Distance effects in electrochemical micromachining

Considering exponential dependence of currents on double-layer voltage and the feedback effect of the electrolyte resistance, a distance effect in electrochemical micromachining is found, namely that both time constant and double-layer voltage depend on the separation of electrodes. The double-layer voltage is the real voltage used in processing. Under DC voltage, the apparent voltages between two electrodes are constant for different separations, but the real voltages change with the separations. Small separations exert substantial effects on the real voltages. Accordingly, a DC-voltage small-separation electrochemical micromachining technique was proposed. The double-layer voltage drops sharply as the small separation increases. Thus, the electrochemical reactions are confined to electrode regions in very close proximity even under DC voltage. The machining precision can be significantly enhanced by reducing the voltage and separation between electrodes. With this technique, the machining of conducting materials with submicrometre precision was achieved.

. Effects of the electrolyte concentrations on the achievable machining precision; triangles, test values; solid lines, fited values.

B. Determination of the over-potential
In the electrochemical machining Ni film, the electrochemical reaction is the dissolution of Ni at an anode and the generation of hydrogen gas at a cathode 30 . At the anode, a passive film forms on the surface and the reaction current is very low. As the potential increases, the passive film is broken, and the reaction current increases, which is called trans-passive dissolution. Here, the workpiece potential should be located in the region between the passive region and the trans-passive region. Therefore, the equilibrium potential at the anode should be taken as its passive potential near to trans-passive region which can be obtained by test (it is 600mV). At the cathode, the electrochemical reaction is: 2H + +2e=H 2 . In 0.1 M H 2 SO 4 , the electrolyte resistance is 50ohm.cm and i 0 =1.7mA/cm 2 (ref. 31), and PH value is small and the equilibrium potential is near to zero (it is taken as 0mV). Thus, the electromotive potential caused by the equilibrium potentials at anode and cathode is 600mV-0mV=600mV.
As Φ 1 is equal to 475mV, the total over-potential at anode and cathode is equal to 2x475mV-600mV=350mV. In the electrochemical machining, a balance electrode is used to control the over-potential between the workpiece and electrolyte to be equal to half of the total over-potential. So, in equation d=(Φ-Φ 1 )/2ρ L i 0 shβ(Φ 1 -φ e ), Φ 1 -φ e is equal to 175mV.
In solution of NaNO 3 , stainless steel is in passive state and Fe 2 O 3 is formed on the stainless steel. So, at an anode, trans-passive reaction occurs from Fe 2 O 3 to Fe 2+ . Its equilibrium potential is taken as its trans-passive potential (+810mV 32 ). At a cathode, the electrochemical reaction is still the generation of hydrogen gas. Here, PH value is 7. So, the equilibrium potential for reaction 2H + +2e=H 2 is -420mV. Thus, the electromotive potential caused by the equilibrium potentials at anode and cathode is 810mV+420mV=1230mV.
From intersection point of the voltage axis and fit line of the test date in Fig.5A, we can obtain dissolution voltage Φ 1 of Fe 2 O 3 (it is 925mV). The experimental electrolyte resistance is 18 ohm.cm. In order to fit a simulated data to the experimental data, i 0 is was determined to 0.16mA/cm 2 .
The total over-potential at anode and cathode is equal to 2x925mV-1230mV=620mV. In the electrochemical machining, a balance electrode is also used to control the over-potential between the workpiece and electrolyte to be equal to half of the total over-potential. So, in equation d=(Φ-Φ 1 )/2ρ L i 0 shβ(Φ 1 -φ e ), Φ 1 -φ e is equal to 310mV.

C. Determining threshold current
In order to finish static voltage-small separation electrochemical micromachining, an intelligent control technique was developed. Here, the current-feedback control is used. As the tool is near to the workpiece, the current flowing through the cell grows significantly. The current value directly monitors the tool-workpiece separation, which is used in a feedback loop for automated adjustment of the gap width between tool-workpiece.
A threshold current is set at which the tool-workpiece separation is equal to a quite small value. If the loop current is smaller than the threshold current, the tool is driven to feed continuously. As soon as the loop current is equal to the threshold current, the tool stops, which makes the workpiece be machined rapidly under a relatively large current. As the machining causes increase of the tool-workpiece separation, the loop current drops rapidly to one value smaller than threshold current, and then the continuous feed begins again. Thus, a relatively large current micromachining process is achieved under small voltage. Of course, another larger threshold current is set at which short circuit occurs. As soon as the loop current gets to the threshold current, the tool goes back 1μm rapidly.
Before machining nickel film in solution of 0.1 M H 2 SO 4 , the threshold current above mentioned was determined by test. Here, the applied voltage between two electrodes is 980mV for etching (half of the voltage between two electrodes is 490mV), and the threshold current was taken as 0.1mA, 0.3mA, 0.5mA, and 1.0mA. The achievable machining precision as a function of the threshold current I t was given in Figure S2. It shows that the best machining precision with this technique is obtained when the threshold current I t is taken as 0.3mA. It corresponds to the tool-workpiece separation of about 1.3μm. Figure S2. Achievable machining precision as a function of the threshold current I t (electrolyte is 0.1 M H 2 SO 4 ); triangles, test values; solid lines, fited values.