two nozzle arrays has two staggered rows of nozzles, each row having a nozzle density of 600 per inch. The effective nozzle density then in each array is 1200 per inch (i.e. d= 1/1200 inch in  FIG. 1 ). If pixels on the recording medium  20  were sequentially numbered along the paper advance direction, the nozzles from one row of an array would print the odd numbered pixels, while the nozzles from the other row of the array would print the even numbered pixels. 
         [0027]    In fluid communication with each nozzle array is a corresponding ink delivery pathway. Ink delivery pathway  122  is in fluid communication with the first nozzle array  120 , and ink delivery pathway  132  is in fluid communication with the second nozzle array  130 . Portions of ink delivery pathways  122  and  132  are shown in  FIG. 1  as openings through printhead die substrate  111 . One or more inkjet printhead die  110  will be included in inkjet printhead  100 , but for greater clarity only one inkjet printhead die  110  is shown in  FIG. 1 . The printhead die are arranged on a mounting support member as discussed below relative to  FIG. 3 . In  FIG. 1 , first fluid source  18  supplies ink to first nozzle array  120  via ink delivery pathway  122 , and second fluid source  19  supplies ink to second nozzle array  130  via ink delivery pathway  132 . Although distinct fluid sources  18  and  19  are shown, in some applications it may be beneficial to have a single fluid source supplying ink to both the first nozzle array  120  and the second nozzle array  130  via ink delivery pathways  122  and  132  respectively. Also, in some embodiments, fewer than two or more than two nozzle arrays can be included on printhead die  110 . In some embodiments, all nozzles on inkjet printhead die  110  can be the same size, rather than having multiple sized nozzles on inkjet printhead die  110 . 
         [0028]    Not shown in  FIG. 1 , are the drop forming mechanisms associated with the nozzles. Drop forming mechanisms can be of a variety of types, some of which include a heating element to vaporize a portion of ink and thereby cause ejection of a droplet, or a piezoelectric transducer to constrict the volume of a fluid chamber and thereby cause ejection, or an actuator which is made to move (for example, by heating a bi-layer element or by electrostatic forces) and thereby cause ejection. In any case, electrical pulses from electrical pulse source  16  are sent to the various drop ejectors according to the desired deposition pattern. In the example of  FIG. 1 , droplets  181  ejected from the first nozzle array  120  are larger than droplets  182  ejected from the second nozzle array  130 , due to the larger nozzle opening area. Typically other aspects of the drop forming mechanisms (not shown) associated respectively with nozzle arrays  120  and  130  are also sized differently in order to optimize the drop ejection process for the different sized drops. During operation, droplets of ink are deposited on a recording medium  20 . 
         [0029]    A printhead die  110  having array lengths of a half inch with nozzles at 1200 per inch will have about 600 nozzles per array. For printhead die  110  that have more than one hundred nozzles, logic electronics  142  and driver transistors  144  are typically integrated onto the printhead die  110  so that the number of interconnection pads  148  can be reduced, as illustrated in the schematic printhead die layout of  FIG. 2 . Rather than requiring an interconnection pad  148  for each nozzle in nozzle arrays  120  and  130  in order to power the associated drop forming mechanisms, a few inputs, such as serial data, clock, ejector power, logic power, ground, and other control signals are connected to interconnection pads  148 . Electrical input signals, plus power and ground are connected to the logic electronics and driver transistors by wiring (not shown) that is patterned on the printhead die  110 . Electrical leads  146  bring power pulses from the driver transistors  144  to the drop forming mechanisms associated with the nozzles in nozzle arrays  120  and  130 . Also shown in  FIG. 2  are ink feed openings  123  and  133  that are part of ink delivery pathways  122  and  132  (with reference to  FIG. 1 ) for nozzle arrays  120  and  130  respectively. For staggered arrays, a typical ink feed opening design is a slot that extends parallel to array direction  254  between the two rows of nozzles in a staggered array. For mechanical strength, rather than a continuous ink feed slot that extends the length of the nozzle array, there can be a series of ink feed slots with strengthening ribs  134  between adjacent slots, as illustrated in  FIG. 2 . 
         [0030]      FIG. 3  is a cross-sectional view of a portion of printhead die  110  along direction A-A seen in  FIG. 2 . Note that direction A-A jogs as it crosses ink feed slot  133 , so that the cross section goes through nozzles  131  on each side of the staggered array of nozzles. Each nozzle  131  is opposite a resistive heater  114 , which serves as the drop forming mechanism in this example. The heater  114  is located in an ink-filled chamber  116 . The floor of the chamber  116  typically includes a plurality of thin film layers  112 , including a thermal barrier layer below the heater  114 . The nozzle  131  is formed in nozzle plate  118 , which forms the roof of chamber  116 . Chamber walls  117  support the nozzle plate  118  and separate it from the floor of the chamber  116 . 
         [0031]    Also shown in  FIG. 3  is a schematic representation of drop ejection behavior for the comparative example of circular nozzles. Drops of ink are ejected when heater  114  is pulsed and heats rapidly to form a bubble which expands and pushes ink from chamber  116  through nozzle  131 . The drop from the nozzle  131  at right was ejected earlier than the drop from the nozzle  131  at left. Drop shapes in  FIG. 3  are similar to those seen about 20 microseconds after pulsing the heater  114  (for the drop at right) and about 10 microseconds after pulsing the heater  114  (for the drop at left). Note that the drop at right has a length L 1c  from head  183  to tail  184  that is somewhat longer than the length L 2c  from head  185  to tail  186  for the drop at the left. In other words, as the drop continues to travel, it elongates. This is because the velocity of the head of the drop is faster than that of the tail of the drop. 
         [0032]      FIG. 4  shows a perspective view of a portion of a printhead chassis  250 . Printhead chassis  250  includes two printhead die  251  (similar to printhead die  110  of  FIGS. 1 and 2 ) that are affixed to a common mounting support  255 . Each printhead die  251  contains two nozzle arrays  253 , so that printhead chassis  250  contains four nozzle arrays  253  altogether. The four nozzle arrays  253  in this example can each be connected to separate ink sources (not shown in  FIG. 4 ), such as cyan, magenta, yellow, and black. Each of the four nozzle arrays  253  is disposed along nozzle array direction  254 , and the length of each nozzle array along nozzle array direction  254  is typically on the order of 1 inch or less. Typical lengths of recording media are 6 inches for photographic prints (4 inches by 6 inches) or 11 inches for paper (8.5 by 11 inches). Thus, in order to print a full image, a number of swaths are successively printed while moving printhead chassis  250  across the recording medium  20 . Following the printing of a swath, the recording medium  20  is advanced along a media advance direction that is substantially parallel to nozzle array direction  254 . 
         [0033]    Also shown in  FIG. 4  is a flex circuit  257  to which the printhead die  251  are electrically interconnected, for example, by wire bonding or TAB bonding. The interconnections and interconnection pads  148  (with reference to  FIG. 2 ) are covered by an encapsulant  256  to protect them. Flex circuit  257  bends around a portion of printhead chassis  250  and connects to connector board  258 . When printhead chassis  250  is mounted into the carriage  200  (see  FIG. 5 ), connector board  258  is electrically connected to a connector (not shown) on the carriage  200 , so that electrical signals can be transmitted from there to the printhead die  251 . 
         [0034]      FIG. 5  shows a portion of a desktop carriage printer. Some of the parts of the printer have been hidden in the view shown in  FIG. 5  so that other parts can be more clearly seen. Printer chassis  300  has a print region  303  across which carriage  200  is moved back and forth in carriage scan direction  305  along the X axis, between the right side  306  and the left side  307  of printer chassis  300 , while drops are ejected from printhead die  251  (not shown in  FIG. 5 ) on printhead chassis  250  that is mounted on carriage  200 . Carriage motor  380  moves belt  384  to move carriage  200  along carriage guide rail  382 . An encoder sensor (not shown) is mounted on carriage  200  and indicates carriage location relative to an encoder fence  383 . 
         [0035]    Printhead chassis  250  is mounted in carriage  200 , and multi-chamber ink supply  262  and single-chamber ink supply  264  are mounted in the printhead chassis  250 . The mounting orientation of printhead chassis  250  is rotated relative to the view in  FIG. 4 , so that the printhead die  251  are located at the bottom side of printhead chassis  250 , the droplets of ink being ejected downward onto the recording medium in print region  303  in the view of  FIG. 5 . Multi-chamber ink supply  262 , for example, contains three ink sources: cyan, magenta, and yellow ink; while single-chamber ink supply  264  contains the ink source for black. Paper or other recording medium (sometimes generically referred to as paper or media herein) is loaded along paper load entry direction  302  toward the front of printer chassis  308 . 
         [0036]    A variety of paper-advance rollers are used to advance the medium through the printer. The motor that powers the paper advance rollers is not shown in  FIG. 5 , but the hole  310  at the right side of the printer chassis  306  is where the motor gear (not shown) protrudes through in order to engage feed roller gear  311 , as well as the gear for the discharge roller (not shown). For normal paper pick-up and feeding, it is desired that all rollers rotate in forward rotation direction  313 . Toward the left side of the printer chassis  307 , in the example of  FIG. 5 , is the maintenance station  330 . 
         [0037]    Toward the rear of the printer chassis  309 , in this example, is located the electronics board  390 , which includes cable connectors  392  for communicating via cables (not shown) to the printhead carriage  200  and from there to the printhead chassis  250 . Also on the electronics board are typically mounted motor controllers for the carriage motor  380  and for the paper advance motor, a processor and/or other control electronics (shown schematically as controller  14  and image processing unit  15  in  FIG. 1 ) for controlling the printing process, and an optional connector for a cable to a host computer. 
         [0038]    Inventive aspects of the present invention relate to a nozzle design having a plurality of lobes that are narrower toward the central region of the nozzle and wider at a portion that is more distant from the central region of the nozzle.  FIGS. 6A-6G  show top views of a variety of multi-lobed nozzle configurations that are embodiments of the invention, but it can be appreciated that many other configurations are possible. 
         [0039]    The embodiment shown in  FIG. 6A  is a nozzle opening made up of two intersecting circles having centers that are displaced from each other. The nonintersecting portion of each of the intersecting circles is a lobe  410 . The nozzle opening also has a central region that is the intersection of the two circles. The central region includes the centroid  420  of the nozzle opening. The two lobes  410  extend in opposite directions away from centroid  420  along radial direction  430 . Radial direction  430  is also an axis of symmetry of the nozzle. The nozzle of  FIG. 6A  is mirror symmetric about radial direction  430 . The two lobes  410  are disposed symmetrically about the central region of the opening. The points of intersection of the two circles define a narrow portion  440  of the nozzle where the two lobes  410  each have a width w 1 . This narrow portion  440  is relatively near the centroid  420 , and therefore is proximate the central region of the nozzle. The lobes  410  also each have a wider portion  450  where the width is w 2  (i.e. w 2 &gt;w 1 ). The wider portion  450  is farther away from centroid  420  than the narrow portion  440  is. In particular, for two intersecting circles having the same radius R and an intersection width w 1  (as in  FIG. 6A ) the distance D from centroid  420  to the wider portion  450  is D=(2R 2 −(0.5w 1 ) 2 ) 1/2 . If the centers of the two intersecting circles are not coincident, then 0.5 w 1  is less than R. Therefore, if the centers of the two intersecting circles are not coincident, D is greater than R, so that wider portion  450  is farther away from centroid  420  than the narrow portion  440  is (i.e. D&gt;0.5w 1 ) 
         [0040]      FIG. 6B  is a nozzle opening embodiment made up of two intersecting triangles. The nonintersecting portion of each of the intersecting triangles is a lobe  410 . Although a common definition of“lobe” is a “rounded projection”, herein the term lobe will have the more general definition “any projection”. Thus the term lobe is used to refer to two portions of  FIG. 6B , as well as two portions of  FIG. 6A . The nozzle opening also has a central region that is the intersection of the two triangles. The central region includes the centroid  420  of the nozzle opening. The two lobes  410  extend in opposite directions away from centroid  420  along radial direction  430 . Radial direction  430  is also an axis of symmetry of the nozzle. The two lobes  410  are disposed symmetrically about the central region of the opening. The nozzle of  FIG. 6B  is mirror symmetric about radial direction  430 . The points of intersection of the two triangles define a narrow portion  440  of the nozzle where the two lobes  410  each have a width w 1 . This narrow portion  440  is relatively near the centroid  420 , and therefore is proximate the central region of the nozzle. The lobes  410  also each have a wider portion  450  where the width is w 2  (i.e. w 2 &gt;w 1 ). The wider portion  450  is farther away from centroid  420  than the narrow portion  440  is. Because of its shape, the nozzle configuration of  FIG. 6B  is sometimes called a bowtie nozzle. Some embodiments of a bowtie nozzle have rounded corners (not shown). 
         [0041]      FIG. 6C  is a nozzle configuration embodiment made up of two intersecting teardrop shaped portions. The general characteristics of two-lobed nozzles where the lobes have the same shape and area, as in  FIGS. 6A and 6B  also apply to the embodiment of  FIG. 6C . Another property is shown with respect to  FIG. 6C , which is also true of a number of other embodiments. In particular, the distance D 1  from the centroid  420  to the nearest portion of nozzle wall at narrow portion  440  is less than the distance D 2  from that nearest portion of wall at narrow portion  440  to the most distal edge  445  of the corresponding lobe  410 . 
         [0042]      FIG. 6D  is a nozzle opening embodiment made up of four intersecting teardrop shaped forms. The axes of symmetry  430  of the four lobes are at 90 degrees to each other (i.e. α 1 =α 2 =90 degrees). All four lobes in  FIG. 6D  have the same size and shape. Other properties of the two-lobed structures described with reference to  FIGS. 6A to 6C  also apply to the nozzle configuration of  FIG. 6D . 
         [0043]      FIG. 6E  is a nozzle opening embodiment made up of three intersecting teardrop shaped forms. In the embodiment of  FIG. 6E , the axes of symmetry (radial direction  430 ) are not all at equal angles with respect to one another for adjacent lobes. In particular α 1 =45 degrees while α 2 =90 degrees. In other words, the plurality of lobes  410  in  FIG. 6E  have at least two different angles between two pairs of axes of symmetry of adjacent lobes. 
         [0044]      FIG. 6F  is a nozzle opening embodiment having three intersecting teardrop shaped forms as in  FIG. 6E . However, in  FIG. 6F , there is a wide lobe  460  and two narrow lobes  465 . Wide lobe  460  has a larger width W 1  and larger area than the width W 2  and area respectively of a narrow lobe  465 . 
         [0045]      FIG. 6G  is a nozzle opening embodiment having six lobes  410 . Although in  FIGS. 6A-6G , embodiments having less than or equal to six lobes have been shown, there also can be embodiments having more than six lobes. 
         [0046]    The multi-lobed nozzle embodiments of the present invention have several performance advantages relative to circular, polygonal, or even star-shaped nozzles of the prior art. Some of these advantages are related to an increased ratio of perimeter to area of the nozzle opening of embodiments of the present invention. The nozzle area is related to the volume of the drop that is ejected. A large ratio of perimeter to area of nozzle opening allows increased nozzle wall interaction with the ink, both before and during drop ejection. Before drop ejection, a high perimeter to area ratio increases refill speed of the drop ejector by pulling ink into the nozzle. This enables higher frequency drop ejection, and higher speed printing as a result. In addition, the meniscus of the ink in the nozzle is pinned more stably by the large perimeter surface forces, thereby reducing the occurrence of nozzle plate flooding due to outward bulging of the meniscus. Such outward bulging of the meniscus can be caused by the momentum of ink flow to refill the nozzles, as well as by cross-talk due to firing neighboring nozzles. Furthermore, larger perimeter to area ratio of the nozzle increases the effectiveness of the surface tension force pulling the tail towards the head of the drop. This prevents the tail of the drop from breaking up into small satellite drops, or results in high satellite velocity relative to prior art nozzles, so that there is a small difference in the velocity of main drops and satellite drops. This reduces misting inside the printer caused by small satellite drops slowing down and stopping in flight by viscous air drag. This also leads to smaller displacement between satellite dots and main dots even during bidirectional printing. Typical inkjet inks have a surface tension of around 30 dynes/cm. 
         [0047]      FIGS. 7A to 7D  illustrate the increased perimeter to area ratio of the two-lobed bowtie nozzle of  FIG. 6B  relative to triangular or six-pointed star nozzles of the prior art.  FIG. 7A  is an equilateral triangle having three equal sides of length s. Triangle centroid  422  is located at the intersection of the three medians (dotted lines in  FIG. 7A ) of the triangle. For an equilateral triangle, it can be shown that the centroid is located a distance h/3 from each of the sides, where h=s√3/2 is the height of the triangle. The area of the equilateral triangle is √3 s 2 /4, while the perimeter is 3s, so the ratio of the perimeter to area is 4√3/s=6.93/s. 
         [0048]      FIG. 7B  is a six-pointed star made up of two mirrored equilateral triangles (solid lines) where the centroids of the two triangles (intersection of dotted line medians) are coincident at the centroid  420  of the star. Each of the mirrored triangles has a side of length a. The star points have sides of length a/3, and the hexagon at the center of the star also has sides of length a/3. The area of the star is a 2 /√3, while the perimeter is 4a. The perimeter to area ratio has a similar expression as that of a single equilateral triangle (4√3/a). However, if the areas of the triangle of  FIG. 7A  and the star of  FIG. 7B  are constrained to be the same (to provide similar drop volumes), √3 s 2 /4=a 2 /√3, so that a=√3 s/2. Thus for similar nozzle areas, the perimeter to area ratio is increased for the star of  FIG. 7B  relative to the triangle of  FIG. 7A  by 2/√3, i.e. a 15.4% increase. 
         [0049]      FIG. 7C  is a bowtie made up of two mirrored equilateral triangles each having sides of length b and having coincident vertices at bowtie centroid  420 . The centroids  422  of each individual triangle are displaced from one another by a distance 2b/√3. The perimeter of the bowtie of  FIG. 7C  is 6b and the area is √3 b 2 /2. The perimeter to area ratio for the bowtie of  FIG. 7C  is 4√3/b. If the area of the bowtie of  FIG. 7C  is set equal to the area of the star of  FIG. 7B , then √3 b 2 /2=a 2 /√3, so that b=a√(2/3). Thus for similar nozzle areas, the perimeter to area ratio is increased for the bowtie of  FIG. 7C  relative to the star of  FIG. 7B  by √(3/2), i.e. a 22.5% increase over the star. 
         [0050]    The bowtie of  FIG. 7D  is made up of two mirrored equilateral triangles each having sides of length c and having an overlap length of h 1 /3, where h 1 =c√3/2 is the height of the triangle. The shape of the overlapping bowtie of  FIG. 7D  is more nearly similar to the bowtie of  FIG. 6B , although rotated by 90 degrees. Its perimeter is 16c/3 and its area is 35√3 c 2 /72. If the area of the overlapping bowtie of  FIG. 7D  is set equal to the area of the six pointed star of  FIG. 7B , the perimeter to area ratio of the overlapping bowtie is increased by 10.4% relative to the star. 
         [0051]    Sometimes perimeter to area ratio is calculated with reference to a circle having the same area. A circle has a perimeter to area ratio of 2/R where R is the radius of the circle. A circle has the minimum ratio of perimeter to area of any plane geometrical shape. A single equilateral triangle (as in  FIG. 7A ) has a perimeter to area ratio of 2.57/R ef , where R ef  is an effective radius determined by setting the area of the triangle equal to the area of the circle. Similarly a square has a perimeter to area ratio of 2.26/R ef  and a regular hexagon has a perimeter to area ratio of 2.10/R ef . As the number of sides of a polygon increases, its perimeter to area ratio approaches 2/R ef . The star of  FIG. 7B  has a perimeter to area ratio of 2.97/R ef . The nonoverlapping bowtie of  FIG. 7C  has a perimeter to area ratio of 3.64/R ef . The overlapping bowtie of  FIG. 7D  has a perimeter to area ratio of 3.28/R ef . Thus, although the star has a higher perimeter to area ratio than any of the regular polygons, the bowtie (even with some overlap as in  FIG. 6B  or  7 D) has a higher perimeter to area ratio than a star. 
         [0052]    Other performance advantages of embodiments of multi-lobed nozzles of the present invention relate to the small central region of the nozzle opening. The nozzle includes opposing sidewalls that converge toward each other in a central region of the nozzle for constricting a central region of the drop of liquid as the drop is ejected through the nozzle. The small opening in the central region causes the ink ligament to pinch off at the center of the nozzle, resulting in straighter jet trajectories for improved drop placement accuracy. In addition, the tail of the jet is shorter than for prior art nozzles, because the small opening at the central region causes the tail to pinch off sooner. This reduces ink volume available to form satellites, so that satellites are smaller and/or less numerous. 
         [0053]      FIG. 8  shows a schematic representation of drop ejection behavior for the embodiment of a multi-lobed nozzle  400  having four lobes. Drops of ink are ejected when heater  114  is pulsed and heats rapidly to form a bubble which expands and pushes ink from chamber  116  through nozzle  400 . The drop from the nozzle  400  at right was ejected earlier than the drop from the nozzle  400  at left. Drop shapes in  FIG. 8  are similar to those seen about  20  microseconds after pulsing the heater  114  (for the drop at right) and about 10 microseconds after pulsing the heater  114  (for the drop at left). Note that the length L 1M  from head  185  to tail  186  for the drop at the left is about the same as the length L 2M  from head  183  to tail  184  for the drop at the right. In other words, as the drop continues to travel, it does not elongate, as does the drop ejected by circular nozzles shown in  FIG. 3 . This is because the velocity of the head of the drop is similar to that of the tail of the drop in the embodiment of  FIG. 8 . 
         [0054]    Furthermore, for a drop ejector having multi-lobed nozzle according to embodiments of the present invention, when the drop forming mechanism (such as heater  114 ) is actuated, the liquid ink (having a surface tension of around 30 dynes/cm for example) is ejected through the nozzle such that a quantity of liquid is forced through each of the plurality of lobes  410 . The lobes of the present invention are more effective in applying surface forces to the ink than the points of a star of a star-shaped nozzle of the prior art. This is because for a star shaped nozzle, the liquid ink primarily goes through the large central region of the star. Not much liquid is forced through the points of the star so that the liquid near the points is substantially stagnant. For the present invention, ink at the narrow central region of the multi-lobed nozzle is not stagnant, but initially travels at a slower velocity due to higher viscous drag. As a result, as the extruded ink  187  is just being ejected from the multi-lobed nozzle  400 , head and tail regions corresponding to each lobe can be observed, although they are still connected together, as schematically illustrated in  FIG. 9 .  FIG. 9  represents an earlier time relative to  FIG. 8 , soon after actuating the drop forming mechanism, such as heater  114 . Between  FIG. 8  and  FIG. 9 , surface tension of the ink tends to collapse the heads from separate lobes into a single head, and also to collapse the tails from separate lobes into a single tail. By the time of  FIG. 8 , the drop head  183  and the drop tail  184  are traveling at substantially equal velocities before striking a receiving substrate (such as paper or other recording medium). 
         [0055]      FIG. 10  shows a printhead die  251  having an array of multi-lobed nozzles  400  disposed along array direction  254 . In embodiments of the present invention, such a printhead die can be assembled into a printhead  250  such as the one shown in  FIG. 4 . In the particular example of  FIG. 10 , the nozzles have two lobes  410  and the nozzle configuration is the overlapping bowtie. For some nozzle configuration embodiments, such as the bowtie nozzle, the dimension H along the radial direction  430  from centroid  420  can be larger than the width w 2  of wide portion  450  of lobe  410 . In order to space the nozzles close together for a high resolution printhead, it can be advantageous to have the largest dimension of the nozzle perpendicular to array direction  254 . For the example of  FIG. 10  this is the same as the radial direction  430  along which a lobe  410  extends away from centroid  420  being perpendicular to array direction  254 . 
         [0056]    A drop ejector having a multi-lobed nozzle can be fabricated in a variety of ways.  FIGS. 11A and 11B  show two-lobed and four-lobed nozzles, respectively, that were formed using the method described in published US Patent Application No. 2008/0136867, which is incorporated herein by reference in its entirety.  FIGS. 12A-12I  show the process of forming the drop ejector structure having a multi-lobed nozzle as shown in  FIGS. 11A and 11B . In  FIG. 12A , the heater  114  and associated thin film layers  112  (including thermal barrier layer  24 , for example, silicon dioxide, electrically resistive layer  26  (which forms resistive heating element  113 ), for example, tantalum silicon nitride, electrically conductive layer  28  (which carries electrical current to resistive heating element  113  and defines the length of resistive heating element  113 ), for example aluminum, insulating passivation layer  30 , for example silicon nitride, and protection layer  32 , for example, tantalum) have been formed on substrate  111  using commonly known processes. Two ink feed ports  6  (one for each row of nozzles) are etched through the thin film layers  112  down to the substrate  111 . Between the two ink feed ports  6  is a chamber center support region  8 . 
         [0057]    As shown in  FIG. 12B , an organic material  48 , such as polyimide, is deposited on the structure in a thickness that will define the height of the ink chamber.  FIG. 12C  shows a hard mask  52 , such as silicon nitride, and a photoresist layer  51  deposited on the hard mask in order to pattern hard mask  51 , as shown, by plasma etching. In  FIG. 12D , the organic material  48  is patterned by oxygen plasma etching through hard mask  52  in order to form openings corresponding to subsequently formed features including chamber walls  117  and center support region walls  56  (see  FIG. 12E ). As part of this plasma etching process, photoresist layer  51  is removed. The organic material  48  is divided into three regions: a passivation region  40  that protects circuitry (not shown) formed on substrate  111  and provides support of the subsequently formed nozzle plate in regions away from the chamber; a center feed support  41  that provides structural support for the nozzle plate over the ink feed opening; and the sacrificial region  54  that defines the region where ink will be located in the printhead die, including the ink chamber. 
         [0058]    As shown in  FIG. 12E , an inorganic material such as silicon oxide is then deposited, for example by plasma enhanced chemical vapor deposition. A portion of this inorganic material that is deposited within the openings becomes the chamber walls  117  and the center support region walls  56 . Another portion of this inorganic material that is deposited over the organic material  48  becomes the nozzle plate  118 . 
         [0059]    As shown in  FIGS. 12F and 12G , multi-lobed nozzles  400  are formed in nozzle plate  118  in alignment with the corresponding heaters by using a mask  402  including multi-lobed regions  403 . Mask  402  is aligned to the heater pattern and light  401  is transmitted through the transparent regions of mask  402  toward photoresist  406  that has been applied to the surface of the nozzle plate  118 . (Multi-lobed regions  403  of mask  402  can be designed to be either transparent or opaque, depending upon the type of photoresist  406  that is used.) The photoresist  406  is thus exposed to form multi-lobed patterns  404 , which are developed and cured. Then the nozzle plate  118  is etched through multi-lobed openings in the photopatterned photoresist  406 , for example with a fluorine based plasma to form multi-lobed nozzles  400  in alignment with heaters  114  as shown in cross-section in  FIG. 12G  (after the photoresist  406  has been removed). 
         [0060]    The feed opening  123  is then formed from the back of the substrate  111  by using deep reactive ion etching, as shown in  FIG. 12H . At this point, organic material  48  is still disposed in sacrificial regions  54 . As illustrated in  FIG. 12I , an oxygen plasma is then used to etch out the organic material in sacrificial region  54  that defines ink chamber  116  and ink feed ports  6 . By this method, a completed drop ejector is formed, having a silicon oxide nozzle plate  118  with multi-lobed nozzles  400  having been integrally formed as part of the wafer fabrication process and aligned to heaters  114 . 
         [0061]    Alternatively, multi-lobed nozzles can be formed using a fabrication process such as described in U.S. Pat. No. 4,789,425, incorporated by reference herein in its entirety. In that process, after the heater is formed on one side of the substrate, the ink delivery passageway is etched through the substrate from the opposite side using orientation dependent etching. A layer of photopatternable material such as photosensitive polyimide is applied and patterned to form chamber walls. Then a dry film photopatternable material is placed over the patterned chamber wall layer to serve as a nozzle plate. Multi-lobed nozzles  400  are formed in the dry film photopatternable material by using a mask including multi-lobed nozzle patterns. The mask is aligned relative to the heaters such that the multi-lobed nozzle patterns in the mask are aligned with the corresponding heaters. The dry film photopatternable material is exposed by transmitting light through the mask toward the dry film photopatternable material, which is then developed and cured to provide a nozzle plate having multi-lobed nozzles. 
         [0062]    In other exemplary methods, the device including the heaters can be fabricated on a substrate, and a nozzle plate can be separately made having multi-lobed nozzles such that after the multi-lobed nozzles are formed in the nozzle plate, the nozzle plate is adhesively bonded to the substrate having the heaters. For example, the nozzle plate can be laser ablated to form multi-lobed nozzles according to the laser ablation process described in U.S. Pat. No. 5,305,018, incorporated by reference herein in its entirety. A strip of polymer film such as Teflon or polyimide is positioned under a laser (e.g. an Excimer laser) with a metal lithographic mask interposed between the laser and the polymer film. In this case, the metal lithographic mask is provided with multi-lobed transparent regions for the laser light to pass through. When the laser is turned on and directed toward the polymer film, it ablates the regions in the film corresponding to where the laser beam goes through the mask, thus forming multi-lobed nozzles in the film. The nozzle plate is subsequently affixed to the substrate having the heaters, such that the multi-lobed nozzles are aligned with the corresponding heaters. The ink chambers can be fabricated on the heater substrate prior to affixing the nozzle plate. Alternatively, the ink chamber structures can also be laser ablated as a separate piece (or as part of the nozzle plate) which is subsequently aligned and bonded to the device having the heaters. 
         [0063]    The invention has been described in detail with particular reference to certain preferred embodiments thereof, but it will be understood that variations and modifications can be effected within the spirit and scope of the invention. 
       Parts List 
       [0000]    
       
           6  Ink feed ports 
           8  Center support region 
           10  Inkjet printer system 
           12  Image data source 
           14  Controller 
           15  Image processing unit 
           16  Electrical pulse source 
           18  First fluid source 
           19  Second fluid source 
           20  Recording medium 
           24  Thermal barrier layer 
           26  Electrically resistive layer 
           28  Electrically conductive layer 
           30  Insulating passivation layer 
           32  Protection layer 
           40  Passivation region 
           41  Center feed support 
           48  Organic material 
           51  Photoresist layer 
           52  Hard mask 
           54  Sacrificial layer 
           56  Center support region walls 
           100  Inkjet printhead 
           110  Inkjet printhead die 
           111  Substrate 
           112  Thin film layers 
           114  Heater 
           116  Chamber 
           117  Chamber wall 
           118  Nozzle plate 
           120  First nozzle array 
           121  Nozzle(s) 
           122  Ink delivery pathway (for first nozzle array) 
           123  Ink feed opening 
           130  Second nozzle array 
           131  Nozzle(s) 
           132  Ink delivery pathway (for second nozzle array) 
           133  Ink feed opening 
           134  Rib 
           142  Logic electronics 
           144  Driver transistors 
           146  Electrical leads 
           148  Interconnection pads 
           181  Droplet(s) (ejected from first nozzle array) 
           182  Droplet(s) (ejected from second nozzle array) 
           183  Drop head 
           184  Drop tail 
           185  Drop head 
           186  Drop tail 
           187  Extruded ink 
           200  Carriage 
           250  Printhead chassis 
           251  Printhead die 
           253  Nozzle array 
           254  Nozzle array direction 
           255  Mounting support member 
           256  Encapsulant 
           257  Flex circuit 
           258  Connector board 
           262  Multi-chamber ink supply 
           264  Single-chamber ink supply 
           300  Printer chassis 
           302  Paper load entry direction 
           303  Print region 
           304  Media advance direction 
           305  Carriage scan direction 
           306  Right side of printer chassis 
           307  Left side of printer chassis 
           308  Front of printer chassis 
           309  Rear of printer chassis 
           310  Hole (for paper advance motor drive gear) 
           311  Feed roller gear 
           313  Forward rotation direction (of feed roller) 
           330  Maintenance station 
           380  Carriage motor 
           382  Carriage guide rail 
           383  Encoder fence 
           384  Belt 
           390  Printer electronics board 
           392  Cable connectors 
           400  Multi-lobed nozzle 
           401  Light 
           402  Mask 
           403  Multi-lobed transparent regions 
           404  Multi-lobed patterns 
           406  Photoresist 
           410  Lobe 
           420  Centroid 
           422  Triangle centroid 
           430  Radial direction from centroid 
           440  Narrow portion 
           445  Most distal edge 
           450  Wide portion 
           460  Wide lobe 
           465  Narrow lobe