Patent Publication Number: US-2022212255-A1

Title: Additive method of forming a metallic nanoparticle microdot on a substrate, a metallic nanoparticle microdot, and an elongate metallic nanoparticle feature

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This application claims benefit under 35 U.S.C. § 119(e) to U.S. Provisional Application No. 63/131,725, filed Dec. 29, 2020, entitled “AN ADDITIVE METHOD OF FORMING A METALLIC NANO PARTICLE MICRODOT ON A SUBSTRATE, A METALLIC NANOPARTICLE MICRODOT, AND AN ELONGATE METALLIC NANOPARTICLE FEATURE,” the entire disclosure of which is hereby incorporated by reference herein. 
    
    
     BACKGROUND 
     Various conductive features can be formed by extruding a metallic nanoparticle composition through a capillary tube onto a substrate. Conductive features include lines and microdots. Conductive features could be useful in applications such as interconnection and integration of semiconductor devices and optoelectronic devices and open defect repair (ODR). Furthermore, conductive features could be optimized to enable conformal coatings overlying them. For these and other reasons, improved methods of forming conductive features are desired. 
     SUMMARY OF THE INVENTION 
     In one aspect, an additive method of forming a metallic nanoparticle microdot on a substrate includes the following steps: (A) estimating or obtaining a position of an outlet of a capillary tube at zero height above the substrate (zero-height position); (B) extruding a metallic nanoparticle composition from the outlet at a first height h 1  above the zero-height position, including forming a fluid bridge between the outlet and the substrate; (C) optionally lifting the capillary tube relative to the substrate by a height increment of Δh while continuing to extrude the metallic nanoparticle composition from the outlet; and (D) rapidly lifting the capillary tube to separate the outlet from the fluid bridge. 
     In another aspect, a metallic nanoparticle microdot on a substrate includes metallic nanoparticles bounded by a substrate surface and a curved surface intersecting the substrate surface. The substrate extends principally along an X-axis and a Y-axis perpendicular to the X-axis. The curved surface protrudes away from the substrate along a Z-axis perpendicular to the X-axis and to the Y-axis. The curved surface includes a peak and a curved line traversing the peak and extending along the X-axis and the Z-axis. The curved line is approximated by a parabolic function of a form: z=ax 2 +bx+c, where xis displacement along the X-axis, z is displacement along the Z-axis, and a, b, and c are respective constants. A correlation of the parabolic function to the curved line is characterized by a coefficient of determination R 2 , where R 2  is in a range of 0.95 to 1.0. 
     In yet another aspect, an elongate metallic nanoparticle feature on a substrate includes metallic nanoparticles bounded by a substrate surface and a curved surface intersecting the substrate surface. The substrate extends principally along an X-axis and a Y-axis perpendicular to the X-axis. The curved surface extends longitudinally along the Y-axis and protrudes along a Z-axis perpendicular to the X-axis and to the Y-axis. The curved surface includes a curved line extending along the X-axis and the Z-axis. The curved line is approximated by a parabolic function of a form: z=ax 2 +bx+c, where x is displacement along the X-axis, z is displacement along the Z-axis, and a, b, and c are respective constants. A correlation of the parabolic function to the curved line is characterized by a coefficient of determination R 2 , where R 2  is in a range of 0.95 to 1.0. 
     The above summary of the present invention is not intended to describe each disclosed embodiment or every implementation of the present invention. The description that follows more particularly exemplifies illustrative embodiments. In several places throughout the application, guidance is provided through examples, which examples can be used in various combinations. In each instance of a list, the recited list serves only as a representative group and should not be interpreted as an exclusive list. 
    
    
     
       BRIEF DESCRIPTION OF THE FIGURES 
       The disclosure may be more completely understood in consideration of the following detailed description of various embodiments of the disclosure in connection with the accompanying drawings, in which: 
         FIG. 1  is a schematic block diagram view of an illustrative nanoparticle composition printing apparatus. 
         FIG. 2  is a flow diagram of an additive method of forming a metallic nanoparticle microdot on a substrate. 
         FIG. 3  is a flow diagram of an additive method of forming an elongate metallic nanoparticle feature on a substrate. 
         FIG. 4  is a schematic side view of a glass capillary tube. 
         FIG. 5  is a scanning electron microscope (SEM) view of a portion of a glass capillary tube. 
         FIG. 6  is a scanning electron microscope (SEM) view of a tapering portion of the glass capillary tube, under low magnification. 
         FIG. 7  is a scanning electron microscope (SEM) view of a tapering portion of the glass capillary tube, under high magnification. 
         FIG. 8  is a scanning electron microscope (SEM) view of the output portion after focused-ion beam treatment, under high magnification. 
         FIG. 9  is a schematic side view and partial cross-sectional view of a piston-cylinder assembly. 
         FIG. 10  is a schematic side view and partial cross-sectional view of a metallic nanoparticle composition dispenser. 
         FIG. 11  is a schematic perspective view of a metallic nanoparticle composition dispenser and an associated dispenser holder. 
         FIG. 12  is a schematic perspective view of an implementation of an additive method of forming a metallic nanoparticle microdot on a substrate. 
         FIG. 13  is a schematic perspective view of an implementation of an additive method of forming an elongate metallic nanoparticle feature on a substrate. 
         FIG. 14  is an SEM image of a first metallic nanoparticle microdot. 
         FIG. 15  is an SEM image of a cross section of the first metallic nanoparticle microdot of  FIG. 14 . 
         FIG. 16  is a graphical plot of a parabolic approximation of the curved line in  FIG. 15 . 
         FIG. 17  is an SEM image of a second metallic nanoparticle microdot. 
         FIG. 18  is an SEM image of a cross section of the second metallic nanoparticle microdot of  FIG. 17 . 
         FIG. 19  is a graphical plot of a parabolic approximation of the curved line in  FIG. 18 . 
         FIGS. 20 and 21  are SEM images of metallic nanoparticle lines. 
         FIG. 22  is an SEM image of a cross section of one of the metallic nanoparticle lines of  FIGS. 20 and 21 . 
         FIG. 23  is a graphical plot of a parabolic approximation of the curved line in  FIG. 22 . 
         FIG. 24  is a graphical plot of heights of metallic nanoparticle microdots as a function of a final height of the outlet of the capillary tube above a substrate. 
         FIG. 25  is a graphical plot of aspect ratios of metallic nanoparticle microdots as a function of a final height of the outlet of the capillary tube above a substrate. 
         FIG. 26  is a graphical plot of diameters (widths) of metallic nanoparticle microdots as a function of time duration of extrusion. 
         FIG. 27  shows illustrative parabolic lines defined by certain values of constants. 
     
    
    
     DETAILED DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS 
     The present disclosure relates to an additive method of forming a metallic nanoparticle microdot on a substrate, a metallic nanoparticle microdot, and an elongate metallic nanoparticle feature. 
     The words “preferred” and “preferably” refer to embodiments of the invention that may afford certain benefits, under certain circumstances. However, other embodiments may also be preferred, under the same or other circumstances. Furthermore, the recitation of one or more preferred embodiments does not imply that other embodiments are not useful and is not intended to exclude other embodiments from the scope of the invention. 
     The terms “comprises” and variations thereof do not have a limiting meaning where these terms appear in the description and claims. 
     Unless otherwise specified, “a,” “an,” “the,” and “at least one” are used interchangeably and mean one or more than one. 
     The recitations of numerical ranges by endpoints include all numbers subsumed within that range (e.g., 1 to 5 includes 1, 1.5, 2, 2.75, 3, 3.80, 4, 5, etc.). 
     For any method disclosed herein that includes discrete steps, the steps may be conducted in any feasible order. As appropriate, any combination of two or more steps may be conducted simultaneously. 
     In carrying out additive methods of forming a metallic nanoparticle microdot or an elongate metallic nanoparticle feature on a substrate, a printing apparatus is typically used.  FIG. 1  is a schematic block diagram view of an illustrative printing apparatus  10 . The printing apparatus  10  includes a substrate stage  102 , a print head  104 , a regulated pneumatic system  106 , and a print head positioning system  108 . A substrate  110  is fixed in position on the substrate stage  102  during the printing (dispensing) and has a printable surface  112 , which is facing upward and facing towards the print head  104 . The print head  104  is positioned above the substrate  110 . The print head  104  includes a metallic nanoparticle composition dispenser  116  and a cartridge holder (dispenser holder)  118 . The metallic nanoparticle composition dispenser  116  includes a piston-cylinder assembly  114  and a capillary tube  120 , as described with reference to  FIG. 10 . Typically, the regulated pneumatic system  106  includes a pump and a pressure regulator. In the example shown in  FIGS. 1, 2, and 3 , a pneumatic port  184  of the piston cylinder assembly  114  is coupled to the regulated pneumatic system  106  via tubing  107 . Preferably, the regulated pneumatic system  106  is capable of applying pressure in a range of 0 bar to 10 bar to the pneumatic port  184 . 
     The print head positioning system  108  controls the vertical displacement (along Z-axis direction  44 ) of the print head  104  and the lateral displacement (along X-axis direction  40  and/or Y-axis direction  42 ) of the print head  104  relative to the substrate. During dispensing of the metallic nanoparticle composition onto the substrate, the print head  104  is moved laterally and/or vertically. 
     The piston-cylinder assembly  114  is sometimes referred to as a printer cartridge. A schematic side view and partial cross-sectional view of an exemplary piston-cylinder assembly  114  is shown in  FIG. 9 . In the example shown, the piston-cylinder assembly  114  includes a cylinder  150 , a cylinder cover  170 , a pneumatic connector  180 , and an intermediate sealing sleeve  190 . The cylinder  150  is shown in cross-section to show a cylindrical cavity portion  154  and a conical cavity portion  156 . A piston  158  is located inside cylinder  150 . The cylinder  150  has a first end (top end) portion  160  and a second end (bottom end) portion  162  opposite the first end. The cylinder cover  170  is sealably mated to the cylinder  150  at the first end portion  160 . In the example shown, an interior surface of the cylinder cover  170  and an exterior surface of the cylinder  150  at its first end portion  160  form a threaded joint. A flat gasket  174  is under compression between the cylinder cover  170  and the cylinder  150  and forms a seal. The intermediate sealing sleeve  190  is sealably mated to the cylinder  150  at the second end portion  162 . In the example shown, an exterior surface of the intermediate sealing sleeve  190  and an interior surface of the cylinder  150  at its second end portion  162  form a threaded joint. A flat gasket  194  is under compression between the intermediate sealing sleeve  190  and the cylinder  150  and forms a seal. 
     The cylinder cover  170  has an opening  172 , which retains the pneumatic connector  180 . A pneumatic port  184  extends longitudinally through the pneumatic connector  180 . The cylinder  150  has a first end  164 , in the first end portion  160 , and a second end  166 , in the second end portion  162 . Accordingly, the pneumatic port is at the first end of the cylinder. Air or fluid enters the cylinder from the pneumatic port  184 . Inside the cylinder, air or fluid first travels through the cylindrical cavity portion  154  and then a conical cavity portion  156 , which tapers to an outlet port  188  at its apex. The outlet port  188  is at the second end  166  opposite the first end  164 . The piston  158  is movable in the cylinder  150  between the first end  164  and the second end  166 . 
       FIG. 10  is a schematic side view and partial cross-sectional view of a dispenser  116 . The dispenser  116  includes a piston-cylinder assembly  114  ( FIG. 9 ) and a capillary tube (nozzle)  120 . Capillary tube  120  has a tube inlet  124  and a tube outlet  132 . Capillary tube  120  is described in greater detail with reference to  FIG. 4 . In the example shown, there is a handle  122 , including a threaded portion  126 , attached to the capillary tube. The threaded portion  126  and an interior surface  192  of the intermediate sealing sleeve  190  form a threaded joint. Accordingly, the intermediate sealing sleeve retains the handle that is attached to the capillary tube. The tube inlet  124  of capillary tube  120  is coupled to the outlet port  188  at the second end  166  of the cylinder  150 . A capillary tube  120  is installed in the piston-cylinder assembly  114 , to form a dispenser  116 . The dispenser is particularly suited to dispense metallic nanoparticle compositions described herein. Accordingly, the dispenser is sometimes referred to as a metallic nanoparticle composition dispenser. 
     Commercially available glass capillary tubes can be used in the dispenser. For example, glass capillary tubes (Eppendorf™ Femtotips™ II Microinjection Capillary Tips), having an inner diameter at the tip of 0.5 μm and an outer diameter at the tip of 0.7 μm, are available from Fisher Scientific. A commercially available glass capillary tube  120  is shown schematically in  FIG. 4 . The glass capillary tube has an inlet  124  at a first end, and outlet  132  at a second end opposite the first end, and an elongate fluid passageway between the inlet  124  and outlet  132 . A plastic handle  122  is attached to the glass capillary tube  120  around its circumference. The plastic handle  122  includes an inlet (input end)  124  and a threaded portion  126  near the inlet  124  which enables a threaded connection to an external body or external conduit (see  FIG. 10 ). The inlet  124  has an inner diameter of 1.2 mm. 
     The glass capillary tube includes an elongate input portion  128  and a tapering portion  130 . There is an externally visible portion  134  of the glass capillary tube  120 . Some of the elongate input portion  128  may be obscured by the surrounding plastic handle  122 . The tapering portion  130  tapers to an outlet (output end)  132  (having an inner diameter of 0.5 μm and an outer diameter at the tip of 0.7 μm in the case of the certain Femtotips™ II Microinjection Capillary Tips). Stainless-steel capillary tubes can also be used. The reduction of diameter along the tapering portion  130  from the elongate input portion  128  to the outlet  132  is more clearly illustrated in  FIGS. 5 through 7 .  FIG. 5  is a scanning electron micrograph view (formed from stitching together multiple SEM images) of the entire externally visible portion  134  of the glass capillary tube  120 . A first magnification region  136  of the tapering portion  130  including the outlet  132 , observed under low magnification in a scanning electron microscope (SEM), is shown in  FIG. 6 . Furthermore, a second magnification region  138  located within the first magnification region  136 , observed under high magnification in a scanning electron microscope (SEM), is shown in  FIG. 7 . The outer diameter is smallest at the outlet  132  ( FIG. 7 ) and increases with increasing longitudinal distance from the outlet  132 . 
     In many cases it is desirable to increase the size of the outlet (outlet size). It is possible to increase the outlet size by cutting the glass capillary tube  120  at a suitable longitudinal location along the tapering portion  130 . Cutting may be done using a focused-ion beam (FIB) apparatus. For example, a plasma-source Xe +  FIB (also called PFIB) is used. The capillary tube is installed in the FIB apparatus. A longitudinal location along the tapering portion  130  is selected, and the focused ion beam is directed to it, with sufficient energy density for cutting the glass tube. A cut is made using the focused-ion beam across the tapering portion at the selected longitudinal location. A scanning electron microscope (in the FIB apparatus) is used to measure the outer diameter or inner diameter or both at the tip. If the measured inner diameter or outer diameter or both are too small, the cutting is carried out at another longitudinal location along the tapering portion. In the example shown in  FIG. 8 , the outlet inner diameter is measured to be 2.153 μm and the outlet outer diameter is measured to be 2.504 μm. We refer to the outlet outer diameter as the outlet size. For glass capillary tubes  120 , outlet sizes in a range of 0.7 μm to 8 μm are possible and have been tried. 
     In preparing a printing apparatus for use, a metallic nanoparticle composition is injected into the cylinder  150 . In the case of the piston-cylinder assembly shown in  FIG. 9 , this can be accomplished by injecting the metallic nanoparticle composition into the cylinder  150  via its first end  164  using a syringe, with the piston  158  removed from the cylinder and the cover  170  and the pneumatic connector  180  detached from the cylinder  150 . Subsequently, the piston is positioned in the cylinder. Additionally, in the example shown in  FIG. 9 , the cylinder cover  170  and the pneumatic connector  180  are attached to the cylinder  150 . The pneumatic port  184  is coupled to a regulated pneumatic system  106  via tubing  107 . 
       FIG. 11  is a schematic perspective view of a metallic nanoparticle composition dispenser  116  and an associated dispenser holder  118 . The dispenser holder  118  includes a fork  198 . When assembled, the fork is inserted into a groove  195  between two annular protrusions  194 ,  196  that protrude radially outward from the outer walls of the cylinder  150 . Accordingly, the dispenser holder  118  retains the dispenser. The dispenser holder  118  is mechanically coupled to the print head positioning system  108 . In preparing a printing apparatus for use, the dispenser  116  is installed in the dispenser holder  118 . 
     The nanoparticle composition printing apparatus  10  ( FIG. 1 ) is used to carry out an additive method of forming a metallic nanoparticle microdot on a substrate (method  50  of  FIG. 2 ) or an additive method of forming an elongate metallic nanoparticle feature on a substrate (method  70  of  FIG. 3 ). The printing apparatus  10  includes an imaging system  12 , which includes a camera  14 . In addition to the camera  14 , the imaging system  12  may include image processing software resident on a computer, with the computer being coupled to the camera  14 . The imaging system  12  is coupled to the positioning system  108 . The positioning system  108  controls the positioning of the nanoparticle composition dispenser  116  and the camera  14 . Preferably, the position of the camera  14 , including its orientation, is adjusted as needed such that the capillary tube  120  and a portion of the substrate  110  near the capillary tube  120  are within the field-of-view of the camera  14 . 
     Method  50  ( FIG. 2 ) includes steps  52 ,  54 ,  56 ,  58 ,  60 ,  62 ,  64 ,  66 , and  68 . At step  52 , a metallic nanoparticle composition is prepared. This includes synthesizing metallic nanoparticles unless metallic nanoparticles are already available. Generally, the synthesis of metallic nanoparticles in solution employs three components: (1) metal precursors (e.g., AgNO3 for silver nanoparticles and Cu(NO3)2 for copper nanoparticles); (2) reducing agents (e.g., ethylene glycol for silver nanoparticles and sodium hypophosphite for copper nanoparticles); and (3) stabilizing (capping) agents (e.g., polyvinylpyrrolidone). Polyvinylpyrrolidone, abbreviated as PVP, is soluble in water and other polar solvents. When PVP is effectively used as a dispersant, stable colloidal silver nanoparticles or copper nanoparticles covered (capped) with PVP polymer can be obtained in small size (&lt;250 nm) because the PVP reduces the aggregation of the silver or copper nanoparticles. 
     The average size of the silver nanoparticles can be controlled to within a range of 20 nm to 80 nm. The average size of the copper nanoparticles can be controlled to within a range of 60 nm to 160 nm. The average particle size and dispersity can be controlled by controlling thermodynamic and kinetic reaction parameters. Reaction temperature, temperature ramp, and reaction time are the important thermodynamic reaction parameters. The rate of adding reagents and molar ratio of used metal precursor to stabilizing agent (PVP) are the important kinetic reaction parameters. An appropriate combination of these parameters leads to obtaining nanoparticles that exhibit the desired properties of small particles size, low dispersity, and high dispersion stability (low occurrence of aggregation). 
     Furthermore, at step  52 , a metallic nanoparticle composition is made from the metallic nanoparticles. Generally, the nanoparticles are separated, to remove impurities and excess PVP, and dispersed in a solvent mixture including a first solvent and an optional second solvent. The metallic nanoparticle composition may optionally include additives to better control its physicochemical properties. These additives include surfactants, binders, adhesion promoters, and antifoaming agents. We have found that the concentration of such additives should not exceed 3% by weight in the metallic nanoparticle composition. 
     The preparation of an example composition is described in detail in the Example 1 hereinbelow. The Example 1 composition contains silver nanoparticles and triethylene glycol as a solvent. It has been found that solvents having a boiling point of at least 280° C. at a pressure of 760 mm Hg are preferable. It has been found that non-aqueous polar protic solvents having two hydroxyl groups are preferable. It has been found that solvents having a viscosity in a range of 45 cP to 65 cP at 20° C. are preferable. Triethylene glycol and tetraethylene glycol are non-aqueous polar protic solvents having two hydroxyl groups. Triethylene glycol has a boiling point of 288.0° C. at a pressure of 760 mm Hg and a viscosity of 49.0 cP at 20° C. Tetraethylene glycol has a boiling point of 329.7° C. (decomposes) at a pressure of 760 mm Hg and a viscosity of 58.3 cP at 20° C. It has been found that triethylene glycol and tetraethylene glycol are preferable as solvents. On the other hand, it is preferable to reduce or avoid the use of lower-boiling point solvents having a boiling point of less than 280° C. at a pressure of 760 mm Hg. Examples of such lower-boiling point solvents are water, methanol, and ethanol. In a preferred metallic nanoparticle composition, a concentration, in aggregate, of solvents having a boiling point of less than 280° C. at a pressure of 760 mm Hg in the metallic nanoparticle composition does not exceed 3 wt %. In a preferred metallic nanoparticle composition, a concentration of metals (this can be estimated by estimating the concentration of metallic nanoparticles excluding the PVP capping layer) in the metallic nanoparticle composition is in a range of 60 wt % to 90 wt %, or in a range of 76 wt % to 84 wt %. In the Example 1 composition, the concentration of silver nanoparticles solids is approximately 85 wt %, and a concentration of silver is estimated to be in a range of 79 wt % to 83 wt %. 
     At step  54 , a printing apparatus (printer) is prepared for use. An example printer  10  has been described with reference to  FIG. 1 . Step  54  can also include preparing a capillary tube  120  ( FIGS. 4, 5, 6, 7, and 8 ), a piston-cylinder assembly (printer cartridge)  114  ( FIG. 9 ), a dispenser  116  including the capillary tube  120  and the printer cartridge  114  ( FIGS. 10, 11 ). At step  54 , the metallic nanoparticle composition can be injected into the cylinder  150 . At step  54 , the nanoparticle composition dispenser  116 , which includes the capillary tube  120 , is positioned above the substrate  110 , and the capillary tube is oriented such that its outlet points toward the substrate. 
     At step  56 , a position of the outlet  132  of the capillary tube  120  at zero height above the substrate is estimated or obtained. This position is referred to as the zero-height position.  FIG. 12  shows two schematic perspective views ( 206 ,  208 ) of the tapering portion  130  and the outlet  132  of a capillary tube, suspended above a substrate  110 . The two views  206 ,  208  correspond to different times. For ease of illustration, only a small portion of the tapering portion is shown. In this implementation, the tapering portion  130  (the capillary tube  120 ) is tilted at an oblique angle relative to a vertical axis (Z-axis  44 ). In view  206 , the outlet  132  (tip of the capillary tube) is at a height  200  above zero-height position  202 . The imaging system  12  can be used to estimate or obtain the zero-height position. In this case, a reflection  210  of the tapering portion  130 , including a reflection  212  of the outlet  132 , from the substrate&#39;s printable surface  112  is visible. For example, the imaging system  12  could estimate a midpoint between outlet  132  and its reflection  212  to be the zero-height position or could discern a position of the printable surface  112  of the substrate  110  and determine this position to be the zero-height position. 
     At step  58 , the capillary tube  120  (more specifically, the outlet  132 ) is displaced to a start position. The start position is a lateral position, typically expressed in coordinates along the substrate plane (along X-axis  40  and Y-axis  42 ), at which the metallic nanoparticle microdot is to be formed. At step  60 , the metallic nanoparticle composition is extruded from the outlet at a first height h 1  above the zero-height position. For example, view  206  ( FIG. 12 ) can be regarded as a view of the outlet  132  at a first height h 1  above the zero-height position if height  200  is equal to first height h 1 . This step  60  includes forming a fluid bridge (a bridge of the metallic nanoparticle composition) between the outlet  132  and the substrate  110 . Accordingly, the first height h 1  should be chosen to be sufficiently short such that a fluid bridge spanning the outlet  132  and the substrate  110  can be formed. Under typical conditions, the first height h 1  can be in a range of 1 μm to 10 μm. The metallic nanoparticle composition is extruded from the outlet under a pressure applied to the metallic nanoparticle composition. In the example shown in  FIGS. 1 and 9 , the regulated pneumatic system  106  applies pressure to the pneumatic port  184  of the dispenser  116 . The pressure applied to the metallic nanoparticle composition in the dispenser is preferably in a range of 0 bar to 10 bar. No electric fields need to be applied to the nanoparticle composition to carry out this extrusion. At step  60 , the extrusion can be carried out for a predetermined time. 
     Step  62  is an optional step and is illustrated in view  208  of  FIG. 12 . At step  62 , the capillary tube is lifted relative to the substrate (along Z-axis  44 ) by a height increment Δh ( 204 ) while continuing to extrude the metallic nanoparticle composition from the outlet. At step  62 , it is preferably that the fluid bridge remains intact while the capillary tube is lifted. Accordingly, at step  62 , it is preferably to lift the capillary tube slowly enough that the fluid bridge remains intact. At step  62 , the outlet reaches a height of h 1 +Δh. At step  62 , extrusion of the metallic nanoparticle composition can continue after the outlet reaches a height of h 1 +Δh. Under typical conditions, the height increment Δh can be in a range of 1 μm to 15 μm. It is also possible to repeat step  62 . For example, at a second iteration of step  62 , the outlet would reach a height of h 1 +2Δh and at a third iteration of step  62 , the outlet would reach a height of h 1 +3Δh. 
     At step  64 , the capillary tube is rapidly lifted to separate the outlet from the fluid bridge. The extrusion of metallic nanoparticle composition to the microdot is complete upon the separation of the outlet from the fluid bridge. Steps  58 ,  60 ,  62 , and  64  are repeated until all of the desired microdots have been formed on the substrate (decision step  66 ). 
     At step  68 , the workpiece is sintered. The workpiece includes the substrate, the microdots, and any other features (including elongate metallic nanoparticle features, discussed hereinbelow) on the substrate. The workpiece can be sintered in an atmosphere of air or in a protective atmosphere. Examples of protective atmospheres are: Argon, Nitrogen, and a mixture of Hydrogen (5 vol. %) and Nitrogen (95 vol. %). For example, the workpiece can be sintered at a temperature of 140° C. or lower. Photonic sintering can also be used. Photonic sintering can be carried out using a laser or a flash lamp. If a laser is used, emission wavelengths of 1064 nm, 532 nm, and 450 nm have been effective. The laser can be operated in continuous-wave mode or pulsed mode. 
       FIG. 14  is an SEM image of a metallic nanoparticle microdot  230 , formed from the silver nanoparticle composition of Example 1. Microdot  230  has been formed on printable surface  112  of substrate  110 . In this example, the substrate  110  is a bare glass substrate. In general, the substrate need not be a bare substrate. In other examples, the substrate can include a bare substrate and a thin-film coating on the bare substrate. In other examples, the substrate can include other previously existing features (e.g., conductive traces, transistors, light-emitting diodes, organic light-emitting diodes) on a bare substrate. Microdot  230  is bounded below by the printable surface  112  and bounded above by a curved surface  232 . Curved surface  232  has a peak  238 . 
     Method  50  was used to form microdot  230 , with the optional step  62  omitted (no lifting of the capillary tube relative to the substrate by a height increment of Δh while continuing to extrude the metallic nanoparticle composition from the outlet). The following conditions were used: capillary tube outlet outer diameter: 3.5 μm, pressure applied to the metallic nanoparticle composition: 9 bar, first height h 1  above the zero-height position: 5 μm, and time duration of extrusion at step  60 : 10 sec. 
       FIG. 15  is an SEM image of a cross section of the metallic nanoparticle microdot  230 . Microdot  230  has been formed on substrate  110 , which is a glass substrate in this example. The substrate extends principally along an X-axis  40  and a Y-axis perpendicular to the X-axis. In this example, this means that a major surface of the substrate extends along the X-axis and the Y-axis, while the substrate has a thickness along a Z-axis  44  perpendicular to the X-axis  40  and Y-axis. The curved surface  232  protrudes away from the substrate along the Z-axis  44 . The cross section has been chosen to include the peak  238  of the curved surface  232 . In the cross-sectional image of  FIG. 15 , a line  234  contained in the substrate surface  112  and a curved line  236  contained in the curved surface  232  are visible. The curved line  236  traverses the peak  238 . The X-axis  40  and the Y-axis have been chosen such that the curved line  236  extends along the X-axis and the Z-axis. In the background of the image of  FIG. 15 , a portion of the curved surface  232  is visible. There is a platinum layer  246  that was formed on top of the curved surface  232  in preparing the cross-sectional sample. Accordingly, the platinum layer is not part of the microdot  230 . Curved line  236  has been marked by circular marks that are used in a curve-fit shown in  FIG. 16 . The curved surface  232  intersects the substrate surface  112  ( FIG. 14 ). The curved line  236  intersects the substrate surface  112  (substrate line  234 ) at endpoints  242  and  244  ( FIGS. 15, 16 ). 
       FIG. 16  shows a graphical plot of curved line  236  (as circular markers). A curve-fit was conducted on the curved line  236  and it was found that the curved line was approximated very well by a parabolic function of the form: z=ax 2 +bx+c, where x is displacement along the X-axis  40 , z is displacement along the Z-axis  44 , and a, b, and c are respective constants. Displacement is expressed in μm. The following values were calculated for the respective constants: a=−0.0386 μm-2, b=0.384 μm −1 , and c=5.65×10 −3  μm. The coefficient of determination R 2  was determined to be 0.998. Generally, the coefficient of determination R 2  is expected to be in a range of 0.95 to 1.0. Preferably, R 2  is in a range of 0.98 to 1.0. Preferably, R 2  is in a range of 0.99 to 1.0. Line  240  is a parabolic line defined by these respective values for the constants a, b, and c. It is possible to measure the X-axis and Z-axis coordinates from an arbitrarily selected origin. However, in the examples discussed in  FIGS. 16  (microdot  230 ),  19  (microdot  250 ), and  23  (line  270 ), the origin was chosen to position the respective left endpoint ( 244  in  FIG. 16, 264  in  FIGS. 19, and 304  in  FIG. 23 ) at or near the origin. In these examples, the right endpoints ( 242  in  FIG. 16, 262  in  FIGS. 19, and 302  in  FIG. 23 ) were positioned near z=0. If the left endpoint is positioned sufficiently close to the origin such that the constant c is sufficiently small (preferably, c is in a range of −0.5×10 −2  μm to 0.5×10 −2  μm, or more preferably c is in a range of −1×10 −2  μm to 1×10 −2  μm), then the width of the parabolic shape (along the X-axis) can be approximated as w=−b/a, a height of the parabolic shape (along the Z-axis) can be approximated as h=−b 2 /(4a), and an aspect ratio AR, defined as height divided by width, can be approximated as AR=b/4. As shown in  FIG. 16 , the microdot width  246  is the distance (along X-axis  40 ) between the two endpoints  242 ,  244  and the microdot height  248  is the distance (along Z-axis) between the peak  238  and the substrate line  234  (approximately corresponding to z=0 line). In this example, the following quantities are calculated: w=9.9 h=0.96 μm, and AR=0.096. With changes in process conditions (e.g., lowering the viscosity of the metallic nanoparticle composition), it should be possible to achieve aspect ratios as low as 0.05 in metallic nanoparticle microdots and elongate metallic nanoparticle features. 
       FIG. 17  is an SEM image of a metallic nanoparticle microdot  250 , formed from the silver nanoparticle composition of Example 1. Microdot  250  has been formed on printable surface  112  of substrate  110 . In this example, the substrate  110  is a bare glass substrate. Microdot  250  is bounded below by the printable surface  112  and bounded above by a curved surface  252 . Curved surface  252  has a peak  258 . Method  50  was used to form microdot  250 , with the optional step  62  omitted (no lifting of the capillary tube relative to the substrate by a height increment of Δh while continuing to extrude the metallic nanoparticle composition from the outlet). The following conditions were used: capillary tube outlet outer diameter: 3.5 μm, pressure applied to the metallic nanoparticle composition: 9 bar, first height h 1  above the zero-height position: 1 μm, and time duration of extrusion at step  60 : 15 sec. 
       FIG. 18  is an SEM image of a cross section of the metallic nanoparticle microdot  250 . Microdot  250  has been formed on substrate  110 , which is a glass substrate in this example. The substrate extends principally along an X-axis  40  and a Y-axis perpendicular to the X-axis. The curved surface  252  protrudes away from the substrate along the Z-axis  44 . The cross section has been chosen to include the peak  258  of the curved surface  252 . In the cross-sectional image of  FIG. 18 , a line  254  contained in the substrate surface  112  and a curved line  256  contained in the curved surface  252  are visible. The curved line  256  traverses the peak  258 . The X-axis  40  and the Y-axis have been chosen such that the curved line  256  extends along the X-axis and the Z-axis. In the background of the image of  FIG. 18 , a portion of the curved surface  252  is visible. Curved line  256  has been marked by circular marks that are used in a curve-fit shown in  FIG. 19 . The curved surface  252  intersects the substrate surface  112  ( FIG. 17 ). The curved line  256  intersects the substrate surface  112  (substrate line  254 ) at endpoints  262  and  264  ( FIGS. 18, 19 ). 
       FIG. 19  shows a graphical plot of curved line  256  (as circular markers). A curve-fit was conducted on the curved line  256  and it was found that the curved line was approximated very well by a parabolic function of the form: z=ax 2 +bx+c, where x is displacement along the X-axis  40 , z is displacement along the Z-axis  44 , and a, b, and c are respective constants. Displacement is expressed in μm. The following values were calculated for the respective constants: a=−0.0363 μm −2 , b=0.394 μm −1 , and c=8.26×10 −3  μm. The coefficient of determination R 2  was determined to be 0.997. Line  260  is a parabolic line defined by these respective values for the constants a, b, and c. As shown in  FIG. 19 , the microdot width  266  is the distance (along X-axis  40 ) between the two endpoints  262 ,  264  and the height  268  is the distance (along Z-axis) between the peak  258  and the substrate line  254  (approximately corresponding to z=0 line). In this example, the following quantities are calculated: w=10.9 h=1.07 μm, and AR=0.099. 
       FIGS. 24 and 25  are graphical plots of data measured from metallic nanoparticle microdots as a function of a final height of the outlet of the capillary tube above the substrate. The microdots were formed from the silver nanoparticle composition of Example 1 on a bare glass substrate. Method  50 , including optional step  62  (lifting of the capillary tube relative to the substrate by a height increment of Dh while continuing to extrude the metallic nanoparticle composition from the outlet) was used to form the microdots. The following conditions were used: capillary tube outlet outer diameter: 3.5 μm, pressure applied to the metallic nanoparticle composition: 7 bar, first height h 1  above the zero-height position: 1 μm, height increment Dh: 1 μm. The final heights are the heights of the capillary tube outlet above the substrate at which step  64  (rapidly lifting the capillary tube to separate the outlet from the fluid bridge) is carried out. For each microdot, step  62  was repeated until the final height was reached. The final heights shown in  FIGS. 24 and 25  range between 1 μm and 13 μm. For example, for a final height of 3 μm, step  62  is carried out twice: (1) lifting from a height of 1 μm to 2 μm, and (2) lifting from a height of 2 μm to 3 μm. A time duration of step  60  was set at 3 sec and a time duration of each duration of step  62  was set at 3 sec. 
       FIG. 24  is a graphical plot  310  of heights of metallic nanoparticle microdots as a function of a final height of the outlet of the capillary tube above the substrate. The heights of the microdots were measured using a surface profilometer.  FIG. 25  is a graphical plot  320  of aspect ratios of metallic nanoparticle microdots as a function of a final height of the outlet of the capillary tube above the substrate. The aspect ratio of a microdot is defined as the height of the microdot divided by the diameter (width) of the microdot. The heights and widths of the microdots were measured using a surface profilometer. The microdot heights ranged between 1.3 μm (at a final height of 1 μm) and 4.56 μm (at a final height of 9 μm) ( FIG. 24 ). For smaller final outlet heights, in a range of 1 μm to 5 μm, the microdot heights increased with increasing final outlet heights. The microdot heights appear to saturate in a range of 4.1 μm to 4.6 μm for final outlet heights of 8 μm and greater. The microdot diameters (widths) ranged between 3.82 μm (at a final outlet height of 1 μm) and 13.14 μm (at a final outlet height of 13 μm). Generally, the microdot diameters increased with increasing final outlet heights. The microdot aspect ratio reaches a peak of 0.5 at a final height of 6 μm (diameter 5.69 μm, height 2.84 μm). The microdot aspect ratios are lower for final heights of 8 μm and greater because the diameters are larger for these final heights (9.1 μm diameter at final height of 8 μm and 13.14 μm diameter at final height of 13 μm) and the microdot heights are saturated. With changes in process conditions (e.g., increasing the viscosity of the metallic nanoparticle composition), it should be possible to achieve microdot aspect ratios greater than 0.5 and microdot heights greater than 4.5 μm. Microdot heights as large as 10 μm should be possible. On the other hand, if the metallic nanoparticles have diameters of less than 100 nm, a minimum microdot height can be 0.1 μm. Accordingly, heights of metallic nanoparticle microdots can be in a range of 0.1 μm to 10 μm. Similarly, heights of elongate metallic nanoparticle features can be in a range of 0.1 μm to 10 μm. 
       FIG. 26  is a graphical plot  330  of diameters of metallic nanoparticle microdots as a function of a time duration of extrusion at step  60 . The microdots were formed from the silver nanoparticle composition of Example 1 on a bare glass substrate. Method  50  was used to form the microdots, with optional step  62  omitted (no lifting of the capillary tube relative to the substrate by a height increment of Δh while continuing to extrude the metallic nanoparticle composition from the outlet). The following conditions were used: capillary tube outlet outer diameter: 3.5 μm, pressure applied to the metallic nanoparticle composition: 9 bar, first height h 1  above the zero-height position: 5 μm. The microdot diameter (width) increases monotonically from 9.57 μm for extrusion time duration of 10 sec to 25.51 μm for extrusion time duration of 30 sec. 
     It should be possible to form microdots as small as 1 μm in diameter by using a suitable combination of capillary tubes of outlet outer diameter smaller than 3.5 μm and extrusion times shorter than 10 sec. For example, in the case of lines, a line width of 2.6 μm was achieved using a capillary tube of outlet outer diameter 1.5 μm ( FIG. 23 ). It should be possible to form microdots as large as 50 μm in diameter by using a suitable combination of capillary tubes of outlet outer diameter greater than 3.5 μm and extrusion times longer than 30 sec. Metallic nanoparticle microdots with widths in a range of 1 μm to 50 μm should be possible. Similarly, elongate metallic nanoparticle features with line widths in a range of 1 μm to 50 μm should be possible. 
       FIG. 27  shows selected illustrative parabolic lines defined by certain values of constants a and b. In these graphical plots, the constant c is set to zero.  FIG. 27  shows the following: parabolic line  340  (circles, a=−0.05, b=0.5, w=10 μm, h=1.25 μm, AR=0.125), parabolic line  342  (triangles, a=−0.1, b=1.0, w=10 μm, h=2.5 μm, AR=0.25), parabolic line  344  (diamonds, a=−0.2, b=2.0, w=10 μm, h=5.0 μm, AR=0.5), and parabolic line  346  (x&#39;s, a=−0.35, b=2.0, w=5.714 μm, h=2.857 μm, AR=0.5). If feasible aspect ratios (AR) are in a range of 0.05 to 1, possible values of constant b would be in a range of 0.2 μm-1 to 4 μm-1 for microdots and lines. If the microdot widths or line widths are in a range of 1 μm to 50 μm, then the values of the ratio −b/a would be in a range of 1 μm to 50 μm. In accordance with the constraints on the values of aspect ratios, microdot heights or line heights, and microdot widths or line widths, the values of a would be in a range of −4 μm −2  to −0.01 μm −2 . 
     Method  70  of  FIG. 3  is an additive method of forming an elongate metallic nanoparticle feature on a substrate. Method  70  includes steps  52 ,  54 ,  56 ,  58 ,  72 ,  64 ,  76 , and  68 . Steps  52 ,  54 ,  56 ,  58 ,  64 , and  68  have been described with reference to method  50  ( FIG. 2 ). At step  52 , a metallic nanoparticle composition is prepared. At step  54 , a printing apparatus (printer) is prepared for use. At step  56 , a position of the outlet  132  of the capillary tube  120  at zero height above the substrate (zero-height position) is estimated or obtained. 
       FIG. 13  shows a perspective view of the tapering portion  130  and the outlet  132  of a capillary tube, suspended above a substrate  110 . The two views  206 ,  208  correspond to different times. For ease of illustration, only a small portion of the tapering portion is shown. In this implementation, the tapering portion  130  (the capillary tube  120 ) is tilted at an oblique angle relative to a vertical axis (Z-axis  44 ). In view  206 , the outlet  132  (tip of the capillary tube) is at a height  200  above zero-height position  202 . 
     At step  58 , the capillary tube  120  (more specifically, the outlet  132 ) is displaced to a start position.  FIG. 13  shows a view of a tapering portion  130  and an outlet  132  of a capillary tube at a start position  222 , which is a lateral position expressed in X-coordinates and Y-coordinates. At the start position  222 , the outlet  132  is at a first height h 1  ( 200 ). At step  72 , the metallic nanoparticle composition is extruded from the outlet while laterally displacing the capillary tube is laterally displaced along a trajectory ( 220 ) on the substrate from a start position  222  to an end position  224 . The height of the outlet above the substrate is at the first height h 1  ( 200 ) at the start position but the height may change as the capillary tube is displaced to the end position  224 . This may occur, for example, if the capillary tube traverses existing microscopic steps or other existing features. The height of the outlet above the substrate may stay approximately constant during step  72 . Step  72  includes forming and maintaining a fluid bridge (a bridge of the metallic nanoparticle composition) between the outlet  132  and the substrate  110 . Accordingly, the first height h 1  should be chosen to be sufficiently short such that a fluid bridge spanning the outlet  132  and the substrate  110  can be formed. Under typical conditions, the first height h 1  can be in a range of 1 μm to 10 μm. The pressure applied to the metallic nanoparticle composition in the dispenser is preferably in a range of 0 bar to 10 bar. No electric fields need to be applied to the nanoparticle composition to carry out this extrusion. 
     At step  64 , the capillary tube is rapidly lifted to separate the outlet from the fluid bridge. The extrusion of metallic nanoparticle composition to the elongate feature is complete upon the separation of the outlet from the fluid bridge. Steps  58 ,  72 , and  64  are repeated until all of the desired elongate features have been formed on the substrate (decision step  76 ). At step  68 , the workpiece is sintered. 
       FIG. 20  is an SEM image of metallic nanoparticle lines  270 ,  272 , and  274 , formed from the silver nanoparticle composition of Example 1. Metallic nanoparticle lines are examples of elongate metallic nanoparticle features. Lines  270 ,  272 , and  274  have been formed on printable surface  112 . The substrate extends principally along an X-axis  40  and a Y-axis  42  perpendicular to the X-axis. The lines  270 ,  272 , and  274  extend longitudinally along the Y-axis  42 . In this example, the printable surface has two portions: a higher surface portion  276  and a lower surface portion  286 . Surface portion  276  is aluminum (Al) and surface portion  284  is silicon nitride (SiN x ). There is a microscopic step  278  down from surface portion  276  to surface portion  284 . A height of the microscopic step  278  is approximately 370 nm. The lines  270 ,  272 , and  274  traverse the microscopic step without any breakage. Method  70  was used to form lines  270 ,  272 , and  274 . The following conditions were used: capillary tube outlet outer diameter: 1.5 μm, pressure applied to the metallic nanoparticle composition: 10 bar, first height h 1  above the zero-height position: 1 μm, and speed of lateral displacement at step  72 : 0.05 mm/sec. For each of the lines, the start position was in the higher surface portion  276  and the end position was in the lower surface portion  284 . 
       FIG. 21  is an SEM image of a portion  280  of the workpiece ( FIG. 20 ). In this portion  280 , the lines  270 ,  272 , and  274  are on a silicon nitride surface. In the portion  280  shown in  FIG. 21 , the line  270  is bounded below by substrate surface  284  and bounded above by a curved surface  292 . In the portion  280  shown in  FIG. 21 , curved surface  292  extends longitudinally along the Y-axis  42 . A cross section  282  of line  270  was obtained as shown in  FIG. 21 .  FIG. 22  is an SEM image of the cross section  282  of the metallic nanoparticle line  270 . The curved surface  292  protrudes away from the substrate along the Z-axis  44 . In the cross-sectional image of  FIG. 22 , a line  294  contained in the substrate surface  284  and a curved line  296  contained in the curved surface  292  are visible. The cross section  282  has been chosen to be transverse to the longitudinal direction (Y-axis  42 ) along which the curved surface  292  extends. Accordingly, the curved line  296  extends along the X-axis  40  and the Z-axis  44 . The curved surface  292  intersects the substrate surface  284  ( FIG. 21 ). The curved line  296  intersects the substrate surface  284  (or substrate line  294 ) at two endpoints  302 ,  304  ( FIGS. 22, 23 ). In the background of the image of  FIG. 22 , a portion of the curved surface  292  is visible. The curved line  296  traverses its peak  298 . Curved line  296  has been marked by circular marks that are used in a curve-fit shown in  FIG. 23 . 
       FIG. 23  shows a graphical plot of curved line  296  (as circular markers). A curve-fit was conducted on the curved line  296  and it was found that the curved line was approximated very well by a parabolic function of the form: z=ax 2 +bx+c, where x is displacement along the X-axis  40 , z is displacement along the Z-axis, and a, b, and c are respective constants. Displacement is expressed in p.m. The following values were calculated for the respective constants: a=−0.19 nm −2 , b=0.503 μm −1 , and c=−2.62×10 −3  μm. The coefficient of determination R 2  was determined to be 0.995. Line  300  is a parabolic line defined by these respective values for the constants a, b, and c. As shown in  FIG. 23 , the line width  306  is the distance (along X-axis  40 ) between the two endpoints  302 ,  3044  and the height  308  is the distance (along Z-axis) between the peak  298  and the substrate line  294  (approximately corresponding to z=0 line). In this example, the following quantities are calculated: w=2.6 h=0.33 μm, and AR=0.126. 
     Metallic nanoparticle microdots and features having parabolic profiles are significant in that there are no sharp edges. Methods of forming these metallic nanoparticle microdots and features are additive manufacturing methods. Subtractive manufacturing methods such as photolithography and nanoimprint lithography are available but conventional features that are formed using these subtractive manufacturing methods do not have parabolic surfaces. Conventional features that are formed using subtractive manufacturing methods have sharper edges or sidewalls that are closer to vertical. Accordingly, there are frequently difficulties in forming subsequent conformal coatings over conventional features without breakage. The development of these metallic nanoparticle microdots and features will enable higher throughput manufacturing of multi-layer conductive features in the semiconductor and optoelectronics applications. 
     EXAMPLES 
     Example 1: Silver Nanoparticle Paste Composition (85 wt %) in Triethylene Glycol, Including Dispersing Agent 2 wt % 
     Reagents: 
     AgNO3—12.5 g 
     PVP (K30 grade)—100.1 g 
     Ethylene glycol—560 ml 
     Acetone—1520 ml 
     Ethanol 96%—300 ml 
     Triethylene glycol—1.326 ml 
     Dispersing agent, alkylammonium salt of a copolymer with acidic groups—235.2 μl 
     1) Synthesis 
     Two synthesis reactions were done in parallel. For each synthesis reaction: AgNO3 (12.5 g) was dissolved in 50 ml of Ethylene Glycol at room temperature. In a three-necked flask, PVP (100.2 g) was dissolved in 250 ml of Ethylene Glycol, under reflux, while heating at 140° C. AgNO3 solution was poured in a quick movement (via funnel) into hot PVP dissolved in Ethylene Glycol. Mixtures were heated at 140° C. for 60 min under vigorous stirring. Finally, cooled in cold water bath until room temperature was reached. 
     2) Purification 
     Mixture from each synthesis was poured into a 2.5 liter beaker. 100 ml of Ethylene Glycol was added to the three-necked reaction flask, sonicated for 1 min under stirring and pooled with the previously mentioned fraction. 1440 ml of Acetone and 160 ml of Ethylene Glycol were mixed in a 2 liter beaker and poured into the beaker containing the Ag NPs suspension, under stirring first at 500 rpm, then 900 rpm. Another 40 ml of acetone was then added, then another 40 ml of acetone was added. There was a change in the color of the solution from dark green to brown. The contents of the beaker were poured equally into six 500 ml centrifuge bottles and were centrifuged for 15 min @ 4000×g. Clear orange supernatants were discarded. Silver pellets were re-dispersed in 40 ml of ethanol (per bottle) under sonication and shaking (10 min). The solution were poured into two bottles (120 ml per bottle), followed by centrifugation for 35 min @ 11000×g. The pellet were individually re-dispersed in premixtures of 30 ml EtOH and 58.8 μl dispersing agent (for each of 4 bottles of the double synthesis) under sonication and shaking (10 min). 
     3) Formulation 
     Approximately 120 ml of obtained dispersion were transferred into a syringe and filtered through 1.0 μm PA filter directly into round-bottom flask. 1.326 ml of triethylene glycol were added. Flask was placed on rotary evaporator at 43° C., 110 mbar for 40 min and then set to 35 mbar. Time taken to reach the set pressure was 30 min, and when reached, the condition was maintained for 5 min. Paste-like composition was transferred into a syringe and filtered through a 0.45 μm PVDF filter directly into 5 ml PE syringe (filled from top). Obtained dispersion is estimated to have a solid content concentration of 85 wt % ±2 wt % (based on TGA measurement). Silver content is estimated to be in a range of 79 wt % to 83 wt (based on ICP or AAS measurement). The concentration of the dispersing agent in the composition is estimated to be approximately 2 wt %.