Patent Publication Number: US-5892524-A

Title: Apparatus for printing multiple drop sizes and fabrication thereof

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     Reference is made to my commonly assigned, co-pending U.S. patent applications Ser. No. 08/701,021 entitled CMOS PROCESS COMPATIBLE FABRICATION OF PRINT HEADS filed Aug. 21, 1996; Ser. No. 08/733,711 entitled CONSTRUCTION AND MANUFACTURING PROCESS FOR DROP ON DEMAND PRINT HEADS WITH NOZZLE HEATERS filed Oct. 17, 1996; Ser. No. 08/734,822 entitled A MODULAR PRINT HEAD ASSEMBLY filed Oct. 22, 1996; Ser. No. 08/736,537 entitled PRINT HEAD CONSTRUCTIONS FOR REDUCED ELECTROSTATIC INTERACTION BETWEEN PRINTED DROPLETS filed Oct. 24, 1996; Ser. No. 08/750,320 entitled NOZZLE DUPLICATION FOR FAULT TOLERANCE IN INTEGRATED PRINTING HEADS and Ser. No. 08/750,312 entitled HIGH CAPACITY COMPRESSED DOCUMENT IMAGE STORAGE FOR DIGITAL COLOR PRINTERS both filed Nov. 26, 1996; Ser. No. 08/753,718 entitled NOZZLE PLACEMENT IN MONOLITHIC DROP-ON-DEMAND PRINT HEADS and Ser. No. 08/750,606 entitled A COLOR VIDEO PRINTER AND A PHOTO CD SYSTEM WITH INTEGRATED PRINTER both filed on Nov. 27, 1996; Ser. No. 08/750,438 entitled A LIQUID INK PRINTING APPARATUS AND SYSTEM, Ser. No. 08/750,599 entitled COINCIDENT DROP SELECTION, DROP SEPARATION PRINTING METHOD AND SYSTEM, Ser. No. 08/750,435 entitled MONOLITHIC PRINT HEAD STRUCTURE AND A MANUFACTURING PROCESS THEREFOR USING ANISTROPIC WET ETCHING, Ser. No. 08/750,436 entitled POWER SUPPLY CONNECTION FOR MONOLITHIC PRINT HEADS, Ser. No. 08/750,437 entitled MODULAR DIGITAL PRINTING, Ser. No. 08/750,439 entitled A HIGH SPEED DIGITAL FABRIC PRINTER, Ser. No. 08/750,763 entitled A COLOR PHOTOCOPIER USING A DROP ON DEMAND INK JET PRINTING SYSTEM, Ser. No. 08/765,756 entitled PHOTOGRAPH PROCESSING AND COPYING SYSTEMS, Ser. No. 08/750,646 entitled FAX MACHINE WITH CONCURRENT DROP SELECTION AND DROP SEPARATION INK JET PRINTING, Ser. No. 08/759,774 entitled FAULT TOLERANCE IN HIGH VOLUME PRINTING PRESSES, Ser. No. 08/750,429 entitled INTEGRATED DRIVE CIRCUITRY IN DROP ON DEMAND PRINT HEADS, Ser. No. 08/750,433 entitled HEATER POWER COMPENSATION FOR TEMPERATURE IN THERMAL PRINTING SYSTEMS, Ser. No. 08/750,640 entitled HEATER POWER COMPENSATION FOR THERMAL LAG IN THERMAL PRINTING SYSTEMS, Ser. No. 08/750,650 entitled DATA DISTRIBUTION IN MONOLITHIC PRINT HEADS, and Ser. No. 08/750,642 entitled PRESSURIZABLE LIQUID INK CARTRIDGE FOR COINCIDENT FORCES PRINTERS all filed Dec. 3, 1996; Ser. No. 08/750,647 entitled MONOLITHIC PRINTING HEADS AND MANUFACTURING PROCESSES THEREFOR, Ser. No. 08/750,604 entitled INTEGRATED FOUR COLOR PRINT HEADS, Ser. No. 08/750,605 entitled A SELF-ALIGNED CONSTRUCTION AND MANUFACTURING PROCESS FOR MONOLITHIC PRINT HEADS, Ser. No. 08/682,603 entitled A COLOR PLOTTER USING CONCURRENT DROP SELECTION AND DROP SEPARATION INK JET PRINTING TECHNOLOGY, Ser. No. 08/750,603 entitled A NOTEBOOK COMPUTER WITH INTEGRATED CONCURRENT DROP SELECTION AND DROP SEPARATION COLOR PRINTING SYSTEM, Ser. No. 08/765,130 entitled INTEGRATED FAULT TOLERANCE IN PRINTING MECHANISMS; Ser. No. 08/750,431 entitled BLOCK FAULT TOLERANCE IN INTEGRATED PRINTING HEADS, Ser. No. 08/750,607 entitled FOUR LEVEL INK SET FOR BI-LEVEL COLOR PRINTING, Ser. No. 08/750,430 entitled A NOZZLE CLEARING PROCEDURE FOR LIQUID INK PRINTING, Ser. No. 08/750,600 entitled METHOD AND APPARATUS FOR ACCURATE CONTROL OF TEMPERATURE PULSES IN PRINTING HEADS, Ser. No. 08/750,608 entitled A PORTABLE PRINTER USING A CONCURRENT DROP SELECTION AND DROP SEPARATION PRINTING SYSTEM, and Ser. No. 08/750,602 entitled IMPROVEMENTS IN IMAGE HALFTONING all filed Dec. 4, 1996; Ser. No. 08/765,127 entitled PRINTING METHOD AND APPARATUS EMPLOYING ELECTROSTATIC DROP SEPARATION, Ser. No. 08/750,643 entitled COLOR OFFICE PRINTER WITH A HIGH CAPACITY DIGITAL PAGE IMAGE STORE, and Ser. No. 08/765,035 entitled HEATER POWER COMPENSATION FOR PRINTING LOAD IN THERMAL PRINTING SYSTEMS all filed Dec. 5, 1996; Ser. No. 08/765,017 entitled HEATER STRUCTURE AND FABRICATION PROCESS FOR MONOLITHIC PRINT HEADS, Ser. No. 08/750,772 entitled DETECTION OF FAULTY ACTUATORS IN PRINTING HEADS, Ser. No. 08/765,037 entitled PAGE IMAGE AND FAULT TOLERANCE CONTROL APPARATUS FOR PRINTING SYSTEMS all filed Dec. 9, 1996; and Ser. No. 08/765,038 entitled CONSTRUCTIONS AND MANUFACTURING PROCESSES FOR THERMALLY ACTIVATED PRINT HEADS filed Dec. 10, 1996. 
    
    
     CROSS REFERENCE TO RELATED APPLICATIONS 
     Reference is made to my commonly assigned, co-pending U.S. patent applications Ser. No. 08/701,021 entitled CMOS PROCESS COMPATIBLE FABRICATION OF PRINT HEADS filed Aug. 21, 1996; Ser. No. 08/733,711 entitled CONSTRUCTION AND MANUFACTURING PROCESS FOR DROP ON DEMAND PRINT HEADS WITH NOZZLE HEATERS filed Oct. 17, 1996; Ser. No. 08/734,822 entitled A MODULAR PRINT HEAD ASSEMBLY filed Oct. 22, 1996; Ser. No. 08/736,537 entitled PRINT HEAD CONSTRUCTIONS FOR REDUCED ELECTROSTATIC INTERACTION BETWEEN PRINTED DROPLETS filed Oct. 24, 1996; Ser. No. 08/750,320 entitled NOZZLE DUPLICATION FOR FAULT TOLERANCE IN INTEGRATED PRINTING HEADS and Ser. No. 08/750,312 entitled HIGH CAPACITY COMPRESSED DOCUMENT IMAGE STORAGE FOR DIGITAL COLOR PRINTERS both filed Nov. 26, 1996; Ser. No. 08/753,718 entitled NOZZLE PLACEMENT IN MONOLITHIC DROP-ON-DEMAND PRINT HEADS and Ser. No. 08/750,606 entitled A COLOR VIDEO PRINTER AND A PHOTO CD SYSTEM WITH INTEGRATED PRINTER both filed on Nov. 27, 1996; Ser. No. 08/750,438 entitled A LIQUID INK PRINTING APPARATUS AND SYSTEM, Ser. No. 08/750,599 entitled COINCIDENT DROP SELECTION, DROP SEPARATION PRINTING METHOD AND SYSTEM, Ser. No. 08/750,435 entitled MONOLITHIC PRINT HEAD STRUCTURE AND A MANUFACTURING PROCESS THEREFOR USING ANISTROPIC WET ETCHING, Ser. No. 08/750,436 entitled POWER SUPPLY CONNECTION FOR MONOLITHIC PRINT HEADS, Ser. No. 08/750,437 entitled MODULAR DIGITAL PRINTING, Ser. No. 08/750,439 entitled A HIGH SPEED DIGITAL FABRIC PRINTER, Ser. No. 08/750,763 entitled A COLOR PHOTOCOPIER USING A DROP ON DEMAND INK JET PRINTING SYSTEM, Ser. No. 08/765,756 entitled PHOTOGRAPH PROCESSING AND COPYING SYSTEMS, Ser. No. 08/750,646 entitled FAX MACHINE WITH CONCURRENT DROP SELECTION AND DROP SEPARATION INK JET PRINTING, Ser. No. 08/759,774 entitled FAULT TOLERANCE IN HIGH VOLUME PRINTING PRESSES, Ser. No. 08/750,429 entitled INTEGRATED DRIVE CIRCUITRY IN DROP ON DEMAND PRINT HEADS, Ser. No. 08/750,433 entitled HEATER POWER COMPENSATION FOR TEMPERATURE IN THERMAL PRINTING SYSTEMS, Ser. No. 08/750,640 entitled HEATER POWER COMPENSATION FOR THERMAL LAG IN THERMAL PRINTING SYSTEMS, Ser. No. 08/750,650 entitled DATA DISTRIBUTION IN MONOLITHIC PRINT HEADS, and Ser. No. 08/750,642 entitled PRESSURIZABLE LIQUID INK CARTRIDGE FOR COINCIDENT FORCES PRINTERS all filed Dec. 3, 1996; Ser. No. 08/750,647 entitled MONOLITHIC PRINTING HEADS AND MANUFACTURING PROCESSES THEREFOR, Ser. No. 08/750,604 entitled INTEGRATED FOUR COLOR PRINT HEADS, Ser. No. 08/750,605 entitled A SELF-ALIGNED CONSTRUCTION AND MANUFACTURING PROCESS FOR MONOLITHIC PRINT HEADS, Ser. No. 08/682,603 entitled A COLOR PLOTTER USING CONCURRENT DROP SELECTION AND DROP SEPARATION INK JET PRINTING TECHNOLOGY, Ser. No. 08/750,603 entitled A NOTEBOOK COMPUTER WITH INTEGRATED CONCURRENT DROP SELECTION AND DROP SEPARATION COLOR PRINTING SYSTEM, Ser. No. 08/765,130 entitled INTEGRATED FAULT TOLERANCE IN PRINTING MECHANISMS; Ser. No. 08/750,431 entitled BLOCK FAULT TOLERANCE IN INTEGRATED PRINTING HEADS, Ser. No. 08/750,607 entitled FOUR LEVEL INK SET FOR BI-LEVEL COLOR PRINTING, Ser. No. 08/750,430 entitled A NOZZLE CLEARING PROCEDURE FOR LIQUID INK PRINTING, Ser. No. 08/750,600 entitled METHOD AND APPARATUS FOR ACCURATE CONTROL OF TEMPERATURE PULSES IN PRINTING HEADS, Ser. No. 08/750,608 entitled A PORTABLE PRINTER USING A CONCURRENT DROP SELECTION AND DROP SEPARATION PRINTING SYSTEM, and Ser. No. 08/750,602 entitled IMPROVEMENTS IN IMAGE HALFTONING all filed Dec. 4, 1996; Ser. No. 08/765,127 entitled PRINTING METHOD AND APPARATUS EMPLOYING ELECTROSTATIC DROP SEPARATION, Ser. No. 08/750,643 entitled COLOR OFFICE PRINTER WITH A HIGH CAPACITY DIGITAL PAGE IMAGE STORE, and Ser. No. 08/765,035 entitled HEATER POWER COMPENSATION FOR PRINTING LOAD IN THERMAL PRINTING SYSTEMS all filed Dec. 5, 1996; Ser. No. 08/765,017 entitled HEATER STRUCTURE AND FABRICATION PROCESS FOR MONOLITHIC PRINT HEADS, Ser. No. 08/750,772 entitled DETECTION OF FAULTY ACTUATORS IN PRINTING HEADS, Ser. No. 08/765,037 entitled PAGE IMAGE AND FAULT TOLERANCE CONTROL APPARATUS FOR PRINTING SYSTEMS all filed Dec. 9, 1996; and Ser. No. 08/765,038 entitled CONSTRUCTIONS AND MANUFACTURING PROCESSES FOR THERMALLY ACTIVATED PRINT HEADS filed Dec. 10, 1996. 
     FIELD OF THE INVENTION 
     The present invention is in the field of computer controlled printing devices. In particular, the field is print head configurations for drop on demand (DOD) printing systems. 
     BACKGROUND OF THE INVENTION 
     Many different types of digitally controlled printing systems have been invented, and many types are currently in production. These printing systems use a variety of actuation mechanisms, a variety of marking materials, and a variety of recording media. Examples of digital printing systems in current use include: laser electrophotographic printers; LED electrophotographic printers; dot matrix impact printers; thermal paper printers; film recorders; thermal wax printers; dye diffusion thermal transfer printers; and ink jet printers. However, at present, such electronic printing systems have not significantly replaced mechanical printing presses, even though this conventional method requires very expensive setup and is seldom commercially viable unless a few thousand copies of a particular page are to be printed. Thus, there is a need for improved digitally controlled printing systems, for example, being able to produce high quality color images at a high-speed and low cost, using standard paper. 
     Inkjet printing has become recognized as a prominent contender in the digitally controlled, electronic printing arena because, e.g., of its non-impact, low-noise characteristics, its use of plain paper and its avoidance of toner transfers and fixing. 
     Many types of ink jet printing mechanisms have been invented. These can be categorized as either continuous ink jet (CIJ) or drop on demand (DOD) ink jet. Continuous ink jet printing dates back to at least 1929: Hansell, U.S. Pat. No. 1,941,001. 
     Sweet et al U.S. Pat. No. 3,373,437, 1967, discloses an array of continuous ink jet nozzles where ink drops to be printed are selectively charged and deflected towards the recording medium. This technique is known as binary deflection IJ, and is used by several manufacturers, including Elmjet and Scitex. 
     Hertz et al U.S. Pat. No. 3,416,153, 1966, discloses a method of achieving variable optical density of printed spots in CU printing using the electrostatic dispersion of a charged drop stream to modulate the number of droplets which pass through a small aperture. This technique is used in ink jet printers manufactured by Iris Graphics. 
     Kyser et al U.S. Pat. No. 3,946,398, 1970, discloses a DOD ink jet printer which applies a high voltage to a piezoelectric crystal, causing the crystal to bend, applying pressure on an ink reservoir and jetting drops on demand. Many types of piezoelectric drop on demand printers have subsequently been invented, which utilize piezoelectric crystals in bend mode, push mode, shear mode, and squeeze mode. Piezoelectric DOD printers have achieved commercial success using hot melt inks (for example, Tektronix and Dataproducts printers), and at image resolutions up to 720 dpi for home and office printers (Seiko Epson). Piezoelectric DOD printers have an advantage in being able to use a wide range of inks. However, piezoelectric printing mechanisms usually require complex high voltage drive circuitry and bulky piezoelectric crystal arrays, which are disadvantageous in regard to manufacturability and performance. 
     Endo et al GB Pat. No. 2,007,162, 1979, discloses an electrothermal DOD ink jet printer which applies a power pulse to an electrothermal transducer (heater) which is in thermal contact with ink in a nozzle. The heater rapidly heats water based ink to a high temperature, whereupon a small quantity of ink rapidly evaporates, forming a bubble. The formation of these bubbles results in a pressure wave which cause drops of ink to be ejected from small apertures along the edge of the heater substrate. This technology is known as Bubblejet™ (trademark of Canon K.K. of Japan), and is used in a wide range of printing systems from Canon, Xerox, and other manufacturers. 
     Vaught et al U.S. Pat. No. 4,490,728, 1982, discloses an electrothermal drop ejection system which also operates by bubble formation. In this system, drops are ejected in a direction normal to the plane of the heater substrate, through nozzles formed in an aperture plate positioned above the heater. This system is known as Thermal Ink Jet, and is manufactured by Hewlett-Packard. In this document, the term Thermal Ink Jet is used to refer to both the HewlettPackard system and systems commonly known as Bubblejet™. 
     Thermal Ink Jet printing typically requires approximately 20 μJ over a period of approximately 2 μs to eject each drop. The 10 Watt active power consumption of each heater is disadvantageous in itself and also necessitates special inks, complicates the driver electronics and precipitates deterioration of heater elements. 
     Other ink jet printing systems have also been described in technical literature, but are not currently used on a commercial basis. For example, U.S. Pat. No. 4,275,290 discloses a system wherein the coincident address of predetermined print head nozzles with heat pulses and hydrostatic pressure, allows ink to flow freely to spacer-separated paper, passing beneath the print head. U.S. Pat. Nos. 4,737,803; 4,737,803 and 4,748,458 disclose ink jet recording systems wherein the coincident address of ink in print head nozzles with heat pulses and an electrostatically attractive field cause ejection of ink drops to a print sheet. 
     Each of the above-described inkjet printing systems has advantages and disadvantages. However, there remains a widely recognized need for an improved ink jet printing approach, providing advantages for example, as to cost, speed, quality, reliability, power usage, simplicity of construction and operation, durability and consumables. 
     SUMMARY OF THE INVENTION 
     The invention provides a print head for a drop on demand printing system the print head including a first plurality of nozzles for printing ink of a first predetermined color, and containing a second plurality of nozzles of different radius to the first plurality of nozzles, whereupon the second plurality of nozzles is adapted to print ink drops of the first predetermined color, but of a different volume than, the ink drops printed by the first plurality of nozzles. 
     A preferred aspect of the invention is that the print head is useful with the coincident forces printing system described in my concurrently filed application, entitled &#34;Liquid Ink Printing Apparatus and System&#34;. 
     A further preferred aspect of the invention is that the print head also contains at least a third plurality of nozzles which print a color different than the first and second pluralities of nozzles. 
     A further preferred aspect of the invention is that the print head prints the colors cyan, magenta, and yellow, wherein two pluralities of nozzles of differing radii are provided for at least the cyan and magenta inks. 
     A further preferred aspect of the invention is that the print head also contains a plurality of nozzle which print black ink. 
     A further preferred aspect of the invention is that the radius of the second plurality of nozzles is between 50% and 90% of the radius of the first plurality of nozzles. 
     A further preferred aspect of the invention is that the radius of the second plurality of nozzles is between 60% and 80% of the radius of the first plurality of nozzles. 
     Another preferred form of the invention is a manufacturing process for a print head for a drop on demand printing system wherein the second plurality of nozzles are formed simultaneously to the first plurality of nozzles. 
     A further preferred aspect of the invention is a manufacturing process for a print head for a drop on demand printing system wherein the nozzles are formed by microelectronic lithographic processes on a silicon substrate. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1(a) shows a simplified block schematic diagram of one exemplary printing apparatus according to the present invention. 
     FIG. 1(b) shows a cross section of one variety of nozzle tip in accordance with the invention. 
     FIGS. 2(a) to 2(f) show fluid dynamic simulations of drop selection. 
     FIG. 3(a) shows a finite element fluid dynamic simulation of a nozzle in operation according to an embodiment of the invention. 
     FIG. 3(b) shows successive meniscus positions during drop selection and separation. 
     FIG. 3(c) shows the temperatures at various points during a drop selection cycle. 
     FIG. 3(d) shows measured surface tension versus temperature curves for various ink additives. 
     FIG. 3(e) shows the power pulses which are applied to the nozzle heater to generate the temperature curves of FIG. 3(c) 
     FIG. 4 shows a block schematic diagram of print head drive circuitry for practice of the invention. 
     FIG. 5 shows projected manufacturing yields for an A4 page width color print head embodying features of the invention, with and without fault tolerance. 
     FIG. 6 shows a generalized block diagram of a printing system using one embodiment of the present invention. 
     FIG. 7 shows a cross section of an example print head nozzle embodiment of the invention used for computer simulations shown in FIGS. 8 to 18. 
     FIG. 8(a) shows the power sub-pulses applied to the print head for a single heater energizing pulse. 
     FIG. 8(b) shows the temperature at various points in the nozzle during the drop selection process. 
     FIG. 9 is a graph of meniscus position versus time for the drop selection process. 
     FIG. 10 is a plot of meniscus position and shape at 5 μs intervals during the drop selection process. 
     FIG. 11 shows the quiescent position of the ink meniscus before the drop selection process. 
     FIGS. 12 to 17 show the meniscus position and thermal contours at various stages during the drop selection process. 
     FIG. 18 shows fluid streamlines 50 μs after the beginning of the drop selection heater pulse. 
     FIG. 19 shows a single silicon substrate with a multitude of nozzles etched in it. 
     FIG. 20 shows a possible nozzle layout for a section of a print head in accordance with the invention. 
     FIG. 21 shows a halftoned pattern of 800 dpi dots of four differing intensities magnified 288 times. 
     FIG. 22 is a graph of dot probability versus pixel intensity used for of FIG. 9. 
     FIGS. 23(a), 23(c), and 23(e) are graphs of the position of the centre of the meniscus versus time for various nozzle radii. 
     FIGS. 23(b), 23(d), and 23(f) are plots of the meniscus shape at various instants for various nozzle radii. 
    
    
     DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS 
     In one general aspect, the invention constitutes a drop-on-demand printing mechanism wherein the means of selecting drops to be printed produces a difference in position between selected drops and drops which are not selected, but which is insufficient to cause the ink drops to overcome the ink surface tension and separate from the body of ink, and wherein an alternative means is provided to cause separation of the selected drops from the body of ink. 
     The separation of drop selection means from drop separation means significantly reduces the energy required to select which ink drops are to be printed. Only the drop selection means must be driven by individual signals to each nozzle. The drop separation means can be a field or condition applied simultaneously to all nozzles. 
     The drop selection means may be chosen from, but is not limited to, the following list: 
     1) Electrothermal reduction of surface tension of pressurized ink 
     2) Electrothermal bubble generation, with insufficient bubble volume to cause drop ejection 
     3) Piezoelectric, with insufficient volume change to cause drop ejection 
     4) Electrostatic attraction with one electrode per nozzle The drop separation means may be chosen from, but is not limited to, the following list: 
     1) Proximity (recording medium in close proximity to print head) 
     2) Proximity with oscillating ink pressure 
     3) Electrostatic attraction 
     4) Magnetic attraction 
     The table &#34;DOD printing technology targets&#34; shows some desirable characteristics of drop on demand printing technology. The table also lists some methods by which some embodiments described herein, or in other of my related applications, provide improvements over the prior art. 
     DOD printing technology targets 
     
         ______________________________________
Target      Method of achieving improvement over prior art
______________________________________
High speed operation
            Practical, low cost, pagewidth printing heads with
            more than 10,000 nozzles. Monolithic A4
            pagewidth print heads can be manufactured using
            standard 300 mm (12&#34;) silicon wafers
High image quality
            High resolution (800 dpi is sufficient for most
            applications), six color process to reduce image
            noise
Full color operation
            Halftoned process color at 800 dpi using
            stochastic screening
Ink flexibility
            Low operating ink temperature and no
            requirement for bubble formation
Low power   Low power operation results from drop selection
requirements
            means not being required to fully eject drop
Low cost    Monolithic print head without aperture plate, high
            manufacturing yield, small number of electrical
            connections, use of modified existing CMOS
            manufacturing facilities
High manufacturing
            Integrated fault tolerance in printing head
yield
High reliability
            Integrated fault tolerance in printing head.
            Elimination of cavitation and kogation. Reduction
            of thermal shock.
Small number of
            Shift registers, control logic, and drive circuitry
electrical connections
            can be integrated on a monolithic print head using
            standard CMOS processes
Use of existing VLSI
            CMOS compatibility. This can be achieved
manufacturing
            because the heater drive power is less is than 1%
facilities  of Thermal Ink Jet heater drive power
Electronic collation
            A new page compression system which can
            achieve 100:1 compression with insignificant
            image degradation, resulting in a compressed data
            rate low enough to allow real-time printing of any
            combination of thousands of pages stored on a
            low cost magnetic disk drive.
______________________________________
 
    
     In thermal ink jet (TIJ) and piezoelectric ink jet systems, a drop velocity of approximately 10 meters per second is preferred to ensure that the selected ink drops overcome ink surface tension, separate from the body of the ink, and strike the recording medium. These systems have a very low efficiency of conversion of electrical energy into drop kinetic energy. The efficiency of TIJ systems is approximately 0.02%). This means that the drive circuits for TIJ print heads must switch high currents. The drive circuits for piezoelectric ink jet heads must either switch high voltages, or drive highly capacitive loads. The total power consumption of pagewidth TIJ printheads is also very high. An 800 dpi A4 full color pagewidth TIJ print head printing a four color black image in one second would consume approximately 6 kW of electrical power, most of which is converted to waste heat. The difficulties of removal of this amount of heat precludes the production of low cost, high speed, high resolution compact pagewidth TIJ systems. 
     One important feature of embodiments of the invention is a means of significantly reducing the energy required to select which ink drops are to be printed. This is achieved by separating the means for selecting ink drops from the means for ensuring that selected drops separate from the body of ink and form dots on the recording medium. Only the drop selection means must be driven by individual signals to each nozzle. The drop separation means can be a field or condition applied simultaneously to all nozzles. 
     The table &#34;Drop selection means&#34; shows some of the possible means for selecting drops in accordance with the invention. The drop selection means is only required to create sufficient change in the position of selected drops that the drop separation means can discriminate between selected and unselected drops. 
     
         ______________________________________
Method    Advantage      Limitation
______________________________________
1. Electrothermal
          Low temperature
                         Requires ink pressure
reduction of
          increase and low drop
                         regulating mechanism. Ink
surface tension of
          selection energy. Can be
                         surface tension must reduce
pressurized ink
          used with many ink
                         substantially as temperature
          types. Simple fabrication.
                         increases
          CMOS drive circuits can
          be fabricated on same
          substrate
2. Electrothermal
          Medium drop selection
                         Requires ink pressure
reduction of ink
          energy, suitable for hot
                         oscillation mechanism. Ink
viscosity,
          melt and oil based inks.
                         must have a large decrease
combined with
          Simple fabrication.
                         in viscosity as temperature
oscillating ink
          CMOS drive circuits can
                         increases
pressure  be fabricated on same
          substrate
3. Electrothermal
          Well known technology,
                         High drop selection energy,
bubble genera-
          simple fabrication,
                         requires water based ink,
tion, with
          bipolar drive circuits can
                         problems with kogation,
insufficient
          be fabricated on same
                         cavitation, thermal stress
bubble volume to
          substrate.
cause drop
ejection
4. Piezoelectric,
          Many types of ink base
                         High manufacturing cost,
with insufficient
          can be used    incompatible with
volume change            integrated circuit processes,
to cause drop            high drive voltage,
ejection                 mechanical complexity,
                         bulky
5. Electrostatic
          Simple electrode
                         Nozzle pitch must be
attraction with
          fabrication    relatively large. Crosstalk
electrode per            between adjacent electric
nozzle                   fields. Requires high
                         voltage drive circuits
______________________________________
 
    
     Other drop selection means may also be used. 
     The preferred drop selection means for water based inks is method 1: &#34;Electrothermal reduction of surface tension of pressurized ink&#34;. This drop selection means provides many advantages over other systems, including; low power operation (approximately 1% of TIJ), compatibility with CMOS VLSI chip fabrication, low voltage operation (approx. 10 V), high nozzle density, low temperature operation, and wide range of suitable ink formulations. The ink must exhibit a reduction in surface tension with increasing temperature. 
     The preferred drop selection means for hot melt or oil based inks is method 2: &#34;Electrothermal reduction of ink viscosity, combined with oscillating ink pressure&#34;. This drop selection means is particularly suited for use with inks which exhibit a large reduction of viscosity with increasing temperature, but only a small reduction in surface tension. This occurs particularly with non-polar ink carriers with relatively high molecular weight. This is especially applicable to hot melt and oil based inks. 
     The table &#34;Drop separation means&#34; shows some of the possible methods for separating selected drops from the body of ink, and ensuring that the selected drops form dots on the printing medium. The drop separation means discriminates between selected drops and unselected drops to ensure that unselected drops do not form dots on the printing medium. 
     
         ______________________________________
Method    Advantage      Limitation
______________________________________
1. Electrostatic
          Can print on rough
                         Requires high voltage
attraction
          surfaces, simple
                         power supply
          implementation
2. AC electric
          Higher field strength is
                         Requires high voltage AC
field     possible than electro-
                         power supply synchronized
          static, operating margins
                         to drop ejection phase.
          can be increased, ink
                         Multiple drop phase
          pressure reduced, and
                         operation is difficult
          dust accumulation is
          reduced
3. Proximity
          Very small spot sizes can
                         Requires print medium to
(print head in
          be achieved. Very low
                         be very close to print head
close proximity
          power dissipation. High
                         surface, not suitable for
to, but not
          drop position accuracy
                         rough print media, usually
touching,                requires transfer roller or
recording                belt
medium)
4. Transfer
          Very small spot sizes can
                         Not compact due to size of
Proximity (print
          be achieved, very low
                         transfer roller or transfer
head is in close
          power dissipation, high
                         belt.
proximity to a
          accuracy, can print on
transfer roller or
          rough paper
belt
5. Proximity with
          Useful for hot melt inks
                         Requires print medium to
oscillating ink
          using viscosity reduction
                         be very close to print head
pressure  drop selection method,
                         surface, not suitable for
          reduces possibility of
                         rough print media. Requires
          nozzle clogging, can use
                         ink pressure oscillation
          pigments instead of dyes
                         apparatus
6. Magnetic
          Can print on rough
                         Requires uniform high
attraction
          surfaces. Low power if
                         magnetic field strength,
          permanent magnets are
                         requires magnetic ink
          used
______________________________________
 
    
     Other drop separation means may also be used. 
     The preferred drop separation means depends upon the intended use. For most applications, method 1: &#34;Electrostatic attraction&#34;, or method 2: &#34;AC electric field&#34; are most appropriate. For applications where smooth coated paper or film is used, and very high speed is not essential, method 3: &#34;Proximity&#34; may be appropriate. For high speed, high quality systems, method 4: &#34;Transfer proximity&#34; can be used. Method 6: &#34;Magnetic attraction&#34; is appropriate for portable printing systems where the print medium is too rough for proximity printing, and the high voltages required for electrostatic drop separation are undesirable. There is no clear `best` drop separation means which is applicable to all circumstances. 
     Further details of various types of printing systems according to the present invention are described in the following Australian patent specifications filed on 12 Apr. 1995, the disclosure of which are hereby incorporated by reference: 
     `A Liquid ink Fault Tolerant (LIFT) printing mechanism` (Filing no.: PN2308); 
     `Electrothermal drop selection in LIFT printing` (Filing no.: PN2309); 
     `Drop separation in LIFT printing by print media proximity` (Filing no.: PN2310); 
     `Drop size adjustment in Proximity LIFT printing by varying head to media distance` (Filing no.: PN2311); 
     `Augmenting Proximity LIFT printing with acoustic ink waves` (Filing no.: PN2312); 
     `Electrostatic drop separation in LIFT printing` (Filing no.: PN2313); 
     `Multiple simultaneous drop sizes in Proximity LEFT printing` (Filing no.: PN2321); 
     `Self cooling operation in thermally activated print heads` (Filing no.: PN2322); and 
     `Thermal Viscosity Reduction LIFT printing` (Filing no.: PN2323). 
     A simplified schematic diagram of one preferred printing system according to the invention appears in FIG. 1(a). 
     An image source 52 may be raster image data from a scanner or computer, or outline image data in the form of a page description language (PDL), or other forms of digital image representation. This image data is converted to a pixel-mapped page image by the image processing system 53. This may be a raster image processor (RIP) in the case of PDL image data, or may be pixel image manipulation in the case of raster image data. Continuous tone data produced by the image processing unit 53 is halftoned. Halftoning is performed by the Digital Halftoning unit 54. Halftoned bitmap image data is stored in the image memory 72. Depending upon the printer and system configuration, the image memory 72 may be a full page memory, or a band memory. Heater control circuits 71 read data from the image memory 72 and apply time-varying electrical pulses to the nozzle heaters (103 in FIG. 1(b)) that are part of the print head 50. These pulses are applied at an appropriate time, and to the appropriate nozzle, so that selected drops will form spots on the recording medium 51 in the appropriate position designated by the data in the image memory 72. 
     The recording medium 51 is moved relative to the head 50 by a paper transport system 65, which is electronically controlled by a paper transport control system 66, which in turn is controlled by a microcontroller 315. The paper transport system shown in FIG. 1(a) is schematic only, and many different mechanical configurations are possible. In the case of pagewidth print heads, it is most convenient to move the recording medium 51 past a stationary head 50. However, in the case of scanning print systems, it is usually most convenient to move the head 50 along one axis (the sub-scanning direction) and the recording medium 51 along the orthogonal axis (the main scanning direction), in a relative raster motion. The microcontroller 315 may also control the ink pressure regulator 63 and the heater control circuits 71. 
     For printing using surface tension reduction, ink is contained in an ink reservoir 64 under pressure. In the quiescent state (with no ink drop ejected), the ink pressure is insufficient to overcome the ink surface tension and eject a drop. A constant ink pressure can be achieved by applying pressure to the ink reservoir 64 under the control of an ink pressure regulator 63. Alternatively, for larger printing systems, the ink pressure can be very accurately generated and controlled by situating the top surface of the ink in the reservoir 64 an appropriate distance above the head 50. This ink level can be regulated by a simple float valve (not shown). 
     For printing using viscosity reduction, ink is contained in an ink reservoir 64 under pressure, and the ink pressure is caused to oscillate. The means of producing this oscillation may be a piezoelectric actuator mounted in the ink channels (not shown). 
     When properly arranged with the drop separation means, selected drops proceed to form spots on the recording medium 51, while unselected drops remain part of the body of ink. 
     The ink is distributed to the back surface of the head 50 by an ink channel device 75. The ink preferably flows through slots and/or holes etched through the silicon substrate of the head 50 to the front surface, where the nozzles and actuators are situated. In the case of thermal selection, the nozzle actuators are electrothermal heaters. 
     In some types of printers according to the invention, an external field 74 is required to ensure that the selected drop separates from the body of the ink and moves towards the recording medium 51. A convenient external field 74 is a constant electric field, as the ink is easily made to be electrically conductive. In this case, the paper guide or platen 67 can be made of electrically conductive material and used as one electrode generating the electric field. The other electrode can be the head 50 itself. Another embodiment uses proximity of the print medium as a means of discriminating between selected drops and unselected drops. 
     For small drop sizes gravitational force on the ink drop is very small; approximately 10 -4  of the surface tension forces, so gravity can be ignored in most cases. This allows the print head 50 and recording medium 51 to be oriented in any direction in relation to the local gravitational field. This is an important requirement for portable printers. 
     FIG. 1(b) is a detail enlargement of a cross section of a single microscopic nozzle tip embodiment of the invention, fabricated using a modified CMOS process. The nozzle is etched in a substrate 101, which may be silicon, glass, metal, or any other suitable material. If substrates which are not semiconductor materials are used, a semiconducting material (such as amorphous silicon) may be deposited on the substrate, and integrated drive transistors and data distribution circuitry may be formed in the surface semiconducting layer. Single crystal silicon (SCS) substrates have several advantages, including: 
     1) High performance drive transistors and other circuitry can be fabricated in SCS; 
     2) Print heads can be fabricated in existing facilities (fabs) using standard VLSI processing equipment; 
     3) SCS has high mechanical strength and rigidity; and 
     4) SCS has a high thermal conductivity. 
     In this example, the nozzle is of cylindrical form, with the heater 103 forming an annulus. The nozzle tip 104 is formed from silicon dioxide layers 102 deposited during the fabrication of the CMOS drive circuitry. The nozzle tip is passivated with silicon nitride. The protruding nozzle tip controls the contact point of the pressurized ink 100 on the print head surface. The print head surface is also hydrophobized to prevent accidental spread of ink across the front of the print head. 
     Many other configurations of nozzles are possible, and nozzle embodiments of the invention may vary in shape, dimensions, and materials used. Monolithic nozzles etched from the substrate upon which the heater and drive electronics are formed have the advantage of not requiring an orifice plate. The elimination of the orifice plate has significant cost savings in manufacture and assembly. Recent methods for eliminating orifice plates include the use of `vortex` actuators such as those described in Domoto et al U.S. Pat. Nos. 4,580,158, 1986, assigned to Xerox, and Miller et al U.S. Pat. No. 5,371,527, 1994 assigned to Hewlett-Packard. These, however are complex to actuate, and difficult to fabricate. The preferred method for elimination of orifice plates for print heads of the invention is incorporation of the orifice into the actuator substrate. 
     This type of nozzle may be used for print heads using various techniques for drop separation. 
     Operation with Electrostatic Drop Separation 
     As a first example, operation using thermal reduction of surface tension and electrostatic drop separation is shown in FIG. 2. 
     FIG. 2 shows the results of energy transport and fluid dynamic simulations performed using FIDAP, a commercial fluid dynamic simulation software package available from Fluid Dynamics Inc., of Illinois, U.S.A. This simulation is of a thermal drop selection nozzle embodiment with a diameter of 8 μm, at an ambient temperature of 30° C. The total energy applied to the heater is 276 nJ, applied as 69 pulses of 4 nJ each. The ink pressure is 10 kPa above ambient air pressure, and the ink viscosity at 30° C. is 1.84 cPs. The ink is water based, and includes a sol of 0.1% palmitic acid to achieve an enhanced decrease in surface tension with increasing temperature. A cross section of the nozzle tip from the central axis of the nozzle to a radial distance of 40 μm is shown. Heat flow in the various materials of the nozzle, including silicon, silicon nitride, amorphous silicon dioxide, crystalline silicon dioxide, and water based ink are simulated using the respective densities, heat capacities, and thermal conductivities of the materials. The time step of the simulation is 0.1 μs. 
     FIG. 2(a) shows a quiescent state, just before the heater is actuated. An equilibrium is created whereby no ink escapes the nozzle in the quiescent state by ensuring that the ink pressure plus external electrostatic field is insufficient to overcome the surface tension of the ink at the ambient temperature. In the quiescent state, the meniscus of the ink does not protrude significantly from the print head surface, so the electrostatic field is not significantly concentrated at the meniscus 
     FIG. 2(b) shows thermal contours at 5° C. intervals 5 μs after the start of the heater energizing pulse. When the heater is energized, the ink in contact with the nozzle tip is rapidly heated. The reduction in surface tension causes the heated portion of the meniscus to rapidly expand relative to the cool ink meniscus. This drives a convective flow which rapidly transports this heat over part of the free surface of the ink at the nozzle tip. It is necessary for the heat to be distributed over the ink surface, and not just where the ink is in contact with the heater. This is because viscous drag against the solid heater prevents the ink directly in contact with the heater from moving. 
     FIG. 2(c) shows thermal contours at 5° C. intervals 10 μs after the start of the heater energizing pulse. The increase in temperature causes a decrease in surface tension, disturbing the equilibrium of forces. As the entire meniscus has been heated, the ink begins to flow. 
     FIG. 2(d) shows thermal contours at 5° C. intervals 20 μs after the start of the heater energizing pulse. The ink pressure has caused the ink to flow to a new meniscus position, which protrudes from the print head. The electrostatic field becomes concentrated by the protruding conductive ink drop. 
     FIG. 2(e) shows thermal contours at 5° C. intervals 30 μs after the start of the heater energizing pulse, which is also 6 μs after the end of the heater pulse, as the heater pulse duration is 24 μs. The nozzle tip has rapidly cooled due to conduction through the oxide layers, and conduction into the flowing ink. The nozzle tip is effectively `water cooled` by the ink. Electrostatic attraction causes the ink drop to begin to accelerate towards the recording medium. Were the heater pulse significantly shorter (less than 16 μs in this case) the ink would not accelerate towards the print medium, but would instead return to the nozzle. 
     FIG. 2(f) shows thermal contours at 5° C. intervals 26 μs after the end of the heater pulse. The temperature at the nozzle tip is now less than 5° C. above ambient temperature. This causes an increase in surface tension around the nozzle tip. When the rate at which the ink is drawn from the nozzle exceeds the viscously limited rate of ink flow through the nozzle, the ink in the region of the nozzle tip `necks`, and the selected drop separates from the body of ink. The selected drop then travels to the recording medium under the influence of the external electrostatic field. The meniscus of the ink at the nozzle tip then returns to its quiescent position, ready for the next heat pulse to select the next ink drop. One ink drop is selected, separated and forms a spot on the recording medium for each heat pulse. As the heat pulses are electrically controlled, drop on demand ink jet operation can be achieved. 
     FIG. 3(a) shows successive meniscus positions during the drop selection cycle at 5 μs intervals, starting at the beginning of the heater energizing pulse. 
     FIG. 3(b) is a graph of meniscus position versus time, showing the movement of the point at the centre of the meniscus. The heater pulse starts 10 μs into the simulation. 
     FIG. 3(c) shows the resultant curve of temperature with respect to time at various points in the nozzle. The vertical axis of the graph is temperature, in units of 100° C. The horizontal axis of the graph is time, in units of 10 μs. The temperature curve shown in FIG. 3(b) was calculated by FIDAP, using 0.1 μs time steps. The local ambient temperature is 30 degrees C. Temperature histories at three points are shown: 
     A--Nozzle tip: This shows the temperature history at the circle of contact between the passivation layer, the ink, and air. 
     B--Meniscus midpoint: This is at a circle on the ink meniscus midway between the nozzle tip and the centre of the meniscus. 
     C--Chip surface: This is at a point on the print head surface 20 μm from the centre of the nozzle. The temperature only rises a few degrees. This indicates that active circuitry can be located very close to the nozzles without experiencing performance or lifetime degradation due to elevated temperatures. 
     FIG. 3(e) shows the power applied to the heater. Optimum operation requires a sharp rise in temperature at the start of the heater pulse, a maintenance of the temperature a little below the boiling point of the ink for the duration of the pulse, and a rapid fall in temperature at the end of the pulse. To achieve this, the average energy applied to the heater is varied over the duration of the pulse. In this case, the variation is achieved by pulse frequency modulation of 0.1 μs sub-pulses, each with an energy of 4 nJ. The peak power applied to the heater is 40 mW, and the average power over the duration of the heater pulse is 11.5 mW. The sub-pulse frequency in this case is 5 Mhz. This can readily be varied without significantly affecting the operation of the print head. A higher sub-pulse frequency allows finer control over the power applied to the heater. A sub-pulse frequency of 13.5 Mhz is suitable, as this frequency is also suitable for minimizing the effect of radio frequency interference (RFI). 
     Inks with a negative temperature coefficient of surface tension 
     The requirement for the surface tension of the ink to decrease with increasing temperature is not a major restriction, as most pure liquids and many mixtures have this property. Exact equations relating surface tension to temperature for arbitrary liquids are not available. However, the following empirical equation derived by Ramsay and Shields is satisfactory for many liquids: ##EQU1## 
     Where γ T  is the surface tension at temperature T, k is a constant, T c  is the critical temperature of the liquid, M is the molar mass of the liquid, x is the degree of association of the liquid, and ρ is the density of the liquid. This equation indicates that the surface tension of most liquids falls to zero as the temperature reaches the critical temperature of the liquid. For most liquids, the critical temperature is substantially above the boiling point at atmospheric pressure, so to achieve an ink with a large change in surface tension with a small change in temperature around a practical ejection temperature, the admixture of surfactants is recommended. 
     The choice of surfactant is important. For example, water based ink for thermal ink jet printers often contains isopropyl alcohol (2-propanol) to reduce the surface tension and promote rapid drying. Isopropyl alcohol has a boiling point of 82.4° C., lower than that of water. As the temperature rises, the alcohol evaporates faster than the water, decreasing the alcohol concentration and causing an increase in surface tension. A surfactant such as 1-Hexanol (b.p. 158° C.) can be used to reverse this effect, and achieve a surface tension which decreases slightly with temperature. However, a relatively large decrease in surface tension with temperature is desirable to maximize operating latitude. A surface tension decrease of 20 mN/m over a 30° C. temperature range is preferred to achieve large operating margins, while as little as 10 mN/m can be used to achieve operation of the print head according to the present invention. 
     Inks With Large Δγ T   
     Several methods may be used to achieve a large negative change in surface tension with increasing temperature. Two such methods are: 
     1) The ink may contain a low concentration sol of a surfactant which is solid at ambient temperatures, but melts at a threshold temperature. Particle sizes less than 1,000 Å are desirable. Suitable surfactant melting points for a water based ink are between 50° C. and 90° C., and preferably between 60° C. and 80° C. 
     2) The ink may contain an oil/water microemulsion with a phase inversion temperature (PIT) which is above the maximum ambient temperature, but below the boiling point of the ink. For stability, the PIT of the microemulsion is preferably 20° C. or more above the maximum non-operating temperature encountered by the ink. A PIT of approximately 80° C. is suitable. 
     Inks with Surfactant Sols 
     Inks can be prepared as a sol of small particles of a surfactant which melts in the desired operating temperature range. Examples of such surfactants include carboxylic acids with between 14 and 30 carbon atoms, such as: 
     
         ______________________________________
Name         Formula      m.p.    Synonym
______________________________________
Tetradecanoic acid
             CH.sub.3 (CH.sub.2).sub.12 COOH
                          58° C.
                                  Myristic acid
Hexadecanoic acid
             CH.sub.3 (CH.sub.2).sub.14 COOH
                          63° C.
                                  Palmitic acid
Octadecanoic acid
             CH.sub.3 (CH.sub.2).sub.15 COOH
                          71° C.
                                  Stearic acid
Eicosanoic acid
             CH.sub.3 (CH.sub.2).sub.16 COOH
                          77° C.
                                  Arachidic acid
Docosanoic acid
             CH.sub.3 (CH.sub.2).sub.20 COOH
                          80° C.
                                  Behenic acid
______________________________________
 
    
     As the melting point of sols with a small particle size is usually slightly less than of the bulk material, it is preferable to choose a carboxylic acid with a melting point slightly above the desired drop selection temperature. A good example is Arachidic acid. 
     These carboxylic acids are available in high purity and at low cost. The amount of surfactant required is very small, so the cost of adding them to the ink is insignificant. A mixture of carboxylic acids with slightly varying chain lengths can be used to spread the melting points over a range of temperatures. Such 
     It is not necessary to restrict the choice of surfactant to simple unbranched carboxylic acids. Surfactants with branched chains or phenyl groups, or other hydrophobic moieties can be used. It is also not necessary to use a carboxylic acid. Many highly polar moieties are suitable for the hydrophilic end of the surfactant. It is desirable that the polar end be ionizable in water, so that the surface of the surfactant particles can be charged to aid dispersion and prevent flocculation. In the case of carboxylic acids, this can be achieved by adding an alkali such as sodium hydroxide or potassium hydroxide. 
     Preparation of Inks with Surfactant Sols 
     The surfactant sol can be prepared separately at high concentration, and added to the ink in the required concentration. 
     An example process for creating the surfactant sol is as follows: 
     1) Add the carboxylic acid to purified water in an oxygen free atmosphere. 
     2) Heat the mixture to above the melting point of the carboxylic acid. The water can be brought to a boil. 
     3) Ultrasonicate the mixture, until the typical size of the carboxylic acid droplets is between 100 Å and 1,000 Å. 
     4) Allow the mixture to cool. 
     5) Decant the larger particles from the top of the mixture. 
     6) Add an alkali such as NaOH to ionize the carboxylic acid molecules on the surface of the particles. A pH of approximately 8 is suitable. This step is not absolutely necessary, but helps stabilize the sol. 
     7) Centrifuge the sol. As the density of the carboxylic acid is lower than water, smaller particles will accumulate at the outside of the centrifuge, and larger particles in the centre. 
     8) Filter the sol using a microporous filter to eliminate any particles above 5000 Å. 
     9) Add the surfactant sol to the ink preparation. The sol is required only in very dilute concentration. 
     The ink preparation will also contain either dye(s) or pigment(s), bactericidal agents, agents to enhance the electrical conductivity of the ink if electrostatic drop separation is used, humectants, and other agents as required. 
     Anti-foaming agents will generally not be required, as there is no bubble formation during the drop ejection process. 
     Cationic surfactant sols 
     Inks made with anionic surfactant sols are generally unsuitable for use with cationic dyes or pigments. This is because the cationic dye or pigment may precipitate or flocculate with the anionic surfactant. To allow the use of cationic dyes and pigments, a cationic surfactant sol is required. The family of alkylamines is suitable for this purpose. 
     Various suitable alkylamines are shown in the following table: 
     
         ______________________________________
Name         Formula        Synonym
______________________________________
Hexadecylamine
             CH.sub.3 (CH.sub.2).sub.14 CH.sub.2 NH.sub.2
                            Palmityl amine
Octadecylamine
             CH.sub.3 (CH.sub.2).sub.16 CH.sub.2 NH.sub.2
                            Stearyl amine
Eicosylamine CH.sub.3 (CH.sub.2).sub.18 CH.sub.2 NH.sub.2
                            Arachidyl amine
Docosylamine CH.sub.3 (CH.sub.2).sub.20 CH.sub.2 NH.sub.2
                            Behenyl amine
______________________________________
 
    
     The method of preparation of cationic surfactant sols is essentially similar to that of anionic surfactant sols, except that an acid instead of an alkali is used to adjust the pH balance and increase the charge on the surfactant particles. A pH of 6 using HCl is suitable. 
     Microemulsion Based Inks 
     An alternative means of achieving a large reduction in surface tension as some temperature threshold is to base the ink on a microemulsion. A microemulsion is chosen with a phase inversion temperature (PIT) around the desired ejection threshold temperature. Below the PIT, the microemulsion is oil in water (O/W), and above the PIT the microemulsion is water in oil (W/O). At low temperatures, the surfactant forming the microemulsion prefers a high curvature surface around oil, and at temperatures significantly above the PIT, the surfactant prefers a high curvature surface around water. At temperatures close to the PIT, the microemulsion forms a continuous `sponge` of topologically connected water and oil. 
     There are two mechanisms whereby this reduces the surface tension. Around the PIT, the surfactant prefers surfaces with very low curvature. As a result, surfactant molecules migrate to the ink/air interface, which has a curvature which is much less than the curvature of the oil emulsion. This lowers the surface tension of the water. Above the phase inversion temperature, the microemulsion changes from O/W to W/O, and therefore the ink/air interface changes from water/air to oil/air. The oil/air interface has a lower surface tension. 
     There is a wide range of possibilities for the preparation of microemulsion based inks. 
     For fast drop ejection, it is preferable to chose a low viscosity oil. 
     In many instances, water is a suitable polar solvent. However, in some cases different polar solvents may be required. In these cases, polar solvents with a high surface tension should be chosen, so that a large decrease in surface tension is achievable. 
     The surfactant can be chosen to result in a phase inversion temperature in the desired range. For example, surfactants of the group poly(oxyethylene)alkylphenyl ether (ethoxylated alkyl phenols, general formula: C n  H 2n+1  C 4  H 6  (CH 2  CH 2  O) m  OH) can be used. The hydrophilicity of the surfactant can be increased by increasing m, and the hydrophobicity can be increased by increasing n. Values of m of approximately 10, and n of approximately 8 are suitable. 
     Low cost commercial preparations are the result of a polymerization of various molar ratios of ethylene oxide and alkyl phenols, and the exact number of oxyethylene groups varies around the chosen mean. These commercial preparations are adequate, and highly pure surfactants with a specific number of oxyethylene groups are not required. 
     The formula for this surfactant is C 8  H 17  C 4  H 6  (CH 2  CH 2  O) n  OH (average n=10). 
     Synonyms include Octoxynol-10, PEG-10 octyl phenyl ether and POE (10) octyl phenyl ether 
     The HLB is 13.6, the melting point is 7° C., and the cloud point is 65° C. 
     Commercial preparations of this surfactant are available under various brand names. Suppliers and brand names are listed in the following table: 
     
         ______________________________________
Trade name    Supplier
______________________________________
Akyporox OP100
              Chem-Y GmbH
Alkasurf OP-10
              Rhone-Poulenc Surfactants and Specialties
Dehydrophen POP 10
              Pulcra SA
Hyonic OP-10  Henkel Corp.
Iconol OP-10  BASF Corp.
Igepal O      Rhone-Poulenc France
Macol OP-10   PPG Industries
Malorphen 810 Huls AG
Nikkol OP-10  Nikko Chem. Co. Ltd.
Renex 750     ICI Americas Inc.
Rexol 45/10   Hart Chemical Ltd.
Synperonic OP10
              ICI PLC
Teric X10     ICI Australia
______________________________________
 
    
     These are available in large volumes at low cost (less than one dollar per pound in quantity), and so contribute less than 10 cents per liter to prepared microemulsion ink with a 5% surfactant concentration. 
     Other suitable ethoxylated alkyl phenols include those listed in the following table: 
     
         ______________________________________
Trivial name
         Formula           HLB    Cloud Point
______________________________________
Nonoxynol-9
         C.sub.9 H.sub.19 C.sub.4 H.sub.6 (CH.sub.2 CH.sub.2 O).sub..about
         .9 OH             13     54° C.
Nonoxynol-10
         C.sub.9 H.sub.19 C.sub.4 H.sub.6 (CH.sub.2 CH.sub.2 O).sub..about
         .10 OH            13.2   62° C.
Nonoxynol-11
         C.sub.9 H.sub.19 C.sub.4 H.sub.6 (CH.sub.2 CH.sub.2 O).sub..about
         .11 OH            13.8   72° C.
Nonoxynol-12
         C.sub.9 H.sub.19 C.sub.4 H.sub.6 (CH.sub.2 CH.sub.2 O).sub..about
         .12 OH            14.5   81° C.
Octoxynol-9
         C.sub.8 H.sub.17 C.sub.4 H.sub.6 (CH.sub.2 CH.sub.2 O).sub..about
         .9 OH             12.1   61° C.
Octoxynol-10
         C.sub.8 H.sub.17 C.sub.4 H.sub.6 (CH.sub.2 CH.sub.2 O).sub..about
         .10 OH            13.6   65° C.
Octoxynol-12
         C.sub.8 H.sub.17 C.sub.4 H.sub.6 (CH.sub.2 CH.sub.2 O).sub..about
         .12 OH            14.6   88° C.
Dodoxynol-10
         C.sub.12 H.sub.25 C.sub.4 H.sub.6 (CH.sub.2 CH.sub.2 O).sub..abou
         t.10 OH           12.6   42° C.
Dodoxynol-11
         C.sub.12 H.sub.25 C.sub.4 H.sub.6 (CH.sub.2 CH.sub.2 O).sub..abou
         t.11 OH           13.5   56° C.
Dodoxynol-14
         C.sub.12 H.sub.25 C.sub.4 H.sub.6 (CH.sub.2 CH.sub.2 O).sub..abou
         t.14 OH           14.5   87° C.
______________________________________
 
    
     Microemulsion based inks have advantages other than surface tension control: 
     1) Microemulsions are thermodynamically stable, and will not separate. Therefore, the storage time can be very long. This is especially significant for office and portable printers, which may be used sporadically. 
     2) The microemulsion will form spontaneously with a particular drop size, and does not require extensive stirring, centrifuging, or filtering to ensure a particular range of emulsified oil drop sizes. 
     3) The amount of oil contained in the ink can be quite high, so dyes which are soluble in oil or soluble in water, or both, can be used. It is also possible to use a mixture of dyes, one soluble in water, and the other soluble in oil, to obtain specific colors. 
     4) Oil miscible pigments are prevented from flocculating, as they are trapped in the oil microdroplets. 
     5) The use of a microemulsion can reduce the mixing of different dye colors on the surface of the print medium. 
     6) The viscosity of microemulsions is very low. 
     7) The requirement for humectants can be reduced or eliminated. 
     Dyes and pigments in microemulsion based inks 
     Oil in water mixtures can have high oil contents--as high as 40%--and still form O/W microemulsions. This allows a high dye or pigment loading. 
     Mixtures of dyes and pigments can be used. An example of a microemulsion based ink mixture with both dye and pigment is as follows: 
     1) 70% water 
     2) 5% water soluble dye 
     3) 5% surfactant 
     4) 10% oil 
     5) 10% oil miscible pigment 
     The following table shows the nine basic combinations of colorants in the oil and water phases of the microemulsion that may be used. 
     
         ______________________________________
Combination
         Colorant in water phase
                          Colorant in oil phase
______________________________________
1        none             oil miscible pigment
2        none             oil soluble dye
3        water soluble dye
                          none
4        water soluble dye
                          oil miscible pigment
5        water soluble dye
                          oil soluble dye
6        pigment dispersed in water
                          none
7        pigment dispersed in water
                          oil miscible pigment
8        pigment dispersed in water
                          oil soluble dye
9        none             none
______________________________________
 
    
     The ninth combination, with no colorants, is useful for printing transparent coatings, UV ink, and selective gloss highlights. 
     As many dyes are amphiphilic, large quantities of dyes can also be solubilized in the oil-water boundary layer as this layer has a very large surface area. 
     It is also possible to have multiple dyes or pigments in each phase, and to have a mixture of dyes and pigments in each phase. 
     When using multiple dyes or pigments the absorption spectrum of the resultant ink will be the weighted average of the absorption spectra of the different colorants used. This presents two problems: 
     1) The absorption spectrum will tend to become broader, as the absorption peaks of both colorants are averaged. This has a tendency to `muddy` the colors. To obtain brilliant color, careful choice of dyes and pigments based on their absorption spectra, not just their human-perceptible color, needs to be made. 
     2) The color of the ink may be different on different substrates. If a dye and a pigment are used in combination, the color of the dye will tend to have a smaller contribution to the printed ink color on more absorptive papers, as the dye will be absorbed into the paper, while the pigment will tend to `sit on top` of the paper. This may be used as an advantage in some circumstances. 
     Surfactants with a Krafft point in the drop selection temperature range 
     For ionic surfactants there is a temperature (the Krafft point) below which the solubility is quite low, and the solution contains essentially no micelles. Above the Krafft temperature micelle formation becomes possible and there is a rapid increase in solubility of the surfactant. If the critical micelle concentration (CMC) exceeds the solubility of a surfactant at a particular temperature, then the minimum surface tension will be achieved at the point of maximum solubility, rather than at the CMC. Surfactants are usually much less effective below the Krafft point. 
     This factor can be used to achieve an increased reduction in surface tension with increasing temperature. At ambient temperatures, only a portion of the surfactant is in solution. When the nozzle heater is turned on, the temperature rises, and more of the surfactant goes into solution, decreasing the surface tension. 
     A surfactant should be chosen with a Krafft point which is near the top of the range of temperatures to which the ink is raised. This gives a maximum margin between the concentration of surfactant in solution at ambient temperatures, and the concentration of surfactant in solution at the drop selection temperature. 
     The concentration of surfactant should be approximately equal to the CMC at the Krafft point. In this manner, the surface tension is reduced to the maximum amount at elevated temperatures, and is reduced to a minimum amount at ambient temperatures. 
     The following table shows some commercially available surfactants with Krafft points in the desired range. 
     
         ______________________________________
Formula                Krafft point
______________________________________
C.sub.16 H.sub.33 SO.sub.3.sup.- Na.sup.+
                       57° C.
C.sub.18 H.sub.37 SO.sub.3.sup.- Na.sup.+
                       70° C.
C.sub.16 H.sub.33 SO.sub.4.sup.- Na.sup.+
                       45° C.
Na.sup.+- O.sub.4 S(CH.sub.2).sub.16 SO.sub.4.sup.- Na.sup.+
                       44.9° C.
K.sup.+- O.sub.4 S(CH.sub.2).sub.16 SO.sub.4.sup.- K.sup.+
                       55° C.
C.sub.16 H.sub.33 CH(CH.sub.3)C.sub.4 H.sub.6 SO.sub.3.sup.- Na.sup.+
                       60.8° C.
______________________________________
 
    
     Surfactants with a cloud point in the drop selection temperature range 
     Non-ionic surfactants using polyoxyethylene (POE) chains can be used to create an ink where the surface tension falls with increasing temperature. At low temperatures, the POE chain is hydrophilic, and maintains the surfactant in solution. As the temperature increases, the structured water around the POE section of the molecule is disrupted, and the POE section becomes hydrophobic. The surfactant is increasingly rejected by the water at higher temperatures, resulting in increasing concentration of surfactant at the air/ink interface, thereby lowering surface tension. The temperature at which the POE section of a nonionic surfactant becomes hydrophilic is related to the cloud point of that surfactant. POE chains by themselves are not particularly suitable, as the cloud point is generally above 100° C. 
     Polyoxypropylene (POP) can be combined with POE in POE/POP block copolymers to lower the cloud point of POE chains without introducing a strong hydrophobicity at low temperatures. 
     Two main configurations of symmetrical POE/POP block copolymers are available. These are: 
     1) Surfactants with POE segments at the ends of the molecules, and a POP segment in the centre, such as the poloxamer class of surfactants (generically CAS 9003-11-6) 
     2) Surfactants with POP segments at the ends of the molecules, and a POE segment in the centre, such as the meroxapol class of surfactants (generically also CAS 9003-11-6) 
     Some commercially available varieties of poloxamer and meroxapol with a high surface tension at room temperature, combined with a cloud point above 40° C. and below 100° C. are shown in the following table: 
     
         __________________________________________________________________________
                                         Surface
       BASF Trade                        Tension
                                             Cloud
Trivial name
       name  Formula                     (mN/m)
                                             point
__________________________________________________________________________
Meroxapol
       Pluronic
             HO(CHCH.sub.3 CH.sub.2 O).sub.˜7 --(CH.sub.2 CH.sub.2
             O).sub.˜22 --(CHCH.sub.3 CH.sub.2 O).sub.˜7
                                         50.9
                                             69° C.
105    10R5
Meroxapol
       Pluronic
             HO(CHCH.sub.3 CH.sub.2 O).sub.˜7 --(CH.sub.2 CH.sub.2
             O).sub.˜91 --(CHCH.sub.3 CH.sub.2 O).sub.˜7
                                         54.1
                                             99° C.
108    10R8
Meroxapol
       Pluronic
             HO(CHCH.sub.3 CH.sub.2 O).sub.˜12 --(CH.sub.2 CH.sub.2
             O).sub.˜136 --(CHCH.sub.3 CH.sub.2 O).sub.˜12
                                         47.3
                                             81° C.
178    17R8
Meroxapol
       Pluronic
             HO(CHCH.sub.3 CH.sub.2 O).sub.˜18 --(CH.sub.2 CH.sub.2
             O).sub.˜163 --(CHCH.sub.3 CH.sub.2 O).sub.˜18
                                         46.1
                                             80° C.
258    25R8
Poloxamer 105
       Pluronic L35
             HO(CH.sub.2 CH.sub.2 O).sub.˜11 --(CHCH.sub.3 CH.sub.2
             O).sub.˜16 --(CH.sub.2 CH.sub.2 O).sub.˜11
                                         48.8
                                             77° C.
Poloxamer 124
       Pluronic L44
             HO(CH.sub.2 CH.sub.2 O).sub.˜11 --(CHCH.sub.3 CH.sub.2
             O).sub.˜21 --(CH.sub.2 CH.sub.2 O).sub.˜11
                                         45.3
                                             65° C.
__________________________________________________________________________
 
    
     Other varieties of poloxamer and meroxapol can readily be synthesized using well known techniques. Desirable characteristics are a room temperature surface tension which is as high as possible, and a cloud point between 40° C. and 100° C., and preferably between 60° C. and 80° C. 
     Meroxapol  HO(CHCH 3  CH 2  O) x  (CH 2  CH 2  O) y  (CHCH 3  CH 2  O) z  OH! varieties where the average x and z are approximately 4, and the average y is approximately 15 may be suitable. 
     If salts are used to increase the electrical conductivity of the ink, then the effect of this salt on the cloud point of the surfactant should be considered. 
     The cloud point of POE surfactants is increased by ions that disrupt water structure (such as I - ), as this makes more water molecules available to form hydrogen bonds with the POE oxygen lone pairs. The cloud point of POE surfactants is decreased by ions that form water structure (such as Cl - , OHS), as fewer water molecules are available to form hydrogen bonds. Bromide ions have relatively little effect. The ink composition can be `tuned` for a desired temperature range by altering the lengths of POE and POP chains in a block copolymer surfactant, and by changing the choice of salts (e.g Cl -   to Br to I - ) that are added to increase electrical conductivity. NaCl is likely to be the best choice of salts to increase ink conductivity, due to low cost and non-toxicity. NaCl slightly lowers the cloud point of nonionic surfactants. 
     Hot Melt Inks 
     The ink need not be in a liquid state at room temperature. Solid `hot melt` inks can be used by heating the printing head and ink reservoir above the melting point of the ink. The hot melt ink must be formulated so that the surface tension of the molten ink decreases with temperature. A decrease of approximately 2 mN/m will be typical of many such preparations using waxes and other substances. However, a reduction in surface tension of approximately 20 mN/m is desirable in order to achieve good operating margins when relying on a reduction in surface tension rather than a reduction in viscosity. 
     The temperature difference between quiescent temperature and drop selection temperature may be greater for a hot melt ink than for a water based ink, as water based inks are constrained by the boiling point of the water. 
     The ink must be liquid at the quiescent temperature. The quiescent temperature should be higher than the highest ambient temperature likely to be encountered by the printed page. The quiescent temperature should also be as low as practical, to reduce the power needed to heat the print head, and to provide a maximum margin between the quiescent and the drop ejection temperatures. A quiescent temperature between 60° C. and 90° C. is generally suitable, though other temperatures may be used. A drop ejection temperature of between 160° C. and 200° C. is generally suitable. 
     There are several methods of achieving an enhanced reduction in surface tension with increasing temperature. 
     1) A dispersion of microfine particles of a surfactant with a melting point substantially above the quiescent temperature, but substantially below the drop ejection temperature, can be added to the hot melt ink while in the liquid phase. 
     2) A polar/non-polar microemulsion with a PIT which is preferably at least 20° C. above the melting points of both the polar and non-polar compounds. 
     To achieve a large reduction in surface tension with temperature, it is desirable that the hot melt ink carrier have a relatively large surface tension (above 30 mN/m) when at the quiescent temperature. This generally excludes alkanes such as waxes. Suitable materials will generally have a strong intermolecular attraction, which may be achieved by multiple hydrogen bonds, for example, polyols, such as Hexanetetrol, which has a melting point of 88° C. 
     Surface tension reduction of various solutions 
     FIG. 3(d) shows the measured effect of temperature on the surface tension of various aqueous preparations containing the following additives: 
     1) 0.1% sol of Stearic Acid 
     2) 0.1% sol of Palmitic acid 
     3) 0.1% solution of Pluronic 10R5 (trade mark of BASF) 
     4) 0.1% solution of Pluronic L35 (trade mark of BASF) 
     5) 0.1% solution of Pluronic L44 (trade mark of BASF) 
     Inks suitable for printing systems of the present invention are described in the following Australian patent specifications, the disclosure of which are hereby incorporated by reference: 
     `Ink composition based on a microemulsion` (Filing no.: PN5223, filed on 6 Sep. 1995); 
     `Ink composition containing surfactant sol` (Filing no.: PN5224, filed on Sep. 6. 1995); 
     `Ink composition for DOD printers with Krafft point near the drop selection temperature sol` (Filing no.: PN6240, filed on 30 Oct. 1995); and 
     `Dye and pigment in a microemulsion based ink` (Filing no.: PN6241, filed on 30 Oct. 1995). 
     Operation Using Reduction of Viscosity 
     As a second example, operation of an embodiment using thermal reduction of viscosity and proximity drop separation, in combination with hot melt ink, is as follows. Prior to operation of the printer, solid ink is melted in the reservoir 64. The reservoir, ink passage to the print head, ink channels 75, and print head 50 are maintained at a temperature at which the ink 100 is liquid, but exhibits a relatively high viscosity (for example, approximately 100 cP). The Ink 100 is retained in the nozzle by the surface tension of the ink. The ink 100 is formulated so that the viscosity of the ink reduces with increasing temperature. The ink pressure oscillates at a frequency which is an integral multiple of the drop ejection frequency from the nozzle. The ink pressure oscillation causes oscillations of the ink meniscus at the nozzle tips, but this oscillation is small due to the high ink viscosity. At the normal operating temperature, these oscillations are of insufficient amplitude to result in drop separation. When the heater 103 is energized, the ink forming the selected drop is heated, causing a reduction in viscosity to a value which is preferably less than 5 cP. The reduced viscosity results in the ink meniscus moving further during the high pressure part of the ink pressure cycle. The recording medium 51 is arranged sufficiently close to the print head 50 so that the selected drops contact the recording medium 51, but sufficiently far away that the unselected drops do not contact the recording medium 51. Upon contact with the recording medium 51, part of the selected drop freezes, and attaches to the recording medium. As the ink pressure falls, ink begins to move back into the nozzle. The body of ink separates from the ink which is frozen onto the recording medium. The meniscus of the ink 100 at the nozzle tip then returns to low amplitude oscillation. The viscosity of the ink increases to its quiescent level as remaining heat is dissipated to the bulk ink and print head. One ink drop is selected, separated and forms a spot on the recording medium 51 for each heat pulse. As the heat pulses are electrically controlled, drop on demand ink jet operation can be achieved. 
     Manufacturing of Print Heads 
     Manufacturing processes for monolithic print heads in accordance with the present invention are described in the following Australian patent specifications filed on 12 Apr. 1995, the disclosure of which are hereby incorporated by reference: 
     `A monolithic LIFT printing head` (Filing no.: PN2301); 
     `A manufacturing process for monolithic LIFT printing heads` (Filing no.: PN2302); 
     `A self-aligned heater design for LIFT print heads` (Filing no.: PN2303); 
     `Integrated four color LIFT print heads` (Filing no.: PN2304); 
     `Power requirement reduction in monolithic LIFT printing heads` (Filing no.: PN2305); 
     `A manufacturing process for monolithic LIFT print heads using anisotropic wet etching` (Filing no.: PN2306); 
     `Nozzle placement in monolithic drop-on-demand print heads` (Filing no.: PN2307); 
     `Heater structure for monolithic LIFT print heads` (Filing no.: PN2346); 
     `Power supply connection for monolithic LIFT print heads` (Filing no.: PN2347); 
     `External connections for Proximity LIFT print heads` (Filing no.: PN2348); and 
     `A self-aligned manufacturing process for monolithic LIFT print heads` (Filing no.: PN2349); and 
     `CMOS process compatible fabrication of LIFT print heads` (Filing no.: PN5222, 6 Sep. 1995). 
     `A manufacturing process for LIFT print heads with nozzle rim heaters` (Filing no.: PN6238, Oct. 30, 1995); 
     `A modular LIFT print head` (Filing no.: PN6237, 30 Oct. 1995); 
     `Method of increasing packing density of printing nozzles` (Filing no.: PN6236, Oct. 30, 1995); and 
     `Nozzle dispersion for reduced electrostatic interaction between simultaneously printed droplets` (Filing no.: PN6239, 30 Oct. 1995). 
     Control of Print Heads 
     Means of providing page image data and controlling heater temperature in print heads of the present invention is described in the following Australian patent specifications filed on 12 Apr. 1995, the disclosure of which are hereby incorporated by reference: 
     `Integrated drive circuitry in LIFT print heads` (Filing no.: PN2295); 
     `A nozzle clearing procedure for Liquid Ink Fault Tolerant (LIFT) printing` (Filing no.: PN2294); 
     `Heater power compensation for temperature in LIFT printing systems` (Filing no.: PN2314); 
     `Heater power compensation for thermal lag in LIFT printing systems` (Filing no.: PN2315); 
     `Heater power compensation for print density in LIFT printing systems` (Filing no.: PN2316); 
     `Accurate control of temperature pulses in printing heads` (Filing no.: PN2317); 
     `Data distribution in monolithic LIFT print heads` (Filing no.: PN2318); 
     `Page image and fault tolerance routing device for LIFT printing systems` (Filing no.: PN2319); and 
     `A removable pressurized liquid ink cartridge for LIFT printers` (Filing no.: PN2320). 
     Image Processing for Print Heads 
     An objective of printing systems according to the invention is to attain a print quality which is equal to that which people are accustomed to in quality color publications printed using offset printing. This can be achieved using a print resolution of approximately 1,600 dpi. However, 1,600 dpi printing is difficult and expensive to achieve. Similar results can be achieved using 800 dpi printing, with 2 bits per pixel for cyan and magenta, and one bit per pixel for yellow and black. This color model is herein called CC&#39;MM&#39;YK. Where high quality monochrome image printing is also required, two bits per pixel can also be used for black. This color model is herein called CC&#39;MM&#39;YKK&#39;. Color models, halftoning, data compression, and real-time expansion systems suitable for use in systems of this invention and other printing systems are described in the following Australian patent specifications filed on 12 Apr. 1995, the disclosure of which are hereby incorporated by reference: 
     `Four level ink set for bi-level color printing` (Filing no.: PN2339); 
     `Compression system for page images` (Filing no.: PN2340); 
     `Real-time expansion apparatus for compressed page images` (Filing no.: PN2341); and 
     `High capacity compressed document image storage for digital color printers` (Filing no.: PN2342); 
     `Improving JPEG compression in the presence of text` (Filing no.: PN2343); 
     `An expansion and halftoning device for compressed page images` (Filing no.: PN2344); and 
     `Improvements in image halftoning` (Filing no.: PN2345). 
     Applications Using Print Heads According to this Invention 
     Printing apparatus and methods of this invention are suitable for a wide range of applications, including (but not limited to) the following: color and monochrome office printing, short run digital printing, high speed digital printing, process color printing, spot color printing, offset press supplemental printing, low cost printers using scanning print heads, high speed printers using pagewidth print heads, portable color and monochrome printers, color and monochrome copiers, color and monochrome facsimile machines, combined printer, facsimile and copying machines, label printing, large format plotters, photographic duplication, printers for digital photographic processing, portable printers incorporated into digital `instant` cameras, video printing, printing of PhotoCD images, portable printers for `Personal Digital Assistants`, wallpaper printing, indoor sign printing, billboard printing, and fabric printing. 
     Printing systems based on this invention are described in the following Australian patent specifications filed on 12 Apr. 1995, the disclosure of which are hereby incorporated by reference: 
     `A high speed color office printer with a high capacity digital page image store` (Filing no.: PN2329); 
     `A short run digital color printer with a high capacity digital page image store` (Filing no.: PN2330); 
     `A digital color printing press using LIFT printing technology` (Filing no.: PN2331); 
     `A modular digital printing press` (Filing no.: PN2332); 
     `A high speed digital fabric printer` (Filing no.: PN2333); 
     `A color photograph copying system` (Filing no.: PN2334); 
     `A high speed color photocopier using a LIFT printing system` (Filing no.: PN2335); 
     `A portable color photocopier using LIFT printing technology` (Filing no.: PN2336); 
     `A photograph processing system using LIFT printing technology` (Filing no.: PN2337); 
     `A plain paper facsimile machine using a LIFT printing system` (Filing no.: PN2338); 
     `A PhotoCD system with integrated printer` (Filing no.: PN2293); 
     `A color plotter using LIFT printing technology` (Filing no.: PN2291); 
     `A notebook computer with integrated LIFT color printing system` (Filing no.: PN2292); 
     `A portable printer using a LIFT printing system` (Filing no.: PN2300); 
     `Fax machine with on-line database interrogation and customized magazine printing` (Filing no.: PN2299); 
     `Miniature portable color printer` (Filing no.: PN2298); 
     `A color video printer using a LIFT printing system` (Filing no.: PN2296); and 
     `An integrated printer, copier, scanner, and facsimile using a LIFT printing system` (Filing no.: PN2297) 
     Compensation of Print Heads for Environmental Conditions 
     It is desirable that drop on demand printing systems have consistent and predictable ink drop size and position. Unwanted variation in ink drop size and position causes variations in the optical density of the resultant print, reducing the perceived print quality. These variations should be kept to a small proportion of the nominal ink drop volume and pixel spacing respectively. Many environmental variables can be compensated to reduce their effect to insignificant levels. Active compensation of some factors can be achieved by varying the power applied to the nozzle heaters. 
     An optimum temperature profile for one print head embodiment involves an instantaneous raising of the active region of the nozzle tip to the ejection temperature, maintenance of this region at the ejection temperature for the duration of the pulse, and instantaneous cooling of the region to the ambient temperature. 
     This optimum is not achievable due to the stored heat capacities and thermal conductivities of the various materials used in the fabrication of the nozzles in accordance with the invention. However, improved performance can be achieved by shaping the power pulse using curves which can be derived by iterative refinement of finite element simulation of the print head. The power applied to the heater can be varied in time by various techniques, including, but not limited to: 
     1) Varying the voltage applied to the heater 
     2) Modulating the width of a series of short pulses (PWM) 
     3) Modulating the frequency of a series of short pulses (PFM) 
     To obtain accurate results, a transient fluid dynamic simulation with free surface modeling is required, as convection in the ink, and ink flow, significantly affect on the temperature achieved with a specific power curve. 
     By the incorporation of appropriate digital circuitry on the print head substrate, it is practical to individually control the power applied to each nozzle. One way to achieve this is by `broadcasting` a variety of different digital pulse trains across the print head chip, and selecting the appropriate pulse train for each nozzle using multiplexing circuits. 
     An example of the environmental factors which may be compensated for is listed in the table &#34;Compensation for environmental factors&#34;. This table identifies which environmental factors are best compensated globally (for the entire print head), per chip (for each chip in a composite multi-chip print head), and per nozzle. 
     Compensation for environmental factors 
     
         __________________________________________________________________________
Factor        Sensing or user
                         Compensation
compensated
          Scope
              control method
                         mechanism
__________________________________________________________________________
Ambient   Global
              Temperature sensor
                         Power supply voltage
Temperature   mounted on print head
                         or global PFM patterns
Power supply
          Global
              Predictive active
                         Power supply voltage
voltage fluctuation
              nozzle count based on
                         or global PFM patterns
with number of
              print data
active nozzles
Local heat build-
          Per Predictive active
                         Selection of
up with successive
          nozzle
              nozzle count based on
                         appropriate PFM
nozzle actuation
              print data pattern for each printed
                         drop
Drop size control
          Per Image data Selection of
for multiple bits
          nozzle         appropriate PFM
per pixel                pattern for each printed
                         drop
Nozzle geometry
          Per Factory measurement,
                         Global PFM patterns
variations between
          chip
              datafile supplied with
                         per print head chip
wafers        print head
Heater resistivity
          Per Factory measurement,
                         Global PFM patterns
variations between
          chip
              datafile supplied with
                         per print head chip
wafers        print head
User image
          Global
              User selection
                         Power supply voltage,
intensity                electrostatic
adjustment               acceleration voltage, or
                         ink pressure
Ink surface tension
          Global
              Ink cartridge sensor or
                         Global PFM patterns
reduction method
              user selection
and threshold
temperature
Ink viscosity
          Global
              Ink cartridge sensor or
                         Global PFM patterns
              user selection
                         and/or clock rate
Ink dye or pigment
          Global
              Ink cartridge sensor or
                         Global PFM patterns
concentration user selection
Ink response time
          Global
              Ink cartridge sensor or
                         Global PFM patterns
              user selection
__________________________________________________________________________
 
    
     Most applications will not require compensation for all of these variables. Some variables have a minor effect, and compensation is only necessary where very high image quality is required. 
     Print head drive circuits 
     FIG. 4 is a block schematic diagram showing electronic operation of an example head driver circuit in accordance with this invention. This control circuit uses analog modulation of the power supply voltage applied to the print head to achieve heater power modulation, and does not have individual control of the power applied to each nozzle. FIG. 4 shows a block diagram for a system using an 800 dpi pagewidth print head which prints process color using the CC&#39;MM&#39;YK color model. The print head 50 has a total of 79,488 nozzles, with 39,744 main nozzles and 39,744 redundant nozzles. The main and redundant nozzles are divided into six colors, and each color is divided into 8 drive phases. Each drive phase has a shift register which converts the serial data from a head control ASIC 400 into parallel data for enabling heater drive circuits. There is a total of 96 shift registers, each providing data for 828 nozzles. Each shift register is composed of 828 shift register stages 217, the outputs of which are logically anded with phase enable signal by a nand gate 215. The output of the nand gate 215 drives an inverting buffer 216, which in turn controls the drive transistor 201. The drive transistor 201 actuates the electrothermal heater 200, which may be a heater 103 as shown in FIG. 1(b). To maintain the shifted data valid during the enable pulse, the clock to the shift register is stopped the enable pulse is active by a clock stopper 218, which is shown as a single gate for clarity, but is preferably any of a range of well known glitch free clock control circuits. Stopping the clock of the shift register removes the requirement for a parallel data latch in the print head, but adds some complexity to the control circuits in the Head Control ASIC 400. Data is routed to either the main nozzles or the redundant nozzles by the data router 219 depending on the state of the appropriate signal of the fault status bus. 
     The print head shown in FIG. 4 is simplified, and does not show various means of improving manufacturing yield, such as block fault tolerance. Drive circuits for different configurations of print head can readily be derived from the apparatus disclosed herein. 
     Digital information representing patterns of dots to be printed on the recording medium is stored in the Page or Band memory 1513, which may be the same as the Image memory 72 in FIG. 1(a). Data in 32 bit words representing dots of one color is read from the Page or Band memory 1513 using addresses selected by the address mux 417 and control signals generated by the Memory Interface 418. These addresses are generated by Address generators 411, which forms part of the `Per color circuits` 410, for which there is one for each of the six color components. The addresses are generated based on the positions of the nozzles in relation to the print medium. As the relative position of the nozzles may be different for different print heads, the Address generators 411 are preferably made programmable. The Address generators 411 normally generate the address corresponding to the position of the main nozzles. However, when faulty nozzles are present, locations of blocks of nozzles containing faults can be marked in the Fault Map RAM 412. The Fault Map RAM 412 is read as the page is printed. If the memory indicates a fault in the block of nozzles, the address is altered so that the Address generators 411 generate the address corresponding to the position of the redundant nozzles. Data read from the Page or Band memory 1513 is latched by the latch 413 and converted to four sequential bytes by the multiplexer 414. Timing of these bytes is adjusted to match that of data representing other colors by the FIFO 415. This data is then buffered by the buffer 430 to form the 48 bit main data bus to the print head 50. The data is buffered as the print head may be located a relatively long distance from the head control ASIC. Data from the Fault Map RAM 412 also forms the input to the FIFO 416. The timing of this data is matched to the data output of the FIFO 415, and buffered by the buffer 431 to form the fault status bus. 
     The programmable power supply 320 provides power for the head 50. The voltage of the power supply 320 is controlled by the DAC 313, which is part of a RAM and DAC combination (RAMDAC) 316. The RAMDAC 316 contains a dual port RAM 317. The contents of the dual port RAM 317 are programmed by the Microcontroller 315. Temperature is compensated by changing the contents of the dual port RAM 317. These values are calculated by the microcontroller 315 based on temperature sensed by a thermal sensor 300. The thermal sensor 300 signal connects to the Analog to Digital Converter (ADC) 311. The ADC 311 is preferably incorporated in the Microcontroller 315. 
     The Head Control ASIC 400 contains control circuits for thermal jag compensation and print density. Thermal lag compensation requires that the power supply voltage to the head 50 is a rapidly time-varying voltage which is synchronized with the enable pulse for the heater. This is achieved by programming the programmable power supply 320 to produce this voltage. An analog time varying programming voltage is produced by the DAC 313 based upon data read from the dual port RAM 317. The data is read according to an address produced by the counter 403. The counter 403 produces one complete cycle of addresses during the period of one enable pulse. This synchronization is ensured, as the counter 403 is clocked by the system clock 408, and the top count of the counter 403 is used to clock the enable counter 404. The count from the enable counter 404 is then decoded by the decoder 405 and buffered by the buffer 432 to produce the enable pulses for the head 50. The counter 403 may include a prescaler if the number of states in the count is less than the number of clock periods in one enable pulse. Sixteen voltage states are adequate to accurately compensate for the heater thermal lag. These sixteen states can be specified by using a four bit connection between the counter 403 and the dual port RAM 317. However, these sixteen states may not be linearly spaced in time. To allow non-linear timing of these states the counter 403 may also include a ROM or other device which causes the counter 403 to count in a non-linear fashion. Alternatively, fewer than sixteen states may be used. 
     For print density compensation, the printing density is detected by counting the number of pixels to which a drop is to be printed (`on` pixels) in each enable period. The `on` pixels are counted by the On pixel counters 402. There is one On pixel counter 402 for each of the eight enable phases. The number of enable phases in a print head in accordance with the invention depend upon the specific design. Four, eight, and sixteen are convenient numbers, though there is no requirement that the number of enable phases is a power of two. The On Pixel Counters 402 can be composed of combinatorial logic pixel counters 420 which determine how many bits in a nibble of data are on. This number is then accumulated by the adder 421 and accumulator 422. A latch 423 holds the accumulated value valid for the duration of the enable pulse. The multiplexer 401 selects the output of the latch 423 which corresponds to the current enable phase, as determined by the enable counter 404. The output of the multiplexer 401 forms part of the address of the dual port RAM 317. An exact count of the number of `on` pixels is not necessary, and the most significant four bits of this count are adequate. 
     Combining the four bits of thermal lag compensation address and the four bits of print density compensation address means that the dual port RAM 317 has an 8 bit address. This means that the dual port RAM 317 contains 256 numbers, which are in a two dimensional array. These two dimensions are time (for thermal lag compensation) and print density. A third dimension--temperature--can be included. As the ambient temperature of the head varies only slowly, the microcontroller 315 has sufficient time to calculate a matrix of 256 numbers compensating for thermal lag and print density at the current temperature. Periodically (for example, a few times a second), the microcontroller senses the current head temperature and calculates this matrix. 
     The clock to the print head 50 is generated from the system clock 408 by the Head clock generator 407, and buffered by the buffer 406. To facilitate testing of the Head control ASIC, JTAG test circuits 499 may be included. 
     Comparison with thermal ink jet technology 
     The table &#34;Comparison between Thermal ink jet and Present Invention&#34; compares the aspects of printing in accordance with the present invention with thermal ink jet printing technology. 
     A direct comparison is made between the present invention and thermal ink jet technology because both are drop on demand systems which operate using thermal actuators and liquid ink. Although they may appear similar, the two technologies operate on different principles. 
     Thermal ink jet printers use the following fundamental operating principle. A thermal impulse caused by electrical resistance heating results in the explosive formation of a bubble in liquid ink. Rapid and consistent bubble formation can be achieved by superheating the ink, so that sufficient heat is transferred to the ink before bubble nucleation is complete. For water based ink, ink temperatures of approximately 280° C. to 400° C. are required. The bubble formation causes a pressure wave which forces a drop of ink from the aperture with high velocity. The bubble then collapses, drawing ink from the ink reservoir to re-fill the nozzle. Thermal ink jet printing has been highly successful commercially due to the high nozzle packing density and the use of well established integrated circuit manufacturing techniques. However, thermal ink jet printing technology faces significant technical problems including multi-part precision fabrication, device yield, image resolution, `pepper` noise, printing speed, drive transistor power, waste power dissipation, satellite drop formation, thermal stress, differential thermal expansion, kogation, cavitation, rectified diffusion, and difficulties in ink formulation. 
     Printing in accordance with the present invention has many of the advantages of thermal ink jet printing, and completely or substantially eliminates many of the inherent problems of thermal ink jet technology. 
     Comparison between Thermal ink jet and Present Invention 
     
         ______________________________________
       Thermal Ink-Jet
                     Present Invention
______________________________________
Drop selection
         Drop ejected by pressure
                         Choice of surface tension or
mechanism
         wave caused by thermally
                         viscosity reduction
         induced bubble  mechanisms
Drop     Same as drop selection
                         Choice of proximity,
separation
         mechanism       electrostatic, magnetic, and
mechanism                other methods
Basic ink
         Water           Water, microemulsion,
carrier                  alcohol, glycol, or hot melt
Head     Precision assembly of
                         Monolithic
construction
         nozzle plate, ink channel,
         and substrate
Per copy Very high due to limited
                         Can be low due to
printing cost
         print head life and
                         permanent print heads and
         expensive inks  wide range of possible inks
Satellite drop
         Significant problem which
                         No satellite drop formation
formation
         degrades image quality
Operating ink
         280° C. to 400° C. (high
                         Approx. 70° C. (depends
temperature
         temperature limits dye use
                         upon ink formulation)
         and ink formulation)
Peak heater
         400° C. to 1,000° C. (high
                         Approx. 130° C.
temperature
         temperature reduces device
         life)
Cavitation
         Serious problem limiting
                         None (no bubbles are
(heater erosion
         head life       formed)
by bubble
collapse)
Kogation Serious problem limiting
                         None (water based ink
(coating of
         head life and ink
                         temperature does not
heater by ink
         formulation     exceed 100° C.)
ash)
Rectified
         Serious problem limiting
                         Does not occur as the ink
diffusion
         ink formulation pressure does not go
(formation of            negative
ink bubbles due
to pressure
cycles)
Resonance
         Serious problem limiting
                         Very small effect as
         nozzle design and
                         pressure waves are small
         repetition rate
Practical
         Approx. 800 dpi max.
                         Approx. 1,600 dpi max.
resolution
Self-cooling
         No (high energy required)
                         Yes: printed ink carries
operation                away drop selection energy
Drop ejection
         High (approx. 10 m/sec)
                         Low (approx. 1 m/sec)
velocity
Crosstalk
         Serious problem requiring
                         Low velocities and
         careful acoustic design,
                         pressures associated with
         which limits nozzle refill
                         drop ejection make
         rate.           crosstalk very small.
Operating
         Serious problem limiting
                         Low: maximum
thermal  print-head life.
                         temperature increase
stress                   approx. 90° C. at centre
                         of heater.
Manufacturing
         Serious problem limiting
                         Same as standard CMOS
thermal stress
         print-head size.
                         manufacturing process.
Drop selection
         Approx. 20 μJ
                         Approx. 270 nJ
energy
Heater pulse
         Approx. 2-3 μs
                         Approx. 15-30 μs
period
Average heater
         Approx. 8 Watts per
                         Approx. 12 mW per heater.
pulse power
         heater.         This is more than 500 times
                         less than Thermal Ink-Jet.
Heater pulse
         Typically approx. 40 V.
                         Approx. 5 to 10 V.
voltage
Heater peak
         Typically approx. 200 mA
                         Aprox. 4 mA per heater.
pulse current
         per heater. This requires
                         This allows the use of small
         bipolar or very large MOS
                         MOS drive transistors.
         drive transistors.
Fault tolerance
         Not implemented. Not
                         Simple implementation
         practical for edge shooter
                         results in better yield and
         type.           reliability
Constraints on
         Many constraints including
                         Temperature coefficient of
ink compo-
         kogation, nucleation, etc.
                         surface tension or viscosity
sition                   must be negative.
Ink pressure
         Atmospheric pressure or
                         Approx. 1.1 atm
         less
Integrated drive
         Bipolar circuitry usually
                         CMOS, nMOS, or bipolar
circuitry
         required due to high drive
         current
Differential
         Significant problem for
                         Monolithic construction
thermal  large print heads
                         reduces problem
expansion
Pagewidth print
         Major problems with yield,
                         High yield, low cost and
heads    cost, precision long life due to fault
         construction, head life, and
                         tolerance. Self cooling due
         power dissipation
                         to low power dissipation.
______________________________________
 
    
     Yield and Fault Tolerance 
     In most cases, monolithic integrated circuits cannot be repaired if they are not completely functional when manufactured. The percentage of operational devices which are produced from a wafer run is known as the yield. Yield has a direct influence on manufacturing cost. A device with a yield of 5% is effectively ten times more expensive to manufacture than an identical device with a yield of 50%. 
     There are three major yield measurements: 
     1) Fab yield 
     2) Wafer sort yield 
     3) Final test yield 
     For large die, it is typically the wafer sort yield which is the most serious limitation on total yield. Full pagewidth color heads in accordance with this invention are very large in comparison with typical VLSI circuits. Good wafer sort yield is critical to the cost-effective manufacture of such heads. 
     FIG. 5 is a graph of wafer sort yield versus defect density for a monolithic full width color A4 head embodiment of the invention. The head is 215 mm long by 5 mm wide. The non fault tolerant yield 198 is calculated according to Murphy&#39;s method, which is a widely used yield prediction method. With a defect density of one defect per square cm, Murphy&#39;s method predicts a yield less than 1%. This means that more than 99% of heads fabricated would have to be discarded. This low yield is highly undesirable, as the print head manufacturing cost becomes unacceptably high. 
     Murphy&#39;s method approximates the effect of an uneven distribution of defects. FIG. 5 also includes a graph of non fault tolerant yield 197 which explicitly models the clustering of defects by introducing a defect clustering factor. The defect clustering factor is not a controllable parameter in manufacturing, but is a characteristic of the manufacturing process. The defect clustering factor for manufacturing processes can be expected to be approximately 2, in which case yield projections closely match Murphy&#39;s method, 
     A solution to the problem of low yield is to incorporate fault tolerance by including redundant functional units on the chip which are used to replace faulty functional units. 
     In memory chips and most Wafer Scale Integration (WSI) devices, the physical location of redundant sub-units on the chip is not important. However, in printing heads the redundant sub-unit may contain one or more printing actuators. These must have a fixed spatial relationship to the page being printed. To be able to print a dot in the same position as a faulty actuator, redundant actuators must not be displaced in the non-scan direction. However, faulty actuators can be replaced with redundant actuators which are displaced in the scan direction. To ensure that the redundant actuator prints the dot in the same position as the faulty actuator, the data timing to the redundant actuator can be altered to compensate for the displacement in the scan direction. 
     To allow replacement of all nozzles, there must be a complete set of spare nozzles, which results in 100% redundancy. The requirement for 100% redundancy would normally more than double the chip area, dramatically reducing the primary yield before substituting redundant units, and thus eliminating most of the advantages of fault tolerance. 
     However, with print head embodiments according to this invention, the minimum physical dimensions of the head chip are determined by the width of the page being printed, the fragility of the head chip, and manufacturing constraints on fabrication of ink channels which supply irk to the back surface of the chip. The minimum practical size for a full width, full color head for printing A4 size paper is approximately 215 mm×5 mm. This size allows the inclusion of 100% redundancy without significantly increasing chip area, when using 1.5 μm CMOS fabrication technology. Therefore, a high level of fault tolerance can be included without significantly decreasing primary yield. 
     When fault tolerance is included in a device, standard yield equations cannot be used. Instead, the mechanisms and degree of fault tolerance must be specifically analyzed and included in the yield equation. FIG. 5 shows the fault tolerant sort yield 199 for a full width color A4 head which includes various forms of fault tolerance, the modeling of which has been included in the yield equation. This graph shows projected yield as a function of both defect density and defect clustering. The yield projection shown in FIG. 5 indicates that thoroughly implemented fault tolerance can increase wafer sort yield from under 1% to more than 90% under identical manufacturing conditions. This can reduce the manufacturing cost by a factor of 100. 
     Fault tolerance is highly recommended to improve yield and reliability of print heads containing thousands of printing nozzles, and thereby make pagewidth printing heads practical. However, fault tolerance is not to be taken as an essential part of the present invention. 
     Fault tolerance in drop-on-demand printing systems is described in the following Australian patent specifications filed on Apr. 12, 1995, the disclosure of which are hereby incorporated by reference: 
     `Integrated fault tolerance in printing mechanisms` (Filing no.: PN2324); 
     `Block fault tolerance in integrated printing heads` (Filing no.: PN2325); 
     `Nozzle duplication for fault tolerance in integrated printing heads` (Filing no.: PN2326); 
     `Detection of faulty nozzles in printing heads` (Filing no.: PN2327); and 
     `Fault tolerance in high volume printing presses` (Filing no.: PN2328). 
     Printing System Embodiments 
     A schematic diagram of a digital electronic printing system using a print head of this invention is shown in FIG. 6. This shows a monolithic printing head 50 printing an image 60 composed of a multitude of ink drops onto a recording medium 51. This medium will typically be paper, but can also be overhead transparency film, cloth, or many other substantially flat surfaces which will accept ink drops. The image to be printed is provided by an image source 52, which may be any image type which can be converted into a two dimensional array of pixels. Typical image sources are image scanners, digitally stored images, images encoded in a page description language (PDL) such as Adobe Postscript, Adobe Postscript level 2, or Hewlett-Packard PCL 5, page images generated by a procedure-call based rasterizer, such as Apple QuickDraw, Apple Quickdraw GX, or Microsoft GDI, or text in an electronic form such as ASCII. This image data is then converted by an image processing system 53 into a two dimensional array of pixels suitable for the particular printing system. This may be color or monochrome, and the data will typically have between 1 and 32 bits per pixel, depending upon the image source and the specifications of the printing system. The image processing system may be a raster image processor (RIP) if the source image is a page description, or may be a two dimensional image processing system if the source image is from a scanner. 
     If continuous tone images are required, then a halftoning system 54 is necessary. Suitable types of halftoning are based on dispersed dot ordered dither or error diffusion. Variations of these, commonly known as stochastic screening or frequency modulation screening are suitable. The halftoning system commonly used for offset printing--clustered dot ordered dither--is not recommended, as effective image resolution is unnecessarily wasted using this technique. The output of the halftoning system is a binary monochrome or color image at the resolution of the printing system according to the present invention. 
     The binary image is processed by a data phasing circuit 55 (which may be incorporated in a Head Control ASIC 400 as shown in FIG. 4) which provides the pixel data in the correct sequence to the data shift registers 56. Data sequencing is required to compensate for the nozzle arrangement and the movement of the paper. When the data has been loaded into the shift registers 56, it is presented in parallel to the heater driver circuits 57. At the correct time, the driver circuits 57 will electronically connect the corresponding heaters 58 with the voltage pulse generated by the pulse shaper circuit 61 and the voltage regulator 62. The heaters 58 heat the tip of the nozzles 59, affecting the physical characteristics of the ink. Ink drops 60 escape from the nozzles in a pattern which corresponds to the digital impulses which have been applied to the heater driver circuits. The pressure of the ink in the ink reservoir 64 is regulated by the pressure regulator 63. Selected drops of ink drops 60 are separated from the body of ink by the chosen drop separation means, and contact the recording medium 51. During printing, the recording medium 51 is continually moved relative to the print head 50 by the paper transport system 65. If the print head 50 is the full width of the print region of the recording medium 51, it is only necessary to move the recording medium 51 in one direction, and the print head 50 can remain fixed. If a smaller print head 50 is used, it is necessary to implement a raster scan system. This is typically achieved by scanning the print head 50 along the short dimension of the recording medium 51, while moving the recording medium 51 along its long dimension. 
     Computer simulation of nozzle dynamics 
     Details of the operation of print heads according to this invention have been extensively simulated by computer. FIGS. 8 to 18 are some results from an example simulation of a preferred nozzle embodiment&#39;s operation using electrothermal drop selection by reduction in surface tension, combined with electrostatic drop separation. 
     Computer simulation is extremely useful in determining the characteristics of phenomena which are difficult to observe directly. Nozzle operation is difficult to observe experimentally for several reasons, including: 
     1) Useful nozzles are microscopic, with important phenomena occurring at dimensions less than 1 μm. 
     2) The time scale of a drop ejection is a few microseconds, requiring very high speed observations. 
     3) Important phenomena occur inside opaque solid materials, making direct observation impossible. 
     4) Some important parameters, such as heat flow and fluid velocity vector fields are difficult to directly observe on any scale. 
     5) The cost of fabrication of experimental nozzles is high. 
     Computer simulation overcomes the above problems. A leading software package for fluid dynamics simulation is FIDAP, produced by Fluid Dynamics International Inc. of Illinois, U.S.A. (FDI). FIDAP is a registered trademark of FDI. Other simulation programs are commercially available, but FIDAP was chosen for its high accuracy in transient fluid dynamic, energy transport, and surface tension calculations. The version of FIDAP used is FIDAP 7.51. 
     The simulations combine energy transport and fluid dynamic aspects. Axi-symmetric simulation is used, as the example nozzle is cylindrical in form. There are four deviations from cylindrical form. These are the connections to the heater, the laminar air flow caused by paper movement, gravity (if the printhead is not vertical), and the presence of adjacent nozzles in the substrate. The effect of these factors on drop ejection is minor. 
     To obtain convergence for transient free surface simulations with variable surface tension at micrometer scales with microsecond transients using FIDAP 7.51, it is necessary to nondimensionalize the simulation. 
     Only the region in the tip of the nozzle is simulated, as most phenomena relevant to drop selection occur in this region. The simulation is from the axis of symmetry of the nozzle out to a distance of 40 μm. 
     A the beginning of the simulation, the entire nozzle and ink is at the device ambient temperature, which in this case is 30° C. During operation, the device ambient temperature will be slightly higher than the air ambient temperature, as an equilibrium temperature based on printing density is reached over the period of many drop ejections. Most of the energy of each drop selection is carried away with the ink drop. The remaining heat in the nozzle becomes very evenly distributed between drop ejections, due to the high thermal conductivity of silicon, and due to convection in the ink. 
     Geometry of the simulated nozzle 
     FIG. 7 shows the geometry and dimensions of the a preferred nozzle embodiment modeled in this simulation. 
     The nozzle is constructed on a single crystal silicon substrate 2020. The substrate has an epitaxial boron doped silicon layer 2018, which is used as an etch stop during nozzle fabrication. An epitaxial silicon layer 2019 provides the active substrate for the fabrication of CMOS drive transistors and data distribution circuits. On this substrate are several layers deposited CMOS processing. These are a thermal oxide layer 2021, a first interlevel oxide layer 2022, first level metal 2023, second interlevel oxide layer 2024, second level metal 2025, and passivation oxide layer 2026. Subsequent processing of the wafers forms the nozzles and heaters. These structures include the active heater 2027(a), an ESD shield formed from `spare` heater material 2027(b), and a silicon nitride passivation layer 2028. 
     The heater is atop a narrow `rim` etched from the various oxide layers. This is to reduce the `thermal mass` of the material around the heater, and to prevent the ink from spreading across the surface of the print head. 
     The print head is filled with electrically conductive ink 2031. An electric field is applied to the print head, using an electrode which is in electrical contact with the ink, and another electrode which is behind the recording medium. 
     The nozzle radius is 8 μm, and the diagram is to scale. 
     Theoretical basis of calculations 
     The theoretical basis for fluid dynamic and energy transport calculations using the Finite Element Method, and the manner that this theoretical basis is applied to the FIDAP computer program, is described in detail in the FIDAP 7.0 Theory Manual (April 1993) published by FDI, the disclosure of which is hereby incorporated by reference. 
     Material characteristics 
     The table &#34;Properties of materials used for FIDAP simulation&#34; gives approximate physical properties of materials which may be used in the fabrication of the print head in accordance with this invention. 
     The properties of `ink` used in this simulation are that of a water based ink with 25% pigment loading. The ink contains a suspension of fine particles of palmitic acid (hexadecanoic acid) to achieve a pronounced reduction in surface tension with temperature. The surface tensions were measured at various temperatures using a surface tensiometer. 
     The values which have been used in the example simulation using the FIDAP program are shown in the table &#34;Properties of materials used for FIDAP simulation&#34;. Most values are from direct measurement, or from the CRC Handbook of Chemistry and Physics, 72nd edition, or Lange&#39;s handbook of chemistry, 14th edition. 
     Properties of materials used for FIDAP simulation 
     
         ______________________________________
             Material or          Dimensionless
Property     Temperature
                       Physical value
                                  value
______________________________________
Characteristic length (L)
             All       1 μm    1
Characteristic velocity
             Ink       1 m/s      1
(U)
Characteristic time
             All       1 μs    1
Time Step    All       0.1 μs  0.25
Ambient temperature
             All       30° C.
                                  30
Boiling point
             Ink       103° C.
                                  103
Viscosity (η)
             At 20° C.
                       2.306 cP   3.530
Viscosity (η)
             At 30° C.
                       1.836 cP   2.810
Viscosity (η)
             At 40° C.
                       1.503 cP   2.301
Viscosity (η)
             At 50° C.
                       1.259 cP   1.927
Viscosity (η)
             At 60° C.
                       1.074 cP   1.643
Viscosity (η)
             At 70° C.
                       0.930 cP   1.423
Viscosity (η)
             At 80° C.
                       0.816 cP   1.249
Viscosity (η)
             At 90° C.
                       0.724 cP   1.108
Viscosity (η)
             At 100° C.
                       0.648 cP   0.993
Surface Tension (γ)
             28° C.
                       59.3 mN/m  90.742
Surface Tension (γ)
             33° C.
                       58.8 mN/m  89.977
Surface Tension (γ)
             38° C.
                       54.1 mN/m  82.785
Surface Tension (γ)
             43° C.
                       49.8 mN/m  76.205
Surface Tension (γ)
             47° C.
                       47.3 mN/m  72.379
Surface Tension (γ)
             53° C.
                       44.7 mN/m  68.401
Surface Tension (γ)
             58° C.
                       39.4 mN/m  60.291
Surface Tension (γ)
             63° C.
                       35.6 mM/m  54.476
Surface Tension (γ)
             68° C.
                       33.8 mN/m  51.721
Surface Tension (γ)
             73° C.
                       33.7 mN/m  51.568
Pressure (p) Ink       10 kPa     15.3
Thermal Conductivity (k)
             Ink       0.631      1
                       Wm.sup.-1 K.sup.-1
Thermal Conductivity (k)
             Silicon   148 Wm.sup.-1 K.sup.-1
                                  234.5
Thermal Conductivity (k)
             SiO.sub.2 1.5 Wm.sup.-1 K.sup.-1
                                  2.377
Thermal Conductivity (k)
             Heater    23 Wm.sup.-1 K.sup.-1
                                  36.45
Thermal Conductivity (k)
             Si.sub.3 N.sub.4
                       19 Wm.sup.-1 K.sup.-1
                                  30.11
Specific Heat (c.sub.p)
             Ink       3,727 Jkg.sup.-1 K.sup.-1
                                  3.8593
Specific Heat (c.sub.p)
             Silicon   711 Jkg.sup.-1 K.sup.-1
                                  0.7362
Specific Heat (c.sub.p)
             SiO.sub.2 738 Jkg.sup.-1 K.sup.-1
                                  0.7642
Specific Heat (c.sub.p)
             Heater    250 Jkg.sup.-1 K.sup.-1
                                  0.2589
Specific Heat (c.sub.p)
             Si.sub.3 N.sub.4
                       712 Jkg.sup.-1 K.sup.-1
                                  0.7373
Density (ρ)
             Ink       1.036 gcm.sup.-1
                                  1.586
Density (ρ)
             Silicon   2.320 gcm.sup.-1
                                  3.551
Density (ρ)
             SiO.sub.2 2.190 gcm.sup.-1
                                  3.352
Density (ρ)
             Heater    10.50 gcm.sup.-1
                                  16.07
Density (ρ)
             Si.sub.3 N.sub.4
                       3.160 gcm.sup.-1
                                  4.836
______________________________________
 
    
     Fluid dynamic simulations 
     FIG. 8(a) shows the power applied to the heater. The maximum power applied to the heater is 40 mW. This power is pulse frequency modulated to obtain a desirable temporal distribution of power to the heater. The power pulses are each of a duration of 0.1 μs, each delivering 4 nJ of energy to the heater. The drop selection pulse is started 10 μs into the simulation, to allow the meniscus to settle to its quiescent position. The total energy delivered to the heater during the drop selection pulse is 276 nJ 
     FIG. 8(b) shows the temperature at various points in the nozzle during the simulation. 
     Point A is at the contact point of the ink meniscus and the nozzle rim. For optimal operation, it is desirable that this point be raised as close as possible to the boiling point of the ink, without exceeding the boiling point, and maintained at this temperature for the duration of the drop selection pulse. The `spiky` temperature curve is due to the pulse frequency modulation of the power applied to the heater. This `spikiness` can be reduced by increasing the pulse frequency, and proportionally reducing the pulse energy. 
     Point B is a point on the ink meniscus, approximately midway between the centre of the meniscus and the nozzle tip. 
     Point C is a point on the surface of the silicon, 20 μm from the centre of the nozzle. This shows that the temperature rise when a drop is selected is very small a short distance away from the nozzle. This allows active devices, such as drive transistors, to be placed very close to the nozzles. 
     FIG. 9 shows the position versus time of a point at the centre of the meniscus. 
     FIG. 10 shows the meniscus position and shape at various times during the drop selection pulse. The times shown are at the start of the drop selection pulse, (10 μs into the simulation), and at 5 μs intervals, until 60 μs after the start of the heater pulse. 
     FIG. 11 shows temperature contours in the nozzle just before the beginning of the drop selection pulse, 9 μs into the simulation. The surface tension balances the combined effect of the ink pressure and the external constant electric field. 
     FIG. 12 shows temperature contours in the nozzle 5 μs after beginning of the drop selection pulse, 15 μs into the simulation. The reduction in surface tension at the nozzle tip causes the surface at this point to expand, rapidly carrying the heat around the meniscus. The ink has begun to move, as the surface tension is no longer high enough to balance the combined effect of the ink pressure and the external constant electric field. The centre of the meniscus begins to move faster than the outside, due to viscous drag at the nozzle walls. In FIGS. 12 to 17 temperature contours are shown starting at 35° C. and increasing in 5° C. intervals. 
     FIG. 13 shows temperature contours in the nozzle 10 μs after beginning of the drop selection pulse, 20 μs into the simulation. 
     FIG. 14 shows temperature contours in the nozzle 20 μs after beginning of the drop selection pulse, 30 μs into the simulation. 
     FIG. 15 shows temperature contours in the nozzle 30 μs after beginning of the drop selection pulse, 40 μs into the simulation. This is 6 μs after the end of the drop selection pulse, and the nozzle has begun to cool down. 
     FIG. 16 shows temperature contours in the nozzle 40 μs after beginning of the drop selection pulse, 50 μs into the simulation. If is clear from this simulation that the vast majority of the energy of the drop selection pulse is carried away with the selected drop. 
     FIG. 17 shows temperature contours in the nozzle 50 μs after beginning of the drop selection pulse, 60 μs into the simulation. At this time, the selected drop is beginning to `neck`, and the drop separation process is beginning. 
     FIG. 18 shows streamlines in the nozzle at the same time as FIG. 17. 
     The approximate duration of three consecutive phases in the drop ejection cycle are: 
     1) 24 μs heater energizing cycle 
     2) 60 μs to reach drop separation 
     3) 40 μs to return to the quiescent position 
     The total of these times is 124 μs, which results in a maximum drop repetition rate (drop frequency) of approximately 8 Khz. 
     A major factor determining drop size in Proximity LIFT printing is nozzle radius. The present invention is a print head with nozzles of differing radii, which allows multiple drop sizes in the same print head. This can be used to weight drop sizes to achieve multi-level printing, allowing higher print quality at the same resolution. 
     Print heads with six rows of nozzles can use the CC&#39;MM&#39;YK color system to attain high print quality. This system requires three differing optical densities: full optical density for yellow and black, 2/3 optical density for the most significant bits of cyan and magenta, and 1/3 optical density for the least significant bits of cyan and magenta. To achieve the various optical densities, the drop volume can be different for the various color components. The required drop volume to achieve particular optical density depends upon the characteristics of the ink and the recording medium. However, the optical density attained will typically be approximately proportional to the drop volume. To achieve the variation in drop volume with other characteristics being equal, the nozzle radius can be approximately in proportion to the required drop volume. For 800 dpi printing, nozzle radii of 10 μm for the yellow and black inks, 8.2 μm for the 2/3 intensity magenta and cyan inks, and 5.8 μm for the 1/3 intensity magenta and cyan inks can be used. 
     The recommended manufacturing method for print heads uses microelectronic lithographic processes on a silicon wafer, with ink channels and individual nozzles etched through the wafer. Many thousands of nozzles can be fabricated simultaneously in one print head. The radius of individual ink nozzles is determined by the mask patterns used during various lithographic processes, and nozzles with differing radii can be simultaneously fabricated without requiring extra manufacturing steps. 
     Multiple nozzles in a single monolithic print head 
     It is desirable that a new printing system intended for use in equipment such as office printers or photocopiers is able to print quickly. A printing speed of 60 A4 pages per minute (one page per second) will generally be adequate for many applications. However, achieving an electronically controlled print speed of 60 pages per minute is not simple. 
     The minimum time taken to print a page is equal to the number of dot positions on the page times the time required to print a dot, divided by the number of dots of each color which can be printed simultaneously. 
     The image quality that can be obtained is affected by the total number of ink dots which can be used to create an image. For full color magazine quality printing using dispersed dot digital halftoning, approximately 800 dots per inch (31.5 dots per mm) are required. The spacing between dots on the paper is 31.75 μm. 
     A standard A4 page is 210 mm times 297 mm. At 31.5 dots per mm, 61,886,632 dots are required for a monochrome full bleed A4 page. High quality process color printing requires four colors--cyan, magenta, yellow, and black. Therefore, the total number of dots required is 247,546,528. While this can be reduced somewhat by not allowing printing in a small margin at the edge of the paper, the total number of dots required is still very large. If the time taken to print a dot is 144 μs, and only one nozzle per color is provided, then it will take more than two hours to print a single page. 
     To achieve high speed, high quality printing with my printing system described above, printing heads with many small nozzles are required. The printing of a 800 dpi color A4 page in one second can be achieved if the printing head is the full width of the paper. The printing head can be stationary, and the paper can travel past it in the one second period. A four color 800 dpi printing head 210 mm wide requires 26,460 nozzles. 
     Such a print head may contain 26,460 active nozzles, and 26,460 redundant (spare) nozzles, giving a total of 52,920 nozzles. There are 6,615 active nozzles for each of the cyan, magenta, yellow, and black process colors. 
     Print heads with large numbers of nozzles can be manufactured at low cost. This can be achieved by using semiconductor manufacturing processes to simultaneously fabricate many thousands of nozzles in a silicon wafer. To eliminate problems with mechanical alignment and differential thermal expansion that would occur if the print head were to be manufactured in several parts and assembled, the head can be manufactured from a single piece of silicon. Nozzles and ink channels are etched into the silicon. Heater elements are formed by evaporation of resistive materials, and subsequent photolithography using standard semiconductor manufacturing processes. 
     To reduce the large number of connections that would be required on a print head with thousands of nozzles, data distribution circuits and drive circuits can also be integrated on the print head. 
     The print head width is related to the number of colors, the arrangement of nozzles, the spacing between the nozzles, and the head area required for drive circuitry and interconnections. For a monochrome head, an appropriate width would be approximately 2 mm. For a process color head, an appropriate width would be approximately 5 mm. For a CC&#39;MM&#39;YK color print head, the appropriate head width is approximately 8 mm. The length of the head depends upon the application. Very low cost applications may use short heads, which must be scanned over a page. High speed applications can use fixed page-width monolithic or multi-chip print heads. A typical range of lengths for print heads is between 1 cm and 21 cm, though print heads longer than 21 cm are appropriate for high volume paper or fabric printing. 
     Example Head Layout 
     FIG. 20 shows one possible basic layout for a 6 color 800 dpi print head. The print head has six groups of nozzles 680 through 685. Many configurations of ink and nozzles are possible with this print head. One examples is to use the CC&#39;MM&#39;YK color model, in which case drops of two different optical densities are required for the cyan and magenta colors. The differing optical densities for cyan and magenta may be printed using the same ink formulation, but with differing drop volumes. The differing drop volumes may be achieved by using nozzles of different radii. An example of an assignment of inks to nozzle groups is the following configuration: 
     1) nozzle group 680 may be used to print cyan ink of 2/3 maximum optical density. The nozzle radius may be 8.2 μm; 
     2) nozzle group 681 may be used to print cyan ink of 1/3 maximum optical density. The nozzle radius may be 5.8 μm; 
     3) nozzle group 682 may be used to print magenta ink of 2/3 maximum optical density. The nozzle radius may be 8.2 μm; 
     4) nozzle group 683 may be used to print magenta ink of 1/3 maximum optical density. The nozzle radius may be 5.8 μm; 
     5) nozzle group 684 may be used to print yellow ink of maximum optical density. The nozzle radius may be 10 μm; and 
     6) nozzle group 685 may be used to print black ink of maximum optical density. The nozzle radius may be 10 μm. 
     In this case, the nozzle radii are approximately scaled to the square root of the ratio in required optical density, with the maximum optical density (resulting from full pixel coverage) being achieved with a nozzle radius of 10 μm. 
     Halftoning 
     The appearance of continuous tone operation is achieved by digital halftoning, preferably using either error diffusion or dispersed dot dithering. When the dot size is small in relation to the viewing distance, the human eye averages a region of dots to perceive an average color. 
     A printing resolution of 1,600 dpi using stochastic dispersed dot dithering or error diffusion can achieve high quality text and continuous tone images. However, 1,600 dpi can be difficult and expensive to achieve. Most commercial ink jet printers for the mass market operate at either 300 dpi, 360 dpi, or 400 dpi. The increase in resolution from 300 dpi to 1,600 dpi requires a 5.3 times decrease in nozzle spacing, and approximately 28 times decrease in drop volume, a 28 times increase in memory for page stores (where used), and requires a 28 times increase in drop ejection rate to maintain the same printing speed. 
     Operation at 600 dpi for office and home printing, and 800 dpi for quality commercial printing provides a good compromise. Text and line art has adequate quality at 600 dpi to 800 dpi that `jaggies` are not normally visible. Continuous tone images are adequate for most home uses and non-critical business use. However, even at 800 dpi, continuous tone images still suffer from `pepper` noise. `Pepper noise` results from the human eye&#39;s interpretation of the scarce arrangement of dark dots on white paper that results when near-white pixel intensities are halftoned. The `lightest` shade of black that can be depicted in most systems is represented by a pixel value of 1 out of a maximum of 255. When halftoned at 800 dpi, the result is an average of 3.9 black dots per square millimeter. At normal reading distances, the human eye fails to perceive this scattering of black dots as a grey tone, and instead resolved the individual dots. The resultant appearance is akin to pepper spread on the paper. 
     Ink System for Improved Image Quality 
     A system of inks for bi-level printing is disclosed. The system includes yellow and black ink spots of fill optical density, cyan, and magenta inks of 1/3 full optical density, and cyan, and magenta inks of 2/3 full optical density. When printed at 800 dpi, this ink system achieves a visual image quality which is superior to printing with four colors (cyan, magenta, yellow, and black) at 1,600 dpi. There is also a significant reduction in the visual effect of `pepper` noise. 
     It is not necessary to provide two intensities of yellow ink, as the luminance contribution of yellow is approximately 22% that of magenta, and 28% that of cyan, so a full optical density yellow ink has a lower luminance contribution than a 1/3 optical density cyan or magenta ink. It is also not normally necessary to provide two intensities of black ink, as black ink is typically not used in the light tones of images where pepper noise is important, and 800 dpi bi-level is generally adequate for text and line art. 
     Inks of differing intensities than 2/3 and 1/3 may be used. The advantage of 1/3 and 2/3 ink intensities is that the four possible combinations of presence or absence of high and low intensity ink drops of a particular color in a pixel results in linearly spaced optical densities as shown in the following table: 
     
         ______________________________________
2/3 intensity drop
            1/3 intensity drop
                        Resultant Optical Density
______________________________________
Absent      Absent      0
Absent      Present     1/3
Present     Absent      2/3
Present     Present     1
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     Obtaining good image quality when halftoning with multiple dot intensities requires caution. As well as the well known spatial artifacts which result from regularities or excessive noise in dither matrices or from error diffusion, there is a problem with visually `flat` regions in color regions which can be closely represented by one of the available optical densities. These regions are due to the human eye&#39;s perception of texture. The transition from a rough texture resulting from dithering between two optical densities, and the smooth texture resulting from the printing of only one optical density is often visible as an undesirable image artifact. The size of these image artifacts depends upon the original image content, and not upon the printing resolution. Therefore, these artifacts are still a problem when printing at high resolution of 800 dpi or more. 
     FIG. 21 shows a halftoned image of 800 dpi dots of four differing intensities magnified 288 times. FIG. 21 was generated by the following Mathematica program, which solves the image artifact problem described above: 
     matrixSize:=Length dither!; 
     overlap:=1/18; 
     multiLevelDither pixel -- ,x -- ,y --  !:=Which pixel&lt;=1/3-overlap, 
     lf 3 pixel&gt;dither  x,y!!/256,1/3,0!, 1/3-overlap&lt;pixel&lt;1/3+overlap, 
     lf 1-3*overlap&gt;dither  Mod x+8,matrixSize!+1,Mod y+8,matrixSize!+1!!/256, 1/3, 
     lf (1/(2*overlap))(pixel-(1/3-overlap))&gt;dither  x,y!!/256,2/3,0!!, 1/3+overlap&lt;pixel&lt;2/3-overlap, 
     lf 3(pixel-1/3)&gt;dither  x,y!!/256,2/3,1/3!, 2/3-overlap&lt;pixel&lt;2/3+overlap, 
     lf 1-3*overlap&gt;dither  Mod x+8,matrixSize!+1,Mod y+8,matrixSize!+1!!/256, 2/3, 
     lf (1/(2*overlap))(pixel-(2/3-overlap))&gt;dither  x,y!!/256,1,1/3!!, 2/3+overlap&lt;=pixel, 
     lf 3(pixel-2/3)&gt;dither  x,y!!/256,1,2/3!!; 
     Show DensityGraphics Table multiLevelDither monaLisa  256*(256-n)+m!!/256, Mod n,matrixSize!+1,Mod m,matrixSize!+1!, {n,1,256}{m, 1,256}!,Mesh→False!! 
     This algorithm is described in the Australian patent specifications lodged concurrently herewith, entitled `Improvements in bi-level color printing`; 
     In FIG. 21, the grey-scales are represented by halftoning using a 45° screen (clustered dot ordered dither) on a 300 dpi laser printer. This representation adds image artifacts (such as the 45 linear artifacts visible in FIG. 21), and obscures the improvements in reduction of pepper noise and in making the grey tones look `smoother` and less noisy. 
     FIG. 22 is a graph of the probability of ink drop presence in a pixel versus the pixel optical density. The pixel optical density is normalized to the range 0 (black) to 1 (white). The overlap parameter in the algorithm controls the width of the overlap region shown in FIG. 23(b). When overlap is 1/18th of the pixel optical density range (5.5%), the result is as shown in FIG. 21. An overlap of between 3% and 10% (depending upon printing resolution, paper type, and ink characteristics) gives optimum results. 
     Fluid dynamic simulations of head with multiple drop sizes 
     The actual diameter of a nozzle required to produce a certain drop volume in a printer depends upon many factors, including: 
     1) the drop separation method used; 
     2) the ink viscosity; 
     3) the ink surface tension, and temperature dependence of the ink surface tension; 
     4) the heater pulse energy; 
     5) the heater pulse duration; 
     6) the thermal coupling between the heater pulse and the ink; 
     7) the ambient temperature (of the print head substrate); 
     8) the method of compensation for ambient temperature changes; and 
     9) the ink pressure. 
     These parameters can be controlled accurately, and with sufficient stability to ensure consistent image quality. 
     To achieve the best possible image quality the ratio of optical density of the high optical density spot to the low optical density spot should be accurate. For binary weighted image formation the high optical density spots are twice the optical density of the low optical density spots. The required ratio of drop volumes to achieve an optical density ratio of 2:1 depends upon the ink and paper types chosen, but are close to 2:1 for combinations of ink and paper in common use. 
     Fluid dynamic simulations of nozzles which can be used for binary weighted drop sizes in the ratio of 4:2:1 have been performed. These simulations are of nozzles which are on the same print head, so the drive voltage, heater pulse duration, ambient temperature, ink characteristics, nozzle construction and materials, and other properties are held constant. 
     The only properties varied are the nozzle diameter, the ink pressure, and the amount of energy delivered to the heater. The amount of energy supplied to the heater can be simply varied by placing a resistor in series with the nozzle heater. This resistor can be fabricated as an extended length of heater material a short distance from the nozzle. 
     The nozzle radii used are 10 μm for the main ink drop, 7 μm for a drop with approximately half the volume, and 5 μm for a drop with approximately one quarter the volume. The head layout shown in FIG. 10 uses only the 10 μm and 7 μm radius nozzles. It is not necessary for the nozzle radii to be exactly adjusted for the desired drop size, as the ink pressure and other parameters can be altered to adjust the drop size without requiring the fabrication of new print heads. 
     FIGS. 23(a) to 23(f) show summarized results of fluid dynamic simulations performed using the FIDAP simulation software. In each case the simulation is over a duration of 100 μs, in 0.1 μs steps. The nozzle tip is cylindrical, and the ambient temperature is 30° C. At the beginning of the simulation the ink meniscus is near its quiescent position, and all velocities are zero. A time varying power pulse is applied to the heater, starting at 20 μs, for a duration of 18 μs. The pulse starts at 20 μs to allow time for the ink meniscus to reach the quiescent position before the drop selection pulse. 
     Only the drop selection process is modeled in these simulations. The drop separation process may be proximity, electrostatic, or other means. Separation of the selected drop from unselected drops relies upon a physical difference in meniscus position between the selected drop and the unselected drops. An axial difference of 15 μm between the position of the centre of the meniscus before and after the drop selection pulse is adequate for drop separation. 
     FIGS. 23(a), 23(c), and 23(e) are graphs of the position of the centre of the meniscus versus time for nozzle radii of 10 μm, 7 μm, and 5 μm respectively. Visual comparison of these graphs should take into account the variation of vertical scale between the graphs. The important characteristic is the attainment of a meniscus position of approximately 20 μm, at which point the drop separation means (not simulated in these simulations) can ensure that selected drops are separated from the body of ink and transferred to the recording medium. Oscillations of the meniscus after the drop selection pulse is removed are due to the initial non-spherical nature of the exuded drop: the drop oscillates between an initial prolate form, through a spherical form, to an oblate form, and back again. These oscillations are unimportant, as the drop separation means becomes the dominant determining factor of ink meniscus position after drop selection. 
     FIGS. 23(b), 23(d), and 23(f) are plots of the meniscus shape at various instants for nozzle radii of 10 μm, 7 μm, and 5 μm respectively. The meniscus positions are shown at 2 μs intervals from the start of the drop selection pulse at 20 μs to 4 μs after the end of the 18 μs pulse, at 42 μs. 
     In FIGS. 23(b), 23(d), and 23(f), 100 is ink, 101 is the silicon substrate, 102 is SiO 2 , 103 marks the position of one side of the annular heater, 108 is a Si 3  N 4  passivation layer and 109 is a hydrophobic surface coating. Although the plots are labeled `Temperature contour plot`, there are no temperature contours shown. 
     It can be seen from the simulation results shown in FIG. 23 that the drop volume varies with nozzle radius, as would be expected. The relationship between drop volume and nozzle radius is not linear, and the drop volume increases with approximately the square of the nozzle radius. 
     Nozzles of differing radii can readily and accurately be fabricated on the same silicon substrate using well known semiconductor and micromechanical fabrications processes. The fabrication process for a print head containing of nozzles of various radii can be identical to the fabrication process of a print head with only one nozzle radius. Multiple nozzles of differing radii can be achieved by altering only the mask patterns for the appropriate lithographic steps. 
     The foregoing describes several preferred embodiments of the present invention. Modifications, obvious to those skilled in the art, can be made thereto without departing from the scope of the invention.