**13. Consumption of nickel ions in the LECD location**

Figure 18 displays the plot of average current measured at steady state in the LECD and the current efficiency against the voltages employed. It is seen in Fig. 18 the average current increases from 0.2 to 1.8 mA, whereas the current efficiency decreases from 53 to 23 % with increasing the biases in the range from 3.2 to 4.6 V. The standard deviation of the average current also increases with the electrical biases. Observation suggested the increase in average current is proportional to the augmenting in the growing rate of columns. The decrease in the current efficiency responds to the phenomenon that bubbles evolve much more generously when increasing the biases. This enlargement in bubbles evolution implies reducing hydrogen ions contributes much more than nickel ions. The higher standard deviation in the average current at higher corresponding biases reflects the greater variation in the diameter of the columns and in the roughness of their surface morphology.

The weight of a single micrometer column is so slight and beyond the detection limit of a usual balance. Three columns fabricated at the same conditions were gathered to overcome this difficulty, thus an average weight for a single column could be estimated (*Westimated by weighing*). The current efficiency (*η*) for the LECD conducted under specific conditions can be estimated by equation (13-1)

$$\eta = \frac{\mathcal{W}\_{\text{estimated by weighing}}}{\mathcal{W}\_{\text{calculated from current}}} \tag{13-1}$$

In which the numerator (*Westimated by weighing*) is the average weight obtained by the aforementioned for a single micrometer column and the denominator (*Westimated by weighing*) was

Mass Transfer Within the Location Where Micro Electroplating Takes Place 229

transverse in compact from those with porous transverse internal. At voltages less than the critical, the columns will lead to a compact transverse, whereas at voltages higher than the critical the columns will lead to a porous one. Considering the LECD performed at 3.2V the supplying rate of nickel ions (that is, 2.77 x10-9 mol s-1) is much higher than the consumption rate (that is, 6.19 x10-10 mol s-1). Nickel ions supplied to the location are more than consumed within the LECD region. Surplus supply of nickel ions leads to a complete filling of internal transverse of the columns. Stable current results in smooth morphology of the columns. On the other hand, as the LECD performed at 4.6V, the supply rate (4.58 x10-10 mol s-1) is much less than the consumption rate (2.24 x10-9 mol s-1). Shortage of nickel ions resultant from a lower rate of supply rate than the consumption leads to formation of internal pores thus resulting in porous transverse in the center of the columns. Greater variation in the deposition current results in rough morphology of the columns. The higher the biases employed in the LECD, the more severe the porous transverse in the columns, and the

There exists a transition zone in a narrow range of the electric bias (from 3.55 to 3.57 V) in Fig. 17. This transition zone arises from the deviation of accuracy in calculating of nickel concentrations and measuring local potentials. Apparently, the accuracy deviation is so small (at 0.02 V) that 3.56 ± 0.01 V is the critical voltage for conducting the intermittent MAGE to separate the micrometer columns with a smooth surface and full compact internal from those with rough surface and porous (or even hollow) internal. At any voltage less than this critical, the nickel ions consumed by electrochemical deposition in the depletion region could be completely compensated by the diffusion of nickel ions from nearby surroundings. This ensures sufficient supply for the need in the electrochemical consumption thus resulting in a full compact internal transverse of the columns. On the contrary, at the overages higher than this critical, the consumption of nickel ions is faster than their supply within the electroplating location. Insufficient supply of nickel ions leads to a porous (and even empty) internal transverse of the columns. Lower current density arising from the cases conducted at lower voltages results in a finely grained smooth surface; higher current density arising from the

cases conducted at higher voltage results in an irregularly nodular rough surface.

LECD is also named as microanode guided electroplating (MAGE) process.

The kinetics of electrochemical processes is determined not only by the strength of electric field but also by the mass transport phenomenon of the electrochemical active ions. In the cases of ordinary electrochemical deposition, the electric field employed is relatively low and the field distribution is homogeneous. Localized electrochemical deposition (LECD) process provides a new concept to fabricate three-dimensional (3D) metal microstructures. However, a super high electrical field is exerted at the electroplating site in the LECD, and the distribution of field strength is ultra heterogeneous. The site chosen to conduct LECD is controlled experimentally to follow the track guided with a microanode. Consequently,

Through discussion on the phenomenon of mass transport in such a strong field distributed in extremely heterogeneous manner, balance between the supply rate and consumption rate of nickel ions in the region where LECD taking place plays a role on the surface morphology and the transverse internal structure. This balance is determined significantly by experimental parameters such as motion modes of the microanode, applied electric voltage, initial gap between the cathode and microanode. In terms of models, we simulate the system with commercial software ANSYS 8.0 to realize the electrochemical mechanism satisfactory.

rougher their surface, as shown in Fig. 11.

**15. Conclusions** 

calculated from the data of electroplating current consumed to grow the column within the duration. The theoretical weight of the column (*Westimated by weighing*) estimated by the data of current and duration measured is believed to obey the following equation (13-2).

$$\mathcal{W}\_{\text{calculated from current}} = \frac{\text{ItA}}{\text{zF}} \tag{13-2}$$

Where *I* is the average current; *t* is the duration to grow a 1000 μm-height column; *A* is the atomic weight of nickel; *z* is the valence; and *F* is the Faraday constant. The average consumption rate of the nickel ions in the local region taking place by LECD could be estimated by the equation (13-3)

$$\text{Consumption} \, rate = \frac{\mathcal{W}}{t \times A} = \frac{I\eta}{zF} \tag{13-3}$$

The average consumption rates calculated from equation (13-3) are plotted with the voltages, as shown in Fig. 17

Fig. 18. The average current measured in the LECD and the current efficiency plotted against the electrical bias (voltage) employed

### **14. Balance between the supply and consumption of nickel ions within the location taking place LECD**

Figure 17 summarizes the variation of supply rate and consumption rate within the location where taking place LECD with the voltage employed in the intermittent MAGE. The increase in the consumption rate and the decrease in the supply rate when increasing the electrical biases tend to meet at a point which reaches a balance. At the balance point the consumption rate of nickel ions in the local region could be compensated by the supply rate. Therefore, this point defines a critical voltage to separate the columns with internal transverse in compact from those with porous transverse internal. At voltages less than the critical, the columns will lead to a compact transverse, whereas at voltages higher than the critical the columns will lead to a porous one. Considering the LECD performed at 3.2V the supplying rate of nickel ions (that is, 2.77 x10-9 mol s-1) is much higher than the consumption rate (that is, 6.19 x10-10 mol s-1). Nickel ions supplied to the location are more than consumed within the LECD region. Surplus supply of nickel ions leads to a complete filling of internal transverse of the columns. Stable current results in smooth morphology of the columns. On the other hand, as the LECD performed at 4.6V, the supply rate (4.58 x10-10 mol s-1) is much less than the consumption rate (2.24 x10-9 mol s-1). Shortage of nickel ions resultant from a lower rate of supply rate than the consumption leads to formation of internal pores thus resulting in porous transverse in the center of the columns. Greater variation in the deposition current results in rough morphology of the columns. The higher the biases employed in the LECD, the more severe the porous transverse in the columns, and the rougher their surface, as shown in Fig. 11.

There exists a transition zone in a narrow range of the electric bias (from 3.55 to 3.57 V) in Fig. 17. This transition zone arises from the deviation of accuracy in calculating of nickel concentrations and measuring local potentials. Apparently, the accuracy deviation is so small (at 0.02 V) that 3.56 ± 0.01 V is the critical voltage for conducting the intermittent MAGE to separate the micrometer columns with a smooth surface and full compact internal from those with rough surface and porous (or even hollow) internal. At any voltage less than this critical, the nickel ions consumed by electrochemical deposition in the depletion region could be completely compensated by the diffusion of nickel ions from nearby surroundings. This ensures sufficient supply for the need in the electrochemical consumption thus resulting in a full compact internal transverse of the columns. On the contrary, at the overages higher than this critical, the consumption of nickel ions is faster than their supply within the electroplating location. Insufficient supply of nickel ions leads to a porous (and even empty) internal transverse of the columns. Lower current density arising from the cases conducted at lower voltages results in a finely grained smooth surface; higher current density arising from the cases conducted at higher voltage results in an irregularly nodular rough surface.

#### **15. Conclusions**

228 Mass Transfer - Advanced Aspects

calculated from the data of electroplating current consumed to grow the column within the duration. The theoretical weight of the column (*Westimated by weighing*) estimated by the data of

> *calculated from current ItA <sup>W</sup>*

Where *I* is the average current; *t* is the duration to grow a 1000 μm-height column; *A* is the atomic weight of nickel; *z* is the valence; and *F* is the Faraday constant. The average consumption rate of the nickel ions in the local region taking place by LECD could be

onsumption *W I C rate*

The average consumption rates calculated from equation (13-3) are plotted with the

Fig. 18. The average current measured in the LECD and the current efficiency plotted

**14. Balance between the supply and consumption of nickel ions within the** 

Figure 17 summarizes the variation of supply rate and consumption rate within the location where taking place LECD with the voltage employed in the intermittent MAGE. The increase in the consumption rate and the decrease in the supply rate when increasing the electrical biases tend to meet at a point which reaches a balance. At the balance point the consumption rate of nickel ions in the local region could be compensated by the supply rate. Therefore, this point defines a critical voltage to separate the columns with internal

against the electrical bias (voltage) employed

**location taking place LECD** 

*t A zF*

η

*zF* <sup>=</sup> (13-2)

= = <sup>×</sup> (13-3)

current and duration measured is believed to obey the following equation (13-2).

estimated by the equation (13-3)

voltages, as shown in Fig. 17

The kinetics of electrochemical processes is determined not only by the strength of electric field but also by the mass transport phenomenon of the electrochemical active ions. In the cases of ordinary electrochemical deposition, the electric field employed is relatively low and the field distribution is homogeneous. Localized electrochemical deposition (LECD) process provides a new concept to fabricate three-dimensional (3D) metal microstructures. However, a super high electrical field is exerted at the electroplating site in the LECD, and the distribution of field strength is ultra heterogeneous. The site chosen to conduct LECD is controlled experimentally to follow the track guided with a microanode. Consequently, LECD is also named as microanode guided electroplating (MAGE) process.

Through discussion on the phenomenon of mass transport in such a strong field distributed in extremely heterogeneous manner, balance between the supply rate and consumption rate of nickel ions in the region where LECD taking place plays a role on the surface morphology and the transverse internal structure. This balance is determined significantly by experimental parameters such as motion modes of the microanode, applied electric voltage, initial gap between the cathode and microanode. In terms of models, we simulate the system with commercial software ANSYS 8.0 to realize the electrochemical mechanism satisfactory.

**Part 3** 

**Advances in Energy and** 

**Environmental Engineering Aspects** 
