Patent Publication Number: US-9409391-B2

Title: Methods of driving hybrid inkjet printing apparatus including resonating ink in a nozzle

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application claims the benefit of Korean Patent Application No. 10-2012-0003456, filed on Jan. 11, 2012, in the Korean Intellectual Property Office, the disclosure of which is incorporated herein in its entirety by reference. 
     BACKGROUND 
     1. Field 
     At least one example embodiment relates to methods of driving a hybrid inkjet printing apparatus that ejects relatively minute droplets (for example, droplets having a volume of less than about 50 femtoliters), the methods including a piezoelectric method and an electrostatic method. 
     2. Description of the Related Art 
     Inkjet printing apparatuses print a desired (or alternatively, predetermined) color image on a surface of a printing sheet by ejecting minute droplets of printing ink onto a desired area of the printing sheet using an inkjet head. Recently, inkjet printing apparatuses have been used in various fields such as flat display fields, for example, liquid crystal displays (LCDs) and organic light emitting devices (OLEDs); flexible display fields, for example, E-paper; printed electronics fields, for example, metal wirings, organic thin film transistors (OTFTs); and the like. When inkjet printing apparatuses are used in the fields of displays or printed electronics, one important technical objective for process technologies is high-resolution and precise printing. 
     Inkjet printing apparatuses use various inkjet ejecting methods, for example, a piezoelectric method or an electrostatic method. The piezoelectric method is a method of ejecting ink by deforming a piezoelectric element. The electrostatic method is a method of ejecting ink using an electrostatic force. The electrostatic method ejects ink using electrostatic induction, which includes accumulating charged pigments using an electrostatic force and then ejecting ink droplets. 
     Since a piezoelectric-type printing inkjet printing apparatus ejects ink by using a drop on demand (DOD) method, printing operations of the piezoelectric-type printing inkjet printing apparatus are easily controlled. Further, piezoelectric-type printing inkjet printing apparatuses use a simple driving method, and ejection energy is generated by mechanically deforming a piezoelectric element. Thus, a piezoelectric-type printing inkjet printing apparatus may use any ink. However, the piezoelectric-type printing inkjet printing apparatus has difficulty ejecting ink in minute droplets of several picoliters or less. The piezoelectric-type printing inkjet apparatus also has difficulty with applications requiring relatively high-precision printing. 
     An electrostatic-type inkjet printing apparatus has been used to address some of the above issues. Electrostatic-type printing apparatuses have a simple driving method, and are capable of ejecting minute ink droplets with a relative precision. However, an electrostatic-induction inkjet printing apparatus of the electrostatic-type inkjet printing apparatus has difficulty in forming separate inkjet paths. Thus, it is difficult to eject ink using a DOD method from a plurality of nozzles. In addition, electrostatic printing methods are limited in ejection speed of ink as well as the kinds of ink used because electrostatic methods require charged pigments with high densities. 
     With regard to inkjet printing apparatuses in general, the size of ejected ink droplets is proportional to a diameter of a nozzle. Thus, in order to eject minute ink droplets, the size of a nozzle needs to be reduced. However, when the size of the nozzle is reduced, it is difficult to obtain precise nozzles and the nozzle is more likely to clog, thereby reducing reliability. 
     SUMMARY 
     At least one example embodiment provides methods of driving a hybrid inkjet printing apparatus that ejects minute droplets using a piezoelectric method and an electrostatic method together. 
     Additional aspects will be set forth in part in the description which follows and, in part, will be apparent from the description, or may be learned by practice of example embodiments. 
     According to an example embodiment, a method of driving a hybrid inkjet printing apparatus includes applying an electrostatic voltage to ink contained in a nozzle; applying a waveform voltage to ink contained in the nozzle, the waveform voltage being applied by a piezoelectric driving device; and applying an ejection voltage so as to eject the ink. 
     In at least one example embodiment, the applying of the electrostatic voltage may be maintained when the ink resonates and the ink is ejected. 
     In at least one example embodiment, the applying of the waveform voltage may include applying a voltage such that the ink oscillates in the nozzle. 
     In at least one example embodiment, the applying of the waveform voltage may applying the waveform voltage for a duration corresponding to a resonance period of a meniscus of the ink. 
     In at least one example embodiment, the method may further include measuring the resonance period of the meniscus using the waveform voltage. 
     In at least one example embodiment, the measuring of the resonance period of the meniscus may include applying the waveform voltage to the piezoelectric driving device such that ink is not ejected; measuring a displacement of the meniscus; and determining a time between two peaks of the displacement as the resonance period. 
     In at least one example embodiment, the applying of the ejection voltage may include applying the ejection voltage when the meniscus of the ink contained in the nozzle is moved in a direction in which the ink contained in the nozzle is ejected. 
     In at least one example embodiment, the ejection voltage may be a pulse voltage having an absolute value greater than an absolute value of the waveform voltage. 
     In at least one example embodiment, ink droplets having a smaller size than a size of the nozzle may be ejected. 
     In at least one example embodiment, the applying of the electrostatic voltage may include applying the electrostatic voltage for a desired period of time after the ejection voltage is applied. 
     According to another example embodiment, a method of driving a hybrid inkjet printing apparatus includes applying a waveform voltage, the waveform voltage being applied by an electrostatic device; applying an ejection voltage so as to eject the ink contained in the nozzle; and applying an electrostatic voltage to the electrostatic driving device during the applying of the ejection voltage. 
     In at least one example embodiment, the waveform voltage and the ejection voltage having a same polarity may be applied. 
     In at least one example embodiment, the applying of the waveform voltage may include applying the waveform voltage such that the ink oscillates in the nozzle. 
     In at least one example embodiment, the applying of the waveform voltage comprises applying the waveform voltage for a duration corresponding a resonance period of a meniscus of the ink. 
     In at least one example embodiment, the method further comprises measuring the resonance period of the meniscus using the waveform voltage. 
     In at least one example embodiment, the measuring of the resonance period of the meniscus comprises: applying the waveform voltage such that ink is not ejected; measuring a displacement of the meniscus; and determining a time between two peaks of the displacement as the resonance period. 
     In at least one example embodiment, the applying of the ejection voltage comprises applying the ejection voltage if the meniscus of the ink contained in the nozzle is moved in a direction in which the ink contained in the nozzle is ejected. 
     In at least one example embodiment, the ejecting of the ink comprises ejecting ink droplets having a smaller size than a size of the nozzle. 
     In at least one example embodiment, the applying of the electrostatic voltage comprises applying the electrostatic voltage for a desired period of time after the ejection voltage is applied. 
     In a driving method according to at least one example embodiment, since an ejection voltage is applied when a meniscus of ink contained in a nozzle resonates, the ejection voltage is low and minute droplets may be ejected. Thus, minute droplets having a volume of 50 femtoliters or less may also be ejected through a nozzle having a relatively great diameter, for example, a diameter of several μm to several tens of μm, without reducing the size of the nozzle. 
     In addition, even if a nozzle having a relatively great diameter may be used, minute droplets may be ejected and thus the nozzle is not likely to clog, thereby increasing reliability of a printing apparatus. 
     Since an electrostatic force acts on minute droplets when the minute droplets are ejected, the minute droplets having a volume of 50 femtoliters or less may proceed to have good straightness without dragging and thus, precise printing may be performed. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       These and/or other aspects will become apparent and more readily appreciated from the following description of example embodiments, taken in conjunction with the accompanying drawings in which: 
         FIG. 1  is a cross-sectional view of a hybrid inkjet printing apparatus according to an example embodiment; 
         FIG. 2  is a graph showing a displacement of a meniscus for measuring a resonance period of a meniscus of ink contained in a nozzle; 
         FIG. 3  is a set of diagrams for explaining a method of driving a hybrid inkjet printing apparatus, according to an example embodiment; 
         FIG. 4  is a timing diagram for explaining a method of driving a hybrid inkjet printing apparatus, according to an example embodiment; 
         FIG. 5  is a timing diagram for explaining a method of driving a hybrid inkjet printing apparatus, according to another example embodiment; 
         FIG. 6  is a set of diagrams for explaining a method of driving a hybrid inkjet printing apparatus, according to another example embodiment; and 
         FIG. 7  is a timing diagram for explaining a method of driving a hybrid inkjet printing apparatus, according to another example embodiment. 
     
    
    
     DETAILED DESCRIPTION OF EXAMPLE EMBODIMENTS 
     Example embodiments will be understood more readily by reference to the following detailed description and the accompanying drawings. Example embodiments may, however, be embodied in many different forms and should not be construed as being limited to those set forth herein. Rather, these example embodiments are provided so that this disclosure will be thorough and complete. In at least some example embodiments, well-known device structures and well-known technologies will not be specifically described in order to avoid ambiguous interpretation. 
     It will be understood that when an element is referred to as being “connected to” or “coupled to” another element, it can be directly on, connected or coupled to the other element or intervening elements may be present. In contrast, when an element is referred to as being “directly connected to” or “directly coupled to” another element, there are no intervening elements present. Like numbers refer to like elements throughout. As used herein, the term “and/or” includes any and all combinations of one or more of the associated listed items. 
     It will be understood that, although the terms first, second, third, etc., may be used herein to describe various elements, components and/or sections, these elements, components and/or sections should not be limited by these terms. These terms are only used to distinguish one element, component or section from another element, component or section. Thus, a first element, component or section discussed below could be termed a second element, component or section without departing from the teachings of example embodiments. 
     The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting. As used herein, the singular forms “a”, “an” and “the” are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms “comprises,” “comprising,” “includes,” and/or “including” when used in this specification, specify the presence of stated components, steps, operations, and/or elements, but do not preclude the presence or addition of one or more other components, steps, operations, elements, and/or groups thereof. 
     Unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which example embodiments belong. It will be further understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the relevant art and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein. 
     Spatially relative terms, such as “below”, “beneath”, “lower”, “above”, “upper”, and the like, may be used herein for ease of description to describe the relationship of one element or feature to another element(s) or feature(s) as illustrated in the figures. It will be understood that the spatially relative terms are intended to encompass different orientations of the device in use or operation, in addition to the orientation depicted in the figures. For example, if the device in the figures is turned over, elements described as “below” or “beneath” other elements or features would then be oriented “above” the other elements or features. Thus, the exemplary term “below” can encompass both an orientation of above and below. The device may be otherwise oriented (rotated 90 degrees or at other orientations) and the spatially relative descriptors used herein interpreted accordingly. 
       FIG. 1  is a cross-sectional view of a hybrid inkjet printing apparatus  100  according to an example embodiment. 
     Referring to  FIG. 1 , the hybrid inkjet printing apparatus  100  includes a flow channel plate  110  on which an ink channel is formed, a piezoelectric actuator  130  providing a driving force for ejecting ink, and an electrostatic force applier  140 . Hereinafter, the piezoelectric actuator  130  and an electrostatic force applier  140  will also be referred to as a piezoelectric driving device and an electrostatic driving device, respectively. 
     The flow channel plate  110  includes an inkjet inlet  121  to which ink is introduced, a plurality of pressure chambers  125  containing the introduced ink, and a plurality of nozzles  128  for ejecting ink droplets. The inkjet inlet  121  is formed in an upper surface of the flow channel plate  110  and is connected to an ink tank (not shown). Ink provided from the ink tank is introduced into the flow channel plate  110  through the inkjet inlet  121 . Manifolds  122  and  123  and a restrictor  124 , which connect the inkjet inlet  121  and the pressure chambers  125  to each other, may be formed in the flow channel plate  110 . 
     The nozzles  128  are respectively connected to the pressure chambers  125  and eject ink in the form of droplets. The plurality of the nozzles  128  may be formed on a lower surface of the flow channel plate  110  and may be disposed in one row or two rows. A plurality of dampers  126  for connecting the pressure chambers  125  and the nozzles  128  to each other may be formed in the flow channel plate  110 . 
     The flow channel plate  110  may be formed of a material having good micromachining properties, for example, silicon. The flow channel plate  110  may be formed by adhering three substrates, that is, a first substrate  111 , a second substrate  112 , and a third substrate  113 , which are sequentially stacked, by silicon direct bonding (SDB). 
     The inkjet inlet  121  may be vertically formed through an uppermost substrate, that is, the third substrate  113 . The pressure chambers  125  may be formed to a desired (or alternatively, predetermined) depth from a lower surface of the third substrate  113 . The nozzles  128  may be vertically formed through a lowermost substrate, that is, the first substrate  111 . The manifolds  122  and  123  may be formed in the third substrate  113  and the second substrate  112  that is an intermediate substrate. The dampers  126  may be vertically formed through the second substrate  112 . 
     Thus far, the case where the flow channel plate  110  includes the first, second, and third substrates  111 ,  112 , and  113  has been described but is just an example and example embodiments are not limited thereto. Thus, the flow channel plate  110  may include a single substrate, two substrates, or four or more substrates. Ink paths formed in the flow channel plate  110  may be variously arranged and may be changed to have various structures. 
     The piezoelectric actuator  130  provides a driving force, that is, a pressure change for ejecting ink to the pressure chambers  125  and is formed on the upper surface of the flow channel plate  110  to correspond to each of the pressure chambers  125 . The piezoelectric actuator  130  may include a lower electrode  131 , a piezoelectric film  132 , and an upper electrode  133 , which are sequentially stacked on the upper surface of the flow channel plate  110 . 
     The lower electrode  131  serves as a common electrode. The upper electrode  133  serves a driving electrode for applying a voltage to the piezoelectric film  132 . A first power source  135  is connected to the lower electrode  131  and the upper electrode  133 . The first power source  135  includes a waveform voltage generator and a pulse voltage generator. The piezoelectric film  132  is deformed by a voltage applied from the first power source  135  to deform an upper wall  125   a  of the pressure chamber  125 . The upper wall  125   a  serves as a vibration plate that is driven by the piezoelectric actuator  130  and is deformed to generate a pressure wave in the pressure chambers  125 . The piezoelectric film  132  may be formed of a desired (or alternatively, predetermined) piezoelectric material, for example, lead zirconate titanate (PZT). 
     The electrostatic force applier  140  applies an electrostatic force to the ink contained in the nozzles  128  and includes a first electrostatic electrode  141  and a second electrostatic electrode  142 , which face each other, and a second power source  145  for applying a voltage between the first electrostatic electrode  141  and the second electrostatic electrode  142 . The second power source  145  includes a high-voltage generator and a pulse generator. The electrostatic force applier  140  may accelerate ejected minute ink droplets so as to reduce (or alternatively, prevent) the minute ink droplets from dragging. 
     The first electrostatic electrode  141  is disposed on the flow channel plate  110 . For example, the first electrostatic electrode  141  may be formed on the upper surface of the flow channel plate  110 , that is, the upper surface of the third substrate  113 . In this case, the first electrostatic electrode  141  may be disposed on an area in which the inkjet inlet  121  is formed so as to be spaced apart from the lower electrode  131  of the piezoelectric actuator  130 . The second electrostatic electrode  142  may be disposed so as to be spaced apart from the lower surface of the flow channel plate  110 . In addition, a printing medium P on which the ink droplets ejected from the nozzles  128  of the flow channel plate  110  are printed may be positioned on the second electrostatic electrode  142 . 
     Since the hybrid inkjet printing apparatus  100  having the above-described structure uses both a piezoelectric method and an electrostatic method as an inkjet ejecting method, the hybrid inkjet printing apparatus  100  may have the advantages of both the piezoelectric method and the electrostatic method. That is, according to at least one example embodiment, since the hybrid inkjet printing apparatus  100  may eject ink by using a drop on demand (DOD) method, it is easy to control a printing operation and to realize minute droplets, and to eject ink droplets straight. Thus, the hybrid inkjet printing apparatus  100  may be advantageously used in precision printing. 
     According to an example embodiment, the resonance characteristics of a meniscus of ink contained in a nozzle may be utilized. 
       FIG. 2  is a graph showing a displacement of a meniscus for measuring a resonance period of a meniscus of ink contained in a nozzle. In order to obtain the resonance period of the meniscus of ink, the resonance period may be calculated by using a volume of ink channels and physical properties of ink. Alternatively, the resonance period may be measured from a displacement of the meniscus of ink at a nozzle while a desired (or alternatively, predetermined) pulse voltage is applied to a piezoelectric actuator such that the ink contained in the nozzle flows and the ink droplets are not ejected from the nozzle. In other words, the resonance period may be determined as the ink oscillates in the nozzle. The resonance period of the meniscus may be referred to as a resonance period of ink contained in the nozzle. 
     Referring to  FIG. 2 , a time between two peaks P 1  and P 2  that are measured when the meniscus is in a convex state corresponds to a resonance period and is measured as about 20 μs. The resonance period of the meniscus may vary according to the size of nozzle and the physical properties of ink. 
       FIG. 3  is diagrams for explaining a method of driving the hybrid inkjet printing apparatus  100 , according to an example embodiment.  FIG. 4  is a timing diagram for explaining a method of driving the hybrid inkjet printing apparatus  100 , according to an example embodiment. 
     Referring to  FIGS. 3 and 4 , in a first operation, a voltage is not applied to the piezoelectric actuator  130  and a desired (or alternatively, predetermined) electrostatic voltage VE is applied between the first electrostatic electrode  141  and the second electrostatic electrode  142  from the second power source  145 . For example, a voltage of −2 kV may be applied and thus positive charges and particles exhibiting positive charges may be moved to a meniscus M from ink  129  toward the second electrostatic electrode  142 . In this case, since an electrostatic force that acts on the ink  129  contained in the nozzle  128  is relatively low, the meniscus M of the ink  129  is in a stationary state. 
     In a second operation, a first waveform voltage VP 1  is applied to the piezoelectric actuator  130  for a time T 1 , which is 1/4 the resonance period of the meniscus M. In this case, a state in which an electrostatic voltage VE is applied between the first electrostatic electrode  141  and the second electrostatic electrode  142  is maintained. 
     The first waveform voltage VP 1  is a voltage for deforming the piezoelectric actuator  130  in a first direction in which the volume of the pressure chamber  125  reduces. The first waveform voltage VP 1  slowly increases from 0 V and reaches about −40 V. In this case, the meniscus M is convex from the nozzle  128  toward the second electrostatic electrode  142 . 
     In a third operation, a second waveform voltage VP 2  is applied to the piezoelectric actuator  130  for a time T 2 , which is 1/2 the resonance period of the meniscus M. In this case, a state in which the electrostatic voltage VE is applied between the first electrostatic electrode  141  and the second electrostatic electrode  142  is maintained. 
     The second waveform voltage VP 2  is a voltage for deforming the piezoelectric actuator  130  in a second direction in which the volume of the pressure chamber  125  increases. The second waveform voltage VP 2  may gradually increase from, for example, −40 V to about 20 V. When the second waveform voltage VP 2  reaches 20V, then the second waveform voltage VP 2  may be maintained for a desired (or alternatively, predetermined) period of time T 3 . In this case, the meniscus M is concave with respect to the nozzle  128 . 
     A maximum voltage of the second waveform voltage VP 2  is smaller than a maximum voltage of the first waveform voltage VP 1  and the maximum voltage of the second waveform voltage VP 2  is maintained for a desired (or alternatively, predetermined) period of time T 3  in order to easily perform a next ejecting operation of droplets. 
     In a fourth operation, a third voltage VP 3  is applied to the piezoelectric actuator  130  in a direction in which the volume of the pressure chamber  125  decreases. The third voltage VP 3  may be a pulse voltage, for example, −70 V. An absolute value of the third voltage VP 3  is greater than an absolute value of the first waveform voltage VP 1  and thus ink is ejected out of the nozzle  128  in the form of droplet  129   a.    
     In general, an electrostatic force FE is proportional to a charge quantity q and an electric field intensity E, as shown in Equation 1 below. In addition, as shown in Equation 2 below, the charge quantity q is also proportional to the electric field intensity E. Thus, as shown in Equation 3 below, the electrostatic force FE is proportional to the square of the electric field intensity E. As shown in Equation 4 below, the electric field intensity E is proportional to the applied electrostatic voltage V E  but is inversely proportional to a radius of curvature r m  of the meniscus M. Thus, as shown in Equation 5 below, the electrostatic force F E  that acts on the ink  129  that sharply protrudes at an end of the nozzle  128  is inversely proportional to the square of the radius of curvature r m  of the meniscus M of the portion. 
     
       
         
           
             
               
                 
                   
                     F 
                     E 
                   
                   ∝ 
                   qE 
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
             
               
                 
                   q 
                   ∝ 
                   E 
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
             
               
                 
                   
                     F 
                     E 
                   
                   ∝ 
                   
                     E 
                     2 
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
             
               
                 
                   E 
                   ∝ 
                   
                     
                       V 
                       E 
                     
                     
                       r 
                       m 
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
             
               
                 
                   
                     F 
                     E 
                   
                   ∝ 
                   
                     
                       ( 
                       
                         
                           V 
                           E 
                         
                         
                           r 
                           m 
                         
                       
                       ) 
                     
                     2 
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
     
     A resonance waveform voltage (i.e., a first waveform voltage and a second waveform voltage) is applied such that ink contained in the nozzle  128  resonates and thus the droplet  129   a  is ejected by a small force, that is, a small piezoelectric voltage. Since the size of the ejected droplet  129   a  is proportional to a piezoelectric voltage, the small droplet  129   a  may be ejected by applying a low piezoelectric voltage. In this case, since the ink  129  is ejected to sharply protrude at a central portion of the nozzle  128 , the droplet  129   a  having a relatively small size compared with the size of the nozzle  128  may be ejected. Thus, when the droplet  129   a  is ejected based on resonance, the droplet  129   a  has a jet shape. 
     The ejected droplet  129   a  is accelerated in a direction toward the second electrostatic electrode  142  by the electrostatic force FE so as to be printed on the printing medium P. Since the ejected droplet  129   a  having a jet shape has a small radius of curvature compared with a spherical droplet having the same value as the ejected droplet  129   a , a relatively high electrostatic driving force acts on the ejected droplet  129   a . Even if the droplet  129   a  having a volume of 50 femtoliters or less is ejected, the droplet  129   a  may be less likely to scatter (or alternatively, be prevented from being scattered) as a result of the electrostatic driving force. Thus, relatively minute droplets may be ejected onto the printing medium P with high precision. 
     As shown in  FIG. 3 , when the third voltage VP 3  applied to the piezoelectric actuator  130  is removed, the piezoelectric actuator  130  returns to an original state and a pressure in the pressure chamber  125  returns to an original state, and the meniscus M having a convex shape returns to an original state. In this case, a state where the electrostatic voltage VE is applied between the first electrostatic electrode  141  and the second electrostatic electrode  142  may be maintained. Thus, the droplet  129   a  having positive charges may precisely reach the printing medium P by an electrostatic force. 
       FIG. 4  shows a case where a piezoelectric voltage for resonating ink has a linear waveform but example embodiments are not limited to this. For example, the piezoelectric voltage may have a curve shape like an alternating current (AC) voltage. 
     As described above, in a driving method according to an example embodiment, ink droplets having a relatively small size compared with the size of a nozzle may be ejected. That is, minute droplets having a volume of 50 femtoliters or less may also be ejected through a nozzle having a relatively great diameter, for example, a diameter of several μm to several tens of μm without reducing the size of a nozzle. In addition, even if a nozzle having a relatively great diameter is used, minute droplets may be ejected and thus the nozzle is not likely to clog, thereby increasing reliability of a printing apparatus. Further, minute droplets may reach a desired position of the printing medium P using an electrostatic force that acts on the minute droplets. 
       FIG. 5  is a timing diagram for explaining a method of driving the hybrid inkjet printing apparatus  100 , according to another example embodiment. Details of substantially the same operations as in  FIGS. 3 and 4  will not be repeated. 
     Referring to  FIG. 5 , a first operation and a second operation are the same as in  FIGS. 3 and 4 . In a third operation, a second waveform voltage VP 2   a  is applied to the piezoelectric actuator  130  for a time T 2 , which is 1/2 the resonance period of the meniscus M. In this case, a state in which the electrostatic voltage VE is applied between the first electrostatic electrode  141  and the second electrostatic electrode  142  is maintained. 
     The second waveform voltage VP 2   a  is a voltage for deforming the piezoelectric actuator  130  in a second direction in which the volume of the pressure chamber  125  increases. The second waveform voltage VP 2   a  may gradually increase from, for example, −40 V to about 40 V. In this case, the meniscus M is concave with respect to the nozzle  128 . 
     In a fourth operation, a third waveform voltage VP 3   a  is applied to the piezoelectric actuator  130  in a direction in which the volume of the pressure chamber  125  decreases. The third waveform voltage VP 3   a  may gradually reduce from, for example, 40 V to about −40 V. In this case, the meniscus M is gradually deformed to be convex from the nozzle  128  toward the second electrostatic electrode  142 . The fourth operation is performed during a time T 3 , which is 3/4 to 5/4 the resonance period of the meniscus M. In the fourth operation, since the meniscus M is moved in a direction in which ink is ejected, a driving voltage for ejecting ink droplets reduces. 
     For the time T 3  of the fourth operation, a fourth voltage VP 4  for deforming the pressure chamber  125  in a direction in which the volume of the pressure chamber  125  decreases is applied to the piezoelectric actuator  130 . The fourth voltage VP 4  may be a pulse voltage, for example, −70 V. An absolute value of the fourth voltage VP 4  is greater than an absolute value of the first waveform voltage VP 1  and thus ink in the form of the droplet  129   a  may be ejected out of the nozzle  128 . 
     A resonance waveform voltage (i.e., a first waveform voltage and a second waveform voltage) is applied such that ink contained in the nozzle  128  resonates and thus the droplet  129   a  is ejected by a small force, that is, a small piezoelectric voltage. Since the size of the ejected droplet  129   a  is proportional to a piezoelectric voltage, the small droplet  129   a  may be ejected by applying a low piezoelectric voltage. In this case, the ink  129  is ejected to sharply protrude at a central portion of the nozzle  128 , the droplet  129   a  having a very small size compared to the size of the nozzle  128  may be ejected. Thus, when the droplet  129   a  is ejected based on resonance, the droplet  129   a  has a jet shape. 
     The ejected droplet  129   a  is accelerated in a direction toward the second electrostatic electrode  142  by the electrostatic force FE so as to be printed on the printing medium P. Since the ejected droplet  129   a  having a jet shape has a small radius of curvature compared with a spherical droplet having the same value as the ejected droplet  129   a , a relatively high electrostatic driving force acts on the ejected droplet  129   a . Even if the droplet  129   a  having a volume of 50 femtoliters or less is ejected, the droplet  129   a  may be less likely to scatter (or alternatively, be prevented from scattering) as a result of the electrostatic driving force. Thus, minute droplets may be ejected onto the printing medium P with high precision. 
       FIG. 6  is a diagram for explaining a method of driving the hybrid inkjet printing apparatus  100 , according to another example embodiment.  FIG. 7  is a timing diagram for explaining a method of driving the hybrid inkjet printing apparatus  100 , according to another example embodiment. 
     In a first operation, a voltage is not applied to the piezoelectric actuator  130  and a first waveform voltage VE 1  is applied between the first electrostatic electrode  141  and the second electrostatic electrode  142  from the second power source  145 . The first waveform voltage VE 1  is applied for a time T 1  that is 1/4 the resonance period of the meniscus M. The first waveform voltage VE 1  varies from 0 V to about −3 kV. Positive charges and particles exhibiting positive charges may be moved to the meniscus M toward the second electrostatic electrode  142 . The meniscus M is deformed to be convex toward a direction in which the ink  129  is ejected from the nozzle  128  by an electrostatic force that acts on the ink  129  contained in the nozzle  128 . 
     The resonance period of the meniscus M may be determined by applying an electrostatic voltage to the electrostatic driving device and calculating the time between two peaks of the displacement of the meniscus M as stated above with  FIG. 2 . 
     In a second operation, a second waveform voltage VE 2  is applied to the piezoelectric actuator  130  for a time that is 2/4 to 1 times the resonance period of the meniscus M. Referring to  FIG. 7 , the second operation is performed for a time T 2  and a time T 3 . For the time T 2 , an electrostatic voltage varies from about −3 kV to 0 V. In this case, the meniscus M is moved in an opposite direction to a direction in which the ink  129  is ejected. A state in which a voltage is not applied to the piezoelectric actuator  130  is maintained. 
     Then, an electrostatic voltage VE 3  may be maintained to 0 V for the time T 3 . A positive voltage is not applied for the time T 3  such that positive charges are maintained in the meniscus M. 
     The time T 2  may correspond to 1/4 the resonance period of the meniscus M. The time T 3  may correspond to 1/4 to 3/4 the resonance period of the meniscus M. During the time T 3 , the meniscus M is in a resonance state by applying the first waveform voltage VE 1  and the second waveform voltage VE 2  and in a state to move in a direction in which the ink  129  is ejected. 
     In a third operation, the third voltage VP 3  is applied to the piezoelectric actuator  130  in a direction in which the volume of the pressure chamber  125  decreases. A fourth voltage VE 4  is applied between the first electrostatic electrode  141  and the second electrostatic electrode  142  from the second power source  145 . The third voltage VP 3  may be a pulse voltage, for example, −70 V. The fourth voltage VE 4  may be, for example, −3 kV. The third voltage VP 3  may be applied for the time T 4 . The fourth voltage VE 4  may be applied for a time T 5  that is longer than the time T 4 . 
     A resonance waveform voltage (i.e., a first waveform voltage and a second waveform voltage) is applied such that ink contained in the nozzle  128  resonates and thus the droplet  129   a  is ejected by a small force, that is, a small piezoelectric voltage. Since the size of the ejected droplet  129   a  is proportional to a piezoelectric voltage, the small droplet  129   a  may be ejected by applying a relatively low third voltage VP 3 . In this case, since the ink  129  is ejected to sharply protrude at a central portion of the nozzle  128 , the droplet  129   a  having a very small size compared with the size of the nozzle  128  may be ejected. Thus, when the droplet  129   a  is ejected based on resonance, the droplet  129   a  has a jet shape. 
     The ejected droplet  129   a  is accelerated in a direction toward the second electrostatic electrode  142  by an electrostatic force so as to be printed on the printing medium P by applying the fourth voltage VE 4 . Since the ejected droplet  129   a  having a jet shape has a small radius of curvature compared with a spherical droplet having the same volume as the ejected droplet  129   a , a relatively high electrostatic driving force acts on the ejected droplet  129   a . Even if the droplet  129   a  having a volume of 50 femtoliters or less is ejected, the droplet  129   a  may be less likely to scatter (or alternatively, be prevented from scattering) as a result of the electrostatic driving force. Thus, minute droplets may be ejected onto the printing medium P with high precision. 
     In a fourth operation, when the fourth voltage VE 4  is removed, the meniscus M having a convex shape returns to an original state. 
     As described above, in a driving method according to at least one example embodiment, ink droplets having a very small size compared with the size of a nozzle may be ejected. That is, minute droplets having a volume of 50 femtoliters or less may be ejected through a nozzle having a relatively great diameter, for example, a diameter of several μm to several tens of μm without reducing the size of a nozzle. In addition, even if a nozzle having a relatively great diameter is used, minute droplets may be ejected and thus the nozzle is not likely to clog, thereby increasing reliability of a printing apparatus. Further, minute droplets may reach a desired position of the printing medium using an electrostatic force. 
     It should be understood that the exemplary embodiments described herein should be considered in a descriptive sense only and not for purposes of limitation. Descriptions of features or aspects within each example embodiment should typically be considered as available for other similar features or aspects in other example embodiments.