Abstract:
A pattern forming method includes the step of ejecting droplets of a liquid containing a functional component, from nozzles of an inkjet recording head onto a surface of a substrate in one direction in sequence so as to form a linear pattern on the surface of the substrate, wherein: the inkjet recording head is controlled in such a manner that 
             p   ≤       π   ⁢           ⁢   d       6   ⁢     (       θ       sin   2     ⁢   θ       -       cos   ⁢           ⁢   θ       sin   ⁢           ⁢   θ         )     ⁢       {     tan   ⁢     θ   2     ⁢     (     3   +       tan   2     ⁢     θ   2         )       }       -     2   3                   
is satisfied where d denotes a diameter of the droplets of the liquid before depositing on the surface of the substrate, θ denotes a contact angle of the droplets of the liquid with respect to the substrate, and p denotes a dot pitch of the droplets of the liquid that are adjacently deposited on the surface of the substrate, and the droplets of the liquid contain a volatile solvent with volume ratio not less than
 
     
       
         
           
             
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Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     The present application claims priority from Japanese Patent Application No. 2008-244234, filed Sep. 24, 2008, the contents of which are herein incorporated by reference in their entirety. 
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to a pattern forming method, and in particularly to a pattern forming method forming a linear pattern on a surface of a substrate with an ink jet head. 
     2. Description of the Related Art 
     Japanese Patent Application Publication No. 2003-80694 discloses a method for ejecting a liquid containing a functional component onto a substrate by means of inkjet so as to form a functional film pattern, wherein the liquid is ejected onto the substrate with a film forming surface having a contact angle falling within a range from 30 degrees to 60 degrees in such a manner that the liquid overlaps with a range of 1% or more and 10% or less of the diameter on the substrate, thereby forming conducting layer wiring. 
     When a liquid is ejected by means of inkjet so as to form a line on a substrate which the ejected liquid does not penetrate through (does not permeate), a bulge (a bunch) may be made in a portion of the line or jaggies may be made rather than a line having a smoothly linear (in the shape of a straight line) contour, depending on the interval or the amount of the liquid (liquid droplets) ejected on the substrate. 
     The method disclosed in Japanese Patent Application Publication No. 2003-80694 tries to avoid the braking or short-circuit of a conducting film wire. However, in cases of a pattern forming apparatus of an inkjet type, the dot pitch varies according to the accuracy of the landing positions (ejection direction and ejection volume) of ink ejected from an inkjet head and the accuracy of the position of a conveyed substrate. Therefore, it is difficult for the method disclosed in Japanese Patent Application Publication No. 2003-80694 to form lines with a uniform width in stable fashion. 
     SUMMARY OF THE INVENTION 
     It is an object of the present invention to provide a pattern forming method based on an inkjet system to form (make) a line-shape pattern with uniform width in a stable fashion. 
     In order to attain an object described above, one aspect of the present invention is directed to a pattern forming method comprising the step of ejecting droplets of a liquid containing a functional component, from nozzles of an inkjet recording head onto a surface of a substrate in one direction in sequence so as to form a linear pattern on the surface of the substrate, wherein: the inkjet recording head is controlled in such a manner that 
             p   ≤       π   ⁢           ⁢   d       6   ⁢     (       θ       sin   2     ⁢   θ       -       cos   ⁢           ⁢   θ       sin   ⁢           ⁢   θ         )     ⁢       {     tan   ⁢     θ   2     ⁢     (     3   +       tan   2     ⁢     θ   2         )       }       -     2   3                   
is satisfied where d denotes a diameter of the droplets of the liquid before depositing on the surface of the substrate, θ denotes a contact angle of the droplets of the liquid with respect to the substrate, and p denotes a dot pitch of the droplets of the liquid that are adjacently deposited on the surface of the substrate, and the droplets of the liquid contain a volatile solvent with volume ratio not less than
 
     
       
         
           
             
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                 1 
                 - 
                 
                   
                     6 
                     ⁢ 
                     
                         
                     
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               ] 
             
             × 
             100 
             ⁢ 
             
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               . 
             
           
         
       
     
     Desirably, time interval from ejection of one of the droplets of the liquid that are to be adjacently deposited on the surface of the substrate until ejection of another one of the droplets of the liquid that are to be adjacently deposited on the surface of the substrate, is set to be 1 millisecond or less. 
     Desirably, the pattern forming method further comprises the step of ejecting droplets of the liquid from the nozzles onto a preliminary area other than the substrate, preliminary to ejection of the droplets of the liquid onto the surface of the substrate from the nozzles, wherein the ejection of the droplets of the liquid onto the surface of the substrate to form the linear pattern is started within one second after ejection of the droplets of the liquid onto the preliminary area. 
     According to the present invention, the dot pitch and the volume ration of a volatile solvent of a liquid are controlled in accordance with the above formulas, and thereby occurrence of jaggies or bulges can be prevented. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The nature of this invention, as well as other objects and benefits thereof, will be explained in the following with reference to the accompanying drawings, in which like reference characters designate the same or similar parts throughout the figures and wherein: 
         FIG. 1  is an oblique perspective view illustrating a pattern forming device related to a first embodiment of the present invention; 
         FIG. 2  is a plan view illustrating a surface in which nozzles of a recording head are formed; 
         FIG. 3  is a cross-sectional diagram illustrating an ejection element; 
         FIG. 4  is a block diagram illustrating a control system of a pattern forming apparatus; 
         FIG. 5  is a diagram illustrating steps of a scanning control for making a pattern L by causing the recording head and a substrate to move relatively in an x direction; 
         FIGS. 6A and 6B  are views (including cross-sectional diagrams and plan views) illustrating the changing state over time of liquid droplets ejected onto the surface of the substrate; 
         FIG. 7  is a plan view illustrating a positional example of a preliminary ejection region; 
         FIG. 8  is a plan view illustrating another positional example of the preliminary ejection region; 
         FIG. 9  is a plan view illustrating another positional example of the preliminary ejection region; and 
         FIG. 10  is a flowchart indicating steps for a pattern forming. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Desirable embodiments of a pattern forming method according to embodiments of the present invention are described below with reference to drawings. 
     Configuration of Pattern Forming Device 
       FIG. 1  is an oblique perspective view illustrating a pattern forming device related to a first embodiment of the present invention. 
     As illustrated in  FIG. 1 , the pattern forming device (ink jet recording device)  10  of the present embodiment includes an ink jet head (referred to hereinbelow as “recording head”)  12  and a support plate  14 . 
     The recording head  12  is a line-type of recording head in which a plurality of nozzles  22  are aligned in the main scanning direction (y direction in  FIG. 1 ). 
     A substrate  16  that is an object onto which a liquid is ejected from the recording head  12 , is placed on the support plate  14 . The support plate  14  is supported so as to maintain a constant clearance gap with the recording head  12 , and is capable of scanning (moving) in the sub-scanning direction (x direction in  FIG. 1 ). 
     By causing the recording head  12  to eject liquid droplets while causing the support plate  14  to move in the x direction, the liquid can be deposited on the entire surface of the imaging region of the substrate  16 . 
       FIG. 2  is a plan view illustrating a surface where the nozzles of the recording head  12  are formed. 
     As illustrated in  FIG. 2 , the recording head  12  has a structure in which ejection elements  20  (see  FIG. 3 ), each having a nozzle  22  and a pressure chamber  24 , are arranged substantially equidistantly in the main scanning direction (y direction) substantially perpendicular to the sub-scanning direction (x direction). 
     A nozzle diameter of the recording head  12  is, for example, 35 μm and the distance between the centers of adjacent liquid droplets on the substrate  16  (nozzle pitch) is, for example, 254 μm (100 npi (nozzles per inch)). The recording head  12  has a jet-out period (ejection cycle) of 1 kHz, and droplets can be continuously jetted out at a head scanning (moving) rate of 0.1 msec. 
       FIG. 3  is a cross-sectional diagram illustrating an ejection element  20 . 
     The pressure chambers  24  provided correspondingly to the nozzles  22  have a substantially square shape in a plan view thereof. An outflow port leading to the corresponding nozzle  22  is provided in one inner corner on a diagonal line of each pressure chamber  24 , and a liquid supply port  26  leading to the corresponding pressure chamber  24  is provided in the other corner. In addition to the aforementioned square shape, the pressure chambers  24  can have a polygonal shape such as tetragonal shape (rhomboidal shape, rectangular shape), pentagonal shape, or hexagonal shape, and also round shape or elliptical shape. 
     As illustrated in  FIG. 3 , the pressure chambers  24  of the ejection elements  20  are linked to a common channel  28  via the supply ports  26 . The common channel  28  is linked to a tank (not illustrated in the figure) that serves as a liquid supply source, and the liquid supplied from the tank is distributed and supplied to the pressure chambers  24  via the common channel  28 . 
     Piezoelectric elements  34  provided with individual electrodes  32  respectively are bonded to a pressure plate (oscillation plate (diaphragm) also serving as a common electrode)  30  constituting parts of the surfaces (top surface in  FIG. 3 ) of the pressure chambers  24 . For example, a piezoelectric material such as lead zirconium titanate (PZT) or barium titanate can be used as a material for the piezoelectric elements  34 . 
     Where a drive signal is applied between an individual electrode  32  and the common electrode, the corresponding piezoelectric element  34  is deformed and the volume of the corresponding pressure chamber  24  changes. As a result, the pressure inside the pressure chamber  24  changes, thereby ejecting a droplet from the corresponding nozzle  22 . After the droplet has been ejected, the displacement of the piezoelectric element  34  returns to the original state, and the pressure chamber  24  is refilled with new liquid from the common channel  28  via the supply port  26 . 
     In the present embodiment, a system is employed by which ink is pressurized by deformation of the piezoelectric elements  34 , but actuators of other systems (for example, a thermal system) may be also employed. 
       FIG. 4  illustrates a block diagram illustrating a control system of the pattern forming device  10 . 
     The pattern forming device  10  includes a communications interface  40 , a system controller  42 , a memory  46 , a motor driver  48 , a heater driver  52 , an ejection control unit  56 , a buffer memory  58  and a head driver  60 . 
     The communications interface  40  functions as an interface unit receiving ejection date sent from a host computer  80 . As the communications interface  40 , USB (Universal Serial Bus), IEEE1394, Ethernet (registered trademark), wireless network, other serial networks, parallel interface such as Centronics may be used. Further, a buffer memory may be mounted on this portion in order to speed up the communications. 
     The system controller  42  includes a CPU (central processing unit) and the peripheral circuits, and functions as a control unit controlling each section of the pattern forming device  10 . This system controller  42  controls the communications with the host computer  80 , controls read-in and writing-in the memory  46 , generates control signals to control the motors  50  of the conveyance drive system and the heater  54 , and performs other control. 
     Control programs of the pattern forming device  10  are stored in a program storage unit  44 . The system controller  42  reads out various sorts of control programs stored in the program storage unit  44  and performs the read-out programs in a proper manner. 
     The memory  46  is a memory device used as a temporary storage area of date and a working area when the system controller  42  carries out various sorts of calculations. As the memory  46 , a memory formed from a semiconductor element, or a magnetic medium such as a hard disk may be used. 
     The motor  50  drives a driving system for driving at least one of the recording head  12  and the support plate  14  in  FIG. 1  so as to cause the recording head  12  and the support plate  14  to move relatively. The motor driver  48  drives the motor in accordance with control commands from the system controller  42 . 
     The heater driver  52  drives the heater  54  in accordance with control signals from the system controller  42 . The heater  54  includes heaters for adjusting temperature provided on parts of the pattern forming device  10 . 
     The ejection date sent from the host computer  80  is sent into the pattern forming device  10  via the communications interface  40 , and is temporarily stored in the memory  46 . 
     The ejection control unit  56  has a signal processing function to carry out various processing and correction to generate signals for controlling the ejection from the ejection data stored in the memory  46  in accordance with the control by the system controller  42 , and supplies the generated print control signals (dot data) to the head driver  60 . Required signal processing is carried out in the ejection control unit  56 , and the ejection amount and the ejection timing of the liquid from the head  12  are controlled via the head driver  60 , on the basis of the ejection data. 
     The head driver  60  drives the piezoelectric elements  34  of the recording head  12  on the basis of the ejection data supplied from the ejection control unit  56 . The head driver  60  may include a feedback control system to keep constant drive conditions of the head. 
     The ejection control unit  56  is provided with a buffer memory  58 ; and ejection data, parameters, and other data are temporarily stored in the buffer memory  58  when the ejection data is processed in the ejection control unit  56 . 
     It is possible to use the buffer memory  58  as the memory  46 . It is also possible to integrate the ejection control unit  56  and the system controller  42  in such a manner that both the ejection control unit  56  and the system controller  42  are realized by one processor. 
     Although not illustrated in the drawings, the pattern forming apparatus  10  comprises a supply system for supplying liquid to the recording head  12  and a maintenance unit which carries out maintenance of the recording head  12 . 
     Liquid Ejection Conditions 
       FIG. 5  is a diagram illustrating a schematic view of a scanning control procedure when recording a pattern L by scanning (moving) the recording head  12  and the substrate  16  relatively in the x direction. 
     As illustrated in  FIG. 5 , in the present embodiment, a linear (for example, a straight line) pattern L is described by ejecting a liquid (ink) formed by mixing a functional component (for example, silver nano-particles) in a volatile solvent (for example, water or tetradecane) while scanning (moving) the recording head  12  and the substrate  16  relatively in the x direction. In this case, if the interval (dot pitch p) between the liquid droplets D ejected onto the substrate  16  is large, then jaggies become liable to occur. Furthermore, if the ratio of the volatile solvent contained in the liquid is large, then bulges become liable to occur. Below, the conditions with respect to the dot pitch p and the ratio of solvent in the liquid in order to prevent the occurrence of jaggies and bulges are determined. 
     Liquid Ejection Condition 1 (Dot Pitch p) 
       FIGS. 6A and 6B  are a diagram illustrating a schematic and plan view of temporal change in liquid droplets ejected onto the surface of a substrate  16 . 
     As illustrated in  FIG. 6A , droplets D 1   eqm  which have been ejected from the recording head  12  and have landed on the surface of the substrate  16  have a substantially round shape at the start of landing and makes contact with an adjacent droplet. As illustrated in  FIG. 6B , each of the droplets D wets and spreads to form a pattern L. 
     Here, it is supposed that the substrate  16  is a medium into which the droplets D do not penetrate (permeate), and the volume of the droplets is the same before and after landing on the substrate  16 . Furthermore, it is supposed that the angle of contact θ (rad) of the droplet D with respect to the substrate  16  is uniform. 
     In this case, the ratio β eqm  between the diameter d eqm  (μm) of a droplet D 1   eqm  after landing on the substrate  16  and the diameter d (μm) of the droplet D before landing (the rate of spreading) is expressed by Formula (1) below. Here, the diameter d is the diameter when the droplet D before landing is converted to a sphere. 
     
       
         
           
             
               
                 
                   
                     β 
                     eqm 
                   
                   = 
                   
                     
                       
                         d 
                         eqm 
                       
                       d 
                     
                     = 
                     
                       2 
                       ⁢ 
                       
                         
                           { 
                           
                             
                               ( 
                               
                                 tan 
                                 ⁢ 
                                 
                                   θ 
                                   2 
                                 
                               
                               ) 
                             
                             ⁢ 
                             
                               ( 
                               
                                 3 
                                 + 
                                 
                                   
                                     tan 
                                     2 
                                   
                                   ⁢ 
                                   
                                     θ 
                                     2 
                                   
                                 
                               
                               ) 
                             
                           
                           } 
                         
                         
                           - 
                           
                             1 
                             3 
                           
                         
                       
                     
                   
                 
               
               
                 
                   Formula 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     1 
                     ) 
                   
                 
               
             
           
         
       
     
     If the width of the pattern L is taken as w (μm), then the cross-sectional surface area S 1  (μm 2 ) of the droplet D 2   eqm  in  FIG. 6B  in a section taken in a plane parallel to the zy plane passing through the center of the droplet D 2   eqm  is expressed by Formula (2) below. 
     
       
         
           
             
               
                 
                   
                     S 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     1 
                   
                   = 
                   
                     
                       1 
                       4 
                     
                     ⁢ 
                     
                       
                         w 
                         2 
                       
                       ⁡ 
                       
                         ( 
                         
                           
                             θ 
                             
                               
                                 sin 
                                 2 
                               
                               ⁢ 
                               θ 
                             
                           
                           - 
                           
                             
                               cos 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               θ 
                             
                             
                               sin 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               θ 
                             
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   Formula 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     2 
                     ) 
                   
                 
               
             
           
         
       
     
     Therefore, if the distance (nozzle pitch) between the centers of adjacently positioned droplets on the substrate  16  is taken as p (μm), then the volume Va (μm 3 ) of the droplet D 2   eqm  is expressed by Formula (3) below. 
     
       
         
           
             
               
                 
                   Va 
                   = 
                   
                     
                       1 
                       4 
                     
                     ⁢ 
                     
                       w 
                       2 
                     
                     ⁢ 
                     
                       p 
                       ⁡ 
                       
                         ( 
                         
                           
                             θ 
                             
                               
                                 sin 
                                 2 
                               
                               ⁢ 
                               θ 
                             
                           
                           - 
                           
                             
                               cos 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               θ 
                             
                             
                               sin 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               θ 
                             
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   Formula 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     3 
                     ) 
                   
                 
               
             
           
         
       
     
     On the other hand, since the diameter of the droplet before landing is d, then the volume Vb (μm 3 ) of the droplet D before landing is expressed by Formula (4) below. 
     
       
         
           
             
               
                 
                   Vb 
                   = 
                   
                     
                       1 
                       6 
                     
                     ⁢ 
                     π 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       d 
                       3 
                     
                   
                 
               
               
                 
                   Formula 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     4 
                     ) 
                   
                 
               
             
           
         
       
     
     From Formula 1 above, the volume of the droplet D remains unchanged, before and after landing. If Va=Vb is solved with respect to the width w, then Formula (5) below is obtained. 
     
       
         
           
             
               
                 
                   w 
                   = 
                   
                     
                       
                         2 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         π 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           d 
                           3 
                         
                       
                       
                         3 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           p 
                           ⁡ 
                           
                             ( 
                             
                               
                                 θ 
                                 
                                   
                                     sin 
                                     2 
                                   
                                   ⁢ 
                                   θ 
                                 
                               
                               - 
                               
                                 
                                   cos 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   θ 
                                 
                                 
                                   sin 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   θ 
                                 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   Formula 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     5 
                     ) 
                   
                 
               
             
           
         
       
     
     Here, since w≧d eqm =β eqm d, then if Formula (5) is solved by taking the dot pitch p as a variable, the conditional Formula (6) for the dot pitch p is obtained. 
     
       
         
           
             
               
                 
                   
                     p 
                     ≤ 
                     
                       
                         2 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         π 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         d 
                       
                       
                         3 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           
                             β 
                             eqm 
                             2 
                           
                           ⁡ 
                           
                             ( 
                             
                               
                                 θ 
                                 
                                   
                                     sin 
                                     2 
                                   
                                   ⁢ 
                                   θ 
                                 
                               
                               - 
                               
                                 
                                   cos 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   θ 
                                 
                                 
                                   sin 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   θ 
                                 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                   = 
                   
                     
                       π 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       d 
                     
                     
                       6 
                       ⁢ 
                       
                         ( 
                         
                           
                             θ 
                             
                               
                                 sin 
                                 2 
                               
                               ⁢ 
                               θ 
                             
                           
                           - 
                           
                             
                               cos 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               θ 
                             
                             
                               sin 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               θ 
                             
                           
                         
                         ) 
                       
                       ⁢ 
                       
                         
                           { 
                           
                             tan 
                             ⁢ 
                             
                               θ 
                               2 
                             
                             ⁢ 
                             
                               ( 
                               
                                 3 
                                 + 
                                 
                                   
                                     tan 
                                     2 
                                   
                                   ⁢ 
                                   
                                     θ 
                                     2 
                                   
                                 
                               
                               ) 
                             
                           
                           } 
                         
                         
                           - 
                           
                             2 
                             3 
                           
                         
                       
                     
                   
                 
               
               
                 
                   Formula 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     6 
                     ) 
                   
                 
               
             
           
         
       
     
     By controlling the dot pitch p so as to satisfy the condition in Formula (6) above, it is possible to prevent the occurrence of raggedness (jaggies) in the outline of the pattern L. 
     Liquid Ejection Condition 2 (Condition Relating to Ratio of Solvent (Volatile Component) in Liquid) 
     Next, the condition relating to the ratio of the solvent (volatile component) in the liquid will be described. Here, the liquid ejected onto the substrate  16  is taken to be, for example, a liquid (ink) obtained by dispersing silver nano-particles in a solvent of water or tetradecane (both of which have volatile properties). 
     As described above, when a pattern L is described by ejecting liquid onto the substrate  16 , if the amount of solvent (liquid component) in the pattern L is too great with respect to the line width w, then bulges are liable to occur. In order to prevent the occurrence of bulges, the amount of solvent on the substrate  16  should be reduced to a level whereby bulges do not occur when the solvent is evaporated off after the droplet D has landed on the substrate  16 . More specifically, the amount of solvent is set in such a manner that the diameter d eqm  (μm) of the droplet D after wetting and spreading on the substrate  16  and after the solvent has evaporated off is equal to the line width w (μm). If w=d eqm , then the volume V 1  (μm 3 ) of the droplet D 2   eqm  after wetting and spreading and evaporation of the solvent is represented by Formula (7) below. 
     
       
         
           
             
               
                 
                   
                     V 
                     1 
                   
                   = 
                   
                     p 
                     ⁢ 
                     
                       { 
                       
                         
                           
                             θ 
                             ⁡ 
                             
                               ( 
                               
                                 
                                   d 
                                   eqm 
                                 
                                 
                                   2 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   sin 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   θ 
                                 
                               
                               ) 
                             
                           
                           2 
                         
                         - 
                         
                           
                             
                               d 
                               eqm 
                               2 
                             
                             ⁢ 
                             cos 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             θ 
                           
                           
                             4 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             sin 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             θ 
                           
                         
                       
                       } 
                     
                   
                 
               
               
                 
                   Formula 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     7 
                     ) 
                   
                 
               
             
           
         
       
     
     On the other hand, since the diameter of the droplet before landing is d, then the volume V 2  (μm 3 ) of the droplet D before landing is expressed by Formula (8) below. 
     
       
         
           
             
               
                 
                   
                     V 
                     2 
                   
                   = 
                   
                     
                       4 
                       3 
                     
                     ⁢ 
                     
                       
                         π 
                         ⁡ 
                         
                           ( 
                           
                             d 
                             2 
                           
                           ) 
                         
                       
                       3 
                     
                   
                 
               
               
                 
                   Formula 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     8 
                     ) 
                   
                 
               
             
           
         
       
     
     Consequently, the ratio of the volatile solvent contained in the liquid (volume ratio) {(V 2 −V 1 )/V 2 ×100(%)} is expressed by Formula (9) below. 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             
                               
                                 V 
                                 2 
                               
                               - 
                               
                                 V 
                                 1 
                               
                             
                             
                               V 
                               2 
                             
                           
                           × 
                           100 
                           ⁢ 
                           % 
                         
                         = 
                         
                           
                             [ 
                             
                               1 
                               - 
                               
                                 
                                   p 
                                   ⁢ 
                                   
                                     { 
                                     
                                       
                                         
                                           θ 
                                           ⁡ 
                                           
                                             ( 
                                             
                                               
                                                 d 
                                                 eqm 
                                               
                                               
                                                 2 
                                                 ⁢ 
                                                 
                                                     
                                                 
                                                 ⁢ 
                                                 sin 
                                                 ⁢ 
                                                 
                                                     
                                                 
                                                 ⁢ 
                                                 θ 
                                               
                                             
                                             ) 
                                           
                                         
                                         2 
                                       
                                       - 
                                       
                                         
                                           
                                             d 
                                             eqm 
                                             2 
                                           
                                           ⁢ 
                                           cos 
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           θ 
                                         
                                         
                                           4 
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           sin 
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           θ 
                                         
                                       
                                     
                                     } 
                                   
                                 
                                 
                                   
                                     4 
                                     3 
                                   
                                   ⁢ 
                                   
                                     
                                       π 
                                       ⁡ 
                                       
                                         ( 
                                         
                                           d 
                                           2 
                                         
                                         ) 
                                       
                                     
                                     3 
                                   
                                 
                               
                             
                             ] 
                           
                           × 
                           100 
                           ⁢ 
                           % 
                         
                       
                     
                   
                   
                     
                       
                         = 
                         
                           
                             [ 
                             
                               1 
                               - 
                               
                                 
                                   
                                     
                                       
                                         6 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         
                                           p 
                                           ⁡ 
                                           
                                             ( 
                                             
                                               
                                                 θ 
                                                 
                                                   
                                                     sin 
                                                     2 
                                                   
                                                   ⁢ 
                                                   θ 
                                                 
                                               
                                               - 
                                               
                                                 
                                                   cos 
                                                   ⁢ 
                                                   
                                                       
                                                   
                                                   ⁢ 
                                                   θ 
                                                 
                                                 
                                                   sin 
                                                   ⁢ 
                                                   
                                                       
                                                   
                                                   ⁢ 
                                                   θ 
                                                 
                                               
                                             
                                             ) 
                                           
                                         
                                       
                                     
                                   
                                   
                                     
                                       
                                         
                                           { 
                                           
                                             tan 
                                             ⁢ 
                                             
                                               θ 
                                               2 
                                             
                                             ⁢ 
                                             
                                               ( 
                                               
                                                 3 
                                                 + 
                                                 
                                                   
                                                     tan 
                                                     2 
                                                   
                                                   ⁢ 
                                                   
                                                     θ 
                                                     2 
                                                   
                                                 
                                               
                                               ) 
                                             
                                           
                                           } 
                                         
                                         
                                           - 
                                           
                                             2 
                                             3 
                                           
                                         
                                       
                                     
                                   
                                 
                                 
                                   π 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   d 
                                 
                               
                             
                             ] 
                           
                           × 
                           100 
                           ⁢ 
                           % 
                         
                       
                     
                   
                 
               
               
                 
                   Formula 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     9 
                     ) 
                   
                 
               
             
           
         
       
     
     By setting the ratio of the volume of volatile solvent in the liquid to a value equal to or greater than that expressed by Formula (9) above, it is possible to prevent the occurrence of bulging. 
     Liquid Ejection Condition 3 (Interval Between Droplet Ejection Timings) 
     Next, the interval between droplet ejection timings will be described. Table 1 indicates the stability of the line width w when lines were recorded at different values of the number of droplets D ejected per second (i.e. printing frequency), and different dot pitches, taking droplet diameter as d=26.0 (μm), d eqm =55.5 (μm) and the angle of contact as θ=30(°) (in other words, under conditions which satisfy Formulas (6) and (9) above). 
     
       
         
               
               
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 1 
               
             
             
               
                   
               
               
                 Printing 
                   
                   
               
               
                 Frequency 
                 Dot Pitch [μm] 
               
             
          
           
               
                 [Hz] 
                 20 
                 30 
                 40 
                 50 
               
               
                   
               
             
          
           
               
                 10 
                 Poor 
                 Poor 
                 Poor 
                 Poor 
               
               
                 1000 
                 Good 
                 Good 
                 Average 
                 Poor 
               
               
                 10000 
                 Good 
                 Good 
                 Good 
                 Poor 
               
               
                   
               
             
          
         
       
     
     In Table 1, a case where the line width w of the printed line is stable (for example, a case where the amount of variation in the line width w (for example, the difference between the maximum value and minimum value of the line width w per unit length) is less than a prescribed value) is indicated as “Good”, a case where the amount of variation in the line width w is equal to or greater than the prescribed value but the amount of variation is not as large as a “Poor” case is indicated as “Average”, and a case where the amount of variation in the line width w is greater than the maximum value of the amount of variation in an “Average” case is indicated as “Poor”. According to the experimental results in Table 1, if the printing frequency was equal to or greater than 1000 Hz, then the line width w was stable and results which are free of the occurrence of bulges and jaggies were obtained. 
     Consequently, the interval from printing the n th  droplet until printing the (n+1) th  droplet is set to be 1 millisecond or less. By adopting such an interval, it is possible to prevent the combination on the substrate  16  during printing of portions which are in a balanced state (a state where the droplets D have wet and spread and the shape of the droplets D is stable) and portions which are in an unbalanced state (a state during the wetting and spreading of the droplets D and before the shape of the droplets D has become stable). Consequently, a balanced state is achieved and it becomes possible to obtain recorded lines of uniform width, without the formation of large pools of droplets D in an unbalanced state or thickening of a portion of the pattern L. 
     Liquid Ejection Condition 4 (Preliminary Ejection) 
     Next, preliminary ejection before the start of printing will be described. 
     In a pattern forming apparatus of an inkjet type, if a state where ink is not ejected has continued for a prescribed period of time or longer, the solvent in the ink adhering to the vicinity of the nozzles  22  of the recording head  12  evaporates off, the density of the silver nano-particles of the ink becomes higher and the viscosity becomes higher. If this occurs, then when a piezoelectric element  34  (see  FIG. 3 ) is operated, a liquid ejection error or ejection failure occurs. 
     Consequently, in the present embodiment, ink of high viscosity which is adhering to the vicinity of the nozzles  22  is removed by carrying out preliminary ejection (“dummy ejection”, “purging”, “spit ejection”) in order to eject ink onto a prescribed preliminary ejection region before the start of printing. Furthermore, by carrying out preliminary ejection also after the soiling on the nozzle surface has been wiped by a wiper (not illustrated) of a cleaning blade which is provided as a nozzle surface wiping device, infiltration of foreign matter into the nozzles due to the wiping operation of the wiper is prevented. 
     If the preliminary ejection described above is carried out, desirably, printing is started within one second after preliminary ejection. By this means, it is possible to print lines of a stable uniform width. 
     Carrying out preliminary ejection onto the substrate  16  may possibly cause problems in the product, and therefore it is desirable to provide a preliminary ejection region in the pattern forming apparatus  10 . In order to shorten the time period from the carrying out of preliminary ejection until the start of printing, it is desirable that the preliminary ejection region should be located in the whole of the periphery of the substrate  16  or the print start position ST. 
       FIG. 7  to  FIG. 9  are plan diagrams illustrating examples of the positioning of the preliminary ejection region. 
     In the example illustrated in  FIG. 7 , the recording head  12  is movable in the xy directions and a preliminary ejection region  100  is provided in a region surrounding the substrate  16  on the substrate  16  mounting surface of a support plate  14 . 
     When preliminary ejection is carried out, the perpendicular line L 1  of shortest length of lines connecting to the inner circumference of the preliminary ejection region  100  from the print start position (point) ST of the substrate  16  is selected. Preliminary ejection is carried out at a point (preliminary ejection position) PR on the line obtained by extending the vertical pattern L 1  toward the preliminary ejection region  100  side. The preliminary ejection position PR is set at a position where the distance between the preliminary ejection position PR and the substrate  16  is longer than the predicted radius of the droplet when the liquid ejected by preliminary ejection has landed on the preliminary ejection region  100 . Thereupon, after the end of preliminary ejection, the recording head  12  is moved to the printing start position ST following the perpendicular pattern L 1 . By this means, it is possible to shorten the time from the end of preliminary ejection until the start of printing at the printing start position ST. 
     In the examples illustrated in  FIG. 8  and  FIG. 9 , a preliminary ejection region  100 A is provided on either side of the substrate  16 . In the example illustrated in  FIG. 8 , the recording head  12  is movable in the ±y direction and the substrate  16  is movable in the ±x direction. Furthermore, in the example illustrated in  FIG. 9 , the recording head  12  is movable in the xy directions and the substrate  16  is movable in the +x direction. 
     In the examples illustrated in  FIG. 8  and  FIG. 9 , by setting the preliminary ejection similarly to  FIG. 7 , it is possible to shorten the time period from the end of preliminary ejection until the start of printing at the printing start position ST. 
     It has been confirmed that the phenomenon of large swelling of a portion of the line occurs over a time scale of 2 to 8 seconds. Therefore, by controlling the heater  54 , or the like, to solidify the droplets D on the substrate  16  within one second after landing, it is also possible to prevent the occurrence of bulges. 
     Pattern Forming Procedure 
     Next, steps for pattern forming are described by referring to the flowchart in  FIG. 10 . 
     Firstly, the system controller  42  obtains the co-ordinates of the printing start position ST on the substrate  16  and calculates the co-ordinates of the point where preliminary ejection is possible which is closest to the printing start position ST in the preliminary ejection region  100  (the preliminary ejection position PR). The system controller  42  outputs a control signal to the head driver  60 , thereby moving the recording head  12  to the preliminary ejection position PR (step S 10 ). 
     Next, preliminary ejection is carried out (step S 12 ), the recording head  12  is moved to the printing start position ST (step S 14 ) and printing is started (step S 16 ). Thereupon, printing of a pattern L is carried out using a dot pitch which satisfies the condition in Formula (6) above and at a droplet ejection interval of 1 millisecond or less (step S 18 ). 
     Here, the system controller  42  controls the recording head  12  and the support plate  14  in such a manner that the processes from step S 12  to step S 16  are completed within one second. 
     According to the present embodiment, it is possible to prevent the occurrence of jaggies and bulges by controlling the dot pitch p so as to satisfy the condition in Formula (6) above, by setting the ratio of the volume of volatile solvent in the liquid to a value equal to or greater than that expressed by Formula (9) above, and by setting the droplet ejection time interval and the time interval from preliminary ejection to a prescribed value or less. 
     It should be understood that there is no intention to limit the invention to the specific forms disclosed, but on the contrary, the invention is to cover all modifications, alternate constructions and equivalents falling within the spirit and scope of the invention as expressed in the appended claims.