**4. Current measured in the intermittent MAGE**

Figure 6 demonstrates the current variation with time for the intermittent MAGE conducted at 3.2 and 4.2 V, respectively. The initiate gap between the electrodes was set at 10 μm in each intermittent cycle. Two different time-intervals are concerned: within the initial 20 s, the current profile is displayed in Fig. 6(a); at the final stage to grow a column up to 500 μm, the current profile is shown in Fig. 6 (b). The current exhibits different profiles in Fig. 6(a) depending upon the voltages employed. The current level responsible for on-time intermittent MAGE conducting at 4.2 V is higher than that conducting at 3.2 V (i.e., −3.70 ± 0.19 mA as compared to −2.26 ± 0.07 mA); however, the time period at 4.2 V is shorter than that at 3.2 V (i.e., 0.24–0.95 s against 6.19–8.81 s). Greater current variation is also found at 4.2 V than 3.2 V.

Analysis of the current profile in the initial 20 s indicates that intermittent MAGE conducted at 4.2 V almost completing 10 cycles (each cycle including one on-time half cycle and offtime half cycle) but that conducted at 3.2 V only accomplishing 2.3 cycles. Total height of the micrometer column could be estimated from multiplication of the intermittent gap (i.e., 10 μm per cycle) with the number of off-time cycles (i.e., the height roughly at 100 μm for 4.2 V compared to 23 μm for 3.2 V). Checking with SEM examination, the columns fabricated by intermittent MAGE at 4.2 and 3.2 V revealed their heights at 93 and 22 μm, respectively. Obviously, the intermittent MAGE conducted at 3.2 V revealed better consistency for the column height coming from calculated and observed results.

It is possible to evaluate the time needed to grow a nickel microcolumn up to 500 μm. Fig. 6 (b) displays a few final cycles in the cases of intermittent MAGE conducted at 4.2V (on the left-hand side) and at 3.2V (on the right-hand side), respectively. It takes 107.18 s (overall *t*-on = 35.78 s; overall *t*-off = 71.40 s) at 4.2 V, and 510.03 s (overall *t*-on=438.63; overall *t*-off=71.40 s) at 3.2 V, respectively. If time-consumption for ascending the microanode is ignored, the average growth rates are estimated at 13.97 and 1.14 μm s−1 for the columns fabricated by intermittent MAGE conducted at 4.2 and 3.2 V, respectively. A close examination in Figs 6(a) and (b) indicated that the off-time period is a constant (1.4 s) but the on-time period varies with voltages employed.

growth.

Another plot is given in Fig. 5 to show the current variation against time for MAGE conducted at 3.0 V by controlling the microanode to ascend continuously at a variety of rates from 0.3 to 3.0 μm s−1. In Fig. 5, on the curve responsible for continuous MAGE with ascending rate at 3.0 μm s−1, the current rises abruptly to 2.5 mA, drops to 0.25 mA in 60 s and levels off subsequently. This implies that the nickel column grows very fast in the initial period (less than 60 s) but the growth rate in the subsequent stages decays to very slow. Even the duration of this process lasted for 240 s, the column grew rapidly to a height of 25.1 μm almost within the initial 60 s. In contrast to the case where the microanode ascended continuously at 0.3μm s−1, the current led to a sudden rise in 10 s. The growth rate of the column is much faster than the ascending rate of the microanode. As a result, the column grows so swiftly that facilitates its top to contact the microanode. This short-circuit contact may ruin the apparatus. Therefore, on purpose to protect the apparatus, we designed an automatic switch into the system. Once the current exceeding 20 mA the power of the system is shut off. According to Fig. 5, the ascending rate of the microanode is better controlled in the range from 0.5 to 2.0 μm s−1 to ensure longer duration for column

Figure 6 demonstrates the current variation with time for the intermittent MAGE conducted at 3.2 and 4.2 V, respectively. The initiate gap between the electrodes was set at 10 μm in each intermittent cycle. Two different time-intervals are concerned: within the initial 20 s, the current profile is displayed in Fig. 6(a); at the final stage to grow a column up to 500 μm, the current profile is shown in Fig. 6 (b). The current exhibits different profiles in Fig. 6(a) depending upon the voltages employed. The current level responsible for on-time intermittent MAGE conducting at 4.2 V is higher than that conducting at 3.2 V (i.e., −3.70 ± 0.19 mA as compared to −2.26 ± 0.07 mA); however, the time period at 4.2 V is shorter than that at 3.2 V (i.e., 0.24–0.95 s against 6.19–8.81 s). Greater current variation is also found at

Analysis of the current profile in the initial 20 s indicates that intermittent MAGE conducted at 4.2 V almost completing 10 cycles (each cycle including one on-time half cycle and offtime half cycle) but that conducted at 3.2 V only accomplishing 2.3 cycles. Total height of the micrometer column could be estimated from multiplication of the intermittent gap (i.e., 10 μm per cycle) with the number of off-time cycles (i.e., the height roughly at 100 μm for 4.2 V compared to 23 μm for 3.2 V). Checking with SEM examination, the columns fabricated by intermittent MAGE at 4.2 and 3.2 V revealed their heights at 93 and 22 μm, respectively. Obviously, the intermittent MAGE conducted at 3.2 V revealed better consistency for the

It is possible to evaluate the time needed to grow a nickel microcolumn up to 500 μm. Fig. 6 (b) displays a few final cycles in the cases of intermittent MAGE conducted at 4.2V (on the left-hand side) and at 3.2V (on the right-hand side), respectively. It takes 107.18 s (overall *t*-on = 35.78 s; overall *t*-off = 71.40 s) at 4.2 V, and 510.03 s (overall *t*-on=438.63; overall *t*-off=71.40 s) at 3.2 V, respectively. If time-consumption for ascending the microanode is ignored, the average growth rates are estimated at 13.97 and 1.14 μm s−1 for the columns fabricated by intermittent MAGE conducted at 4.2 and 3.2 V, respectively. A close examination in Figs 6(a) and (b) indicated that the off-time period is a constant (1.4 s) but the

growth.

4.2 V than 3.2 V.

**4. Current measured in the intermittent MAGE** 

column height coming from calculated and observed results.

on-time period varies with voltages employed.

Fig. 6. Variation of current with the electroplating time for the micrometer nickel column fabricated via intermittent MAGE at 3.2 and 4.2 V during (a) the initial stage (in 20 s) and (b) the final stage to reach a column height of 500 μm. The initial gap is at 10 μm in each intermittent cycle

#### **5. Models for column growth in continuous MAGE**

A schematic model is demonstrated in Fig. 7(a) to illustrate the growth of the column fabricated by continuous MAGE. Prior to electrochemical reaction, the microanode was ascended to keep an initial gap of 20 μm from the cathode. As soon as the electrochemical deposition started, the microanode was driven to ascend at a constant rate (V). In response to stages 1, 2, ... and n, as shown in Fig. 7(a1), (a2) and (a3), the micrometer column was growing to various heights (i.e., at h1, h2, ... and hn) with the separation between the microanode and microcolumn at d1, d2, ... and dn, respectively. The dashed region in Fig. 7(a3) was re-plotted in Fig. 7(an) for detailed investigation. Supposedly a column established continuously from the (n-1)th stage to nth. The top surface of the column

Mass Transfer Within the Location Where Micro Electroplating Takes Place 215

Fig. 7. (a) A scheme of sequential models for the continuous MAGE process initiated with a gap of 20 μm between the microanode and the Cu-substrate. In the diagrams, *h*1, *h*2, ..., *h*<sup>n</sup> and *R*1, *R*2, ..., *R*n represent the column height and column radius at a variety of duration *t*1, *t*2...and *t*n, respectively. The eventual gaps in response to different duration are *d*1, *d*2 ... and *d*n. The strength of electric-field strength at *t*n−1 and *t*n is represented by *E*n−1 and *E*n. (b) Distribution map of the electric-field strength simulated with the software ANSYS 8.0 for the system conducted by the continuous MAGE at the final stage. The bias is 5.0 V and the

conductivity of the electrolyte is 42.02 mS cm-1

established at the (n-1)th stage was covered by new deposit coming from the nth stage. It is well known that both deposition rate and surface coverage are determined by the strength of electric field exerted. Accordingly, at the instance of (n-1) stage, the strength at the center top of the column is the strongest, this strength decreases from the center to periphery at the column transverse. Under the condition where the strength of E(n-1) is small enough, no contribution of deposition leads to a confinement of maximal radius at R(n-1) for the column. In the continuous MAGE process, the variation of strength may depend upon the ascending rate of the microanode. Under higher ascending rates, the microanode moves further away from the column in shorter durations. The separation between the microanode and the microcolumn tends to increase in the sequence 20μm < d1< d2 < dn, so that the electric field strength reduces rapidly with time. A field gradient between En and E(n-1) caused by this quick strength change will be intensified and the strength of E(n-1) is soon reduced to an insignificant magnitude. Further proceeding to the process at the nth stage, the deposition would undergo mainly on the top rather than on the periphery of the column. As a result, the columns fabricated by continuous MAGE tended to reduce their radius gradually thus exhibiting the dendrite morphology as shown in Fig 2 (a). The strength difference between the (n-1)th and nth stages may offer an indication of radius uniformity for the column. It is defined by ∆ *<sup>c</sup> E* in Eq (5.1)

$$
\Delta E^{\circ} = E\_n - E\_{\text{(n-1)}} \tag{5.1}
$$

Where E(n-1) and En denote the strength at the (n-1) and nth stages, respectively. Moreover, the mean strength ( *<sup>c</sup> Em* ) defined in Eq (5.2), also based on the strengths arisen from the (n-1)th and nth stages

$$E\_m^c = [\mathbf{E}\_{\text{(n-1)}} + \mathbf{E}\_n]/2\tag{5.2}$$

Both the <sup>∆</sup> *<sup>c</sup> E* and *<sup>c</sup> Em* provide with a criterion to judge whether the microcolumn is possible to grow.

In the case of continuous MAGE conducted at higher voltages under lower ascending rate of the microanode, the strength gets stronger resultant from the growth of the column to diminish the gap between the electrodes. If the growth rate on the column is much higher than the ascending rate of the microanode, the separation between the microanode and the microcolumn will deduce in the order 20 μm > d1 > d2 > dn. Increasing with the elapsed time, this gap is soon reduced so that the field strength and the current responsible for electrochemical deposition are both intensified. Once the current measured exceeding 20 mA, the power of this system is shut off to interrupt MAGE for protection. Theoretically, fabrication of a micrometer column to any height is possible by continuous MAGE via optimal controlling the experimental conditions to balance the growth rate of the microcolumn with the ascending rate of the microanode. It may be accomplished by controlling a constant gap between the microanode and the microcolumn (e.g., 20 μm = d1 = d2 = dn) at any time. However, it is not easy to manipulate in practice. The microcolumn exhibited in figure 2(a) is the longest one we had via continuous MAGE.

Figure 7(b) shows a simulated diagram to elucidate the strength distribution for the electric field strength exerted in the continuous MAGE conducted at 5 V for 240 s, under an initial gap of 20 μm, with ascending rate of the microanode at 2 μm s−1. This simulation is accomplished using the commercial software ANSYS 8.0 by input the data of electrical conductivity of electrolyte with 42.02 mS cm−1. According to the same procedure, we also

established at the (n-1)th stage was covered by new deposit coming from the nth stage. It is well known that both deposition rate and surface coverage are determined by the strength of electric field exerted. Accordingly, at the instance of (n-1) stage, the strength at the center top of the column is the strongest, this strength decreases from the center to periphery at the column transverse. Under the condition where the strength of E(n-1) is small enough, no contribution of deposition leads to a confinement of maximal radius at R(n-1) for the column. In the continuous MAGE process, the variation of strength may depend upon the ascending rate of the microanode. Under higher ascending rates, the microanode moves further away from the column in shorter durations. The separation between the microanode and the microcolumn tends to increase in the sequence 20μm < d1< d2 < dn, so that the electric field strength reduces rapidly with time. A field gradient between En and E(n-1) caused by this quick strength change will be intensified and the strength of E(n-1) is soon reduced to an insignificant magnitude. Further proceeding to the process at the nth stage, the deposition would undergo mainly on the top rather than on the periphery of the column. As a result, the columns fabricated by continuous MAGE tended to reduce their radius gradually thus exhibiting the dendrite morphology as shown in Fig 2 (a). The strength difference between the (n-1)th and nth stages may offer an indication of radius uniformity for the column. It is

( 1)

Where E(n-1) and En denote the strength at the (n-1) and nth stages, respectively. Moreover, the mean strength ( *<sup>c</sup> Em* ) defined in Eq (5.2), also based on the strengths arisen from the

Both the <sup>∆</sup> *<sup>c</sup> E* and *<sup>c</sup> Em* provide with a criterion to judge whether the microcolumn is possible

In the case of continuous MAGE conducted at higher voltages under lower ascending rate of the microanode, the strength gets stronger resultant from the growth of the column to diminish the gap between the electrodes. If the growth rate on the column is much higher than the ascending rate of the microanode, the separation between the microanode and the microcolumn will deduce in the order 20 μm > d1 > d2 > dn. Increasing with the elapsed time, this gap is soon reduced so that the field strength and the current responsible for electrochemical deposition are both intensified. Once the current measured exceeding 20 mA, the power of this system is shut off to interrupt MAGE for protection. Theoretically, fabrication of a micrometer column to any height is possible by continuous MAGE via optimal controlling the experimental conditions to balance the growth rate of the microcolumn with the ascending rate of the microanode. It may be accomplished by controlling a constant gap between the microanode and the microcolumn (e.g., 20 μm = d1 = d2 = dn) at any time. However, it is not easy to manipulate in practice. The microcolumn exhibited in figure 2(a)

Figure 7(b) shows a simulated diagram to elucidate the strength distribution for the electric field strength exerted in the continuous MAGE conducted at 5 V for 240 s, under an initial gap of 20 μm, with ascending rate of the microanode at 2 μm s−1. This simulation is accomplished using the commercial software ANSYS 8.0 by input the data of electrical conductivity of electrolyte with 42.02 mS cm−1. According to the same procedure, we also

*<sup>c</sup>* Δ= − *EE E n n*<sup>−</sup> (5.1)

*<sup>c</sup> Em* = [E(n-1) +En]/2 (5.2)

defined by ∆ *<sup>c</sup> E* in Eq (5.1)

(n-1)th and nth stages

is the longest one we had via continuous MAGE.

to grow.

Fig. 7. (a) A scheme of sequential models for the continuous MAGE process initiated with a gap of 20 μm between the microanode and the Cu-substrate. In the diagrams, *h*1, *h*2, ..., *h*<sup>n</sup> and *R*1, *R*2, ..., *R*n represent the column height and column radius at a variety of duration *t*1, *t*2...and *t*n, respectively. The eventual gaps in response to different duration are *d*1, *d*2 ... and *d*n. The strength of electric-field strength at *t*n−1 and *t*n is represented by *E*n−1 and *E*n. (b) Distribution map of the electric-field strength simulated with the software ANSYS 8.0 for the system conducted by the continuous MAGE at the final stage. The bias is 5.0 V and the conductivity of the electrolyte is 42.02 mS cm-1

Mass Transfer Within the Location Where Micro Electroplating Takes Place 217

simulate the continuous MAGE conducted in different conditions. Diagrams were constructed and the data of <sup>∆</sup> *<sup>c</sup> E* and *<sup>c</sup> Em* were evaluated and compared. In a system where the microanode ascended at 2 μm s−1, the profile of the microcolumn is determined by the electric voltage. The relationship between the surface morphology of the microcolumns and

Figure 8(a) shows the schematic models for the intermittent MAGE process. The microanode was first ascended to keep an initial separation of 10 μm from the substrate, and the power was turned on to proceed electrochemical reaction at a certain voltage. This electroplating process was carried out until the microcolumn growing up to almost in contact with the microanode, as shown at stage 1. The power was switched off to interrupt the electrochemical reaction, the microanode was ascended to another gap (at 10 μm), as depicted in stage 1'. Monitoring of the current would provide with a criterion for this on/off decision-making. The power would keep on as the current measured is less than 20 mA; however, it would turn to off as the current is higher than 20 mA. Another gap of 10 μm-gap was set and the second cycle would succeeded to undergo stages 2 and 2', and so on until the nth cycles (via stages n and n') to accomplish a microcolumn with an overall height of hn. It is apparent that microcolumn revealed a periodic variation in radius (from Rmin to Rmax and Rmin again) in response to periodic performance of the intermittent MAGE through positions ( ) <sup>1</sup>

*<sup>n</sup> <sup>E</sup>* again. It is worth noting that the mean strength of electric field (i.e., *<sup>i</sup> Em* ) can

m may offer a criterion to predict whether the microcolumn keeps on growing. In addition,

max min

may offer an estimation of the diameter uniformity for the column fabricated from

Figure 8(b) shows a schematic diagram to elucidate the distribution of the electric field in

gap of each intermittent cycle at 10 μm. This diagram was also established via simulation by using commercial software ANSYS 8.0 through input the data of electrical conductivity for the electrolyte. A number of diagrams were constructed depending upon various experimental parameters and the corresponding data of *<sup>i</sup> Em* and ∆Ei were evaluated. The relationship between the surface morphology and the electric voltage employed in the intermittent

**7. Effect of electric voltages on the surface morphology and radius of the** 

Figure 9 shows the effect of the electric voltages on the average radius (to the left ordinate) of the microcolumns fabricated from continuous MAGE. The radius of the columns was

the intermittent MAGE conducted at an electric bias of 3.2 V, with the initial

*<sup>n</sup> <sup>E</sup>* and min

) of the electric field between positions max

max *<sup>n</sup> E* <sup>−</sup> to

*<sup>n</sup> E* can be

*<sup>n</sup> E* ) in Eq. (6.1) as follows

*<sup>n</sup> E* and min

min max / 2 *inn EE E <sup>m</sup>* = + ⎡ ⎤ ⎣ ⎦ (6.1)

*in n* Δ= − *EE E* (6.2)

the voltage is discussed later in terms of <sup>∆</sup> *<sup>c</sup> E* and *<sup>c</sup> Em* .

be calculated from two different positions (i.e., max

MAGE is discussed later on basis of *<sup>i</sup> Em* and ∆Ei data.

the strength difference (i.e., ∆Ei

intermittent MAGE.

**microcolumns** 

estimated in Eq. (6.2) in the following

min *<sup>n</sup> <sup>E</sup>* and max

Ei

∆Ei

**6. Models for column growth in intermittent MAGE** 

Fig. 8. (a) A scheme of sequential models for the intermittent MAGE process with each cycle initiated with a gap of 10 μm between the microanode and the column top. In the diagrams, *h*n is the column height after *n*-cycles of intermittent MAGE; 1, 2, ..., *n* and 1', 2', ..., *n'* correspond to the on- and off-cycles, respectively, in each complete cycle; *R*max and *R*min represent the maximal and minimal radii of the column corresponding to the points with the highest (*E*max) and the lowest strength (*E*min) in each intermittent cycle. (b) Distribution map of the electric-field strength simulated with the software ANSYS 8.0 for the system conducted by intermittent MAGE at the final stage. The bias is 3.2 V and the conductivity of the electrolyte is 42.02 mS cm-1

Fig. 8. (a) A scheme of sequential models for the intermittent MAGE process with each cycle initiated with a gap of 10 μm between the microanode and the column top. In the diagrams, *h*n is the column height after *n*-cycles of intermittent MAGE; 1, 2, ..., *n* and 1', 2', ..., *n'* correspond to the on- and off-cycles, respectively, in each complete cycle; *R*max and *R*min represent the maximal and minimal radii of the column corresponding to the points with the highest (*E*max) and the lowest strength (*E*min) in each intermittent cycle. (b) Distribution map of the electric-field strength simulated with the software ANSYS 8.0 for the system conducted by intermittent MAGE at the final stage. The bias is 3.2 V and the conductivity of the

electrolyte is 42.02 mS cm-1

simulate the continuous MAGE conducted in different conditions. Diagrams were constructed and the data of <sup>∆</sup> *<sup>c</sup> E* and *<sup>c</sup> Em* were evaluated and compared. In a system where the microanode ascended at 2 μm s−1, the profile of the microcolumn is determined by the electric voltage. The relationship between the surface morphology of the microcolumns and the voltage is discussed later in terms of <sup>∆</sup> *<sup>c</sup> E* and *<sup>c</sup> Em* .

## **6. Models for column growth in intermittent MAGE**

Figure 8(a) shows the schematic models for the intermittent MAGE process. The microanode was first ascended to keep an initial separation of 10 μm from the substrate, and the power was turned on to proceed electrochemical reaction at a certain voltage. This electroplating process was carried out until the microcolumn growing up to almost in contact with the microanode, as shown at stage 1. The power was switched off to interrupt the electrochemical reaction, the microanode was ascended to another gap (at 10 μm), as depicted in stage 1'. Monitoring of the current would provide with a criterion for this on/off decision-making. The power would keep on as the current measured is less than 20 mA; however, it would turn to off as the current is higher than 20 mA. Another gap of 10 μm-gap was set and the second cycle would succeeded to undergo stages 2 and 2', and so on until the nth cycles (via stages n and n') to accomplish a microcolumn with an overall height of hn. It is apparent that microcolumn revealed a periodic variation in radius (from Rmin to Rmax and Rmin again) in response to periodic performance of the intermittent MAGE through positions ( ) <sup>1</sup> max *<sup>n</sup> E* <sup>−</sup> to min *<sup>n</sup> <sup>E</sup>* and max *<sup>n</sup> <sup>E</sup>* again. It is worth noting that the mean strength of electric field (i.e., *<sup>i</sup> Em* ) can be calculated from two different positions (i.e., max *<sup>n</sup> <sup>E</sup>* and min *<sup>n</sup> E* ) in Eq. (6.1) as follows

min max / 2 *inn EE E <sup>m</sup>* = + ⎡ ⎤ ⎣ ⎦ (6.1)

Ei m may offer a criterion to predict whether the microcolumn keeps on growing. In addition, the strength difference (i.e., ∆Ei ) of the electric field between positions max *<sup>n</sup> E* and min *<sup>n</sup> E* can be estimated in Eq. (6.2) in the following

$$
\Delta E^{i} = E\_{\text{max}}^{\prime \prime} - E\_{\text{min}}^{\prime \prime} \tag{6.2}
$$

∆Ei may offer an estimation of the diameter uniformity for the column fabricated from intermittent MAGE.

Figure 8(b) shows a schematic diagram to elucidate the distribution of the electric field in the intermittent MAGE conducted at an electric bias of 3.2 V, with the initial

gap of each intermittent cycle at 10 μm. This diagram was also established via simulation by using commercial software ANSYS 8.0 through input the data of electrical conductivity for the electrolyte. A number of diagrams were constructed depending upon various experimental parameters and the corresponding data of *<sup>i</sup> Em* and ∆Ei were evaluated. The relationship between the surface morphology and the electric voltage employed in the intermittent MAGE is discussed later on basis of *<sup>i</sup> Em* and ∆Ei data.

### **7. Effect of electric voltages on the surface morphology and radius of the microcolumns**

Figure 9 shows the effect of the electric voltages on the average radius (to the left ordinate) of the microcolumns fabricated from continuous MAGE. The radius of the columns was

Mass Transfer Within the Location Where Micro Electroplating Takes Place 219

Figure 10 depicts the dependence of the column radius (to the left ordinate) upon the voltages employed in the intermittent MAGE. The radius increases gradually (from 22.20 to 31.23 μm) with increasing the voltages from 3.2 to 4.2 V, and so does the corresponding

Regarding the dependence of the mean strength ( *<sup>i</sup> Em* ) of electric field (to the right ordinate) upon the voltages applied in the intermittent MAGE. The mean strength displays a gradual increase from 194 324 to 268 163 V m-1 (roughly 1.4 times) in the range from 3.2 to 4.2 V. The gradual change of *<sup>i</sup> Em* reflects the availability to manipulate experimental conditions in fabrication of the columns. The microcolumns fabricated at higher voltages depict greater standard deviation. This result reflects high degree of non-uniformity for the columns

the result is consistent. A comparison is made for fabricating microcolumns by means of intermittent MAGE (in the range from 3.2 to 4.2 V) and continuous MAGE (in the range from 5.0 to 6.0 V). Strength change in the electric field and standard deviation from the mean strength is much higher in the continuous MAGE than in the intermittent MAGE. Due to this fact, intermittent MAGE is better than continuous MAGE to fabricate microcolumn

Fig. 10. Variation of the average radius for the micrometer columns (left coordinate) and the mean strength of the electric field (right coordinate) with the bias employed in the process of intermittent MAGE to a height of 500 μm. In each intermittent cycle, a gap of 10 μm is set

**8. Surface and transverse morphology of micrometer columns influenced by** 

Micrometer nickel columns obtained from intermittent MAGE were treated in the following procedures to observe their cross section. They were first mounted in an epoxy resin. The mounted columns were ground in a plane perpendicular to the longitudinal direction to expose their cross-sections. A series of carbide paper (in the grade of 400, 600, 800, 1000,

( increase from 9909 to 37 391 V m-1),

standard deviation (from 0.25 to 1.75 μm.)

with a uniform diameter at expected length.

between the microanode and the top of the column.

**electrical voltages** 

fabricated at higher voltages. Checking the data of ∆Ei

evaluated from the SEM micrographs. The average radius was calculated from arithmetic average of three microcolumns fabricated under the same conditions. Standard deviation of the data was concerned in the plot. The average radius of the microcolumns tended to increase gradually from 2.59 to 10.34 μm with increasing the voltage from 1 to 5 V; however, it increases suddenly from 10.34 to 26.77 μm with increasing the voltage form 5 to 6 V. The standard deviation of the radius increases from 1.54 to 3.11 μm in the range from 1.0 to 4.0 V but decreases from 3.11 to 0.77 μm in the range from 4.0 to 6.0 V. At voltages below 5 V, a short vertebra-like structure was slowly formed to reveal a smaller radius at the top. When the continuous MAGE conducted in the range from 5 to 6 V, the growth rate of the microfeature seemed to be similar to the ascending rate of the microanode. This led to a longer microcolumn appearing in uniform diameter.

Figure 9 also depicts the dependence of the mean strength ( *<sup>c</sup> Em* , to the right ordinate) on the electric voltages. The magnitude of *<sup>c</sup> Em* almost increases one order of magnitude with increasing the voltage from 1.0 to 5.0V, and roughly 50 times with an increase of voltage from 5.0 to 6.0 V. A sudden rise in *<sup>c</sup> Em* within the range from 5.0 to 6.0 V is ascribed to much higher growth rate of the column compared to the ascending rate of the microanode. In practice, the huge change in *<sup>c</sup> Em* may lead to a problem to balance the growth rate and the ascending rate between the microcolumn and microanode.

Variation of ∆ *<sup>c</sup> E* with the voltages applied in continuous MAGE is also of concern. It reveals gradual increase (from 37 to 1238 V m-1) with increasing the voltage from 1 to 5 V; however, a sudden increase (from 1238 to 140 000 V m-1) within 5 –6V. The gradual increase of ∆ *<sup>c</sup> E* results in a radius discrepancy of the cylinder-like column with the voltages within 1 – 5 V. The sudden rise of ∆ *<sup>c</sup> E* tends to a momentary growth of the micro feature thus leading to rapid touch with the microanode. Thus, conducting continuous MAGE within 5–6 V to fabricate microcolumns is impractical.

Fig. 9. Variation of the average radius for the micrometer columns (left ordinate) and the mean strength of the electric field (right ordinate) with the bias employed in the process of continuous MAGE with various ascending rates of the microanode in 240 s. The initial separation between the microanode and the Cu-substrate was 20 μm

evaluated from the SEM micrographs. The average radius was calculated from arithmetic average of three microcolumns fabricated under the same conditions. Standard deviation of the data was concerned in the plot. The average radius of the microcolumns tended to increase gradually from 2.59 to 10.34 μm with increasing the voltage from 1 to 5 V; however, it increases suddenly from 10.34 to 26.77 μm with increasing the voltage form 5 to 6 V. The standard deviation of the radius increases from 1.54 to 3.11 μm in the range from 1.0 to 4.0 V but decreases from 3.11 to 0.77 μm in the range from 4.0 to 6.0 V. At voltages below 5 V, a short vertebra-like structure was slowly formed to reveal a smaller radius at the top. When the continuous MAGE conducted in the range from 5 to 6 V, the growth rate of the microfeature seemed to be similar to the ascending rate of the microanode. This led to a longer

Figure 9 also depicts the dependence of the mean strength ( *<sup>c</sup> Em* , to the right ordinate) on the electric voltages. The magnitude of *<sup>c</sup> Em* almost increases one order of magnitude with increasing the voltage from 1.0 to 5.0V, and roughly 50 times with an increase of voltage from 5.0 to 6.0 V. A sudden rise in *<sup>c</sup> Em* within the range from 5.0 to 6.0 V is ascribed to much higher growth rate of the column compared to the ascending rate of the microanode. In practice, the huge change in *<sup>c</sup> Em* may lead to a problem to balance the growth rate and the

Variation of ∆ *<sup>c</sup> E* with the voltages applied in continuous MAGE is also of concern. It reveals gradual increase (from 37 to 1238 V m-1) with increasing the voltage from 1 to 5 V; however, a sudden increase (from 1238 to 140 000 V m-1) within 5 –6V. The gradual increase of ∆ *<sup>c</sup> E* results in a radius discrepancy of the cylinder-like column with the voltages within 1 – 5 V. The sudden rise of ∆ *<sup>c</sup> E* tends to a momentary growth of the micro feature thus leading to rapid touch with the microanode. Thus, conducting continuous MAGE within 5–6

Fig. 9. Variation of the average radius for the micrometer columns (left ordinate) and the mean strength of the electric field (right ordinate) with the bias employed in the process of continuous MAGE with various ascending rates of the microanode in 240 s. The initial

separation between the microanode and the Cu-substrate was 20 μm

microcolumn appearing in uniform diameter.

V to fabricate microcolumns is impractical.

ascending rate between the microcolumn and microanode.

Figure 10 depicts the dependence of the column radius (to the left ordinate) upon the voltages employed in the intermittent MAGE. The radius increases gradually (from 22.20 to 31.23 μm) with increasing the voltages from 3.2 to 4.2 V, and so does the corresponding standard deviation (from 0.25 to 1.75 μm.)

Regarding the dependence of the mean strength ( *<sup>i</sup> Em* ) of electric field (to the right ordinate) upon the voltages applied in the intermittent MAGE. The mean strength displays a gradual increase from 194 324 to 268 163 V m-1 (roughly 1.4 times) in the range from 3.2 to 4.2 V. The gradual change of *<sup>i</sup> Em* reflects the availability to manipulate experimental conditions in fabrication of the columns. The microcolumns fabricated at higher voltages depict greater standard deviation. This result reflects high degree of non-uniformity for the columns fabricated at higher voltages. Checking the data of ∆Ei ( increase from 9909 to 37 391 V m-1), the result is consistent. A comparison is made for fabricating microcolumns by means of intermittent MAGE (in the range from 3.2 to 4.2 V) and continuous MAGE (in the range from 5.0 to 6.0 V). Strength change in the electric field and standard deviation from the mean strength is much higher in the continuous MAGE than in the intermittent MAGE. Due to this fact, intermittent MAGE is better than continuous MAGE to fabricate microcolumn with a uniform diameter at expected length.

Fig. 10. Variation of the average radius for the micrometer columns (left coordinate) and the mean strength of the electric field (right coordinate) with the bias employed in the process of intermittent MAGE to a height of 500 μm. In each intermittent cycle, a gap of 10 μm is set between the microanode and the top of the column.

### **8. Surface and transverse morphology of micrometer columns influenced by electrical voltages**

Micrometer nickel columns obtained from intermittent MAGE were treated in the following procedures to observe their cross section. They were first mounted in an epoxy resin. The mounted columns were ground in a plane perpendicular to the longitudinal direction to expose their cross-sections. A series of carbide paper (in the grade of 400, 600, 800, 1000,

Mass Transfer Within the Location Where Micro Electroplating Takes Place 221

Fig. 11. SEM morphologies for the micrometer Ni columns deposited at various voltages and their corresponding transverse section. The columns were deposited at (a) 3.2V,(b) 3.4 V, (c) 3.6 V, (d) 4.4V and (e) 4.6 V with the gap between the electrodes initially set at 10 μm

1200, 2000) were used in the wet grinding, and subsequently slurries with fine powders of Al2O3 (1.0 and 0.3 μm in diameter, respectively) were employed to polish the cross-sectional surface to a mirror. The mirror surface was pickled in a 0.1% HF solution for 30 s, rinsed with water and dried ready for the SEM examination. Figure 11 displays the SEM morphologies and their transverse section at the position marked with a line across the micrometer. Ni columns deposited at 3.2V (Fig. 11(a)), 3.4V (Fig. 11(b)), 3.6 V (Fig. 11(c)), 4.4 V (Fig. 11(d)) and 4.6 V (Fig. 11(e)). Obviously, the surface morphology and transverse structure of the columns revealed a big difference depending on the biases. The micrometer columns deposited at 3.2 V depicted a smooth surface and a regular circular transverse (Fig. 11(a)). Checking the micrographs shown in Fig. 11 (from 11(a)–(e)),we found that by increasing the electrical voltages, the columns grew into shapes with higher irregularity and less smoothness on their surface. The columns deposited at higher voltages (e.g., 4.4 V) displayed an uneven circular profile around the transverse with the surface in nodular morphology. The columns deposited at much higher voltages (e.g., 4.6 V) appeared to have a branched coral with irregular transverses shape. We were concerned with the internal compactness of the columns, which could be estimated by examining their transverse using the SEM. The compactness was found to vary to different extents, depending on the electrical biases employed. Full compactness was observed in the transverse of the columns deposited at 3.2 V (Fig. 11(a)). Less compact were the columns, with porosity in the center of their transverse (Fig. 11(c)), deposited at little higher voltages (e.g., 3.6 V). The compactness was much less for the columns (Fig. 11(c)) deposited at much higher voltages (e.g., 4.4 V), because of radial expansion of the porosity from the transverse center resulting from coarsening and combination of the voids. The interior of the transverse was almost empty and remained a coral shell for the columns fabricated at an extremely high voltage (i.e. 4.6V). The deposit looked like a branched coral with a hollow interior.
