DSpace at VNU: Characterization of silver nanoparticle based inkjet printed lines

DSpace at VNU: Characterization of silver nanoparticle based inkjet printed lines tài liệu, giáo án, bài giảng , luận vă...

Microsyst Technol DOI 10.1007/s00542-013-1743-x TECHNICAL PAPER Characterization of silver nanoparticle based inkjet printed lines Eric Fribourg-Blanc • Dung My Thi Dang Chien Mau Dang • Received: 25 September 2012 / Accepted: 19 January 2013 Ó Springer-Verlag Berlin Heidelberg 2013 Abstract Inkjet of conductive patterns is a topic which already attracted much interesting research Its importance arises from the ability to deposit electrical circuits on almost any kind of substrates Understanding the controlling parameters to obtain lines with suppressed coffee stain effect still remains an important goal The results reported here were obtained with a commercial nanoparticle based silver ink printed with a Dimatix 2800 printer They show the effect of the printing parameters (drop spacing, substrate temperature, ink concentration and substrate type) on the 3D shape of straight lines In particular it is shown that flat lines can be obtained at any ink concentration on the two different substrate types tested but at specific substrate temperature and drop spacing Dependence of line crosssection area and line width on drop spacing is also analyzed Introduction In the last decade, there has been a growing research activity aimed at bringing inkjet process to printing nongraphical inks onto various kinds of substrates (Hor et al 2010; Yang et al 2007; Tien et al 2009; Lin et al 2008; Loffredo et al 2009) Among these developments, a specific emphasis has been put on depositing conducting E Fribourg-Blanc (&) CEA-LETI, MINATEC Campus, 17, rue des Martyrs, 38054 Grenoble Cedex 9, France e-mail: eric.fribourg-blanc@cea.fr D M T Dang Á C M Dang Laboratory for Nanotechnology, Vietnam National University, Community 6, Linh Trung Ward, Thu Duc District, Ho Chi Minh city, Vietnam patterns on polymer substrates with potential applications towards printed electronics (Kim et al 2009, 2007; Szczech et al 2000; Kamata et al 2009; Subramanian et al 2006) In this respect, inkjet printing compares well with other commercial printing techniques on the smallest achievable line width As a non-contact deposition technique, it also provides many advantages over the other techniques However, several issues appear when jetting an ink over a non-absorbing substrate Among the most important ones are: pattern cross-section with a central recess due to inner flow during the solvent evaporation (Li et al 2007), linewidth inhomogeneity due to bulging along the line’s length (Soltman and Subramanian 2008), and linewidth control resulting from surface tension of the ink over the considered substrate (van Osch et al 2008) These difficulties in controlling the pattern 3D shapes may result in problems when using the resulting circuits for conducting electricity (Kim et al 2006) Despite the fact that there already have been demonstrations of deposition of silver patterns with inks not containing nanoparticles, the most widespread commercial silver inks are formulated based on nanoparticles Furthermore, from the point of view of fundamental study, these inks present the interest of a complex behavior due to migration of nanoparticles during the drying of patterns The study of these deposits is of particular interest for many applications, including inkjet printing of conductive patterns (Denneulin et al 2011), catalysts for CNT growth (Chatzikomis et al 2012) or deposition of quantum dots for light emitting purpose (Haverinen et al 2009) Interestingly, it is the use of very diluted colloidal fluids that allowed to progress on the understanding of the flow inside a drying droplet (Deegan et al 1997; Monteux and Lequeux 2011) The tracking of the particles inside a droplet under microscope by standard reflection or through 123 Microsyst Technol Since the spreading of ink on a substrate is dependent on the contact angle, a simple geometrical model can bring 123 À h Á where b ¼ 24 sin h sin h À cos h The line width is thus independent on the nanoparticles’ concentration in the ink As a consequence, the ratio between the cross-section area and the square of the line width ðA=w2 Þ is independent of the drop spacing and it is only dependent on the equilibrium contact angle and the ink concentration in nanoparticles Experimental 3.1 Inks Several commercial silver inks were tested for using on Dimatix DMP-2800 printer Among these inks, good results could be obtained with Sunjet U5603 ink with a silver concentration of 20 wt % (Sun Chemicals) In order to get further insight for the analysis of printed patterns, we characterized this ink by measuring its particle size distribution and contact angles on different substrates Based on TEM images, the particle size distribution of the commercial ink was obtained using ImageJ software (NIH) The histogram in Fig indicates a bimodal distribution with two peaks around and 32 nm There is a direct interest in looking further into the behavior of an ink at several concentrations to get a better understanding of the influence of concentration in the segregation of particles as the droplet dries As the composition of the ink is proprietary, we lack the knowledge of the exact solvent composition and we chose to test the 12 10 Nanoparticle diameter (nm) Fig Particle size distribution of the commercial ink 70 60 50 40 30 ð1Þ ð2Þ 20 Vd A/ p Vd pb 10 There is no simple model to compute the profile of dried patterns since the solvent is evaporated The connection between the jetted droplets and the deposit is not straightforward Nevertheless, the product of the crosssection area of a printed line (A) by a unit length is equal to the volume of this unit length of printed line The areal density of ink is controlled by the number of droplets printed by unit length, i.e., the unit length volume is proportional to the inverse of the drop spacing (p), which is the distance between two consecutive droplets The quantity of nanoparticles being also dependent on the initial droplet volume (Vd), we obtain: w2 ¼ Theoretical considerations interesting relation between the line width and the drop spacing as shown by Stringer et al (2005) Therefore, it is possible to express the square of the line width of the printed lines (w) as a function of the initial droplet volume, the drop spacing, and a factor depending only on the equilibrium contact angle of that ink on the substrate (h) Frequency (%) fluorescence is possible if the number of particles is limited This is of course not the case when working with nanoparticle laden inks where particle concentration is much higher and particles are invisible with standard microscope Therefore, at the moment no direct observation is possible of the behavior of particles in more concentrated droplets It is worth mentioning another work which dealt with concentrated gold nanoparticle ink (Yarin et al 2006) The authors introduce the idea that the mechanisms known for diluted fluids such as coffee drop (i.e., drainage of particles to the contact line and their reflow inside the droplet leading to accumulation at center (Hu and Larson 2006)) are also accompanied with a drainage of the fluid out of the porous structure once the deposit is settled This tends to exert a force which deforms the deposit until it becomes dry At present, it is rather unclear what is the lower limit on particle concentration before this phenomenon starts to occur and what influence it has on the final printed pattern itself Nevertheless, no systematic attempt was made to characterize printed patterns as a function of printing parameters At the same time, the complex behavior of the ink on the substrate is still incompletely understood and no computational model can completely render the printing of nanoparticle laden inks In the present work a parametric study has therefore been performed of the printing of straight lines using a commercial silver ink on several substrates and cross-section profiles of the printed lines obtained with a confocal microscope After presenting a simple model the experiments and characterization of the printed lines are described and the results are discussed in relation with the model Microsyst Technol (a) 70 PET Kapton Glass Silicon 60 Contact angle (°) dilution in its flush fluid (U5747 SunTronic Flush) In order to check that it is a suitable ink solvent we measured the contact angle of the flush fluid and several dilutions of the original ink In our experiments instead of the weight percentage, the most interesting is the volume percentage at different dilutions They are obtained by mixing the right volumes after measuring the density of initial ink and flush fluid 50 40 30 20 10 3.2 Substrates 0 3.3 Printing conditions Another important parameter is the substrate temperature, which strongly influences the evaporation rate In order to Time(s) (b) 70 Contact angle (°) As the width of printed lines is influenced by the surface energy of the substrate, it is interesting to include this parameter in our study Commercially available cheap substrates are of interest for our study so we measured the contact angles on PET, KaptonÒ, silicon and glass with a CAM 101 optical contact meter (KSV Instruments, Finland) This equipment allows for a measurement of contact angle over time PET, KaptonÒ and glass were cleaned in acetone, rinsed in ethanol and DI water, then dried with blown nitrogen Silicon was used out of the wafer box without further treatment, i.e., with its natural oxidized surface Figure 2a shows the contact angle of the flush fluid used to dilute the ink on the different substrates Each measurement was reproduced times and always showed a very small variation (less than 1°) Interestingly, the behavior is very similar on PET and KaptonÒ, which present similar contact angle for water (the main constituent of the ink) Silicon presents the lowest contact angle for the flush fluid As the line width is not strongly influenced by the contact angle in the range from 20° to 40° we decided to discard glass in our study (Stringer et al 2005) Diluting the ink does not change so much its wetting behavior on silicon which is very similar to flush fluid on silicon (Fig 2b) For PET and KaptonÒ, however, some intermediate dilutions present a larger contact angle We could not find any explanation to this behavior Nevertheless, according to Stringer et al (2005), such higher contact angle should contribute to only a slightly narrower line width for these dilutions According to these results, we decided to choose PET and silicon as the two most interesting substrates; PET because it is a common cheap substrate representative of what can be used in printed electronics, and silicon because it presents a very smooth and clean surface Though we are not knowledgeable of the flush fluid composition, it appears that it does not differ much from the ink solvent in terms of surface energy, and we consider their behavior to be identical The jetting behavior of the different inks was confirmed to be independent of nanoparticle concentration 60 Kapton -non diluted Kapton -1vol% Kapton -0.25vol% 50 Kapton -0.05vol% PET -non diluted 40 PET -1vol% PET -0.25vol% 30 PET -0.05vol% Silicon - non diluted Silicon -1vol% 20 Silicon -0.25vol% Silicon -0.05vol% 10 0 Time (s) Fig Contact angle on different substrates for a flush solvent and b several dilutions of the silver ink ensure good control, the substrate is placed on the printer platen and held in place with vacuum, where it is allowed to stabilize before printing Table shows the different samples processed in this study, up to a substrate temperature of 60 °C, the limit on the Dimatix printer We used a 10 pl cartridge supplied by Dimatix In order to ensure the best conditions for comparing printed lines, only one nozzle of the cartridge was used for all experiments We assume the droplet volume to be fairly constant over a printed line as found out in literature (Famili et al 2011; Deravi et al 2007) Printed lines were one droplet wide and mm long for all experiments This length ensures that there is an established jetting condition along a good portion of the pattern, that measurement can be done Table Samples covered in this study PET Si RT 40 °C 0.25 vol (%) X X 0.5 vol (%) X vol (%) X 1.5 vol (%) X vol (%) X Non-diluted (2.35 vol %) X 45 °C 50 °C 55 °C 60 °C 50 °C X X X X X X X X X X X X X RT room temperature 123 Microsyst Technol 123 140 Top width 120 100 80 Side width 60 40 20 Bottom width -25 -20 -15 -10 Width at mid height -5 10 15 Maximum height In this work, it is necessary to obtain an accurate measurement of the 3D shape of annealed printed lines For this purpose, we used a confocal microscope Sensoscan (Sensofar, Spain) which allows for an accuracy in the vertical direction better than nm at 500 magnification This accuracy is sufficient for our purpose, where all the printed patterns presented a height at center greater than 30 nm The lateral resolution is 330 nm, which is suitable for measurement of inkjet printed lines having a minimum width above 10 lm This microscope also possesses an accurate stitching capability which allows for an automatic profile measurement over an arbitrary area We used a 5-image reconstruction along the line direction with 10 % overlap to obtain a 190 lm wide and 1.17 mm long image On both substrates, the metallic nature of the patterns provided a good contrast On PET, blue light was found to provide a better imaging, while white light was more suitable on silicon The 3D data were then handled in Matlab in order to extract quantitative information about the profile Data filtering was necessary for PET substrate as it appears that the surface quality is poor and there exists a high density of spots with height up to several tens of nanometers As shown in Fig 3, the situation was much better on silicon, proving that the spots on PET are from the substrate and are not a consequence of a lack of control in printing, such as satellites for example Between 10 and 20 regularly spaced cross-sections were extracted for each line, and an average profile was computed A representative profile closest to the average profile was extracted and several parameters recorded as described in Fig 4, providing the basis for comparing the profiles of the different lines More specifically, the bottom width is measured at a height of 30 nm from the substrate surface in order to avoid possible errors arising from the substrate surface roughness (necessary condition on PET) It is not computed if the maximum height is less than 90 nm The width at mid height is always computed and it is the most reliable measurement of the line width for patterns on PET since it avoids the problems of surface roughness while still being very close to the line width at the bottom The top width of the pattern is the width between the side peaks (when present) When the top of the pattern is flat or convex, it is not computed The maximum height is the average of the side peak heights (when present); otherwise it is just the height of the central portion The height at center is the average height of the flat central portion of the profile, if the profile is not convex; otherwise it is equal to the maximum height The side width is the average of the side peaks widths (when present) taken at half distance between the height at center and the maximum height All these lengths are averaged between the extracted profiles The final shape of the printed pattern is influenced by the printing parameters described in Sects 3.2 and 3.3, but obviously also by the nature of the solvent whose volatility Height at center 3.4 3D profile Fig Representative examples of non-diluted ink lines on a PET and b silicon at a substrate temperature of 50 °C and a drop spacing of 25 lm Height (nm) over a length representative of the lines, and that measurement is not influenced by the conditions at both ends, where evaporation tends to be higher due to a longer contact line The lines were obtained at drop spacing from to 60 lm with a lm increment It is well-known that the density of patterns influences their drying through the vapor pressure of the solvent (Shimoda et al 2003; Frassy et al 2006) In order to avoid such influence between different lines, we printed the lines 10 mm apart Therefore, in combination with the printing time the previous line is fully dried when the next one is printed The jetting frequency was constant for all experiments at kHz The patterns were annealed after printing in a conventional oven over h at 100 °C This was necessary to stabilize them before transport, since 3D profile measurements had to be done at another location 20 25 Distance (µm) Fig Representative profile showing the parameters extracted for each line Microsyst Technol controls the evaporation rate It was already shown that a mixture of two solvents with different boiling points could lead to an evolution in the printed pattern profile (Kim et al 2006) In our case, this factor is probably at play to some extent because, even though the exact composition of the ink is unknown, the list of solvents from the safety datasheet includes several organic solvents with different boiling points This factor is however fixed for all experiments at a given concentration Results 4.1 Line profile The pictures in Fig show the different 3D shapes of lines printed with non-diluted ink on PET at a substrate temperature of 45 °C This set of pictures shows some features common to all sets of printed lines When the droplets are sufficiently apart (Figs 5a and b), they present an axisymmetric shape When they are closer but still well separated (Figs 5c and d), they present a shape with a recess along the direction of the line When the droplets are close enough, they merge in a continuous pattern The line presents with wavy sides at coalescence of the droplets into a line (Fig 5e) These wavy sides quickly smoothen out when the drop spacing reduces due to the capillary effect For small drop spacing, the line tends to bulge (Fig 5k and l) (Duineveld 2003) The six parameters extracted from the mean profile are shown in Fig as a function of drop spacing There is a general trend of increase of all parameters as drop spacing is decreasing The three parameters characterizing the line widths tend to be evolving in parallel The error bars are shown for center and top widths, showing that they go through a minimum in the drop spacing range where the side waviness at large drop spacing has disappeared and the bulging at small drop spacing is not yet present The height of the side peaks tends to increase faster than the height of the central recess At coalescence, the line presents a profile with a central recess equivalent to the one present on the non-coalesced but close droplets (Fig 5d and e) This profile can be explained by a higher vapor pressure of the solvent along the axis of the line, which tends to induce a higher evaporation rate at the contact line perpendicular to this axis (Yarin et al 2006; Frassy et al 2006) At the same time, for contact angle below 90° this tends to concentrate the nanoparticles away from the center of the droplet towards the edge of the not yet formed line (Deegan et al 1997) When the drop spacing is gradually decreased, an interesting behavior occurs: the line profile top can become flat while the line width does not change much Fig 3D profiles of non-diluted ink on a PET substrate at 45 °C for drop spacing from 60 down to lm every lm The vertical scale is 500 nm Figure shows the couples of drop spacing and substrate temperature for which the line profile top is flat on PET The dots represent lines of coalesced droplets Coalescence was never observed for drop spacing larger than 45 lm Flat tops are only observed at large drop spacing 123 Microsyst Technol 100 Width (µm) (a) 60 Bottom Center Top Side peak 80 60 40 20 0 10 15 20 25 30 35 40 45 Substrate temperature (°C) (a) 120 55 50 45 40 35 30 25 Drop spacing (µm) 10 15 20 25 30 35 40 45 35 40 45 35 40 45 Drop spacing (µm) Maximum Center 450 400 350 300 250 200 150 100 50 0 10 15 20 25 30 35 40 (b) 60 45 Drop spacing (µm) Substrate temperature (°C) Height (nm) (b) 500 55 50 45 40 35 30 25 10 Fig Parameters extracted from the mean profile of the lines in Fig as described in Fig 4.2 Analysis of line density 4.2.1 On PET For a practical purpose, it is important that the printed lines be as dense as possible when annealed Indeed, a central 123 20 25 30 Drop spacing (µm) (c) 60 Substrate temperature (°C) With the available data, it is difficult to draw any conclusion on the underlying mechanisms, since there is no simple trend in the appearance of a flat top as a function of drop spacing, substrate temperature and ink concentration In (Kim et al 2006), it was demonstrated that a flat top could be obtained for a droplet by using the differential evaporation rates of the solvent components in the ink which induce a modulation of the Marangoni flow during evaporation A flat top could be obtained when drying at room temperature It seems this behavior is identical for individual droplets and when coalesced in a line With the present commercial ink this may not be the only factor at play, since it was always possible to obtain a flat profile for lines whatever the nanoparticle concentration despite the fact that individual droplets exhibited some recess However, as seen in Fig flat top on the lines occurs at different drop spacing depending on the substrate temperature The circulation of nanoparticles due to the Marangoni flow, and their subsequent settlement perpendicular to the printing axis are a consequence of their local concentration, the different solvent evaporation rates, and the drying time 15 55 50 45 40 35 30 25 10 15 20 25 30 Drop spacing (µm) Fig Profile tops of lines printed on PET where black dots represent flat top while white dots show concave shape with side peaks for a non-diluted, b vol % and c 0.25 vol % inks focus in the development of conductive inks is to be able to use them on substrates which are temperature sensitive However the final conductive patterns should have conductivity the closest to the bulk to be useful in a wide range of applications In the case of nanoparticle based inks, conductivity is directly related to the porosity of the printed patterns, as it is well known that the sintering of the materials depends on the contact and fusion of adjacent nanoparticles (Greer and Street 2007; Scandurra et al 2010) An indirect way to get information on the apparent density of printed patterns is to determine the cross-section area of their 3D profile First of all, we measured the cross-section areas of lines printed with non-diluted ink on PET at room temperature Microsyst Technol Few measurements were conducted on silicon, since the main focus was to study the situation on PET, which presents more practical applications However, the measurements done (at a substrate temperature of 50 °C) confirmed the behavior described above for PET as illustrated in Fig 11 for cross-section area The curves are very close for the two substrates, as they are representative of dried ink density, which is not expected to vary much 4.3 Line width All other factors being equal and the ink concentration remaining low in volume, the way ink spreads on the substrate is controlled by the relative surface energy of the ink solvent to the substrate At the same time, the concentration is high enough to expect a contact line pinning in all cases (Deegan et al 1997; Sun et al 2009) As the temperature of the substrate essentially impacts the drying, it is expected that the line width of the printed lines should Cross section area (µm²) Room temperature 40°C 50°C 60°C 30 25 20 15 10 0 10 15 20 25 (a) 18 25 20 15 10 40 45 Room temperature 40°C 50°C 60°C 16 14 12 10 0 10 15 20 25 30 35 40 45 Drop spacing (µm) (b) 10 40°C 50°C 60°C 10 15 20 25 30 35 40 45 Drop spacing (µm) Fig 10 Cross-section area as a function of drop spacing for inks with a concentration of a vol % and b 0.25 vol % Cross section area (µm²) Cross section area (µm²) 150°C 100°C 35 Fig Cross-section area of non-diluted ink printed on PET at different temperatures 35 30 30 Drop spacing (µm) Cross section area (µm²) 4.2.2 On silicon 35 Cross section area (µm²) and annealed at 100 and 150 °C for h The profiles shown in Fig indicate very little difference in the cross-section area of these lines whatever the drop spacing Therefore, the higher temperature annealing does not improve their final density in the limit of the substrate thermal stability Figure shows the cross-section areas for non-diluted ink printed on PET substrate as a function of drop spacing The plain curves show the real measurements If we normalize the drop spacing to the smallest drop spacing (5 lm), we obtain the expected cross-section area as shown in Fig by the dashed curves (Eq (1)) There seems to also be a trend where the higher the substrate temperature is the higher the apparent cross-section area appears However, this dependence is not confirmed for diluted inks, and can even appear reversed for low concentration, as seen in Fig 10 The apparent density of the printed lines as a function of substrate temperature does not find a simple explanation at present Non diluted on PET 30 Non diluted on Silicon 25 1vol% on PET 1vol% on Silicon 20 15 10 0 0 10 15 20 25 30 35 40 45 10 15 20 25 30 35 40 45 Drop spacing (µm) Drop spacing (µm) Fig Effect of annealing temperature on cross-section area Fig 11 Comparison of cross-section areas for the lines printed on silicon and PET 123 Microsyst Technol Width at center (µm) Non diluted RT Non diluted 50°C 1vol% RT 1vol% 50°C 0.25vol% 40°C 0.25vol% 60°C 120 110 100 90 80 70 60 50 40 30 20 Non diluted 40°C Non diluted 60°C 1vol% 40°C 1vol% 60°C 0.25vol% 50°C 10 15 20 25 30 35 40 45 Width at center (µm) Drop spacing (µm) (b)120 Room temperature 40°C 50°C 60°C 110 100 90 80 70 60 50 40 30 20 10 15 20 25 30 35 40 45 Drop spacing (µm) (c) 120 40°C 110 100 90 80 70 60 50 40 30 20 50°C 60°C 10 15 20 25 30 35 40 45 Drop spacing (µm) Fig 13 Line width at center as a function of drop spacing for a nondiluted, b vol % and c 0.25 vol % inks Dashed curves show the inverse of the square root normalized to the value at the smallest drop spacing 160 Non diluted on PET Non diluted on Silicon 1vol% on PET 1vol% on Silicon 140 120 100 80 60 40 20 10 15 20 25 30 35 40 45 Drop spacing (µm) Fig 14 Comparison of line width for lines printed on silicon and PET at a substrate temperature of 50 °C 10 15 20 25 30 35 40 45 Drop spacing (µm) Fig 12 Line width as a function of drop spacing on PET for different concentrations and substrate temperatures 123 Width at center (µm) Contrary to the situation for the cross-section area (Fig 11), we notice that the above discussion about the line width independence on printing parameters, including nanoparticle concentration, does not appear valid for printing on silicon as shown in Fig 14 Only the trend is identical, i.e., the dependence in inverse proportion of the square root of the drop spacing This is especially difficult to understand as the contact angle does not appear dependent on ink concentration on silicon (cf Fig 2) We were therefore expecting an even better matching for the line width on silicon at different ink concentrations compared to the situation on PET Interestingly, the cross-section shape of lines printed on silicon differs much from those on PET at the same substrate temperature (50 °C) as shown in Fig 15 (representative profiles have been selected to avoid the figure to be overcrowded) The settling of nanoparticles is notably different between the two substrates It was already demonstrated that the evaporation phase is influenced by the substrate thermal conductivity (Talbot et al 2012) For PET with a thermal conductivity below W m-1 K-1, the drying time is longer than for silicon This increases the time during Room temperature 40°C 50°C 60°C 110 100 90 80 70 60 50 40 30 20 Width at center (µm) 4.4 Comparison between PET and silicon (a) 120 Width at center (µm) be independent of the printing parameters to the first order and only dependent on the wettability of the substrate This assumption seems to be valid on PET as shown in Fig 12, where the average variation over all measured profiles is found to be less than 9.5 % Following this observation, we examined whether the line width varies in inverse proportion of the square root of the drop spacing (Fig 13) as expected from Eq (2) Here again, each fitting curve is normalized at the smallest drop spacing On average, the line width is indeed proportional to the inverse of the square root of the drop spacing, except for few cases where there is a larger departure from this model which the nanoparticles move due to the Marangoni flow and may therefore be a reason why side peaks form more readily on PET compared to silicon Microsyst Technol Silicon (a) 450 400 400 350 40 300 35 250 25 200 15 150 10 100 350 Height (nm) Height (nm) PET 450 35 300 25 250 15 200 10 150 100 50 50 0 -70-60-50-40-30-20-10 10 20 30 40 50 60 70 -70-60-50-40-30-20-10 10 20 30 40 50 60 70 Distance (µm) Distance (µm) (b) 250 250 200 40 35 150 25 15 100 10 50 Height (nm) Height (nm) 200 40 35 25 15 10 150 100 50 -90 -60 -30 30 60 90 Distance (µm) -90 -60 -30 30 60 90 Distance (µm) Fig 15 Cross-section profiles for lines printed on silicon and PET at a substrate temperature of 50 °C for a non-diluted and b vol % inks As shown in Fig 15, the cross-section profiles of the lines on silicon are quite variable There are several cases were the top is flat, and some profiles present a convex shape as summarized in Fig 16 4.5 Comparison with the model From the theoretical considerations developed in Sect 2, we are expecting the ratio between the cross-section area and the square of the line width to be constant for a given substrate and ink Figure 17 shows the computed ratio from the experimental data for the different concentrations and substrates Non-diluted 1vol% 10 15 20 25 30 35 40 45 Drop spacing (µm) Fig 16 Shape of line tops printed on silicon, where black dots represent flat top, white dots show concave shape with side peaks, and grey dots show convex shape We observe that the concentration seems to have a strong influence on the ratio on PET At low concentration (0.25 vol %), the ratio keeps almost constant with the drop spacing with a slight increase when increasing it At vol % the situation is more confused The trend is for a constant ratio as a function of drop spacing, but with a large variability and a dependence on substrate temperature The situation degrades even further for non-diluted ink, where the ratio does not present a constant trend and is very dependent on substrate temperature Overall, it seems that at 50 °C the situation is somewhat closer to the expected constant ratio as a function of drop spacing for the two concentrations tested (Fig 17d) It also correlates with the fact that it was always possible to obtain a flat top at 50 °C (cf Figs and 16) Whether this remains coincidental or is a consequence of an underlying physics remains unclear The difference of contact angle is reflected in different values of the ratio The line width being only dependent on the impact process, it should be independent on the ink concentration which appears valid to the first order on PET On the other hand, the cross-section area is dependent on the way the nanoparticles settle, i.e., on the final density of the pattern This of course depends on the drying process of the ink i.e., on substrate temperature as well These factors can affect the computed ratio, but not explain its evolution for different concentrations and substrates temperatures on PET 123 Microsyst Technol Room temperature 40°C 50°C (b) 60°C 0 10 15 20 25 30 35 40 45 Cross section area / line width² Cross section area / line width² (a) Room temperature 0 10 60°C 0 10 15 20 25 30 15 20 25 30 35 40 45 Drop spacing (µm) Cross section area / line width² Cross section area / line width² 50°C 60°C (d) 40°C 50°C Drop spacing (µm) (c) 40°C 35 40 45 Drop spacing (µm) Non diluted on Si Non diluted on PET 1vol% on Si 1vol% on PET 3,5 2,5 1,5 0,5 0 10 15 20 25 30 35 40 45 Drop spacing (µm) Fig 17 Computed ratio between the cross-section area to the square of the line width for a non-diluted ink, b ink diluted at vol %, c ink diluted at 0.25 vol %, d a comparison between PET and silicon at a substrate temperature of 50 °C There is no satisfactory explanation for the observed behavior since neither the surface quality nor the thermal conductivity of the substrates support a simple account for the observed data Especially for silicon, the line width seems to vary with ink concentration as shown in Fig 14, but still results in a constant ratio as expected from the theoretical considerations Conclusion We showed that it is possible to predict the line width and cross-section area of any printed line to a first order just by measuring the 3D profile of a line printed at the smallest drop spacing (here lm), all other parameters being identical On PET it was found that the standard deviation from the inverse square root fitting for the line width is less than 9.5 % while the standard deviation from the inverse fitting for the cross-section area is less than 15 % This predictive capability is independent of the cross-section shape of the line and the presence or absence of side peaks This should prove useful for reducing the characterization effort for an ink on any non-absorbing substrate We could show that—in the parametric space used in this work—it was always possible to obtain flat cross-sections for 123 straight lines However, the parameters conducing to those patterns were dependent on the substrate type, the ink concentration, the drop spacing as well as the substrate temperature during printing Nevertheless, in this work we could not assess the density of printed lines because it depends on one hand on the real droplet volume and on the other hand on the sintering degree of nanoparticles at low temperature, which remain unknown in our case In first approximation, it might appear that the final density should be rather constant for all experiments, but we suggest that as this final density depends on the settling of nanoparticles, it may vary with the printing parameters This could partly explain the observed variability in the cross-section area This of course acts as a limiting factor on the predictability of deposited ink volume At this stage, we did not identify a general trend of any one printing parameter having a distinct influence on the final ink density A direct measurement of printed line porosity is necessary to provide further insight Acknowledgments The authors appreciate the financial support of the National Foundation for Science and Technology 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inkjet-printing technology IEEE Trans Microw Theory Tech 55:2894–2901 Yarin AL, Szczech JB, Megaridis CM, Zhang J, Gamota DR (2006) Lines of dense nanoparticle colloidal suspensions evaporating on a flat surface: formation of non-uniform dried deposits J Colloid Interface Sci 294:343–354 123 ... different 3D shapes of lines printed with non-diluted ink on PET at a substrate temperature of 45 °C This set of pictures shows some features common to all sets of printed lines When the droplets... volatility Height at center 3.4 3D profile Fig Representative examples of non-diluted ink lines on a PET and b silicon at a substrate temperature of 50 °C and a drop spacing of 25 lm Height (nm)... to get information on the apparent density of printed patterns is to determine the cross-section area of their 3D profile First of all, we measured the cross-section areas of lines printed with