The Simulation and Research of Etching Function Based on Scanning Electrochemical Microscopy
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Scanning electrochemical microscopy (SECM) has already been employed as a micromachining method for a long time. However, coupling effects of some factors, including the voltage of the tool electrode, the distance between the tool electrode and substrates, tip current, and machining time on the machining process, have not been clearly stated. In this study, based on simulation and experimental results, an etching function between the etching depth and the above influencing factors in the machining process with SECM is proposed. First, the influence of the tool electrode, the distance between the tool electrode and substrates, tip current, and machining time on the etching depth was analyzed by a two-dimensional (2D) axisymmetric finite element model. Second, the etching function between these factors and the etching depth was established. Finally, this relationship was then simplified and verified by etching experiments. In summary, the etching function can be used to guide the etching process to machine 2D and 3D microstructures with SECM.
KeywordsEtching function Etching depth Scanning electrochemical microscopy
The machining method of scanning electrochemical microscopy (SECM) was proposed by Bard et al. . Nowadays, this method has been widely used in many fields, including electrocatalysis, corrosion, and elucidation of charge transfer kinetics and mechanisms of heterogeneous processes, biophysical systems, semiconductors or liquid–liquid and liquid–gas interfaces . Among these methods, by combining this method with the piezoelectric element and other systems, the electrode is controlled to access substrates, and the oxidation–reduction reaction generates between the tip and substrates by increasing the voltage of the tool electrode to realize the etching results. The accuracy of etching results could be increased up to the nanometer level by improving parameters, including the size of the tool electrode and the motion control accuracy. This method has the significant advantages of high spatial resolution [3, 4, 5].
In addition to the factors of the reaction system such as the type of substrates and type of solution, the voltage of the tool electrode, the distance between the tool electrode and substrates, machining time, and tip current are all related to the etching results . Mandler and Bard  held the tip at a constant distance near the surface and obtained the feedback current. For the analysis of the influence of these factors on etching results, simulations on a two-dimensional model are one of the most commonly used methods [8, 9, 10, 11, 12, 13]. The results would be consistent with the experimental results and could be traced and obtained quantitatively. Shimizu et al.  and Mirkin and Bard  applied a 2D integral equation to solve the diffusion problem for two quasi-reversible electron-transfer processes occurring between the tool electrode and substrates. For the multiphase reaction, the reaction rate was the extracted flux of the substance generated on substrates that was evaluated through the concentration of the generated substance by the reported the substrate-generation/tip-collection mode . The equilibrium state and kinetic results were studied by introducing a diffusion coefficient . However, the coupling effects of these factors have not been clearly stated. The aim of this article was to propose the etching function using gallium arsenide (GaAs) as an example. The etching function between the parameters of the multiphase reaction and the etching results was studied based on the 2D integral equation. This function enabled us to establish the relationship between machining depth and machining parameters, thus making parameter design more convenient. In theory, according to the relationship between tip current and tip voltage from the Nernst function [18, 19], and the relationship between etching depth and the tip current , we could determine the relationship between the etching depth and the tip voltage. By establishing a two-dimensional numerical simulation model by COMSOL software, we could understand the theoretical etching function. In addition to the voltage of the electrode, the etching time, and the tool electrode–substrate distance could be considered. We could also modify the etching function mentioned above by experiments.
2 Theory and Simulations
3 Experimental Section
3.1 Chemical Solutions and Materials
The analytical grades of H2SO4 and NaBr were provided by Sinopharm Chemical Reagent Co., Ltd. (China). All of the experimental solutions were prepared with deionized water (18.2 MΩ, MilliQ, Millipore, Bedford, MA, USA). The substrates were silicon-doped GaAs wafers with a doping level between 0.8 × 1018 and 2.3 × 1018 cm−3 provided by Chinese Crystal Technologies Co., Ltd. (Hefei, China). Before being used, the substrates were cleaned with deionized water and dried with nitrogen.
3.2 Instrumentation and Procedures
All experiments were performed on the reported homemade precision machining system . The experimental electrode included a tool electrode, a reference electrode, and a counter electrode. The counter electrode was a Pt wire, and the reference electrode was an Ag wire with the same size of 500-μm diameter. The tool electrode was a 100-μm-diameter Pt wire with the sealing glass that had been tapered to RG = 2. The tool electrode had been characterized by optical microscopy and a steady-state volt–ampere curve. The reported tool electrode worked in solution containing 100 mM NaBr and 500 mM H2SO4. All the simulations were calculated by COMSOL Multiphysics 5.3 software (Stockholm, Sweden).
4 Results and Discussion
4.1 Variations of the Tip Current in Steady-State Simulation
There are many factors affecting the etching results. We do not discuss the influence of solution concentration on the etching results here. We fixed the etching concentration as 100 mM NaBr and 500 mM H2SO4. The tip diameter in the following simulation process was set at 100 μm, and the influence of the tip diameter was not introduced in this study.
This formula can be used to predict the tip current under the above-mentioned research situation before an experiment. Additionally, through coupling the voltage of the tool electrode and the distance between the tool electrode and the GaAs substrate, we could face the resolution limit problem caused by the single factor.
4.2 Calculation of the Etching Function in Transient Simulation
By introducing the parameter of machining time, the relationship between tip current and etching depth was studied, and the etching function was obtained during simulations on the relationship between these factors (tip current, voltage of the tool electrode, machining time and distance between the tool electrode and GaAs substrates) and etching depth under the transient condition.
According to this function, the tip current changed with etching time, the voltage of the tool electrode, and the distance between the tool electrode and GaAs substrates. To further modify the etching function, we set the distance between the tool electrode and GaAs substrates at 100 μm to simulate the relationship between the tip current and the other two factors. The simulation results are illustrated in Fig. 3b. The tip current decreases with the increase of etching time, and the greater the voltage of the tool electrode, the more obvious the decrease. This is consistent with function (10), with the error less than 5% and the machining time within 100 s.
Based on the definition of the relationship between the tip current and the above parameters, the relationship between the etching depth and these factors was directly studied. The etching function depends on many parameters, such as the voltage of the tool electrode and the machining time. The simulation results between the maximum etching depth at different etching times and the voltage of the tool electrode are illustrated in Fig. 3c. Similarly, as the etching time increases, the etching depth increases at different voltages, and the relationship between the two is not linear. By fitting these curves, we found that the results were consistent with the above conclusion that the etching depth would increase the distance between the tool electrode and GaAs substrates and affect the final etching depth.
To further analyze the relationship between etching depth and these two factors, these factors were analyzed separately. We analyzed the etching depth under different volts of the tool electrode with a fixed etching time of 100 s. There are two aspects of the influence about the voltage of the tool electrode on etching results: etching profile and etching depth. First, we studied the effect of the voltage of the tool electrode on etching profile. The etching profile within the range of 0.85–1.20 V at 100 s can be obtained by simulation, as illustrated in Fig. 3d. As the voltage of the tool electrode increases, the etching depth increases. The normalized contours remain the same. The differences between contours under different voltages are only different in size. The overall shape is smooth, and there is no inflection point. Although the tool electrode is a 100-μm-diameter Pt disk, the side wall of the etched profile obtained by the simulation is not straight because of the diffusion effect, and there would be a slope. Additionally, the bigger the voltage, the bigger the slope. Similarly, the machining contours at different etching times under 1.2 V were analyzed, as illustrated in Fig. 3e. The maximum etching depth increases with etching time, and the contour slope increases.
This function is consistent with function (10), and the maximum etching depth is approximately 2.57 μm.
4.3 Experimental Verification of the Etching Function
When functions (13) and (14) were compared, the maximum error of parameters was less than 3%. As illustrated in Fig. 4c, the machining contour maps at different voltages of the tool electrode were consistent. The etching depth decreased as the voltage of the tool electrode decreased, and the overall etching contours were consistent with the simulation results. According to the reported results, the slight difference was caused by tip passivation .
We put forward the concept of an etching function to study the process of scanning electrochemical microscopy. First, we studied the relationship by simulation in the process of etching GaAs with NaBr. The relationship between many factors (including machining time, the distance between the tool electrode and GaAs substrates, and the voltage of the tool electrode and tip current) and etching depth was analyzed under steady-state and transient simulation processes, respectively. Then, we established the multifactor etching function and analyzed each single factor. The etching function of the voltage of the tool electrode, the etching depth at the machining time of 100 s, and the parameter d of 10 μm was determined. Moreover, this relationship was verified by experiments and is consistent with that of the simulation results. In conclusion, this model can be used to determine the etching functions under different factors to determine the etching depth by adjusting different parameters. This work also applies to research on the etching function of the other III semiconductors.
The authors gratefully acknowledge financial support from the National Natural Science Foundation of China (21827802, 21573054, 21327002) and the Fundamental Research Funds for the Central Universities (20720190023).
Compliance with Ethical Standards
Conflict of interest
All authors declare that they have no conflicts of interest.