A closed-loop constant deposition current control method based on MCED circuit model

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.

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, N_i is the transport vector, D_i is the ion diffusivity, c_i is the ion concentration, z_i is the ion electronic charge, u_i is the mobility of the charged species, F is the Faraday constant, φ_l 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, V_m, 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, D_w 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 

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 U_dc is the DC bias voltage and U_c is the voltage across the capacitor C₁. If we take U_dc as the input, the output U_c can be obtained by the Laplace transform,

The transfer function is then given as

According to the relationship between U_c and the current I_R1 passed through R₁, we can get the following equation [Eq. (6)]:

If we take U_dc as the input and the I_R1 as the output, the formula by the Laplace transform is then given as

Combining Eqs. (5) and (7), we can get the transfer function between the U_dc and the current I_R1.The transfer function is 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.

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 U_c 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 $Q=Ucεs4πk$⁠, the current across the capacitor C₁, I_c1, is given as

Therefore, during the retraction of the probe, Q is a constant and $v=d1−d2dt$ 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.

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.

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.

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.

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.

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%.

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.

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.

Figure 9 shows the reduction current response for different relationships of the growth rate of the copper pillars, V_g, and the probe retraction speed, V_u, namely, when V_g < V_u = 196 nm/s [Fig. 9(a)], V_g > V_u = 80 nm/s [Fig. 9(b)], and V_g = V_u = 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.

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.

For the closed loop case, however, the current fluctuation is markedly suppressed [Fig. 10(d)] and the resulting copper pillar exhibits a uniform diameter and a higher aspect ratio [Fig. 10(b)].

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.