Meniscus-confined electrodeposition (MCED) is a simple and economical fabrication method for micro/nanoscale three-dimensional metal printing. In most applications of MCED of copper pillars using a deposition pipette probe, there exists a certain probe retraction speed range that can ensure successful pillar deposition. If the probe retraction speed exceeds this range, however, the morphological changes in the contact meniscus droplet bridge between the probe tip and substrate induce deposition current fluctuations. These fluctuations result in uneven pillar diameters (i.e., beaded wire deposition) and can even lead to nanowire breakage and growth termination. To analyze the MCED process, therefore, this paper first proposes a circuit model for the MCED process and then, based on this model, analyzes the mechanism underlying the deposition current fluctuations present as the probe retracts at higher speeds. To effectively suppress these deposition current fluctuations and improve the stability and quality of deposited copper pillars, a closed-loop constant-deposition-current control method is proposed. Compared with deposition using no control strategy, the constant-deposition-current control method is shown by simulations and experiments to significantly suppress the fluctuation of the deposition current and increase the stability of copper pillar growth. In addition, the constant-deposition-current control method is used for the rapid fabrication of copper pillars with high aspect ratios.
Micro/nanoscale three-dimensional (3D) metal printing can produce free structures that enable the fabrication of innovative products such as micro-sensors,1–3 micro-circuits,4 wire bonding,5 micro/nanoelectromechanical systems,6 plasma, and metamaterial structures. Traditional 3D printing methods include selective laser melting (SLM) and electron beam melting (EBM), which both typically rely on the local fusion of metal particles to form solid materials and are primarily used commercially for macroscale 3D metal printing.7–10 The minimum printing line width of SLM and EBM is several tens of micrometers, making these methods unsuitable for sub-microscale fabrication.11,12 Micro-stereolithography covers a wide range of micro/nanoscale processing technologies and has been successfully applied in commercial applications. However, it is restricted in practical application owing to its relatively low spatial resolution and productivity and its limited material selection in conventional techniques.13 To improve the resolution of metal additive manufacturing methods, various new microscale and sub-microscale technologies are being developed such as direct ink writing,14,15 electro-hydrodynamic printing,16,17 laser-assisted electrophoretic deposition,18,19 laser-induced forward transfer,20,21 meniscus-confined electrodeposition (MCED),22–24 and electroplating of locally dispensed ions in liquid (LDIE).25 Among these methods, the configuration of MCED and LDIE is relatively simple. LDIE involves immersing a probe and a conductive substrate in an electrolyte and applying local electric fields between the probe and the substrate to induce electroplating. The structures fabricated by LDIE are typically porous; however, it is difficult to limit the electric field to the nanoscale, so the feature size is usually a few tens of micrometers.26 Compared with other printing methods, MCED is one of the simplest and most economical manufacturing methods. Essentially, in the MCED process, metal cations are electronically reduced to metal atoms. In 2006, Suryavanshi and Yu proposed a template-based electrodeposition method to create free-standing copper nanowires (i.e., copper nanopillars). During nanopillar growth, the reduction current was governed by electro-migration, diffusion, and convection.27 In 2007, Suryavanshi and Yu proposed electrochemical fountain pen nanofabrication to deposit nanowires, enabling the control of several parameters such as micropipette probe retraction speed, bias voltage, humidity, and electrolyte concentration. It was found that, if the micropipette probe pulls away from the substrate at higher speeds than those required for continuous and smooth deposition, the meniscus can break and terminate the nanowire growth or cause the deposition of beaded wires.23 In 2015, Seol et al. reported the effect of surface evaporation of meniscus droplets on deposited copper pillars and successfully fabricated hollow and solid copper pillars and various microstructures by adjusting the voltage between the electrode and the substrate.24 Local pulsed electrodeposition (L-PED) is a micro/nanoscale 3D printing method based on MCED, where metal deposition is produced via controlling the cycle and break time of the electrical deposition current.29–31 Specifically, L-PED uses the voltage switch “OFF” time to wait for ions inside the probe convection to diffuse to the reaction interface. The L-PED process fabricates nanotwinned metal structures with improved mechanical and electrical properties. Both the L-PED deposition method and the work of Seol et al.24 indicate that adjusting the voltage between the electrode and the conductive substrate can change the morphology and speed of the deposition.
The MCED method for copper pillar deposition is accomplished by continuously pulling away the probe tip from the conductive substrate while the copper salt solution cations are reduced and deposited in the meniscus confined substrate surface, thus forming the copper pillars. There is a required range for the deposition probe tip retraction speed, however, where exceeding the upper limit of this range will cause a periodic variation of the pillar diameter. This periodic diameter variation eventually forms a beaded wire owing to the self-adjusting nature of the deposition process at a higher probe retraction speed.28 In addition, fluctuation of the ambient parameters has a certain impact on the quality of the copper pillar deposition.32 However, there are no reports on the analysis of deposition stability and quality from the perspective of circuit models at a higher probe retraction speed. Therefore, based on the analysis of a proposed MCED circuit model, this paper proposes a closed-loop constant-deposition-current control method wherein the bias voltage between the electrode inserted in the micropipette and the working electrode (i.e., conductive substrate) is adjusted in real-time to maintain a constant deposition current.
II. THEORETICAL ANALYSIS
A. Principle of MCED with a single-barrel pipette
In the MCED process, a micropipette filled with a metal salt solution (0.05M CuSO4) is brought close to a conductive substrate (Au), whereupon a liquid meniscus forms between the pipette tip and the substrate upon electrolyte contact [Fig. 1(a)]. To initiate electrochemical reduction, the conductive substrate is negatively polarized (i.e., the cathode) vs a copper counter electrode inside the pipette (i.e., the anode). The liquid meniscus defines the lateral extension of the electrochemical reaction and, therefore, the nucleation and growth of the metallic deposition. At this point, the Cu2+ in the electrolyte is reduced and deposited on the cathode substrate (Cu2+ + 2e = Cu). The atoms of the copper electrode inside the pipette (i.e., anode) lose electrons and are ionized as Cu2+ (Cu − 2e = Cu2+), thus replenishing the Cu2+ in the solution. Figure 1(b) schematically illustrates the “hopping mode” employed by using the MCED system for deposition. First, the probe moves above a target point and gradually approaches the conductive substrate. When the meniscus droplet makes contact with the conductive substrate surface, the probe tip is continuously retracted to form a copper pillar. When the probe tip is retracted at a sufficiently high speed, the meniscus droplet is separated from the conductive substrate surface and the growth of the copper pillar is terminated. The MCED system moves the probe displacement in the x or y direction for electrodeposition of a new copper pillar. Figure 1(c) shows a scanning electron microscope (SEM) image of the probe opening, while Fig. 1(d) shows the control flow chart of the deposition procedure.
The copper pillar growth rate is primarily governed by the ion concentration in the meniscus droplet at the tip of the probe. Because the deposition and growth of a copper pillar is a complex multi-physical process, the electrochemical dynamics in the electrolyte are described by the Nernst–Planck equation,35 given as
where, for the ionic species i, Ni is the transport vector, Di is the ion diffusivity, ci is the ion concentration, zi is the ion electronic charge, ui is the mobility of the charged species, F is the Faraday constant, φl is the electric potential difference in the electrolyte, and u is the fluid velocity. The ion flux within the electrolyte is governed by diffusion, migration, and convection.32 The electro-migration current intensity accounts for up to 50% of the ion flux, and the remaining 50% is primarily governed by ion diffusion and convection.33 To ensure stable electrodeposition of the copper pillar, the probe should be within a certain retraction speed range.4 The report by Hu gives the relationship between the height of the droplet bridge and the diameter of the copper pillar during MCED.28 In addition, the diameter of the deposited copper pillar is affected by the speed difference between the probe retraction and the growth rate of the copper pillar and the profile angle of the meniscus droplet bridge.28 When the probe tip is retracted, the difference in the electrochemical properties of the varying substrate surface and the varying interface profile angle of the meniscus droplet will cause the growth rate of the copper pillar to be not constant.28
Because the electrochemical deposition is a classic Faraday process, the growth rate, Vm, of the copper pillar is described as
where i is the charge transfer current or the local current on the electrode surface, M is the molar mass of copper, ρ is the density of copper, Dw is the diameter of the deposited copper pillar, and n is the number of electrons necessary for ion reduction.34 Therefore, when the convection and diffusion of metal ions are stabilized between the micropipette and the meniscus droplet, the concentration of metal ions in the meniscus droplet is primarily controlled by electro-migration. Regulating the voltage between the copper electrode and the conductive substrate (i.e., the working electrode) can, therefore, govern the current of the deposition and the growth rate of the copper pillar.25
B. Electrodeposition equivalent circuit model
The MCED equivalent circuit model is shown in Fig. 2(c). When the meniscus droplet comes into contact with the substrate surface, the meniscus droplet is equivalent to a resistor and a capacitor connected in parallel, where R2 is the charge transfer resistance between the solution and the conductive substrate and C1 is the double-layer capacitance of the interface between the solution and substrate surface. In addition, R1 is the resistance of the solution in the micropipette.
According to Kirchhoff’s voltage law, we can obtain the following formula:
where Udc is the DC bias voltage and Uc is the voltage across the capacitor C1. If we take Udc as the input, the output Uc can be obtained by the Laplace transform,
The transfer function is then given as
According to the relationship between Uc and the current IR1 passed through R1, we can get the following equation [Eq. (6)]:
If we take Udc as the input and the IR1 as the output, the formula by the Laplace transform is then given as
According to Eq. (8), we can obtain the block diagram of open-loop and closed-loop control systems, as shown in Fig. 3. In Fig. 3(a), Step is the step input signal. In Fig. 3(b), Step_IR1 is the reference for constant current. K_feedback is the gain of the feedback. In Figs. 3(a) and 3(b), Step1 is used to simulate the step interference. 1/R1 is the resistance proportional. Simout is the data for post-processing. Uniform Random Noise is the interference signal that overlaps with the output.
C. Impact factors of current fluctuation in MCED
1. Current fluctuation caused by the capacitance effect in MCED
When the meniscus droplet comes into contact with the conductive surface, we assume that the height of the meniscus droplet of the probe tip changes within a small range while the contact area of the meniscus droplet and the conductive substrate surface remain unchanged. In this case, the height of the meniscus droplet bridge determines the capacitance C1, which is described using
where ε is the dielectric constant, s is the contact area between the solution and conductive substrate surface, k is the electrostatic force constant, and d is the distance between the electrode plates (i.e., the height of the meniscus droplet bridge). According to the linear superposition principle, we assume that the equivalent resistance R2 is constant after the height of the meniscus droplet is changed; therefore, the voltage Uc remains the same. At this moment, the change in stored electrical charge, Δq, by the capacitance C1 is given as
where d1 and d2 are the heights of the meniscus droplet bridge before and after probe retraction, respectively, and C2 is the capacitance of the meniscus droplet bridge after the height has been changed. Assuming that , the current across the capacitor C1, Ic1, is given as
Therefore, during the retraction of the probe, Q is a constant and is the speed difference between the probe retraction and pillar growth rate. Four observations can made from Eq. (11). First, when the probe retraction speed is equal to the growth rate of the copper pillar, then d1 and d2 are the same and the current passed through C1 is almost unchanged. According to Kirchhoff’s current law, the total current remains almost unchanged. Second, when d2 > d1 and the probe retraction speed is greater than the growth rate of the copper pillar, the current change is negative and the total circuit current decreases. Third, when d2 < d1 and the probe retraction speed is less than the growth of the copper pillar, the capacitance is equivalent to the charge, the current change is positive, and the current in the total circuit increases. Fourth and finally, the current passing through the capacitor is proportional to the speed difference between the probe retraction speed and pillar growth rate and is inversely proportional to the product of d1 and d2.
2. Current fluctuation caused by the resistance effect in MCED
According to the linear superposition principle, for a constant capacitance C1 in the equivalent circuit during the probe retraction, and for an equivalent circuit resistance change from R2 to R3, the voltage across the capacitor C1 in the equivalent circuit is given as
From Eq. (12), when R2 = R3, the current does not change. When R3 > R2, owing to the capacitive effect, the voltage across the capacitor increases exponentially and the current flow through R1 decreases exponentially. Conversely, when R3 < R2, the voltage across the capacitor decreases exponentially and the current flow through R1 increases exponentially. More importantly, Eq. (12) shows that a greater difference between the probe retraction speed and the growth rate induces a greater difference between R2 and R3 and, therefore, a greater fluctuation of the deposition current.
According to the above analysis, it can be seen that the deposition current fluctuates as a result of the combined effects of capacitance and resistance, which are determined by the varying height of the meniscus droplet bridge during electrodeposition.
3. Flow chart for the MCED constant-deposition-current control method
Figure 4 shows the proportional integral (PI) control flow chart in MECD, where delta is the difference between the given deposition current and the feedback sample current, Isum is the sum of delta of the integral, Iout is the digital out, Kp is the proportionality factor, T is the response period, and Ti is the integral constant. Owing to the large surface area-to-volume ratio of the meniscus droplet, parameter changes in the ambient environment will interfere with the deposition current; thus, the introduction of differentiation will amplify the system interference. Therefore, we adopted the proportional integral (PI) control method of integral separation and anti-integral saturation.
III. CONFIGURATION AND MATERIAL
A. MCED system configuration
A schematic of the MCED system used herein is given in Fig. 5. In these experiments, we used a home-built MCED system mainly comprising a piezoelectric ceramic (P621.ZCL, Physik Instrument, Germany) and a piezo-driver (E-509, Physik Instrument, Germany), an additional I/V conversion amplifier (SR570, Stanford Research Systems, USA), a micropipette, and home-built PI controllers.
B. Material preparation
The micropipettes were fabricated from single-barrel borosilicate capillaries [Harvard Apparatus, 1.0 mm (outer diameter) × 0.58 mm (inner diameter) × 100 mm (length)] using a laser puller (P-2000, Sutter Instrument). The radii of the micropipette probe openings were approximately 1 μm. The surface morphology of the copper pillars was characterized by using the SEM (JCM-6000, Jeol Ltd.) operating with a 12 kV electron beam and in high-vacuum mode, wherein the substrates were tilted to facilitate imaging. The substrate was a 200 nm-thick gold layer deposited on high-purity conductive glass. A copper electrode (purity of 99.99%) was inserted into the micropipette probe. In this paper, the simulations were carried out by using the SIMULINK module provided by MATLAB. The parameters in the proposed circuit model are that R1 is 21 MΩ, R2 is 29 MΩ, and C1 is 35 nF. In this experiment, the probe tip diameter is approximately 1 µm, the CuSO4 solution concentration is 0.05M, and the voltage between the two electrodes is 0.18 V.
C. Constant environmental humidity platform
Humidity fluctuations in the ambient environment play an important role in the fabrication quality and the stability of the system.32 Therefore, a platform ensuring a constant-humidity environment was designed (Fig. 6), maintaining a stable humidity level of approximately 60%.
IV. RESULTS AND DISCUSSION
A. Control system simulation and cyclic voltammetry in MCED
Recently, a scanning electrochemical cell microscopy (SECCM) circuit model was proposed by our group.36 According to the similar analysis results and experimental data [Fig. 8(b)], it can be calculated that R1 is 21 MΩ, R2 is 29 MΩ, and C1 is 35 nF. Substituting parameters in open-loop [Fig. 3(a)] and closed-loop [Fig. 3(b)] models, the parameter values Kp = 10, T = 1 s, Ti = 1.8, and Ki = Kp*T/Ti = 0.18 in the PI controller, setting the equal proportion noise interference overlaps with the output of the system. We can get the simulation results shown in Fig. 7(a). It can be seen clearly from Fig. 7(a) that the closed-loop control system suppressed noise better than the open-loop system. At the point at which the meniscus droplet came into contact with the conductive substrate surface [point I in Fig. 7(a)]), the circuit is in a first-order zero-state response state. At the point at which a step signal was superimposed on the system [point II in Fig. 7(a)], the closed-loop system can ignore the effect of step interference and quickly stabilize the output signal to the set value, while the open-loop system output was the original value overlapped with the step signal. Therefore, the simulation suggests that the closed-loop system can significantly suppress the interference of the deposition current.
The cyclic voltammetry curves at four positions are shown in Fig. 7(b), where a net reduction current is seen to appear at voltages greater than 0.1 V. Furthermore, an approximately linear relationship is observed between the net reduction current and the voltage between the micropipette electrode and the conductive substrate. Therefore, the voltage between the micropipette electrode and the working electrode (i.e., the conductive substrate surface) can be adjusted to control the amplitude of the reduction current.
B. Analysis of current fluctuations via capacitance and resistance effects
Figure 8(a) shows a simulation of the reduction current response caused by the changes in the capacitance C1 and resistance R2, while Fig. 8(b) plots the corresponding experimental result. Three different stages (stages II–IV) are identified in the simulation [Fig. 8(a)], and four stages (stages I–IV) are identified in the experiment [Fig. 8(b)], wherein stages II–IV correspond to the same stage for both simulation and experiment. Stage I in Fig. 8(b) corresponds to the situation where the meniscus droplet was not in contact with the conductive substrate surface, and thus, the current in this stage was zero. Stage II plots the current response when the meniscus came into contact with the substrate surface. Stage III plots the current response as the distance between the probe tip and the substrate surface induced an increase in the height of the droplet bridge. Finally, stage IV plots the current response when the distance between the probe tip and the substrate surface was reduced, thus reducing the height of the droplet bridge. A comparison of Figs. 8(a) and 8(b) makes it clear that the results of the simulation and the experiment are in agreement.
At the start of stage II, when the meniscus droplet at the probe tip made contact with the sample surface, the state of the circuit was a first-order zero-state response. At this point, the current consisted of two parts: the faradaic current (i.e., reduction current) and the current that was not the faradaic current (i.e., capacitor-charging current). Owing to the capacitive charging effect, the current decayed exponentially in the initial stage of stage II. However, differences exist between the simulation and experiment in the later parts of stage II. In the simulation, after the capacitor was charged, the current tended to be stable [Fig. 8(a)]. In this experiment, however, because the copper ions in the meniscus droplet were consumed and the copper ions in the micropipette were slowly replenished into the meniscus droplet and the substrate surface, the equivalent resistance of the meniscus droplet became large and induced a decrease in the reduction current [Fig. 8(b)]. Initially, at stage III, the meniscus droplet bridge height between the probe tip and substrate surface increased as the probe tip was retracted. Thus, the current initially exhibited a rapid decrease followed by an exponential increase, though the current decreased overall. Stage IV is a current response curve signifying that, when the MCED system moved the tip of the probe toward the substrate, the height of the meniscus droplet bridge decreased. At this point, the current rose sharply and then decreased exponentially. The results again show that changes in the meniscus droplet height cause equivalent capacitive and resistive effects. In addition, the experimental results indicate that, when the height of the meniscus droplet is varied within a certain small range, the resistance effect of the system was more marked than the capacitance effect.
C. Current response with different probe retraction speeds in MCED
Figure 9 shows the reduction current response for different relationships of the growth rate of the copper pillars, Vg, and the probe retraction speed, Vu, namely, when Vg < Vu = 196 nm/s [Fig. 9(a)], Vg > Vu = 80 nm/s [Fig. 9(b)], and Vg = Vu = 137 nm/s [Fig. 9(c)]. Because the Cu2+ inside the meniscus droplet is continuously consumed via reduction on the conductive substrate surface, the convection and diffusion supplementation of the Cu2+ inside the probe has an inherent physical periodicity,28 resulting in the periodic fluctuation of the reduction current. It can be seen from Figs. 9(a) and 9(c) that the natural period of the reduction current fluctuation was about 2.5 s. Figure 9(a) shows that, for a probe retraction speed of 196 nm/s, the growth rate was slower than the probe retraction speed because the height of meniscus droplet bridge was increasing (i.e., equivalent resistance R2 increased). At the same time, the droplet bridge was continuously elongated, which eventually caused the droplet to separate from the conductive substrate. Figure 9(b) shows a growth curve in which the probe retraction speed was 80 nm/s. When the meniscus droplet came into contact with the conductive substrate, the growth current suddenly increased and continued to rise. This experiment shows that, when the growth rate was higher than the probe retraction speed, the current continuously increases and the copper pillar continuously grew toward the probe, increasing the chance of growth into the probe tip that could induce clogging. A microscope image of a clogged micropipette tip is shown in Fig. 9(d). Figure 9(c) shows the current growth curve for a probe retraction speed of 137 nm/s. At this speed, the Cu2+ ions being supplied via convection, diffusion, and electro-migration are almost equal to the Cu2+ ions consumed by reduction.
D. Comparison of copper pillar growth
Figures 10(a) and 10(b) show the SEM images of copper pillars grown under the open-loop and closed-loop configurations, respectively, as well as the corresponding reduction current curves of the copper pillar growth [Figs. 10(c) and 10(d)]. For the open-loop case, it is clear that the reduction current curve exhibits a significant fluctuation [Fig. 10(c)], and the copper pillars [areas marked by red circles in Fig. 10(a)] have a notably rugged surface structure (i.e., periodic diameter thickness variation). The average current amplitude is stable overall, but the fluctuation period of the reduction current is about 2.5 s. The primary reasons for the deposition current fluctuations are twofold: (i) analyzing the equivalent circuit, the capacitive and resistance effects in the equivalent circuit change as the height of the meniscus droplet varies during the probe retraction. (ii) Physically, the Cu2+ inside the probe has a certain inherent periodicity via convection and diffusion to the surface of the substrate, resulting in periodic fluctuation of the reduction current. Moreover, it is challenging to conduct the copper pillar growth operation in the open-loop configuration with a constant probe retraction speed for an extended duration, and thus, it is difficult to obtain high-aspect-ratio copper pillars.
Herein, a circuit model for MCED is introduced and then used to analyze from the circuit perspective the deposition current fluctuation caused by the variation of the droplet bridge height. Simulations and experiments indicate that the deposition current is highly susceptible to resistance and capacitance effects during the growth of copper pillars. In addition, the cyclic voltammetry experiment demonstrates that changing the voltage between the conductive substrate and the probe’s internal electrode within a small range can govern the deposition current. Hence, to maintain a constant deposition current during electrodeposition, this work proposes a closed-loop constant-deposition-current control method that regulates the voltage between the probe electrode and the conductive interface in real-time. The simulation results demonstrate that the closed-loop method can significantly suppress environmental interference and improve the stability of deposition current. Additionally, the microscale copper pillars produced by both methods reveal that the closed-loop method can significantly improve the quality and stability of copper pillar growth compared to the open-loop method at a higher retraction speed. In summary, the closed-loop constant-growth-current control method is shown to be an efficient and clean technique for localized fabrication of a variety of vertically grown metal nanowires and can potentially be used for fabricating freeform 3D nanostructures.
This research work was supported by the National Natural Science Foundation of China (Project No. 51375363), Industrial Research Project of Science and Technology Department of Shannxi Province (Project No. 2013GY2-04), and Sichuan Science and Technology Program (Grant No. 2018Gz0083). The authors thank Professor Yuan Weifeng from the Southwest University of Science and Technology for fruitful discussions and Lu Xingyuan master for contributions to the SEM images of copper pillars. At the same time, the authors are also very grateful to Dr. Li Yabei and Ali Akmal Zia master of Xi’an Jiaotong University for their constructive opinions.
The authors declare no competing financial interest.
The data that support the findings of this study are available from the corresponding author upon reasonable request.