Method for repairing conductor tracks

Abstract

A method for modifying an elongate structure including providing a fluid deposited onto the substrate, the fluid containing a dispersion of electrically polarizable nanoparticles and applying an AC voltage across a portion of the elongate structure so as to cause an alternating electric current to pass through the narrow section such that a break in the elongate structure is formed at the narrow section, the break being defined between a first broken end and a second broken end of the elongate structure, and then cause, when the break is formed, an alternating electric field to be applied to the fluid such that a plurality of the nanoparticles contained in the fluid are assembled to form a continuation of the elongate structure extending from the first broken end towards the second broken end so as to join the first and second broken ends.

Claims

1. A method of modifying an elongate structure, the method comprising: providing on a substrate an elongate structure formed of assembled electrically polarizable nanoparticles, the elongate structure including a narrow section to be modified; providing a fluid deposited onto the substrate, the fluid containing a dispersion of electrically polarizable nanoparticles and being positioned so that at least the narrow section of the elongate structure is immersed therein; and applying an AC voltage across a portion of the elongate structure that includes the narrow section using a first electrode in contact with the elongate structure at a first end of the portion and a second electrode in contact with the elongate structure at a second end of the portion, so as to: cause an alternating electric current to pass through the narrow section such that a break in the elongate structure is formed at the narrow section, the break being defined between a first broken end and a second broken end of the elongate structure, and then cause, when the break is formed, an alternating electric field to be applied to the fluid such that a plurality of the nanoparticles contained in the fluid are assembled to form a continuation of the elongate structure extending from the first broken end towards the second broken end so as to join the first and second broken ends; monitoring the current passing through the continuation of the elongate structure and continuing to apply the AC voltage across the portion of the elongate structure at least until the monitored current is equal to or greater than a target current; wherein the steps of: applying an AC voltage across a portion of the elongate structure that includes a narrow section, monitoring the AC amplitude of the current passing through the continuation of the elongate structure, and continuing to apply the AC voltage across a portion of the elongate structure at least until the monitored current amplitude is equal to or greater than a target current amplitude define one modifying cycle, and wherein the method further comprises: performing one or more further modifying cycles, for each of which each of the amplitude of the applied AC voltage and the target current amplitude is increased with respect to the previously performed modifying cycle.

2. The method according to claim 1, further comprising varying the applied AC voltage in accordance with the monitored current, wherein varying the applied AC voltage comprises varying one or both of the amplitude and the DC bias of the applied AC voltage.

3. The method according to claim 1, wherein the applied AC voltage is varied in accordance with a relationship between the monitored current and a predetermined tempering current.

4. The method according to any of claim 1, wherein the applied AC voltage is varied according to a feedback loop using the monitored current as feedback data.

5. The method according to claim 1, wherein the narrow section is one of a plurality of narrow sections included in the elongate structure, and wherein the AC voltage is applied so as to cause the break in the elongate structure to be formed at the most narrow of the plurality of narrow sections.

6. The method according to claim 1, further comprising, if the formed continuation is as narrow as or narrower than a target width corresponding to a width for which a section of the elongate structure will be caused to break, continuing to apply the AC voltage so as to: cause an alternating electric current to pass through the continuation such that a further break in the elongate structure is formed at the continuation, the break being defined between a further first broken end and a second further broken end of the elongate structure, and then cause, when the further break is formed, an alternating electric field to be applied to the fluid such that a plurality of the nanoparticles contained in the fluid are assembled to form a further continuation of the elongate structure extending from the first further broken end towards the second further broken end so as to join the first further broken end and second further broken end.

7. The method according to claim 1, wherein the providing of the elongate structure formed upon the substrate and the fluid deposited upon the substrate comprises: depositing the fluid onto the substrate so as to define a wetted region; and applying an alternating electric field to the fluid on the region, using a first electrode and a second electrode, so that a plurality of the nanoparticles are assembled to form the elongate structure, extending from the first electrode towards the second electrode; and further comprises, during the step of applying the alternating electric field, increasing the separation between the first and second electrodes by moving the second electrode away from the first electrode so as to extend further the elongate structure towards the second electrode.

8. The method for forming a compound elongate structure upon a substrate, comprising providing and modifying, according to the method of claim 7, a respective elongate structure upon each of a plurality of adjacent regions on the substrate, such that each structure is connected to at least one other structure.

9. The method according to claim 8, comprising forming and modifying each of the plurality of elongate structures in sequence, wherein the modifying of each elongate structure is continued until a completion criterion for the respective elongate structure is fulfilled.

10. The method according to claim 9 and further comprising monitoring the AC amplitude of the current passing through the continuation of the elongate structure, wherein the completion criterion comprises one or both of: the monitored current amplitude being equal to or greater than a predetermined completion target current amplitude for at least a predetermined duration, and a monitored resistance of the respective elongate structure being less than or equal to a predetermined completion resistance.

11. The method according to claim 9, comprising, if the completion criterion for a respective elongate structure is not met during a predetermined duration, repeating the forming and modifying of that structure.

12. The method according to claim 1, further wherein the elongate structure has a width less than 1 μm and a length greater than 100 μm, wherein the width of the structure at its most narrow point is greater than or equal to 70% the average width of the structure.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) Examples of the present invention will now be described, with reference to the accompanying drawings, in which:

(2) FIG. 1 is a schematic drawing of a narrow section in a conductive line;

(3) FIG. 2A is a graph plotting the electric current passing through a portion of an elongate structure over time during a first example method according to the invention;

(4) FIG. 2B is a flow diagram illustrating steps of the first example method according to the invention;

(5) FIG. 2C is a schematic drawing of a section of an elongate structure at several stages during the first example method according to the invention;

(6) FIG. 3 is a schematic drawing of an elongate structure including multiple narrow sections;

(7) FIG. 4 is a graph plotting the electric current passing through a portion of an elongate structure over time during a second example method according to the invention;

(8) FIG. 5A is a circuit diagram showing apparatus used in a third example method according to the invention;

(9) FIG. 5B is a graph plotting the configured variation in applied AC voltage amplitude against monitored variation in current passing through a portion of elongate structure during the third example method according to the invention;

(10) FIG. 5C shows the variation in voltage and current over time as monitored during the third example method according to the invention;

(11) FIG. 6 is a schematic comparison of a method for forming elongate structures according to the prior art and a fourth example method according to the present invention.

DESCRIPTION OF EMBODIMENTS

(12) With reference to FIGS. 1-3 a method 200 of modifying an elongate structure 101 is now described. Part of an elongate structure 101 including a narrow section or bottleneck 103 is depicted schematically in FIG. 1. For the sake of simplicity of illustration, the width of the structure W is shown as being uniform for each of the narrow section 103 and the two wider or normal sections 105A and 105B. However, in practice, owing to the previously discussed randomness involved in the nanoparticle assembly process employing dielectrophoresis, this width uniformity is unlikely to be present.

(13) The width, thickness, diameter, or cross-sectional area perpendicular to the elongate axis of the structure 101 is considerably smaller in the narrow section 103 than in the remainder of the structure 105A, 105B, and is smaller than that of the maximum value for the structure (the average and maximum value for the remainder of the structure being the same in the present illustration owing to the schematic nature of the drawing). Width and thickness may refer to the greatest linear extent of the elongate structure in a plane parallel to the elongate axis of the structure at a given point, parallel to and normal, respectively, to the plane of the substrate upon which the structure is formed at that point. Diameter may refer to a similarly transverse, that is perpendicular to the elongate axis, measure of linear extent, at any orientation in the transverse plane, and typically corresponding to a straight line passing through the geometric centre of the cross-section in that plane. For structures with non-circular cross-sections, diameter might refer to an average diameter for all transverse orientations. The line is formed from a material that is electrically conductive. However, the electrical conducting capability of the structure is limited by the narrow section 103, because the morphology of that narrow section, namely the tapering to a width or cross-sectional area that is smaller than the remainder or average width of the structure. This is because, for a material with a given conductivity, the rate at which electric charge may be carried along a structure made of that material is dependent upon the cross-sectional area of the material at a given point perpendicular to the axis corresponding to the direction of current flow. This bottleneck in the conductor, that is this narrow section 103 that impedes the rate of flow of charge along the structure 101 is illustrated notionally by the circuit diagram section shown at the lower part of FIG. 1. The resistance R.sub.1 of each of the wider or normal sections 105A and 105B is considerably lower than the resistance R.sub.2 of the narrow section 103.

(14) It should be noted that a bottleneck 103 in an elongate structure 101 such as this may still be thought of or classified as such while having a range of different lengths. For example, rather than the extended narrow section 103 depicted in FIG. 1, which has a length comparable to the wider sections 105A and 105B, a narrow section may also exist that has a shorter length, for example a narrow section in which the width or cross-sectional area of the structure tapers or is small relative to the average or maximum width or area of the structure by virtue of being formed as one or more notches coinciding at a point or section of a structure.

(15) FIG. 2A illustrates the current flowing through the line during a modification process, which may be thought of as a tempering process, according to the first example method. FIG. 2B sets out what happens to the line of the elongate structure itself during this line tempering process. Initially, at the stage indicated at 2051, which may correspond to a time during which the line is being grown or assembled by dielectrophoresis, the current flowing through the elongate structure line is zero. This involves some fluid ink, that is fluid within which polarizable nanoparticles are dispersed, being provided upon a substrate and the elongate structure being grown from that dispersion of nanoparticles, in accordance with the previously discussed known method.

(16) The fluid contains electrically polarizable nanoparticles in the form of silver nanoparticles having a diameter of 100 nm. The mass fraction of the nanoparticles within the fluid is 0.2%. The main component of the fluid is a solvent in the form of ethylene glycol. The fluid also contains a stabilizer in the form of glucose, which has a mass fraction within the fluid of 0.6%.

(17) Since the fluid ink is not conductive, or is not sufficiently conductive to carry a current at the given applied voltage amplitude, and because the elongate structure is not in contact with both electrodes, the elongate structure forms part of an incomplete circuit. When the line short circuits with the second electrode, for example by stopping or slowing the moving second electrode so as to allow the growing end of the elongate structure to reach it, the current starts to flow, at point 2053. During step 2055 the elongate structure is sintered or coalesces by means of the heat generated by virtue of the current passing through the line. The current flowing through the elongate structure is in other words a source of Joule heating that sinters nanoparticles or causes them to be compressed or more closely packed, and increases the conductivity of the line by increasing the charge density that the material is capable of carrying.

(18) A schematic illustration of a narrow section of the elongate structure, that section having high resistance relative to the remainder of the line, is shown in FIG. 2C. As this drawing shows, the sintering at stage 2055 results in a break or a line defect being formed at the narrow section at the time represented by 2057. This break or interruption in the elongate structure causes the circuit to be broken and thereby causes the current to cease flowing through the line structure.

(19) Thus the narrow section shown in FIG. 3 at 303 is intentionally broken by way of the application of a voltage across a portion of the line containing the narrow section. The narrow section, and the comparatively wider sections either side of it 205A, 205B are also shown in FIG. 2C.

(20) The gap or break 207 that is formed by the failure of the high-resistance section 203 during sintering results in an alternating electric field being applied to a drop or volume of fluid (not shown) that is deposited so as to envelop or contain at least the narrow section 203. In this way the conditions for dielectrophoretic self-assembly of nanoparticles dispersed within the fluid are created, specifically in the gap region 207.

(21) The AC frequency and amplitude, and the amplitude of the DC bias of the applied electric field are such that the electric field strength and gradient present at the region 207 between the broken ends 209A, 209B results in the polarizable nanoparticles dispersed in the fluid experiencing a dielectrophoretic force which causes them to begin to assemble together upon the first broken end 209A. In the present example, the voltage applied across the electrodes starts with an AC frequency of 10 kHz, an AC amplitude of 70 V and a DC bias of 1.5 V. The inhomogeneous electric field is conducive to assembly via dielectrophoresis, not least because of the gradient or divergence of the electric field towards the electrodes generating the field. The tapering shape of the broken ends, which effectively act as electrodes, is in part responsible for producing such an inhomogeneous electric field.

(22) The potential applied to the electrodes is additionally configured to have a DC bias which results in nanoparticles assembling by preference upon one of the two ends, which in this case is the first end 209A.

(23) Thus at stage 2059, a plurality of nanoparticles are assembled to form a continuation 2011 of the elongate structure 201 extending from the first end 209A towards the second end 209B. This plurality of nanoparticles corresponds to those particles within the fluid that are sufficiently close to the region of assembly, wherein the electric field conditions are beneficial for assembling the particles via dielectrophoresis, in that they are attracted to and agglomerate upon end 209A so as to begin forming the continuation 2011.

(24) Owing to the direction of the electric field between the electrodes, as the continuation 2011 grows via the progressive addition to the structure of particles within the fluid, the assembling continuation grows or extends towards the second end 209B.

(25) When the continuation 2011 grows sufficiently far so as to reach or make electrical contact with the second broken end 209B, the circuit is again completed. This is shown at step 2060, as indicated by the reestablishment of a non-zero current flowing through the portion of the structure 201.

(26) As indicated by FIG. 2A, the current flowing at step 2060 is greater than the current flowing at stage 2053 prior to the breaking of the initial narrow section 203. This is a result of the continuation 2011 being less narrow, and consequently having a lower electrical resistance, than the initial narrow section 203. The amplitude of the current produced by the applied AC voltage is therefore less limited following the dielectrophoretic self-repair, and is therefore greater.

(27) The return of the current flowing in the elongate structure causes the sintering process to resume, owing to the resistive heating generated in the line. However, in those parts of the line 205 having a thickness and/or conductance greater than the desired level, the sintering will have no disruptive impact upon the assembled nanoparticles therein.

(28) It is not certain that, following dielectrophoretic self-repair 2059, the newly built part of the line 2011 will be stronger than the initial bottleneck 203 on every occasion, since as noted earlier in this disclosure, there is a degree of randomness in the DEP assembly process. However, it will be understood that, should the newly formed continuation section 2011 be as weak or weaker than, or at least as resistive as, or equivalently at least as narrow as, the initial bottleneck 203, the current that flows through the too-narrow new section will cause that section to break as it did the initial bottleneck. These cycles will continue, with overly narrow newly formed sections being burned out and repaired again, until such a time as the newly built section is more robust, or less resistive, than the initial bottleneck 203. This cycle of burning out and repairing is so rapid that it does not significantly impact the time of the modifying process.

(29) The graph shown at FIG. 2A can correspond to the occurrence of several iterations of the breaking-sintering process cycle, at stages 2061-2063. The incremental increases in the current re-established after the self-repair of the narrow section at each of these stages is a result of the assembly of progressively stronger or less resistive continuation sections.

(30) Once a line is modified so as to have sufficiently low resistance along the entire length of the portion to which the AC voltage is applied such that no further breaks are formed, at point 2065, the completion target current indicated by I.sub.temp, has been reached. This target current corresponds to the amplitude of the current through the line that is produced by a given applied AC voltage amplitude for a line or elongate structure 201 the overall resistance of which, or equivalently the overall robustness or thickness of which, is at least as great as a desired threshold.

(31) The various stages depicted at FIG. 2A may also correspond to the repair of multiple sections that are included in a length of elongate structure and are narrower than the average, maximum, or desired thickness for the line or the remainder of the line, or a portion thereof.

(32) Such a line is depicted at several stages corresponding to those illustrated in FIG. 2A in FIG. 3. In these figures, like reference numerals represent corresponding stages. At stage 3055 the portion of the elongate structure 301 shown contains three narrow sections 303, 303′, 303″, listed in order of increasing thickness. At stage 3055 an AC voltage modulated so as to cause the portion of the line to be repaired or modified is applied across the portion. Thus the sintering process is initiated, and the most narrow section 303, which has the greatest level of resistance and therefore experiences the greatest level of disruption owing to resistive heating and/or disruptive capacitance, is caused to break. Since the narrowest of the narrow sections, 303, has the greatest tendency to be broken when sintered compared with the other narrow sections, section 303 breaks first, and so causes the circuit to be broken and the current to stop flowing, thereby preventing the other sections 303′, 303″ from being broken at the same moment.

(33) The DEP action is then caused to occur, such that electrically polarizable nanoparticles in fluid ink surrounding the narrow section are assembled to form continuation 3011, thereby re-joining the two broken ends and re-completing the circuit. In this illustrative example, the re-formed section 3011 remains narrower than the desired thickness for which the applied AC voltage is configured to cause the self-repairing line to reach. This first rebuilt section may be thought of as a further narrow section, 303″. This stage is depicted at 3060, during which a current is again flowing in the line through each of the now present narrow sections 303′, 303″, and 303″, which are listed in order of increasing thickness.

(34) The sintering caused by the current flowing during stage 3060 causes the most narrow of the narrow sections present at this stage, section 303′, to be broken. When that broken section is self-repaired, the current again begins to flow, at stage 3061. As indicated by the increased current shown at equivalent stage 2061 in FIG. 2A, the section with the highest resistance, is, at stage 3061, section 303″, and so the current flowing through the line portion is greater still than that flowing at stage 3060.

(35) A further cycle of sintering and reassembly occurs between the stages depicted at 3061 and 3063, such that narrow section 303″ has been replaced by a continuation having similar thickness to the remainder of the line, or to the average thickness of the line. Therefore at stage 3063 the only remaining section that is narrower than the remainder of the line, and is therefore limiting upon the current that a line may conduct for a given applied AC voltage, is the initially repaired section 303′″. In the present example, the applied AC voltage is modulated so as to cause any section of the elongate structure having a thickness less than that of the normal section 305 to experience a disruptively high magnitude of current and consequently be broken. Therefore, the sintering at stage 3063, indicated by the level of current shown at equivalent stage 2063, causes the now limiting narrow section 303′″ to be broken and then reformed as a continuation 3011′, the thickness of which is equivalent to that of wide section 305. Thus, the target current has been reached by the progressive repair of increasingly wide bottlenecks in the portion of the elongate structure. At stage 3065, no section of the portion to which the AC voltage is applied is sufficiently narrow so as to be resistively heated to such a degree that it is disrupted or broken. Therefore, the portion is sufficiently robust, following the cycles of sintering and self-repair, to sustain the target current.

(36) At the end of this process, which may be thought of as a modification cycle, or a tempering cycle, the current is stabilised at the level of the target current. In practice, owing to the sintering that occurs because of the flow of the target current following stage 3065, the resistivity of the line is likely to decrease further, as the assembled nanoparticles therein are caused to coalesce.

(37) The tempering process, or the modification process, can be performed in a number of tempering or modification cycles, with each cycle having its own set or predetermined target current. A second example method according to the invention, comprising several of these modifying cycles, is depicted by way of a graph plotting current versus time in FIG. 4. The graph shows the variation current over four modification cycles, 470, 472, 474, and 476. These four cycles are listed in order of increasing target current amplitude, indicated by I.sub.temp.sup.(1), I.sub.temp.sup.(2), I.sub.temp.sup.(3), and I.sub.temp.sup.(4). In the present example, these four current values are 0.5, 1.0, 1.5, and 2.0 mA, respectively.

(38) The first tempering cycle 470 is equivalent to the process depicted for the previously described example, shown at FIG. 2A. At the end of the cycle 470, the current flowing through the line portion is I.sub.temp.sup.(1), which is the target current for the first cycle, indicating that a sufficient degree of self-repairing has occurred in the narrow sections initially present in the line for the structure or the portion thereof to be able to sustain a current caused by the voltage applied during the cycle 470 without any further breakages being caused by the sintering. In the present example, the duration of the first tempering cycle 470 is 7.5 ms. Likewise, the subsequent cycles 472, 474, and 476 are each 7.5 ms in duration.

(39) The second cycle 472 is then begun by way of increasing the applied AC voltage to a level or magnitude corresponding to a higher target current than that configured for the first cycle. Because of the now-increased applied AC voltage, a greater AC current amplitude is produced in the line, which causes progressive breaks to be caused in narrow sections of the line that were not sufficiently narrow to be caused to break by the voltage applied during the previous cycle 470. In this way, the robustness of the line is increased by the breaking and self-repair processes that are caused to occur during the second cycle 472 to a degree beyond that achievable during the first cycle 470.

(40) Once the target current I.sub.temp.sup.(2) of the second cycle 472 is reached, a third cycle 474 is begun by again increasing the applied AC voltage magnitude. As can be seen in FIG. 4, in the present example two further breakages and rebuilding steps are caused to occur during the third tempering cycle 474. This indicates that at least one narrow section was present in the line being modified at the beginning of the cycle 474 that was sufficiently robust not to have been caused to break by either of the two preceding cycles 470, 472, but which was caused to be broken by the higher voltage amplitude applied during the third cycle 474.

(41) The fourth depicted cycle 476 involves again increasing the applied AC voltage so as to cause narrow sections that are more robust still, which may be in the same locations or different locations as those which were repaired in preceding cycles, to be broken and repaired by dielectrophoresis.

(42) The second example method is advantageous in its inclusion of several modification cycles 470-476 for a number of reasons. Firstly, the elongate structure is caused to be more robust at the end of the tempering process by way of the higher ultimate target current than that of the first described example.

(43) This is achieved in a faster and more controllable way than attempting to repair the line according to the current I.sub.temp.sup.(4). Moreover, by progressively increasing the target current, and correspondingly increasing the applied AC voltage through several tempering cycles, the risk of the line experiencing a physical shock resulting from an abrupt change of temper current is reduced or avoided.

(44) A third example method according to the invention is now described, with reference to FIG. 5. This example involves the use of a feedback loop involving current measurement, the voltage generator used to apply the AC voltage to the line portion, and a printing head for applying an elongate structure to a surface. In order to perform line tempering and assemble an elongate structure, for example, segment by segment, a feedback loop is implemented as illustrated by the circuit diagram at FIG. 5A and the graphs at FIGS. 5B and 5C. The feedback loop works as follows. Resistors R.sub.s are connected in series with the conductive elongate line structure 501. The resistance of these can be varied. Using a voltmeter, V, the voltage drop across one of the resistors is measured, which indicates the current flowing through the resistor. Since the resistors are connected in electrical series with the line 501, the current flowing through the resistors and the line is the same. Based upon the measured or calculated current, the system modifies the value of the amplitude of the generated AC voltage.

(45) A nominal current value is set as a starting parameter. The degree to which the feedback loop system decreases or increases the applied voltage, that is ΔV, depends upon the difference between the measured current and the nominal current value, as shown in FIG. 5B. The dynamics of increment and decrement of the generated voltage may not necessarily have to be the same.

(46) FIG. 5C illustrates how the feedback loop reacts to measured current changes and causes adjustments to the applied voltage. Initially, during formation of a line being assembled by dielectrophoresis, such as a self-repairing assembly of a continuation between two broken ends of an elongate structure, prior to the growing end of the assembling continuation reaching and making electrical contact with the second broken end, the current is zero, at stage 581. During this stage, the system increases the voltage because the measured current is less than the nominal current parameter.

(47) When the short circuit occurs at 582 as a result of the assembled continuation making electrical contact between the two broken ends and completing the circuit, the current value is measured as being above the nominal parameter, and the feedback loop system decreases the generated voltage. This results in the current through the line being decreased and stabilised towards the nominal value, as indicated by the progressively decreasing oscillations about the tempering current value indicated on the lower graph of FIG. 5C.

(48) In practice it has been found that the maximum of the current peak during the short circuit cannot easily be controlled. This maximum value is dependent upon the generated voltage. Therefore, the voltage is decreased for the purposes of safety and limiting the risk of damage.

(49) Although a large current is required in order to intentionally overheat the line and cause weak, narrow sections to be broken, a current with too great an amplitude will be damaging to the line. Therefore, an optimal value or range of values for the voltage and current is used, so that the line will be broken as required but can still recover and repair itself by dielectrophoresis.

(50) Table 1 below lists parameters used to control the signal in accordance with this example according to the invention, alongside respective ranges of suitable values.

(51) TABLE-US-00001 TABLE 1 Parameter Value Number of cycles for line tempering and 1-100 respective currents Max/min voltage used to build the line 4 V-100 V Level at which we want to stabilize the 10 μA-10 mA.sup.  current Voltage change ΔV 10 μV-10 V   Voltage change frequency 1 kHz-10 MHz.sup. 

(52) An example set of parameters which may be used in a modification procedure applied to an elongate structure having a thickness of around 1 μm is: number of cycles=10; minimum/maximum voltage=1-16 V; current=0.3-3 mA; voltage change=0.1-3 V; voltage change frequency=10 MHz.

(53) As mentioned with reference to the above-described example, it is in some applications advantageous to build a long elongate structure in steps, and apply the modification cycle procedure to each formed line segment in turn, so as to repair narrow sections, on a segment-by-segment basis. A fourth example method according to the invention is now described to demonstrate this.

(54) It is known in the prior art to cause an elongate structure formed from assembled polarizable nanoparticles to be printed upon a substrate using a first electrode and a second electrode applying an alternating electric field to a fluid containing electrically polarizable nanoparticles deposited on the substrate, by way of moving the second electrode such that the growing end of the elongate structure continually extends towards that electrode. Although forming such a line in this manner is in many applications virtually unlimited, owing to the ability to move the second electrode and therefore print any arbitrary line morphology, when applying the self-repair technique of the present disclosure to elongate structures, it is advantageous to do so by treating shorter portions of long structures, one at a time. The time efficiency of such a forming and repairing procedure can be increased by repairing each segment of the line after it has been assembled, prior to moving on to assemble the subsequent segment.

(55) In the present example, an elongate structure is formed upon a substrate in steps, that is segment-by-segment. The movement of the printing head is discrete, in that the printing head moves a certain length Δx. The system performing the method is configured such that the print head can only move when a current condition is fulfilled. This current condition may correspond to the target current, or the final target current in a series of tempering cycles, being reached by the current in the structure.

(56) The modifying process is performed for each segment. In FIG. 6 and Table 2 the fourth example method is compared with the conventional approach of the prior art.

(57) Building and repairing a conductive line structure in a stepwise manner has a number of advantages.

(58) Firstly, it is possible to use a much lower voltage, owing to the effect of scale, when performing the method on shorter portions of an elongate structure. It has been found that the use of a lower voltage results in growth and repair that can be more precisely controlled.

(59) Moreover, it is easier to repair a short segment of an elongate structure than it is to repair a comparatively long segment.

(60) Furthermore, the line can be treated as an extension of the starting electrode, that is the first or non-moving electrode, used in forming the elongate structure on the substrate. The tempering and sintering process applied to the line segment in a step-by-step manner improves the quality of each of these effective extensions, by way of reducing the length, and therefore the number of weak or narrow sections, or sections having undesired or deleterious morphology between the electrode end and the end of the segment that is distal to the electrode.

(61) TABLE-US-00002 TABLE 2 Conventional approach - static Present example - dynamic process process Constant shape and amplitude Voltage assembling the line is modified of AC and DC signals based on the feedback loop between the generator and current measurement system Constant frequency of AC Variable frequency of AC signal. This signal allows the width of each segment to be controlled Current is not controlled Current is controlled Velocity of the printing head The line is built in segments, and thus is constant the movement of the printing head is discrete

(62) The condition for the printing head to move on to the next segment, in the present example, is the monitoring of a continuous complete circuit, that is a continuously flowing current through the line, with a minimum duration of t.sub.1. If such a complete circuit is not achieved within a given duration, t.sub.2, the apparatus performing the example method is configured to build the segment again, by moving the printing head back so as to begin once again the formation of an elongate structure upon that respective region of the substrate.

(63) FIG. 6A illustrates a prior art method for forming a line. FIG. 6B depicts the method according to the present example. It can be seen that, in the prior art, electrode 613 is moved at a constant speed, whereas it is moved in a dynamic, incremental manner in the present example. Thus the elongate structure 601 is formed upon the substrate 615, and is subsequently repaired, in a stepwise manner in the present example. As is also indicated in FIG. 6A, in the prior art process, the current is not monitored.

(64) Further conditions for the printing head to move on to subsequent segments are also envisaged. For example, during the sintering and tempering process of the modification procedure, the resistivity of the segment should decrease, as mentioned earlier in this disclosure. It may therefore be advantageous to determine that a completion condition has been fulfilled when the resistivity of a line structure 601 is monitored as being lower than a given or a predetermined completion value.

(65) Table 3 below lists parameters and suitable values thereof for building a line segment-by-segment in accordance with the presently described example.

(66) TABLE-US-00003 TABLE 3 Parameter Value Minimal duration t.sub.1 of the short-circuit before 1 μs-1 s   we decide to move the printing head Maximal time t.sub.2 wait for a short circuit that 1 μs-10 s  lasts at least t.sub.1 Length of a single segment 1 μm-100 μm

(67) By forming and repairing segments having lengths between 1 μm and 100 μm, such that the segments are joined or electrically connected, to one another, an efficient, and controllable method for forming robust elongate structures, free from disadvantageous narrow sections and unlimited in length, is provided.