Fabrication and characterization of microfluidic pedestal nozzles enabling geometric contact line pinning

Microfluidic pedestal nozzles have been fabricated using self-aligned wafer-scale microfabrication methods. Through implementation of these novel fabrication strategies, nozzles with a concentric rim at the nozzle exit were made. The process allows to accurately vary the rim radius, and rim radii ranging between 36 μ m and 111 μ m are reported here. A unique and essential feature of the nozzle, which is made of hydrophilic silicon dioxide, is that the rim edge has an interior angle of 5 ∘ and a radius of curvature smaller than 20 nm. Due to this nanometrically sharp rim edge, geometric contact line pinning of polar liquids is facilitated. With hydrostatic and hydrodynamic measurements, the nozzle functionality is demonstrated for water and ethanol. Due to the un-precedentedly strong contact line pinning, macroscopic contact angles can be increased by more than 150 ∘ . These measurements reveal a pressure point at which the droplet starts to grow uninhibitedly, which is predicted by a thermodynamic model based on the Gibbs free energy of pinned droplets. It is reckoned that the nozzles are useful in applications where liquids with free surfaces have to be confined to a specific micron-sized surface area, as is the case in, e.g., inkjet printing and electrospinning. To show the functionality of the pedestal nozzles, electrohydrodynamic jetting of a typical electrospinning polymer solution is demonstrated.


Introduction
Confining liquids with free surfaces to a designated contact area is crucial to accurately control microfluidic processes.Furthermore, the liquid is required to adhere strongly to the contact area to prevent its unwanted detachment.For example, in droplet tensiometry, a droplet is formed at the nozzle exit and allowed to deform due to gravity prior to the drop shape analysis and calculation of the interfacial surface tension [1][2][3][4]5].In electrospinning [6] and electrospraying [7], a droplet adhering to the nozzle exit is exposed to a strong external electric field.This field causes the droplet to become unstable and starts to emit the liquid [8][9][10].In inkjet printing, the ink needs to be confined to the nozzle exit in order to eject droplets of precise volume in a well-defined direction [11][12][13].
Several strategies to confine droplets to the nozzle exit have been reported.Millimeter-sized stainless steel pedestal nozzles with a sharpened edge at the nozzle exit enabled droplet tensiometry of low-surface tension liquids [14].This sharpened edge pins the contact line, because the macroscopic contact angle must be increased before the contact line is able to move past the edge [15][16][17][18].However, the edge has an angle of 60 ∘ only, and the used fabrication method allowed the rim edge radius of curvature to be defined with a resolution not better than 10μm.These two factors limit the maximum achievable macroscopic contact angle [15][16][17][18].Moreover, the obtained resolution hampers the downscaling of the nozzle size, which can be relevant for, e.g., high-resolution printing applications.
In conventional solution electrospinning setups, a blunt metal capillary is used as a nozzle.One approach to prevent wetting of the outer side of a capillary, i.e., to confine the liquid to the exit of the capillary, is to cover the outer surface with an anti-wetting Teflon sleeve [19,20].Morad et al. mounted 3D-printed hemispherical caps on metal capillaries and allowed the caps to be wetted by the electrospraying liquid.The cap is wetted by the liquid and makes the contact line less mobile, thereby enhancing the stability of the process [21].
With the aim of generating smaller droplets, micromachining technologies have been employed.Electrospray nozzles were made from photoresist [22,23], anti-wetting hydrophobic parylene [24], silicon [25,26], or silicon dioxide [25,26].Photoresist and silicon dioxide are wetted by common polar liquids, and the wetting of these nozzles is mitigated using an additional anti-wetting pillar-based photoresist structure [23] or by shaping the silicon dioxide to facilitate geometric contact line pinning [26].In many applications, nozzles made of anti-wetting materials are not desired because of the limited adhesion offered.Close to the nozzle of an inkjet printhead, a shallow geometric discontinuity is introduced, which prevents mixing of inks originating from adjacent nozzles through geometric contact line pinning [13].Because this discontinuity is used to prevent mixing of ink, it suggests that the inks are poorly confined to the nozzle exit during the emission of droplets.
In this work, a novel wafer-scale microfabrication process for microfluidic pedestal nozzles is presented.The nozzles are made of silicon dioxide and feature a rim at the tube end with a nanometrically sharp rim edge.Because these nozzles are made of a hydrophilic material, polar liquids adhere strongly to the nozzle.Due to the nanometersized rim edge, it is expected that the contact line is robustly pinned at this edge [15][16][17][18].The nozzles protrude from a square silicon base with sides of 3 mm.A hole through the silicon base provides a fluidic interconnection from the back side of the nozzle base to the nozzle.Fig. 1a shows an image of a nozzle that is made with a scanning electron microscope (SEM), and Fig. 1b shows a SEM image of the cross-section of the rim edge.
The pedestal nozzles are fabricated with wafer-scale micromachining technologies, including local oxidation of silicon (LOCOS) and thin film deposition, which are well-established, uniform processes used in the semiconductor industry (see also Section S2 in the supporting information for uniformity data).Over 600 pedestal nozzles were fabricated from a single 100 mm silicon wafer.During one of the LOCOS steps, the nozzle feature is fabricated, and simultaneously, a so-called bird's beak feature grows at the edge of the nozzle rim.Nozzles with rim radii varying between 36 μ m and 111 μ have been fabricated, and due to the bird's beak, the rim edge has a radius of curvature smaller than 20 nm and an interior angle of approximately 5 ∘ .Nozzles without a rim were fabricated and measured as well to highlight the functionality of the rim.The semiconductive silicon base can be electrified and allows the liquid to be electrified as well.Hence, the nozzles enable the electrohydrodynamic processing of fluids, e.g., by means of electrospinning and electrospraying.
To determine the contact line pinning capabilities of the nozzle rim, de-ionized water (DI-water) or ethanol is supplied to nozzles with a hydrostatic pressure.Experiments show that the pinned contact angle can be increased to more than 150 ∘ .Furthermore, a pressure point at which the droplet grows uninhibitedly is observed, and a thermodynamic model is introduced to understand and predict this phenomenon.Preliminary electrohydrodynamic jetting experiments suggest that the pedestal nozzles allow a large operating window in which a polymer liquid can be electrospun.

Hydrostatic stability analysis of droplets pinned on the pedestal nozzle
Fig. 2 shows a schematic drawing of a liquid droplet pinned on the pedestal nozzle rim.The rim has a radius Ω and an interior rim edge angle ϕ.The liquid-vapor interface has a radius of curvature R, and makes a macroscopic contact angle θ with respect to a plane that intersects the nozzle rim.
As long as the macroscopic contact angle θ is too small to form an equilibrium contact angle at the back side of the nozzle rim, the contact line stays pinned on the nozzle rim edge.Suppose the macroscopic equilibrium contact angle between the nozzle-liquid and liquid-vapor interfaces is θ 0 .In that case, the range of pinned contact angles of a pinned contact line is predicted by Gibbs' inequality [15][16][17]: Oliver et al. stressed that Gibbs' inequality only holds for mathematically sharp edges, i.e., if the edge is not rounded off.Since fabricated edges in nearly all cases are rounded off, the maximum theoretically obtainable contact angle θ = (180 • − ϕ) + θ 0 is hardly conceived in experiments [17].
A thermodynamic model based on the Gibbs free energy of spherical droplets pinned onto the nozzle rim has been made.The detailed calculations are presented in Section S1, and the main assumptions and results are presented here.The Gibbs free energy G of a droplet pinned on the rim of the pedestal nozzle is calculated as [15,27,28]: with C a constant accounting for additional surface energies belonging to, for example, the solid-liquid interaction.A LV is the area of the liquidvapor interface, γ the liquid-vapor interfacial surface tension, Δp the pressure difference across the liquid-vapor interface, and V the volume of the droplet.The capillary length scale predicts the characteristic droplet radius at which the pressure inside the droplet caused by gravity is equal to the Laplace pressure [16].In air and at room temperature, the capillary length scale for DI-water and ethanol droplets are 2.7 mm and 1.7 mm, respectively [29,30].Because the droplets are pinned on pedestal nozzle rims of the order of 100 μ m (Ω ≤ 111 μ m), the effect of gravity can safely be omitted in the current analysis.Furthermore, it is assumed that the liquid is incompressible, in thermal equilibrium with its surroundings and that the vapor pressure is independent of the liquid-vapor interface curvature [27,28].Due to the aforementioned arguments, the droplet assumes a spherical equilibrium shape.Minimizing Eq. ( 2)  for a fixed volume V, i.e., computing ∂G∕∂V = 0, yields the following expression for the pressure drop across the liquid-air interface: which is the familiar Laplace equation for spherical droplets of radius R [16], and valid for pinned droplets as well.Eq. ( 2) is plotted in Fig. 3 as a function of the normalized droplet volume V∕V 0 for different hydrostatic pressures Δp.V 0 is defined as half the volume of a spherical droplet that is pinned on the nozzle rim, i.e., V 0 = 2πΩ 3 ∕3.The dotted line in Fig. 3 intersects the local minima of G for pressures calculated by Eq. ( 3).If V∕V 0 > 1, the droplet starts to grow uninhibitedly because the slope of G remains negative, and no local minimum can be achieved anymore.This uninhibited droplet growth shall be referred to as hydrostatic instability, and the condition for this instability is given by: From Eq. ( 4), it follows that the hydrostatic instability indeed occurs if R = Ω, i.e. if θ = 90 ∘ .Alternatively, the hydrostatic instability is understood by analyzing Eq. ( 3): the largest obtainable Laplace pressure of the pinned droplet, corresponding to the maximum curvature, is obtained once the radius of curvature R is equal to the rim radius Ω.

Key nozzle fabrication steps
The key fabrication steps for the nozzles with rim are briefly described here.Details of the fabrication process of nozzles with and without the rim can be found in Sections S2 and S3.The silicon dioxide (SiO 2 ) pedestal nozzles are fabricated by means of LOCOS.With LOCOS, only silicon surfaces that are not masked by a diffusion barrier for oxidant species are oxidized [31], and allow the rim edge to be well defined.The fabrication starts with growing a thin SiO 2 layer on silicon wafers, followed by the low-pressure chemical vapor deposition (LPCVD) of a much thicker low-stress silicon-rich silicon nitride (SiRN) and silicon dioxide (TEOS) layer.The TEOS layer is used to protect the underlying layers during plasma etching, whereas the SiO 2 layer is used to shape the SiRN diffusion barrier.Using UV contact lithography and directional plasma etching methods, circular holes are etched in the layer stack on the front side of the substrate and in the underlying silicon.The same etching process is used to remove the layer stack on the back side of the substrate (Fig. 4a).
A self-aligned etching technology is developed to retract the layer stack from the periphery of the silicon holes.With aqueous hydrofluoric acid (HF) as an isotropic etchant, the SiO 2 and TEOS are selectively etched.The SiO 2 layer is not masked by SiRN at the periphery of the silicon holes, and here the etchant starts to under-etch the SiRN.This strategy, in which material is removed at previously defined edges in a controlled manner, is referred to as edge lithography [32,33], and results in a suspended SiRN layer.This etching process is stopped once the diameter of the under-etched circular region matches the desired rim diameter.Because the etch rate of TEOS is higher than that of SiO 2 and because the TEOS layer is thinner than the under-etched feature size, the TEOS is stripped during the edge lithography (Fig. 4b).The stripping of the TEOS layer is desired because it does not have any functionality anymore at this point.The suspended part of the SiRN layer is removed by isotropically etching the SiRN in aqueous phosphoric acid.Because the etchant wets the suspended SiRN layer in almost all directions, it is removed once the SiRN layer thickness on the SiO 2 is reduced by half of its initial thickness.At this stage, the layer stack is retracted from the silicon holes and the nozzle feature is fabricated by growing a thick SiO layer by means of LOCOS.During this process, oxidant species are diffusing laterally and, thus, underneath the SiRN hard mask.This causes a so-called bird's beak-shaped SiO 2 feature [34] at the edge of the SiRN layer and gives the rim its sharp rim edge (Fig. 4c).After the LOCOS, the SiRN hard mask is selectively removed with aqueous phosphoric acid, and the thin SiO 2 layer on the front side is removed with aqueous HF.
A second etching technology is developed to establish a fluidic interconnection from the nozzle feature to the back side of the substrate.It allows to selectively remove the SiO 2 at the bottom of the nozzle feature, and to remove the underlying silicon.A stoichiometric silicon nitride (Si 3 N 4 ) hard diffusion mask is deposited with LPCVD and subsequently removed from the back side of the substrate using directional plasma etching.With the aid of aligned UV contact lithography and directional plasma etching, holes are etched in the SiO 2 and silicon at the back side of the substrate.These holes are aligned to the nozzle features on the front side of the substrate.Because the silicon plasma etching process is selective towards SiO 2 , the etching process stops on the SiO 2 of the nozzle feature (Fig. 4d).All exposed SiO 2 is selectively etched in aqueous HF, and the etching process is stopped once no SiO 2 is left on the back side of the substrate.Using LOCOS, a thin SiO 2 layer is regrown on the bare silicon surface.This layer is used to protect the silicon against its wet-chemical etchants at a later stage (Fig. 4e).The Si 3 N hard mask is selectively removed in aqueous phosphoric acid, and the exposed crystalline silicon on the front side of the substrate is etched selectively in aqueous tetramethylammonium hydroxide (TMAH).It exposes the nozzle feature that was largely buried in the silicon substrate, and the TMAH etching process is stopped once the nozzle has the required protrusion height (Fig. 4f).
With a SEM (JEOL JSM 7610FPlus FEG), the dimensions of the nozzles are analyzed.The fabricated nozzles that were used during the experiments reported here have an inner tube radius of 25 μ m, 52 μ m, or 100 μ m, and a nozzle rim radius of 36 μ m, 61 μ m, or 111 μ m, respectively.Measured from the silicon base, the nozzle is 70 μ m to μ m tall, but this dimension is not critical for the characterization of the nozzles, as long as the nozzle sufficiently protrudes from the silicon surface.Images such as Fig. 1b were used to analyze the rim edge dimensions.
One nozzle was sacrificed, and a cross-section cut was milled into the rim to determine the dimensions of the nozzle rim edge.Employing image measuring tools, the rim edge has an interior angle of approximately 5 ∘ and a rim edge radius of curvature smaller than 20 nm.Since nozzle features are fabricated by means of LOCOS, which is a wafer-scale process with large wafer-scale uniformity [35,36], the nozzle-to-nozzle variation of the nozzle dimensions is assumed to be small.A picture of a nozzle without a rim is shown in Fig. S13.The outer tube radius of these nozzles is 52 μ m.

Hydrostatic measuring setup
A schematic drawing of the measuring setup is depicted in Fig. 5.A gravity-directed liquid column and syringe pump are connected to the nozzles with a T-junction.The syringe pump is used to thoroughly flush the hydraulic system with the working liquid to reduce the amount of contaminants and air bubbles in the hydraulic system.Either DI-water or ethanol is supplied to the nozzle by changing the height of these working liquids in the column.By adding a fixed volume of the working liquid to the column, the hydrostatic pressure difference Δp across the nozzle is increased in discrete steps, and the droplet is allowed to settle afterward.A self-leveling laser marks the height of the nozzle on the liquid column.This mark is used to determine the liquid level difference with respect to the nozzle exit, and therewith used to calculate Δp.Equilibrium drop shapes were observed by taking pictures of the droplet's side-view and nozzle using a microscope and camera (not shown in Fig. 5).Movies were made once the droplet became hydrodynamically unstable.MAT-LAB programs were used to binarize and subsequently analyze the imagery.
Nozzles were either directed parallel or anti-parallel to gravity.Thus, pendant droplets were measured if the nozzle was directed parallel to gravity, and sessile droplets were measured otherwise.To ensure that no dust particles in air are contaminating the working liquid, the measurements are performed in an ISO class 7 clean room environment.A detailed description of the measuring strategy and measuring setup are found in Section S4.

Hydrostatic pressure vs. droplet radius
Fig. 6 shows a plot of the typical data obtained during one of the experiments in which DI-water was supplied to a nozzle with Ω = 111μ m.The reciprocal radius of curvature R − 1 of the DI-water droplet is plotted as a function of the applied hydrostatic pressure Δp.Guided by Eq. ( 3), the data is fitted as R − 1 = (Δp − b)∕(2a), with a fitting the surface tension γ and b a pressure offset.The pressure offset is introduced to account for experimental errors, such as air bubbles entrapped in the hydraulic system of the measuring setup, or when the hydrostatic pressure was set.The experimental data suggests that the surface tension of the working liquid slightly increases for larger droplets because the slope of R − 1 decreases as a function of Δp.A possible explanation of this phenomenon is given at the end of this section.
The nozzle axis is directed along the direction of gravity; thus, the droplet is pending on the nozzle rim and moves away from the nozzle after it pinches off.The first droplet is growing on the nozzle until Δp ≈ 1.1 ⋅ 10 3 Pa, after which it becomes hydrostatically unstable, i.e., once R − 1 ≈ Ω − 1 = 0.901 ⋅ 10 4 m − 1 and θ = 90 ∘ .A second droplet immediately forms on the nozzle at an apparently higher surface tension.Once the second droplet also detaches from the nozzle, no stable droplet is formed again, and dripping occurs.Considering the measuring errors, the fitted surface tension for the first droplet is 59.51 ± 1.78 mN m − 1 and 72.22 ± 2.26 mN m − 1 for the second.With a tensiometer (Krüss K20 EasyDyne) equipped with a Du Noüy ring, the surface tension was measured to be 68.0 ± 0.1 mN m − 1 at room temperature.Both surface tension values, measured with the tensiometer and obtained by fitting the experimental data, are lower than the surface Fig. 5.A liquid column (left) is connected to the nozzle assembly (middle) and syringe pump (right) via a T-junction and shut-off valves.A syringe filter is placed between the syringe and shut-off valve if DI-water is used as working liquid.A self-leveling laser unit is used to mark the height of the nozzle exit onto the liquid column.The nozzle's exit is directed along the direction of gravity.Fig. 6.The inverse radius R − 1 of the pendant DI-water droplet plotted as function of the applied pressure Δp.The red and green lines fit the data obtained from the first and second droplet, respectively.The droplet radius is measured with an estimated accuracy of R ± 3μ m, and the hydrostatic pressure is set with an accuracy Δp ± 30 Pa. Horizontal error bars are omitted from the graph to enhance its readability.tension of 72.3 mN m − 1 found in literature [37,38], which is likely caused by ambient contaminants dissolving in the liquid drop during the hydrostatic measurement [39].This hypothesis also explains why the fitted surface tension of the first droplet, which stays pinned on the nozzle for the longest time, is lower than that of the second droplet.

Hydrostatic pressure vs. hydrostatic instability
The minimum droplet radius R ins and pressure Δp ins are measured right before the droplet becomes unstable.The results are plotted in Fig. 7, in which R ins is made dimensionless by diving by dividing it with Ω.To rule out the effect of gravity on R ins , pendant and sessile droplets were measured.Nozzles with no rim were measured as well, and in that case, Ω is equal to the inner tube radius (Ω = 52 μ m).
The data in Fig. 7 agree with the presented thermodynamic analysis because R ins ≈ Ω.Furthermore, the direction of gravity does not affect either R ins or Δp ins .Stable DI-water droplets are formed on nozzles without a rim.However, the contact line of ethanol droplets depins from the nozzle tube well before a significant drop is formed.If nozzles are directed anti-parallel to gravity, the unstable droplet depins from the nozzle, spills over, and wets the nozzle and silicon base.Hence, these measurements were difficult to perform.The data is fitted with Eq. ( 3) to determine the surface tension.For ethanol and DI-water droplets, the average surface tension and variance are γ = 24.6 ± 2.46 mN m − 1 and γ = 59.6 ± 15.2 mN m − 1 , respectively.High-surface tension liquids are more sensitive to impurities [39], and this is regarded as the reason why the fitted surface tension variance of ethanol is smaller than that for DI-water.Hence, the hydrostatic pressure Δp ins at which the ethanol droplet becomes unstable correlates better with the nozzle rim radius Ω.
Stable ethanol droplets are difficult to form at the nozzle exit if the nozzle does not contain a rim, and this is the first indication of the functionality of the nozzle rim.Images taken during one of the experiments in which a sessile DI-water droplet is pinned on a nozzle with rim radius Ω = 61μm are shown in Fig. S16.After a pinned droplet on the pedestal nozzle becomes hydrodynamically unstable, either dripping occurs, or a new droplet with an apparently higher surface tension is formed.However, in the case of nozzles without rim, the droplet started to wet the nozzle after it became hydrostatically unstable.Hence, the nozzles without a rim were not able to pin the contact line with a large contact angle.

The maximum pinned contact angle
The equilibrium macroscopic contact angle of the working liquids on silicon dioxide is measured with an optical contact angle measuring system (Dataphysics OCA-20).The liquids are dispensed onto flat substrates and form a sessile droplet if the liquid makes a finite contact angle with the substrate.Photographs of sessile ethanol and DI-water droplets are presented in Fig. S17.The substrate is a silicon wafer covered with a 455 nm thick thermally grown SiO 2 layer.Prior to the measurement, this substrate is rinsed in acetone and subsequently in isopropyl alcohol and ethanol, to mimic the last fabrication step of the nozzles.The rinsing process may change the surface reactivity of the substrate, and makes it equivalent to the SiO 2 nozzles.For DI-water, the contact angle is found to be 34 ∘ ± 6 ∘ .Once ethanol droplets are dispensed on the substrate, they spread out quickly and form a large disc.Although it is not ruled out that ethanol wets the substrate, the contact angle is too small to accurately measure the contact angle.It is approximated that the equilibrium macroscopic contact angle of ethanol on SiO 2 is approximated to be approximately 5 ∘ .
Since the interior angle of the rim edge ϕ is 5 ∘ and the equilibrium contact angles of the working liquids on SiO 2 are known, the maximum theoretically obtainable pinned contact angle can be predicted using Eq. ( 1).For DI-water and ethanol, the maximum theoretically obtainable contact angle on the pedestal nozzle is 209 ± 6 ∘ and 180 ∘ , respectively.Because the microscope setup used in the experiments is viewing the droplets from its side, the liquid-vapor interface close to the nozzle rim cannot be observed if the macroscopic contact angle exceeds 180 ∘ .However, for DI-water and ethanol sessile droplets, the contact angle is observed to be at least 180 ∘ prior to depinning.Fig. S16c shows a picture of a sessile DI-water droplet right before it depins and wets the nozzle.
Once pendant droplets become hydrostatically unstable because the hydrostatic pressure Δp becomes just too large, movies were taken of the dripping droplets, and the macroscopic contact angle θ is determined in time.An example movie is added as Supporting Information.Fig. 8 presents how the contact angle θ typically evolves in time.In this experiment, ethanol is supplied with a pressure of 873 ± 25 Pa to a nozzle with 61μm rim radius.
At t ≈ 0 s, a new droplet starts to grow on the nozzle and the contact angle rapidly increases from θ ≈ 110 ± 3 ∘ to θ = 164 ± 3 ∘ , after which it reduces again.The reduction of the contact angle is caused by gravity which pulls the growing pendant droplet away from the nozzle.At t ≈ 14.6 s the droplet detaches, and the cycle repeats.The movies are taken with a frame rate of 25fps, which is too low to capture the moment Fig. 7.The normalized minimum droplet radius R ins ∕Ω plotted as a function of the applied pressure difference Δp ins .Ω either measures the rim radius or the tube radius in case the nozzle is not equipped with a rim.Measurements with nozzles directed antiparallel to gravity are labeled with anti-parallel, and nozzles with no rim are labeled with no rim.Ω is measured using a SEM and determined with a precision below 100 nm.However, the radius of curvature R ins is measured with an accuracy R ins ± 3μm and may result in R ins ∕Ω ≤ 1, which is not physical.

B.T.H. Borgelink et al.
when a droplet detaches and to accurately determine macroscopic contact angles below 110 ∘ .The maximum macroscopic contact angle θ max during these measurements is summarized in Fig. 9.
The maximum macroscopic contact angle exceeds 155 ∘ for all nozzle rim radii and working liquids used.Larger maximum contact angles are obtained for smaller rim radii.This is explained as follows: as the droplet grows bigger, gravity forces acting on the droplet become larger.As a consequence, a neck forms between the liquid adhering to the nozzle rim and the bulk of the droplet and reduces the contact angle again.For smaller rim radii, the effect of gravity occurs later, and larger maximum macroscopic contact angles are obtained.Eventually, the neck breaks up and causes the droplet to separate from the nozzle.This observation proves that the adhesion of the working liquids to the nozzle is strong enough to suspend pendant droplets with radii approaching its capillary length scale.

Pedestal nozzles for the electrohydrodynamic jetting of polymer solutions
Nozzles with Ω = 111μm rim radius were mounted on a custommade nozzle holder and placed in a custom-made electrospinning setup.A syringe pump (Harvard PHD 2000) is used to pump a polymer solution through the nozzle at a flow rate of 0.5 mL∕h.The solution consists of polyvinylpyrrolidone (M w = 1.3⋅10 6 Da, Sigma-Aldrich) dissolved in ethanol at a 10 wt% concentration.The distance between the nozzle and the flat metal collector is 2 cm.A custom-made highvoltage power supply is used to generate an electrical potential difference V between the metal nozzle holder and collector.Fig. 10 shows a series of pictures taken during the electrohydrodynamic jetting process.While the flow rate is kept equal, the applied potential difference is varied from V ≈ 9 kV to V ≈ 15 kV.Fig. 10 shows images of the nozzle and the electrohydrodynamic jetting of the polymer liquid for different applied electrical voltages V.
For the lowest applied potential difference V, the contact angle is approximately 90 ∘ (Fig. 10a).Due to the electric body force acting on the liquid jet, the jet accelerates towards the collector.The acceleration causes the characteristically tapered meniscus right below the nozzle, and this taper is referred to as Taylor cone [6].This taper gets larger for larger applied potential differences because of the increasing body force acting on the liquid.As can be seen, an increase in body forces leads to a reduction in the macroscopic contact angle (θ, as defined in Fig. 2) and a thinner jet.However, the liquid meniscus remains pinned at the rim.This result is relevant because it demonstrates that the jet diameter can be modified by adjusting the potential difference V.In Fig. 10c, the potential difference V is so large that the body force acting on the jet causes the contact line to recess from the outer perimeter to the inner perimeter of the rim.However, the nozzle successfully confines the Taylor cone to the designated contact area, i.e., the nozzle rim and the electrohydrodynamic jetting can still be continued.It is important to mention here that similar experiments were not successful with nozzles that do not contain a rim.These attempts did not lead to an operating window at which a stable jet could be emitted, because the polymer solution immediately wets the outer side of the jet.

Conclusions
Silicon dioxide pedestal nozzles with rim radii ranging between 36μm and 111μm were successfully fabricated on wafer-scale using two novel self-aligned microfabrication methods.One of these techniques, based on edge lithography, enabled us to isotropically and concentrically etch a layer stack.This layer stack acts as a diffusion barrier for oxidant species during the LOCOS, which is employed to fabricate the hydrophilic silicon dioxide pedestal nozzles.The sharp rim edge is created by the formation of a bird's beak during the LOCOS step, and is used to pin polar liquids to the rim.A cross-section cut from the nozzle rim edge was analyzed, and the angle of the rim edge was determined to be approximately 5 ∘ , and the sharpness of the rim edge, i.e., the radius of curvature of the rim edge, is less than 20 nm.
Hydrostatic measurements were performed to analyze the functionality of the nozzle rim.During these measurements, it is observed that the droplets start to grow uninhibitedly once the droplet radius is equal to the nozzle rim radius.This observation is in agreement with predictions made by a thermodynamic model based on the Gibbs free energy of pinned droplets, which is developed to also qualitatively understand the phenomenon.DI-water and ethanol droplets of sizes equal to their capillary length scale are pending on the nozzle, thereby proving the strong adhesion between these working liquids and the nozzle.The sharp rim edge increases the macroscopic contact angle up to at least 150 ∘ with respect to the equilibrium contact angle.
Although macroscopic contact angles larger than 180 ∘ cannot be measured with the presented measuring technique, it is expected that the maximum pinned contact angle is close to the theoretically predicted maximum pinned contact angle.To the best of our knowledge, such strong geometrical contact line pinning has not been reported in Fig. 8.The evolution of the contact angle θ in time, once the applied pressure is just too large to maintain a steady pendant droplet at the pedestal nozzle exit.Within an average time of 14.6 s, a droplet is growing on the nozzle and pinching off.The absolute error of the macroscopic contact angle is expected to be θ ± 3 ∘ .The pedestal nozzles effectively confine the contact area of polar liquids with free surfaces.Examples include, but are not limited to, droplet tensiometry and inkjet printing.Because the nozzles facilitate strong geometric contact line pinning, no anti-wetting layers are necessary to prevent wetting of the nozzle.Based on the work of De Jong et al., the nozzles are practical for inkjet printing because the nozzle is expected not to age and is resistant to most chemicals and heat [12].The nozzles were employed successfully for the electrohydrodynamic jetting of polymer liquids and are regarded as a first step toward electrospinning.While the polymer solution was supplied to the nozzle at a constant flow rate, the applied electrical potential difference could be varied over a relatively large range, while the polymer solution remained confined to the nozzle rim.

Fig. 1 .
Fig. 1. a-b) SEM images of one of the pedestal nozzles: a) Silicon dioxide pedestal nozzle protruding the silicon base.b) Cross-section view of the sharp nozzle rim edge (black).The arrow points at the bird's beak-shaped rim edge, which has a radius of curvature smaller than 20 nm and an interior edge angle of approximately 5 ∘ .Platinum has been deposited on the nozzle rim to protect the rim edge during the focused ion beam milling to make a cross-section cut of the nozzle rim.The platinum deposition and its re-deposition during the milling process causes the roughness visible at the rim edge.The scale bar size in a) is 50μm and in b) 900 m.

Fig. 2 .
Fig. 2. A schematic drawing of a liquid droplet (light blue) pinned onto the pedestal nozzle rim (dark blue).The definitions of macroscopic contact angle θ and interior rim edge angle ϕ are depicted in the magnified nozzle rim edge.

Fig. 3 .
Fig. 3. Gibbs free energy plotted as a function of the normalized droplet volume V∕V 0 .The dotted line represents the local minimum of G.For a droplet in thermal equilibrium, its volume increases for increasing hydrostatic pressure difference Δp across the liquid-air interface.

Fig. 4 .
Fig. 4. a-f) Cross-sectional drawings at highlighted stages of the nozzle fabrication process.a) Etching concentric circular holes in TEOS (green), SiRN (red), SiO 2 (blue) and silicon (gray) by means of directional plasma etching.b) Timed isotropic etching of the SiO 2 and removal of TEOS.c) Selective wet-chemical etching of the suspended SiRN layer, and LOCOS.d) LPCVD of Si 3 N 4 and directional plasma etching of circular holes in the SiO 2 and silicon at the back side of the substrate.e) Etching of the exposed SiO 2 and LOCOS.f) Removal of the Si 3 N 4 and etching of crystalline silicon such that the nozzle protrudes the silicon surface.

Fig. 9 .
Fig. 9.The maximum contact angle θ max bundled by the rim radii Ω of the pedestal nozzle.

Fig. 10 .
Fig.10.Pictures of a pedestal nozzle with Ω = 111μm used for the electrohydrodynamic jetting a polymer solution.In a), the applied potential difference V is lowest and of the order of V ≈ 9 kV, whereas in b) and c), the potential differences are of the order of V ≈ 13 kV and V ≈ 15 kV.