Effectiveness of Electrode Design Methodologies for Fast EDM Slotting of Thick Silicon Wafers

Abstract

Silicon is the most commonly used material in the electronic industries due to its unique properties, which also make it very difficult to machine using conventional machining. Electrical discharge machining (EDM) is a non-traditional process that is gaining popularity for machining silicon, although a slower machining rate is one of its limitations. This study investigates two electrode design strategies to enhance the efficiency of EDM by improving the material removal rates, reducing tool wear, and refining the quality of machined features. The first approach involves using graphite electrodes in various array configurations (1 × 4 to 6 × 4) and leg heights (0.2″ and 0.3″). The second approach employs hollow electrodes with differing wall thicknesses (0.04″, 0.08″, and 0.12″). The effects of these variables on performance were evaluated by maintaining constant EDM parameters. The results indicate that increasing the number of electrode legs improves the flushing conditions, resulting in shorter machining times. Meanwhile, the shorter electrode height outperforms the taller electrode, providing a higher machining speed. The thinnest wall thickness for hollow electrodes yielded the best performance due to the increased energy distribution. Both electrode design methodologies can be used for the mass fabrication of features with targeted profiles on silicon using the die-sinking EDM process.

1. Introduction

Due to silicon’s distinctive characteristics, including resistance to radiation and high temperature, crystalline perfection, and high conversation efficiency in thermoelectric energy, it has been used widely in electronics and photovoltaic industries [1,2]. Silicon is utilized to fabricate micro features for micro-electro-mechanical systems (MEMSs), microprocessors, solid-state devices, integrated circuits, computer chips, solar cells, infrared optical technologies, and other components. At present, the applications of silicon are no longer limited to the electronics sector only; it also has a vast application in aerospace, telecommunication, architecture, automobile, textiles, biomedical, and many more fields [3,4].

Silicon is a brittle material with a low fracture toughness (~1 MPa √m) and high hardness (12–14 GPa), which poses several obstacles for machining regarding the material removal rate. Surface defects (micro-cracks), tool wear, low machining efficiency, accuracy, and high cost are some drawbacks of using the conventional machining process for machining silicon, as these processes use cutting force during machining [3].

The two major conventional methods used to slice silicon wafers from ingots are inner diameter (ID) saws and wire saws. However, both techniques have limitations, such as low efficiency, high surface roughness, high kerf loss, and restriction on the thickness. Defects such as transverse cracks, chipping, saw marks, and waste material have been found in these two processes due to the vibration and deformation of the saw blades and the quick movement of abrasive material in the wire saw. Slicing using multi-wire saws is a cost-effective method for cutting silicon wafers of lower thickness only [5,6,7,8].

Due to the drawbacks of the conventional machining process, new approaches have been developed for machining silicon. Non-traditional/no-contact machining processes that avoid cutting force for machining silicon have recently gained more viability and popularity. Non-conventional techniques like plasma and wet chemical etching were investigated to fabricate micro-electro-mechanical system (MEMS) components in silicon. However, properties such as crystal orientations and masking material selectivity make it very difficult to produce truly three-dimensional structures using these processes. Due to the complexity of producing plasma via the de-ionization of etching gas, plasma is still unsuitable for slicing silicon wafers. Processes like X-ray, Lithographie, Galvanoformung, Abformung—lithography, electroplating, and molding (LIGA), and micro stereolithography are developed to solve these problems, but expensive operational costs restrict their usage [8,9]. Laser beam machining has excellent potential for fabricating intricate curves and three-dimensional shapes in silicon. It offers remarkable machining speed and is not constrained by material conductivity. However, defects such as micro cracks, thermal flaws, etc., have a negative impact on the surface integrity and efficiency of the fabricated parts. To eliminate these defects for machining silicon using laser beams, research has been going on to develop hybrid methods such as laser-induced plasma micromachining (LIPMM), magnetically controlled LIPMM, etc. [3,5]. For machining fine details, lithography and chemical etching have been introduced, but the restriction on the minimum feature size due to the wavelength in lithography and the slow machining rate in chemical etching limits the use of silicon machining [10].

Another non-conventional method is electrical discharge machining (EDM), which has the potential for machining hard and difficult-to-cut materials like silicon. It is an electrothermal technique that removes material via melting and vaporizing as a result of the extreme heat generated by the spark that occurs between the workpiece and the tool. As there is no mechanical contact between the workpiece and tool during this process, it provides advantages over other contact-based conventional and non-conventional machining methods [2]. However, the main bottleneck of machining silicon using EDM is the slow material removal rate. Extensive research has been conducted to improve the removal rate of material during EDM using different approaches, which range from parametric optimization, improving the flushing rate, material of the electrode, or shape of the electrode, and reducing contact resistance to hybrid machining.

Many research studies have focused on improving the material removal rate and machining performance by optimizing the process parameters for EDM. Ganapathy et al. [11] investigated the effects of the peak current, pulse on time, dielectric pressure, and tool size on the material removal rate and tool wear rate and carried out parametric optimization to increase the material removal rate (MRR) and decrease the tool wear rate (TWR) during EDM of EN-31 using copper electrodes. Using the analysis of variance, it was found that the MRR was influenced by the peak current by far the most, which accounted for almost 97%, followed by the pulse on time and size of the tool. The pulse on time, however, produced the greatest impact on the TWR, followed by the tool size. Świercz et al. [12] also investigated the optimization of process parameters for an increased material removal rate and reduced surface roughness for EDM of 55NiCrMoV7 using EDM-3 POCO graphite electrodes. It was found that the peak current had a dominant influence on the MRR and surface roughness, followed by the pulse on time. The pulse off time had a negligible effect on the output parameters, but played a vital role in stabilizing the EDM process. Joshi et al. [8] examined a carbon composite as a workpiece, which is a 2 mm rectangular plate, and electrolytic cylindrical copper as a tool electrode with a diameter of 1.6 mm. It was found that the gap voltage had the most significant effect in both cases on the material removal rate and tool wear ratio, followed by the pulse current and pulse on time. Verma et al. [4] analyzed the influence of open voltage, servo voltage, pulse on time (Ton), pulse off time (Toff), and wire tension for slicing the monocrystalline silicon using WEDM in terms of the material removal rate, slicing rate, and surface roughness. The Taguchi methodology and Grey Relational Analysis were utilized to analyze the experimental data. The output parameters primarily depended on the pulse on time, with the wire tension and open voltage coming in second and third. In parametric optimization, the pulse off time had the least impact. The surface roughness and material removal rate were both enhanced by reduced wire tension. Verma et al. [13] further investigated the effects of the peak current, pulse on time, pulse off time, wire tension, and feed rate on the slicing rate and surface roughness during wire EDM of silicon. From the experiments, the maximum slicing rate was obtained at a higher value of pulse on time and peak current, and to obtain the least possible surface roughness, the pulse on time and peak current need to be the smallest. Dongre et al. [14] investigated the effects of process parameters on the EDM performance and carried out the optimization of parameters for slicing silicon ingots using wire EDM. The response surface methodology was used to optimize the process parameters. It was found that the kerf width increased with the increase in the peak current and wire diameter. The duty cycle and workpiece height have a negligible influence on the kerf width. The wire diameter has the maximum effect on the kerf width. The current was the most dominant factor in increasing the slicing rate. The slicing speed increased by 3.5 times when the value of the current changed from 1 A to 5 A. The height of the workpiece had a significant negative effect on the slicing rate. Joshi et al. [8] performed parametric optimization of the process parameters for slicing ultra-thin silicon wafers to achieve the minimum kerf loss and maximum slicing rate in wire EDM of silicon wafers. It was found that the servo voltage, open voltage, and their combination with other parameters influenced the output parameters the most. As the open voltage increases, there is an increment in the slicing rate, and vice versa for the kerf loss. There is an increment in the kerf loss and vice versa for the slicing speed with increased servo voltage. The pulse on time and pulse off time have negligible effects on the slicing speed and kerf loss when machining silicon wafers.

Tool electrodes and dielectric materials can also influence the machining performance during EDM. Maccarini et al. [15] investigated the effects of the tool electrode material and type of dielectric fluid on the material removal rate, tool wear rate, and quality of the machined parts during EDM. For their experiments, the authors used AISI316L and Ti6Al4V as workpiece materials, brass and tungsten carbide as tool electrode materials, and kerosene, demineralized water, and vegetable oil as dielectric fluid materials. It was found that demineralized water performed better regarding the MRR than kerosene and vegetable oil for both types of workpieces and tool electrodes. For the tool wear ratio, water is still ranked at the top, whereas kerosine rests at the bottom for both the workpiece materials and tool electrodes. However, the material of the tool electrode played a significant role in the quality of the machined parts. For brass, the quality of the machined parts was lower in water compared to those machined in kerosene and vegetable oil. Meanwhile, vegetable oil performed worst in terms of the machining quality of the parts for tungsten carbide. For the material removal rate, the brass electrode performed better than the tungsten carbide electrode, and vice versa for the tool wear ratio. Regarding the quality of the machined parts, the overall performance of the tungsten carbide electrode was better than that of the brass tool electrode. Bhaumik et al. [16] discussed the effects of the tool electrode materials during EDM of Ti-5Al-2.5Sn titanium alloy in terms of the MRR and TWR. Copper, brass, and zinc electrodes with a diameter of 10 mm were used to machine titanium alloy. Brass and zinc electrodes provided a higher material removal rate during EDM than copper electrodes overall. Copper electrodes exhibited a lower tool wear rate, followed by brass and zinc tool electrodes. Compared to brass and zinc electrodes, copper electrodes created a smoother surface finish, lesser recast layer thickness, and a smaller crack width. Rahul et al. [17] investigated the effects of electrode materials on the EDM performance of Ti-6Al-4V using tungsten, copper, and cryogenically treated copper electrodes. The tungsten electrode displayed a lower MRR and rougher surface finish for machining the Ti-6Al-4V workpiece. Cryogenically treated copper electrodes exhibited the highest material removal rate, lowest tool wear rate, and smoothest surface finish, followed by normal copper electrodes. Cryogenically treated copper electrodes also showed higher microhardness compared to normal copper electrodes. Elumalai et al. [18] analyzed the effects of nano silicon carbide (SiC) abrasive powder mixed with dielectric fluid for micro-EDM-milling of Inconel 718. A solid tungsten carbide electrode was used to create micro slots on Inconel, and commercially available EDM oil was used as the dielectric fluid. The three distinct concentrations of silicon carbide abrasive powder were 0.2 g/L, 0.3 g/L, and 0.4 g/L. For analysis, the discharge energy was selected in three regimes: low, medium, and high ranges, and varied for 3.2 to 7.2 J (low), 32 to 72 J (medium), and 320 to 720 J (high). The MRR, TWR, and surface roughness of nano-powder-mixed micro-EDM (NP-MEDM) significantly improved compared to those of conventional micro-EDM. At a medium discharge energy level and powder concentration of 0.4 g/l, the nano additive boosted the MRR by 163% while reducing the TWR and SR by 24% and 17%, respectively. Murugesh et al. [19] investigated the influence of different types of dielectric fluid on the EDM of AISI D2 steel using copper electrodes with square and round cross-sections. The dielectric fluids used were kerosine, canola oil, and jatropha oil. It was found that canola oil performed better, followed by jatropha oil and kerosine in the case of the MRR for round and square-shaped electrodes. For the TWR and SR, kerosine oil suffered less tool wear and provided a better surface finish, followed by jatropha oil and canola oil for both shapes of electrodes. Liu et al. [20] studied the impact of adding silver nano powder to the dielectric during the micro-EDM of high-aspect-ratio micro-holes in Ti-6Al-4V, whereas Niamat et al. [21] investigated the effects of kerosine and water dielectric on the MRR and TWR during the EDM of Aluminum 6061T6 using a copper electrode of a 25 mm diameter. Both studies confirmed that the EDM performance is influenced by the dielectric material and the presence of additives in the dielectric fluid.

The geometry of the tool electrode plays an important role in influencing the machining speed during EDM. Murugesh et al. [19] investigated the influence of the shape of the tool electrode in EDM for making blind holes. The workpiece and tool electrode materials were AISI D2 steel and copper, respectively. The shapes of the tool electrodes were square and round. For the square-shaped electrode, the dimension of the side was 8 mm; for the round electrode, the diameter was 8 mm. It was found that square-shaped electrodes outperformed round-shaped electrodes in terms of the MRR and surface roughness for all three types of dielectric fluid, namely EDM oil, canola oil, and jatropha oil. Goiogana et al. [22] also investigated the effects of the geometry of electrodes on the MRR and TWR. They investigated the effectiveness of hexagonal, square, and triangular-shaped electrodes with round and sharp corners. The study showed that round corners outperformed square corners for a higher MRR and lower TWR. Round-cornered square electrodes provided the highest MRR among all electrodes, and sharp-cornered square electrodes performed the worst. For the TWR, round-cornered square-shaped electrodes performed the best, while round-corned hexagonal electrodes displayed the worst performance. Ti-6Al-4V and POCO EDM-3 graphite were used as workpieces and tool electrodes, respectively, for this study. Kachhap et al. [23] looked into how electrode geometry affected the MRR and TWR in the EDM of aluminum-based MMC (Al6063/10%SiC) using copper electrodes. The shapes of the electrodes were varied by preparing conical, hollow, hollow slotted, hemispherical, and solid slotted electrodes. The highest MRR was obtained by a hollow slotted electrode, followed by hollow, conical, solid slotted, and hemispherical electrodes. For the TWR, the solid slotted electrode performed the best, while the hollow slotted electrode performed the worst. Abbas et al. [24] investigated the influence of the hollowness of tool electrodes on the MRR and TWR during the EDM of high-speed steel using copper electrodes. For this experiment, five geometric electrode shapes were used: hollow square, hollow triangular, hollow polygon, hollow round, and solid round. It was found that hollow square-shaped electrodes outperformed the other shapes of electrodes in terms of the MRR, whereas solid round electrodes ranked the lowest. A similar pattern was also seen for the TWR. Lin et al. [25] investigated the effectiveness of hollow round and hexagonal electrodes for the EDM of particle-reinforced aluminum metal matrix composite (MMC). It was found that hexagonal hollow electrodes generated a higher material removal rate than hollow round electrodes.

Many research studies have focused on designing different hybrid machining processes to improve machining performance. Khosrozadeh et al. [26] analyzed the influence of ultrasonic EDM, powder-mixed EDM, and powder-mixed ultrasonic EDM on the machining of Ti-6Al-4V for an increased material removal rate and reduced surface roughness. Silica (SiO₂) nano powder was mixed with dielectric fluid, and tools vibrated at a 20 kHz ultrasonic frequency. Two different types of dielectrics (i.e., with and without nano powder) and two different electrode modes (i.e., with and without ultrasonic vibration) and their combinations were used. Each hybrid machining method was found to have a higher rate of material removal than the standard EDM. For powder-mixed ultrasonic EDM (PM-US-EDM), the vibration was magnified in the presence of nanoparticles. As a result, it generated the roughest surface roughness (SR) and highest MRR among ultrasonic (US) EDM, powder-mixed (PM) EDM, and standard EDM. Meanwhile, PM-EDM exhibited the least surface roughness among all the processes discussed. The addition of nanoparticles to the dielectric resulted in an increase in the machining gap and spark frequency, which generated low and uniform energy for each spark, causing smaller sparks, shallower cavities, and a smoother surface finish. Munz et al. [27] investigated the effect of pressure flushing in the EDM of X153CrMoV12-1 using brass electrodes. The dielectric flow rate varied from 5 to 25 L/h. It was found that the feed rate increased with the increasing flow rate of the dielectric fluid. However, there was a limit in the maximum feed rate, and after that, there was a reduction in the feed rate, which was seen as being over this maximum. The superior cooling behavior of the dielectric during pressure flushing is thought to be the cause of the decreased electrode wear. Higher flow rates increased the removal of the heat that developed during discharge and reduced the wear in the tool electrode. The surface properties gradually deteriorated at the increasing flow rates due to hydraulic pressure, which resulted in poor surface quality. Chuvaree et al. [28] investigated the effects of side flushing and multi-aperture inner flushing on machining performance during the EDM of AISI P20 plastic mold steel using copper electrodes. The flushing pressure was set to 0.098 MPa for both side flushing and multi-aperture flushing. Side-flushing and multi-aperture flushing were found to improve the MRR process with increasing pulse on time, current, and electrode rotation. The electrode rotation and pulse on time had an inverse relationship with the TWR of side flushing and multi-aperture flushing, but a positive relationship with the current. Uhlmann et al. [29] analyzed the EDM of nickel-based alloy MARM247 using two different graphite electrodes, EDM-3 and HK-6, with and without the assistance of vibration. It was found that the vibration amplitude had a significant influence on the machining time and MRR and a negligible influence on the TWR. The maximum rate of material removal with the optimal amplitude and frequency was reported to be 53.71 mm³/min, whereas it was 50.6 mm³/min in the absence of vibration. Therefore, when utilizing the HK-6 electrode, there was an increase in the MRR of about 6.15% when vibration-assisted EDM was employed. When vibration-assisted technology was applied using EDM-3 electrodes as opposed to HK-6 electrodes, the rate of material removal dramatically increased. The MRR was 32.9 mm³/min without vibration and 56.6 mm³/mm with vibration. Compared to HK-6, the rate of tool wear of the EDM-3 electrode increased significantly with vibration. It was found that neither the electrode material nor the vibration had an impact on the surface roughness, which was mostly influenced by the electrical parameters. Moreover, Amorim et al. [30] also investigated the effect of polarity on the MRR for graphite and copper electrodes where the workpiece was AISI P20 tool steel and found that the performance of the EDM process can be manipulated by the selection of electrode polarity.

Okamoto et al. [31] examined multi-wire EDM for slicing silicon ingots to improve productivity so that it could replace conventional multi-wire saws. It was reported that a constant kerf width was required on each of the processing wire electrodes to cut the uniform thickness of the silicon wafer. Kane et al. [32] evaluated the electric forces on multi-wire EDM for machining silicon wafers. It was found that single-wire EDM was able to slice thinner wafers with less kerf loss compared to conventional machining, but it lagged behind multi-wire saws in terms of productivity when slicing silicon ingots. To overcome this problem, multi-wire EDM was introduced. However, in the case of multi-wire EDM, the vibration was higher than in single-wire EDM. Hydrodynamic, electrostatic, and electromagnetics forces were the main sources of this wire vibration or deflection. They analyzed the electromagnetic forces during the slicing of silicon ingots and predicted the vibration of wire in terms of electromagnetic force. Kunieda et al. [33] tried to improve the EDM efficiency by using ohmic contact in slicing silicon ingots. To improve the MRR, the contact resistance between silicon and metal was reduced via ohmic contact, which was a process of changing the rectifying contact resistance to non-rectifying contact resistance. Ohmic contact was carried out by doping another metal in a silicon workpiece. For this study, p-type silicon and n-type silicon were doped with aluminum and gold antimony, respectively. It was found that for both cases of doped silicon (p-type and n-type), the slicing speed was higher than that of silicon without doping.

Extensive research has been conducted on the effectiveness of the electrode material, shape, and design in improving the EDM performance of various functional materials, with a limited focus on silicon. The electrode design methodologies for the EDM of silicon have not been investigated in detail. In addition, although it is reported that flushing mechanisms influence the EDM performance, limited studies have focused on investigating various flushing mechanisms for the EDM of silicon. Furthermore, not many studies have focused on increasing the material removal rate or machining speed during the EDM of silicon using innovative electrode design strategies, although the majority of the studies have reported comparatively slower material removal rates in the EDM of silicon. Therefore, in this study, rather than focusing on the effects of electrode shape, we will look into two electrode design methodologies that have not yet been explored on any type of workpiece, let alone silicon. The impacts of electrode arrays designed with different electrode leg heights and variations in the wall thickness of hollow electrodes on the EDM performance of silicon in terms of the MRR, TWR, and quality of the machined parts have been examined.

2. Materials and Methods

2.1. Experimental Setup

All the experiments in this study have been conducted on the silicon workpiece. The initial shape of the silicon workpiece was round, with a diameter of 300 mm. EXCETEK W 350G wire EDM, Taichung City, Taiwan, was used to cut the round silicon into a rectangular shape to fit in the vise of the die-sinking EDM. The dimension and specifications of the silicon workpiece are shown in

Table 1. Material properties and specification of Silicon workpiece.

Description	Data
Workpiece material	Silicon
Workpiece length	~110 mm
Workpiece width	~80 mm
Workpiece thickness	~3.74 mm
Density	2.33 gm/cm3
Resistivity	0.0–0.05 Ωcm
Melting point	1414 °C
Boiling point	3265 °C

.

The higher melting point and brittleness of silicon make the selection of the EDM electrode tricky and crucial. Graphite has good electrical conductivity, thermal conductivity, and a very high melting point compared to silicon. The machinability of the electrode, along with other electro-thermal properties, was considered while choosing an electrode material for this study, since the electrodes were machined to produce different arrays and heights of electrode legs. In this research study, graphite material of grade Poco-3 was used as an electrode (Entegris, Poco Materials, Billerica, MA, USA). The properties of Poco-3 graphite, as obtained from the product specification from Entegris website, are shown in

Table 2. Material properties of graphite electrode [34] (obtained from the open-source product specification from Entegris website).

Description	Data
Electrode material	Graphite
Grade	Poco-3
Average particle size	<5 µm
Flexural strength	13,300 psi (935 kg/cm2)
Compressive strength	18,100 psi (1273 kg/cm2)
Hardness	73 shore
Electrical resistivity	615 µΩ-in
Melting point	3650 °C

. The dimensions of the Poco-3 graphite block are 1″ × 1″ × 2″ in length, breadth, and height, respectively. The tolerance of the Poco-3 electrode is ±0.005″ and grounded on 6 sides.

All the experiments for slotting silicon workpieces using graphite electrodes were carried out on the die-sinking EDM machine EXCETEK^® ED 400, Taichung City, Taiwan. EDM oil (hydrocarbon oil) was used as a dielectric and all the experiments were carried out in submerged conditions, where a low and constant dielectric flow was used for flushing debris efficiently. The specifications of the EXCETEK^® ED 400 die-sinking machine, Taichung City, Taiwan, are listed in

Table 3. Specifications of EXCETEK ED 400 die-sinking EDM.

Criteria	Description
X-Axis travel	400 mm
Y-Axis travel	300 mm
Z-Axis travel	350 mm
Maximum workpiece weight	1200 kg
Maximum electrode weight	60 kg
C codes	2000 sets
Peak current	0–288 amps
Pulse on time	0–2000 µs
Pulse off time	0–4000 µs
Discharge voltage	140 V–235 V DC
Discharge time	0.1 s–99.9 s
Gap voltage	20–120 V
Swing radius	0–999.99 mm
Electrode polarity	Reversible
Discharge server speed	Controllable (1 to 100%)
Slag removing speed	Controllable (1 to 100%)

.

2.2. Methodology

2.2.1. Electrode Fabrication

To create different shapes of the electrode from the Poco-3 block, the Bridgeport^® milling machine, Bridgeport, CT, USA, was used. Figure 1 shows the machining of a block electrode to an array of electrodes (3 × 4 legs) using the milling process. The Poco-3 block was placed on the fixed vice with the help of parallels in the milling machine. Face milling has been applied at the top surface of all the blocks to smoothen the surface of the electrodes. To locate the origin (0, 0) of the graphite electrode, an edge finder was used. The diameter of the edge finder was 0.2″. A tool rotational speed of 1200 rpm was used for this edge finder to locate the origin accurately. For creating arrays of electrode legs with different heights and hollow electrodes with different thicknesses, square-end mills were used. The diameter of the end mill was 0.125″ and the spindle speed was 2500 rpm. The brand of square-end mill was Accupro^®, Chicago, IL, USA. The specifications of the square-end mill are as follows: material = solid carbide, diameter = 0.125″, length of cut = 0.75″, shank diameter = 0.25″, overall diameter = 2.5″, and number of flutes = 4 [35].

Varying Arrays of Electrode Legs

For this method, different arrays of electrode legs were used. The dimensions, shape, and depth of electrode legs were kept similar, but the numbers of electrode legs were different. The shape and dimension of the whole graphite block were the same for all the experiments. To conduct the experiments, columns of arrays were fixed to 4 and rows gradually increased to 1, 2, 3, 4, 5, and 6. The number of electrode legs was 4, 8, 12, 16, 20, and 24 for 1 × 4, 2 × 4, 3 × 4, 4 × 4, 5 × 4, and 6 × 4 arrays of electrode legs in sequence, respectively. Experiments were repeated three times with each set of electrodes. For this experiment, the hypothesis is that with an increased number of legs, there will be an increased number of channels, which will eventually increase the flushing velocity, thus improving the machining performance in EDM. As a result, there will be an improvement in the machining speed or material removal rate. For different arrays, the quality of the machined parts and electrode wear rate were also investigated.

Varying Depth of Electrode Legs

For this method, electrodes were designed in such a way that the size, shape, and number of electrode legs were the same, but the depth of electrode legs was different in different sets of experiments. The shape and dimension of the whole graphite electrode block were the same for all the experiments. The experiments were carried out for 1 × 4, 2 × 3, 3 × 4, 4 × 4, 5 × 4, and 6 × 4 electrodes where the numbers of legs were 4, 8, 12, 16, 20, and 24, respectively. For the 1st set of electrodes, the depth of the legs was 0.2″, and for the 2nd set of electrodes, the depth of the legs was 0.3″. Each set of electrodes was repeated three times. The hypothesis for this method is that low-depth legs will have better flushing conditions. The material removal rate, electrode tool wear rate, and quality of the machined parts will be scrutinized for the 0.2″ and 0.3″ depths of electrode legs.

Varying Thickness of Hollow Electrodes

For this method, hollow electrodes with different thicknesses were used. The outer shape, size, and depth of all the electrodes were the same, but the thickness of the perimeter of hollow electrodes was different in different sets of experiments. The thicknesses of the hollow electrodes were 0.04″, 0.08″, and 0.12″. The shape, size, and depth of hollow electrodes were square, 1″ × 1″, and 0.2″, respectively. Furthermore, the performance of a block electrode of the same size and shape was also compared with hollow electrodes. The hypothesis for this method is that the thickness of the perimeter should be as small as possible, as the sparking will occur only on the surface area of the wall thickness that is facing the silicon workpiece, and that area will be eroded. As a result, the energy per area will be increased for the smaller thickness of the EDM power unit and will have a better machining speed or higher MRR.

2.2.2. Machining Parameters for EDM of Silicon

After preparing the silicon workpiece by cutting it using wire EDM and the tool electrode by machining graphite electrodes using the milling machine, die-sinking EDM was used for machining silicon. Figure 2 shows the experimental setup before and during the EDM of silicon. The EDM performance was assessed via the output parameters, such as the material removal rate, tool wear rate, quality of the machined parts, and surface roughness. From the literature review, it has been observed that the peak current is the most important parameter that affects the output parameters, followed by the pulse on time and pulse off time. That is why in this experiment, we were mainly concerned about the peak current, pulse on time, and pulse off time. The peak current values varied for 4 A, 6 A, and 8 A. The pulse on time and pulse off time parameters were varied for 200 μs, 150 μs, and 100 μs (T_on) and 50 μs, 75 μs, and 100 μs (T_off), respectively. Other parameters were kept unchanged for all the experiments. The machining time and depth of machining were recorded. Each experiment was repeated three times. The depth of machining for different parameters is listed in

Table 4. Various process parameters for die-sinking EDM for silicon workpieces and graphite electrodes.

Optimization Level	Peak Current (A)	Pulse on Time (μs)	Pulse off Time (μs)	Discharge Time (s)	Machining Time (min)	Depth of Machining (in)
Level 1	4	100	50	0.8	49.5	0.128
Level 2	6	150	75	0.8	49.5	0.0672
Level 3	8	200	100	0.8	49.5	0.0227

. It can be seen that the depth of machining obtained by the Level 1 parameters is higher than those obtained by Levels 2 and 3 parameters by approximately 1.9 times and 5.63 times. Therefore, the optimized process parameters for die-sinking EDM for slotting silicon using graphite electrodes are shown in

Table 5. Optimized process parameters for die-sinking EDM for silicon workpieces and graphite electrodes.

Criteria	Description
C code	408
Peak current	4 A
Pulse on time	100 µs
Pulse off time	50 µs
Discharge voltage	235 V (DC)
Discharge time	0.8 s
Discharge height	0.039″
Slag removing speed	60%
Discharge server speed	70%
Gap voltage	50
Swing radius	0
Electrode polarity	Positive

.

2.3. Characterization of Tool Electrodes and Silicon Workpieces

An Olympus SZX-12 optical microscope, Takeshi Yamashita, Tokyo, Japan, with Image Pro Plus 7, (version 7), Media Cybernetics, Stoneham, MA, USA, has been used for characterization. To characterize the tool electrodes, exposure was set to −2/3, light intensity set to 8~10, and magnification set to 3.5×, 6.25×, 10×, 12.5×, or 16× depending on the size and shape of the electrode under the optical microscope. For each magnification, the image of the ruler with the marking was taken using the same magnification, which was used as a measurement base for Image Pro Plus 7, Media Cybernetics, Stoneham, MA, USA, to determine the dimensions of the legs and other areas of tool electrodes.

The material removal rate (MRR) is the amount of material removed from the workpiece for a unit period. There are two ways to calculate the material removal rate. For the 1st case, the dimensions of the machined geometry can be measured through the microscope and image processing software. After that, the volume is calculated by multiplying the length, breadth, and depth of the hole. The machining time is recorded in the EDM machine and the MRR can be determined. The second way of estimating the MRR is to calculate the weight difference before and after machining. Using the density of the workpiece material and machining time, the material removal rate can be calculated. The commonly used unit for the MRR is mm³/min. In this work, the MRR was computed both ways and then cross-checked for accuracy.

3. Results and Discussion

3.1. Effect of Electrode Arrays on Machining Speed with Varied Electrode Leg Heights

3.1.1. Fabrication of Electrodes, Measurements, and Analysis

Figure 3 represents the steps of how a square block transformed into 1 × 4, 2 × 4, 3 × 4, 4 × 4, 5 × 4, and 6 × 4 arrays of graphite electrodes for heights 0.2″ and 0.3″. For 1 × 4, 2 × 4, 3 × 4, 4 × 4, 5 × 4, and 6 × 4 arrays, the number of electrode legs is 4, 8, 12, 16, 20, and 24, respectively. The first digit of an array denotes the number of rows, while the second digit denotes the fixed number of columns, which is four in this case for both of the heights.

Figure 4 represents explicitly how the markings of each leg have been assigned for arrays of electrodes and the titles of each measurement entity that have been used in the characterization. In Figure 4a, green (hollow), blue (solid), red (square dotted), and yellow (round dotted) color arrows indicate leg length, leg width, length amid/between legs, and width between legs, respectively. Orange (square dotted) and olive green (round dotted) color arrows indicate electrode legs with heights of 0.3″ and 0.2″, respectively, in Figure 4b. The marking method of electrode legs for 3 × 4 arrays of electrodes is shown in Figure 4c, where counting starts from the upper left corner of each electrode and stops at the bottom of the right side of the electrode. For 1 × 4 arrays, legs are marked as Leg-1, Leg-2, Leg-3, and Leg-4. The same pattern also goes for 2 × 4, 4 × 4, 5 × 4, and 6 × 4 arrays of electrodes. Characterization of the electrode leg has been conducted for each sample and the overview of this full process is shown in Figure 4d–i. Each electrode was repeated three times for measurement and characterization. The average height and cross-sectional dimensions (length and width) of the electrode leg and the dimension of the gap in between electrodes (average length and width between electrode legs) of Case-1 and Case-2 are listed in Appendix A as

Table A1. Dimensional characterizations of arrays of electrode legs.

Case-1 (Intended Electrode Leg Height is 0.2″ = 5080 μm)
Number of Arrays	Sample	Leg Length (μm)	Leg Width (μm)	Leg Height (μm)	Length Amid Legs (μm)	Width Amid Legs (μm)
1 × 4 (Row × Column)	Sample-1	3620.94	3627.12	5082.35	3620.69	-
	Sample-2	3615.54	3631.29	5058.82	3628.02	-
	Sample-3	3611.45	3623.38	5094.12	3628.02	-
2 × 4 (Rows × Column)	Sample-1	3615.19	3644.08	5070.58	3627.13	3606.01
	Sample-2	3642.29	3613.25	5062.87	3610.35	3631.65
	Sample-3	3628.18	3614.26	5072.15	3619.15	3621.95
3 × 4 (Row × Column)	Sample-1	3632.31	3614.86	5095.38	3607.91	3615.18
	Sample-2	3634.92	3625.58	5085.02	3611.24	3625.27
	Sample-3	3614.10	3630.18	5069.86	3625.35	3614.75
4 × 4 (Row × Column)	Sample-1	3634.34	3615.87	5076.62	3637.20	3623.07
	Sample-2	3643.89	3608.79	5070.25	3629.68	3637.49
	Sample-3	3635.58	3621.96	5082.68	3630.88	3630.57
5 × 4 (Row × Column)	Sample-1	3651.33	3615.25	5065.45	3627.32	3619.25
	Sample-2	3660.39	3614.68	5071.01	3633.31	3626.16
	Sample-3	3663.03	3620.53	5063.13	3621.87	3630.28
6 × 4 (Row × Column)	Sample-1	3644.85	3625.16	5059.87	3620.35	3607.91
	Sample-2	3635.58	3620.53	5076.26	3619.15	3611.24
	Sample-3	3626.43	3608.13	5070.25	3607.91	3625.35
Case-2 (Intended Electrode Leg Height is 0.3″ = 7620 μm)
1 × 4 (Row × Column)	Sample-1	3597.76	3566.58	7714.29	3641.47	-
	Sample-2	3619.24	3598.64	7733.33	3631.69	-
	Sample-3	3585.15	3619.34	7704.76	3643.70	-
2 × 4 (Row × Column)	Sample-1	3595.47	3604.18	7742.86	3639.03	3639.39
	Sample-2	3618.25	3626.59	7701.15	3625.18	3614.18
	Sample-3	3605.92	3615.21	7695.24	3631.84	3621.17
3 × 4 (Row × Column)	Sample-1	3619.16	3602.66	7712.38	3619.63	3631.59
	Sample-2	3625.72	3615.91	7730.56	3607.92	3626.62
	Sample-3	3632.29	3642.27	7733.33	3604.75	3601.58
4 × 4 (Row × Column)	Sample-1	3652.33	3616.23	7729.35	3629.27	3630.57
	Sample-2	3659.72	3624.80	7737.89	3643.89	3619.25
	Sample-3	3661.03	3621.43	7740.56	3635.58	3626.16
5 × 4 (Row × Column)	Sample-1	3645.96	3660.88	7719.25	3625.35	3625.35
	Sample-2	3656.63	3657.32	7722.88	3637.20	3637.20
	Sample-3	3648.16	3663.66	7720.75	3629.68	3629.68
6 × 4 (Row × Column)	Sample-1	3639.29	3640.35	7735.75	3630.57	3566.58
	Sample-2	3645.89	3625.26	7740.02	3619.25	3598.64
	Sample-3	3635.58	3641.43	7727.63	3626.16	3619.34

.

3.1.2. Analysis of Machining Time and Material Removal Rate (MRR)

The influence of different arrays and heights of electrode legs on the material removal rate and machining time for machined features on silicon has been investigated. Figure 5a,b show the average machining time of through-hole machining on silicon workpieces for each entire array of electrode legs of heights of 0.2″ and 0.3″. The machining time for 1 × 4 (4 legs), 2 × 4 (8 legs), 3 × 4 (12 legs), 4 × 4 (16 legs), 5 × 4 (20 legs), and 6 × 4 (24 legs) arrays were 131.416, 58.383, 41.4, 38.949, 45.310, and 45.078 min, respectively, for electrode legs of height 0.2″, and 166.045, 94.167,41.917, 39.392, 46.550, and 48.16 min, respectively, for electrode legs of height 0.3″. It can be said that for both heights (0.2″ and 0.3″), the time required for machining 6 × 4 arrays (24 legs) was shorter compared to 1 × 4 arrays (4 legs). It would be quite unfair to compare the machining time with different arrays of electrode legs rather than comparing the machining time for a single feature on silicon or machining time per electrode leg.

The time required for machining a single feature in silicon using each electrode leg for different arrays and heights was investigated while keeping the EDM process parameters unchanged. Figure 6 represents the average time required per through hole for machining silicon using arrays of electrodes with two different leg heights of 0.2″ and 0.3″. For machining a single feature or through slots in silicon using electrode arrays with a 0.2″ leg height, the machining times have been calculated as 32.854 min, 7.298 min, 3.45 min, 2.434 min, 2.266 min, and 1.878 min for 1 × 4, 2 × 4, 3 × 4, 4 × 4, 5 × 4, and 6 × 4 arrays, respectively. There is a drastic improvement in reducing the machining time per square feature/hole on silicon with the increased number of arrays of electrode legs, demonstrating the effective mass fabrication of square features on silicon using the proposed electrode design strategy. This will allow users to use arrays of electrodes rather than a traditional method of single electrodes when a large number of features are required. On the other hand, the average machining times required per through hole for the electrode leg height of 0.3″ have been calculated as 41.511 min, 11.771 min, 3.493 min, 2.462 min, 2.327 min, and 3.45 min for 1 × 4, 2 × 4, 3 × 4, 4 × 4, 5 × 4, and 6 × 4 arrays, respectively. It is found that with variation in arrays, it takes significantly less time to machine unit through holes for 6 × 4 arrays compared to 1 × 4 arrays, which can be observed for both cases of leg heights.

From Figure 6, it is observed that when it comes to productivity or cutting down the amount of time required to machine each through hole in each array of electrode legs, smaller heights perform better than bigger heights. For 1 × 4 arrays, the machining time for each through hole is 32.85 and 41.51 min for heights 0.2″ and 0.3″, respectively. Similarly, 2 × 4, 3 × 4, 4 × 4, 5 × 4, and 6 × 4 arrays of electrode legs show the same trend. Another significant takeaway is that the influence of the leg height is only significant for smaller arrays of electrodes (1 × 4 and 2 × 4). With the increased arrays of electrodes, both heights of electrodes perform quite similarly. For machining a unit through hole with a height of 0.2″ as opposed to 0.3″, less time is required. When a smaller leg (0.2″) is utilized in the electrode arrays, the machining time per through hole is decreased by 8.66, 4.47, 0.04, 0.043, 0.061, and 0.129 min for 1 × 4, 2 × 4, 3 × 4, 4 × 4, 5 × 4, and 6 × 4 arrays of electrode legs, respectively, compared to bigger legs (0.3″). It is worth mentioning that the machining time for slotting silicon for the smaller height (0.2″) is more consistent than for the bigger height (0.3″) of electrode legs. Because of this, we have selected the 0.2″ depth for hollow electrodes with different thicknesses for our study.

Figure 7 presents the variation in the MRR for 1 × 4, 2 × 4, 3 × 4, 4 × 4, 5 × 4, and 6 × 4 arrays of electrodes with two electrode leg heights of 0.2″ and 0.3″. It can be observed that there is an increase in the MRR with the increment in arrays of electrode legs for both leg heights of 0.2″ and 0.3″. The values of the MRR are 2.003, 7.986, 16.691, 23.463, 25.313, and 30.499 mm³/min for 1 × 4, 2 × 4, 3 × 4, 4 × 4, 5 × 4, and 6 × 4 arrays of electrodes, respectively, for an electrode leg height of 0.2″. In the case of 6 × 4 arrays, the MRR is around 15 times more than for 1 × 4 arrays, approximately 4 times more than for 2 × 4 arrays, and around 2 times more than for 3 × 4 arrays of electrode legs. The same trend can also be seen in the case of the electrode leg height of 0.3″, where with the increased arrays of the electrode, there is an increment in the MRR. The values of the MRR are found to be 1.643, 5.180, 16.245, 23.016, 24.433, and 28.390 mm³/min for 1 × 4, 2 × 4, 3 × 4, 4 × 4, 5 × 4, and 6 × 4 arrays of electrodes, respectively, for the electrode leg height of 0.3″. It is clear from comparing these findings side by side, as shown in Figure 7, that a smaller electrode height performs better than bigger height in terms of productivity or the material removal rate in general, but that the performance gap is not that significant.

3.1.3. Analysis of Quality of the Machined Features on Silicon

This section presents the quality of the machined features on silicon workpieces for mirror images of graphite electrodes.

Firstly, visual analysis of the entry and exit side of the workpieces for 1 × 4, 2 × 4, 3 × 4, and 6 × 4 arrays of electrodes for the two heights will be shown in Figure 8 and Figure 9, and for 4 × 4 and 5 × 4 arrays, can be seen in Appendix B as Figure A1 and Figure A2. It can be observed that the quality of the machined features improved with increased arrays of electrodes, especially at the exit side.

For higher arrays of electrodes, there is less chipping observed at the exit side of machined features on the silicon surface compared to lower arrays of electrodes. Overall, it is found that the quality of the machined slots suffers lesser defects at the entrance compared to the exit side, although the dimensions of the slots were found to be slightly higher at the entrance. The defects at the exit holes come mostly in the form of chipping at the edges or more specifically at the corners. This is due to the accumulation of carbon at the side and bottom surfaces of the electrode legs, which causes secondary sparking at the side wall and exit corners of the electrode legs.

The most interesting finding is that the amounts of defects found were reduced with the increase in arrays of electrodes. It is hypothesized that the ‘jump’ action of the electrode holder results in increased dielectric fluid flow at the narrow channels of electrode arrays, and that as the number of channels increases with the number of arrays, the flushing becomes more effective. The spaces between the electrode legs in different rows (horizontal) and columns (vertical) work as narrow channels for dielectric fluid flow during die-sinking EDM, which is a probable explanation for why the material removal rate improves and the number of defects reduces on the machined slots, with larger electrode arrays, regardless of the electrode leg height. As we know from the equation of continuity of the fluid flow, the flow velocity of non-compressive fluid is inversely proportional to the cross-sectional area of the pipe at any given flow rate, meaning that the fluid flow inside a smaller diameter pipe has a higher velocity than that of a larger diameter. In a die-sinking EDM dielectric tank, the flow rate and direction of the dielectric fluid are fixed. Therefore, the channels created between rows in the electrode, that are parallel to the direction of the flow, effectively control the dielectric fluid flow during machining. When the fluid goes through these narrow channels, the velocity increases significantly compared to the fluid velocity at other areas of the machining zone, which improves the flushing condition, and thus results in an increment in the MRR. This hypothesis is explained in Figure 10.

Figure 10 demonstrates the channel formation with increased arrays of electrodes and the direction of the dielectric fluid flow. In Figure 10, a solid red arrow indicates the direction of the dielectric fluid flow, dotted red arrows represent the vertical channel, which is normal to the direction of the dielectric fluid flow, and solid yellow arrows indicate the horizontal channel, which is parallel to the direction of the dielectric fluid flow. In the case of 1 × 4 arrays of electrode legs, there is a single row, and no channels exist in the horizontal direction. Three channels can be seen in the vertical direction, but those are normal to the direction of the flow of dielectric fluid. As a result, these channels do not have any effect on improving the flushing conditions. However, in the case of 2 × 4 arrays, there is one channel in the horizontal direction, and it is parallel to the direction of the dielectric fluid. The number of channels in the vertical direction is fixed, which is three for all the arrays of electrodes regardless of height. In the horizontal channel, there is a rise in velocity, which improves the flushing conditions as well as the MRR. It can be seen that there is a significant improvement in the MRR, that is, almost 4-fold, due to the improvement in debris removal from the workpiece compared to 1 × 4 arrays of electrodes. In the case of 3 × 4, 4 × 4, 5 × 4, and 6 × 4 arrays, the increased velocity in two, three, four, and five horizontal channels, respectively, further improved the flushing conditions compared to 1 × 4 and 2 × 4.

The graphite electrodes’ “jump” action toward the silicon workpiece during machining is the principal source of effective flushing during machining. This ‘built-in’ jumping action of the electrode in the die-sinking EDM machine periodically changes the gap between the electrode and the workpiece due to the up-and-down movement and also introduces turbulence into the gap, which helps in flushing the debris out of the machining zone. This jumping action of the electrode also improves the MRR. As the electrode jumps, the dielectric fluid between the workpiece and the electrode becomes turbulent, cleaning the debris from the spark gap [36]. Figure 11 shows a simple graphical representation of how the jump action works in die-sinking EDM [37].

It can be seen that when the electrode goes upward during the pulse off time (Figure 11a), high-velocity dielectric fluid clears debris from the workpiece, and when the electrode moves down toward the silicon workpiece, it creates turbulence and efficiently sweeps out the remaining debris from the machining zone. With more electrode arrays, turbulence became more intense, due to an increase in the number of electrode legs, which effectively removed debris from the workpiece. As a result, the rate of material removal increased with the number of electrode arrays. Combining these two factors increases the productivity of machining silicon workpieces for increased arrays of electrode legs. Also, it is found that an increase in the number of electrode arrays has an inverse relationship with the buildup of carbon deposition on the graphite electrode. With larger arrays of electrodes, this factor may also hasten improvements in the material removal rate.

For the same arrays of electrode legs, electrodes of a 0.2″ height perform better than those of a 0.3″ height in terms of the MRR. The reasoning for this can be referred to as the 1st cause of improving the MRR, which is the increased velocity in narrow channels of electrodes with higher arrays of electrode legs. Because electrode legs of a 0.2″ height create smaller cross-sectional area channels compared to 0.3″ electrode legs at a fixed flow rate, this results in a higher velocity at the channels of the 0.2″ electrode legs. Increased flushing velocity at the channels enhances the flushing conditions by effectively eliminating debris from the workpiece. However, because of the predominance of the electrode’s jump action, this (1st) effect becomes less significant with more electrode arrays. Because of this, the MRR for higher arrays of electrode (3 × 4, 4 × 4, 5 × 4, and 6 × 4) legs is relatively comparable for both heights of electrode legs.

Using the Olympus SZX-12 optical microscope, Takeshi Yamashita, Tokyo, Japan and Image Pro Plus 7 software, (version 7), Media Cybernetics, Stoneham, MA, USA, the characteristics of the graphite electrode (length and width) and the workpiece at the entry and exit sides (length and width) were determined. The characterization of Sample-1 for 1 × 4, 2 × 4, and 3 × 4; Sample-2 for 4 × 4; and Sample-3 for 5 × 4 and 6 × 4 arrays of electrodes comprising 4, 8, 12, 16, 20, and 24 electrode legs, respectively, for heights of 0.2″ and 0.3″ are listed in

Table 6. Characterization of graphite electrodes and silicon workpieces for height 0.2″.

Number of Electrode Legs	Marking of Legs	Electrode		Workpiece (Entry)		Workpiece (Exit)
		Length (μm)	Width (μm)	Length (μm)	Width (μm)	Length (μm)	Width (μm)
4 (1 × 4)	Leg-1	3639.03	3618.86	4162.74	4092.19	3739.43	3965.19
	Leg-2	3628.03	3622.55	4280.34	4120.41	3777.05	3781.75
	Leg-3	3625.36	3635.36	4068.67	4162.75	3838.19	3805.27
	Leg-4	3591.34	3631.70	4040.45	4106.30	3800.56	4007.53
8 (2 × 4)	Leg-1	3639.03	3624.36	3974.60	3969.90	3908.75	3894.64
	Leg-2	3609.69	3620.69	3998.12	3951.08	3951.08	4125.12
	Leg-3	3617.02	3672.05	4016.93	3965.19	4021.64	3993.42
	Leg-4	3606.02	3672.05	4054.56	3984.01	3777.05	3805.27
	Leg-5	3650.04	3613.35	3974.60	3998.12	3974.60	3852.31
	Leg-6	3606.02	3609.69	3951.08	4016.93	3941.68	3988.71
	Leg-7	3609.69	3675.72	4021.64	4040.45	4101.60	4134.55
	Leg-8	3584.01	3664.73	3965.19	4054.56	3767.64	3814.69
12 (3 × 4)	Leg-1	3609.69	3635.37	3913.45	4002.83	3781.75	3932.27
	Leg-2	3613.35	3639.03	4007.53	3974.60	3814.68	3777.06
	Leg-3	3620.69	3628.03	3988.71	3998.12	3852.31	3786.46
	Leg-4	3653.71	3617.03	3984.01	3955.80	3998.12	4139.24
	Leg-5	3617.02	3609.69	3899.34	3993.42	3786.45	3777.05
	Leg-6	3639.03	3609.69	3988.71	3993.42	3819.38	3781.75
	Leg-7	3613.36	3606.02	3998.12	3998.13	3791.16	3795.86
	Leg-8	3661.04	3606.02	3979.30	3979.30	3842.90	3800.56
	Leg-9	3620.69	3617.03	3959.51	3997.18	3871.12	3828.79
	Leg-10	3646.38	3613.35	4002.82	4002.82	3828.79	3814.68
	Leg-11	3635.38	3598.70	3988.71	3936.97	3805.27	3758.23
	Leg-12	3657.38	3598.69	3998.12	3918.16	3819.38	3805.27
16 (4 × 4)	Leg (Average)	3637.94	3615.54	3945.25	3911.92	3834.66	3828.55
20 (5 × 4)	Leg (Average)	3658.25	3616.62	3969.73	3914.67	3828.06	3780.69
24 (6 × 4)	Leg (Average)	3635.62	3617.94	3923.05	3856.27	3781.76	3799.85

and

Table 7. Characterization of graphite electrodes and silicon workpieces for height 0.3″.

Number of Electrode Legs	Marking of Leg	Electrode		Workpiece (Entry)		Workpiece (Exit)
		Length (μm)	Width (μm)	Length (μm)	Width (μm)	Length (μm)	Width (μm)
4 (1 × 4)	Leg-1	3576.67	3580.34	3951.09	4176.86	3786.45	3781.75
	Leg-2	3602.35	3580.34	4087.49	4139.24	3748.82	3715.90
	Leg-3	3587.67	3554.66	4068.67	4026.34	3805.27	3730.01
	Leg-4	3624.36	3550.99	4059.27	4233.30	3744.12	3767.64
8 (2 × 4)	Leg-1	3631.70	3591.34	3955.79	3979.30	4025.42	3997.18
	Leg-2	3591.34	3595.01	3899.34	3969.90	3781.75	3946.39
	Leg-3	3595.01	3650.04	3965.20	3960.49	4045.16	3833.49
	Leg-4	3565.67	3646.37	3932.50	3941.68	3857.01	3922.86
	Leg-5	3631.70	3591.34	4073.38	3960.49	3800.57	3786.46
	Leg-6	3591.35	3591.35	3899.34	3894.64	3828.79	3781.75
	Leg-7	3587.67	3580.34	3913.46	3960.49	3998.12	3852.31
	Leg-8	3569.33	3587.67	3951.08	4002.82	3908.75	3795.87
12 (3 × 4)	Leg-1	3686.72	3573.00	3974.60	3889.93	3866.42	3781.75
	Leg-2	3624.36	3587.67	3955.79	3908.75	3805.27	3809.98
	Leg-3	3609.69	3587.68	3984.01	3965.19	3819.43	3772.39
	Leg-4	3569.33	3591.34	3913.45	3955.79	3781.75	3828.79
	Leg-5	3657.37	3606.02	3960.49	3922.86	3828.79	3795.86
	Leg-6	3617.02	3606.02	3941.68	3984.01	3875.82	3842.90
	Leg-7	3609.69	3606.02	3918.16	3941.68	3889.95	3904.05
	Leg-8	3591.35	3606.02	3904.05	3946.38	3748.83	3894.64
	Leg-9	3639.03	3613.35	3932.27	3951.08	3828.80	3809.98
	Leg-10	3613.35	3617.04	3927.57	3960.49	3810.02	3824.11
	Leg-11	3606.02	3617.02	3927.56	3988.71	3960.49	3894.71
	Leg-12	3606.02	3620.78	3894.64	3927.56	4120.42	4068.67
16 (4 × 4)	Leg (Average)	3657.69	3620.82	3981.47	3941.92	3858.51	3821.98
20 (5 × 4)	Leg (Average)	3650.25	3660.62	3950.78	3960.34	3908.87	3855.48
24 (6 × 4)	Leg (Average)	3640.25	3635.68	3922.43	3931.98	3818.56	3805.02

. This also shows that the dimensions of machined square features are higher than the dimensions of the electrodes used to machine them, due to the spark gap around the electrode. As the machining parameters are kept constant, the spark gap should be constant as well, and hence, the variations in the dimensions of machined features are associated with the effectiveness of the flushing conditions.

The entry and exit sides of Sample-1 (height 0.2″ of Leg-1) for 1 × 4, 2 × 4, and 3 × 4 arrays of the electrode are shown in Figure 12. It can be seen from the images that the exits are more damaged than the entry sides, as shown in Figure 12. This pattern occurs because during the machining of the entry side, the surface of the graphite electrode was not worn out or the carbon accumulation was very little. Nevertheless, when cutting into the workpiece’s exit side, there is a significant buildup of carbon on the graphite electrode surface, which creates unwanted sparks and causes damage at the edges of the machined features on the silicon workpiece.

The percentage deviations of machined features on the silicon workpiece for the electrode length and width for various arrays and varied heights (0.2″ and 0.3″) were compared. The overall percentages of deviation for the heights of 0.2″ and 0.3″ have also been compared. From

Table 8. Quality of the machined parts of the workpiece with arrays of electrodes and height.

Number of Legs	Percentage of Deviation in Arrays (%) for Height 0.2″		Overall Percentage of Deviation in Arrays (%) for Height 0.2″		Percentage of Deviation in Arrays (%) for Height 0.3″		Overall Percentage of Deviation in Arrays (%) for Height 0.3″
	Length	Width	Length	Width	Length	Width	Length	Width
4 (1 × 4)	9.46	10.42	7.67	7.88	8.58	10.65	7.73	7.95
8 (2 × 4)	9.61	9.61			8.93	8.47
12 (3 × 4)	7.51	8.06			7.73	8.22
16 (4 × 4)	6.93	7.04			7.17	7.21
20 (5 × 4)	6.57	6.38			7.66	6.76
24 (6 × 4)	5.96	5.81			6.33	6.41

and Figure 13 and Figure 14, it can be seen that the average percentage of deviation in the case of the width and length decreases with the increased number of arrays. The average percentages of deviation (%) for the width are 10.42, 9.61, 8.06, 7.04, 6.38, and 5.81 for the electrode height 0.2″ and 10.65, 8.47, 8.22, 7.21, 6.76, and 6.41 for the electrode height 0.3″, for 1 × 4, 2 × 4, 3 × 4, 4 × 4, 5 × 4, and 6 × 4 electrode arrays, respectively. The average percentages of deviation (%) for the length are 9.46, 9.61, 7.51, 6.93, 6.57, and 5.96 for the electrode height 0.2″ and 8.58, 8.93, 7.73, 7.17, 7.66, and 6.33 for the electrode 0.3″, for arrays of 1 × 4, 2 × 4, 3 × 4, 4 × 4, 5 × 4, and 6 × 4, respectively. The reduction in the percentage array indicates the improved dimensional accuracy of the machined features with the increase in arrays of electrodes. Therefore, it can be said that both the surface quality and dimensional accuracy of machined features improve with increased arrays of electrodes, and this may be related to the improvement in the flushing conditions associated with larger arrays due to a higher number of flushing channels and increased dielectric flow in those channels.

Figure 13 and Figure 14 show that for both heights of electrode legs (0.2″ and 0.3″), higher arrays of electrode legs (6 × 4, 5 × 4, and 4 × 4) were more accurate than lower (3 × 4, 2 × 4, and 1 × 4) arrays of electrode legs, with the exception of 2 × 4 arrays. In the case of 2 × 4 arrays of electrode legs, they were found to be less precise compared to 1 × 4 and 3 × 4 arrays of electrodes. This percentage of deviation has been analyzed for other samples too. As shown in Table 8 the overall percentage of deviation for electrode leg heights of 0.2″ and 0.3″ is relatively close, with length percentages of 7.67% and 7.73% and width percentages of 7.88% and 7.95%, respectively. For 1 × 4 and 2 × 4 arrays, an electrode with a leg height of 0.3″ performs slightly better in terms of accuracy than an electrode with a leg height of 0.2″. However, for higher arrays of electrodes, the performance was found to be the opposite and more consistent with the claim that higher arrays of electrodes provide better quality features on the silicon workpiece.

3.1.4. Analysis of Tool Wear Ratio

The tool wear rate (TWR) is the volume of material removed from the tool electrode for the unit time during machining. The commonly used unit for the TWR is mm³/min. In our cases, the tool wear rate was negative due to the addition of foreign material (mostly carbon from the graphite electrode and the decomposition of hydrocarbon oil) on the tool electrode. The accumulation of foreign material is due to the migration and deposition of carbon from the hydrocarbon dielectric fluid on the electrode surface facing the workpiece. This phenomenon is not unique to our experiments and can be seen in different instances. J. Marafona [38] investigated black layer characterization and the electrode wear ratio for machining BS 4695 D2 (a high carbon, high chromium tool steel) using a tungsten copper electrode (W/Cu) through EDM. Before machining, EDS-SEM (Energy Dispersive X-ray Spectroscopy–Scanning Electron Microscope) (Model: Zeiss Supra V5, Carl Zeiss AG, Oberkochen, Germany) shows that the electrode (W/Cu) only contains tungsten and copper. But later, during machining, tool electrodes accumulated C, Fe, Cr, V, and Mo from the workpiece and dielectric oil. Higher elemental migration and a higher carbon presence were observed in the low EWR (0.26%) conditions, while a higher EWR (3.48%) showed lower carbon and fewer migrated elements at the end of the machining. Zan et al. [39] investigated tool wear in graphite using various dielectrics, including deionized water, EDM oil, an emulsion (a mixture of EDM oil and deionized water), and Polyethylene Glycol (PEG) solution (a combination of deionized water and PEG). It was found that dielectrics with a higher carbon content led to a reduction in the tool wear rate due to increased carbon deposition on the electrode. Jahan et al. [40] also found similar results in micro-EDM; carbon migration on tool electrodes was evident through EDS analysis. They also noted that both the amount of migrated material and the black layer increased with longer discharge durations and higher discharge currents. Additionally, Klocke et al. [41] mentioned that the porous nature of graphite electrodes allowed them to absorb some EDM oil during machining, which lead to an increase in their weight. Figure 15a–c depicts the carbon deposition on the graphite electrodes after machining silicon for arrays of electrodes 1 × 4, 2 × 4, and 3 × 4 with a leg height of 0.2″. It is clear that for 1 × 4 arrays, carbon deposition is higher and quite uniform across all legs. However, for 2 × 4 arrays, carbon accumulation mainly occurs on the left and rightmost columns for row-1 and row-2. The probable explanation for this phenomenon is that the velocity of the dielectric fluid at the first column and fourth column is lesser than at other columns as those are entry and exit points for 2 × 4 arrays of electrodes. When it comes to 3 × 4 arrays, carbon deposits mostly appear in row-1 (top) and row-3 (bottom), respectively. The reason for decreased carbon deposition on electrode legs in the middle row is that there is a high-velocity flow of dielectric fluid on channels on both sides of the middle row compared to one side’s high velocity of dielectric flow for row-1 and row-3. Figure 15d–f depicts carbon deposition for higher arrays of electrodes (4 × 4, 5 × 4, and 6 × 4); it can be observed that for higher arrays of electrodes, there is significantly less carbon deposition than for lower arrays of electrodes. All of the higher arrays of electrodes have a similar pattern, and carbon deposition mostly occurs at the entry point of the dielectric fluid, where velocity is the lowest. Figure 16 and

Table 9. Carbon accumulation per electrode leg for different arrays of height 0.2″.

Arrays of Electrode	The Average Weight of the Electrode Before Machining (gm)	The Average Weight of the Electrode After Machining (gm)	Average Carbon Accumulation per Leg (gm)
1 × 4	51.91	54.71	0.6993
2 × 4	51.73	54.83	0.3875
3 × 4	52.81	56.58	0.3142
4 × 4	52.15	54.94	0.1744
5 × 4	72.36	76.25	0.1945
6 × 4	99.80	101.67	0.0779

show the amount of carbon deposition per electrode leg for various arrays of electrodes with a leg height of 0.2″. It was observed that, with increased arrays of electrodes, the carbon deposition per electrode leg gradually decreased, in general, except for the 5 × 4 array, which has slightly higher carbon accumulation than the 4 × 4 array. For a constant electrode leg height of 0.2″, the average carbon deposition per leg is 0.6993, 0.3875, 0.3142, 0.1744, 0.1945, and 0.0779 gm for 1 × 4, 2 × 4, 3 × 4, 4 × 4, 5 × 4, and 6 × 4 arrays, respectively.

In Figure 17 and

Table 10. Carbon accumulation per electrode leg for different arrays of height 0.3″.

Arrays of Electrode	Average Weight of Electrode Before Machining (gm)	Average Weight of Electrode After Machining (gm)	Average Carbon Accumulation per Leg (gm)
1 × 4	49.24	52.14	0.7250
2 × 4	50.02	53.23	0.4013
3 × 4	51.86	55.02	0.2633
4 × 4	50.52	53.26	0.1713
5 × 4	68.92	72.63	0.1855
6 × 4	94.32	96.04	0.0717

, the amount of carbon deposition is shown for electrode legs with a height of 0.3″. It has been shown that, with increased arrays of electrodes, the carbon deposition per electrode leg gradually decreased for an electrode leg height of 0.3″ in general. For both cases of electrode heights (0.2″ and 0.3″), the carbon deposition per electrode leg exhibited the same pattern. The average carbon accumulation per leg is 0.725, 0.4013, 0.2633, 0.1713, 0.1855, and 0.0717 gm for 1 × 4, 2 × 4, 3 × 4, 4 × 4, 5 × 4, and 6 × 4 arrays, respectively, for an electrode leg height of 0.3″.

In die-sinking EDM, the velocity of the dielectric fluid is crucial for minimizing the carbon deposition on the tool electrode during the machining process. It has been observed that a lower dielectric fluid velocity results in a higher carbon deposition [42]. As discussed earlier, the flushing conditions improve as the electrode arrays are increased for both cases of electrode leg heights, as the dielectric fluid velocity at the channels within the electrode arrays is higher. Because of this, for both electrode leg heights, higher electrode arrays resulted in less carbon accumulation than for lower arrays. It can also be claimed that because lower arrays of electrodes accumulate more carbon than higher arrays of electrodes, the machining time is higher in the lower arrays. In addition, the higher accumulation of carbon at the electrode legs of lower arrays causes secondary sparking at the exit during machining, causing chipped exit edges of machined features.

3.2. Effects of Hollow Electrodes on Machining Speed with Varied Wall Thickness

3.2.1. Fabrication of Electrodes, Measurements, and Analysis

Figure 18a–d show how square blocks were machined to different wall thicknesses of 0.04″, 0.08″, and 0.12″. Figure 18e–g show different dimensions of measurements that were taken to analyze the dimensional accuracy and tool wear. Figure 18h–j shows the actual measurement of different dimensions of the hollow electrode. The depth of each hollow electrode was 0.2″, as suggested as the electrode height. The machining of graphite creates a huge amount of dust. For this reason, the vacuum cleaner was attached close to the machining area so that it could consume the dust as much as possible at a very early stage. For the safety of the operator, a mask and safety glass were used during machining, as the dust produced from the graphite electrode is harmful to human health. The average length, breadth, and thickness of the block and hollow electrodes are listed in

Table 11. Dimensional characterizations of arrays of block and hollow electrodes.

Electrode	Sample	Length (μm)	Width (μm)	Thickness (μm)
Block Electrode	Sample-1	25,463.50	25,476.20	-
	Sample-2	25,463.50	25,463.50	-
	Sample-3	25,463.50	25,463.50	-
0.12″ Hollow Electrode	Sample-1	25,463.50	25,476.20	3018.841
	Sample-2	25,463.50	25,476.20	2981.047
	Sample-3	25,476.20	25,463.50	2981.286
0.08″ Hollow Electrode	Sample-1	25,476.20	25,463.50	2056.545
	Sample-2	25,476.20	25,463.50	1962.208
	Sample-3	25,463.50	25,476.20	1962.299
0.04″ Hollow Electrode	Sample-1	25,463.50	25,476.20	1056.742
	Sample-2	25,463.50	25,476.20	1113.336
	Sample-3	25,476.20	25,463.50	1094.308

.

3.2.2. Analysis of Machining Time and Material Removal Rate

The machining time required for slotting silicon in the case of block electrodes and hollow electrodes with different thicknesses was investigated. The outer shape of all the electrodes was the same, which was square with a length and width of 1″ and 1″, respectively. The depth of hollow electrodes was 0.2″. Figure 19 shows the average machining time of through-hole machining on silicon workpieces for block and hollow electrodes with various wall thicknesses. The machining time for block electrodes (1″ square) and hollow electrodes with 0.12″, 0.08″, and 0.04″ wall thicknesses were 68.867, 51.5, 36.128, and 22.200 min, respectively. From Figure 19, it can be seen that with the decrease in the wall thickness from 1″ (solid block electrode) to the hollow electrode of a 0.04″ wall thickness, the machining time decreased from 68.867 min to 22.20 min, which is a significant leap in terms of improving productivity. It was found that for machining the same size through a square hole (1 in × 1 in), hollow electrodes are more effective in terms of the machining speed, compared to solid block electrodes. For each case of wall thickness, the hollow electrode performs better than the solid electrode. This can be explained using the carbon accumulation phenomenon discussed in the earlier section. The solid block electrode has a large surface area facing the workpiece during machining, although in EDM, there is no direct contact between the workpiece and the electrode. However, the amount of carbon accumulation was significantly higher in the solid block electrode due to the higher surface area compared to the hollow electrode. This carbon accumulation causes secondary sparking and arcing, thus increasing the number of ineffective pulses during machining, and increasing the machining time [43]. The discharge energy for each spark in EDM is as follows:

$$\mathrm{E}=\mathrm{V}\times \mathrm{I}\times {\mathrm{T}}_{\mathrm{o}\mathrm{n}}$$

where V = discharge voltage, I = discharge current, and T_on = Pulse on time. Furthermore, in an ideal scenario in EDM, where the machining parameters, dielectric oil, material of tool electrode, and workpiece are the same, the number of sparks (n) for a given period will be identical. So, the spark energy density for the same period will be as follows:

$${\mathrm{E}}_{\mathrm{S}}={\displaystyle \frac{\mathrm{V}\times \mathrm{I}\times {\mathrm{T}}_{\mathrm{o}\mathrm{n}}}{\mathrm{A}}}$$

where A = effective discharge/machining area. So, for the same amount of discharge energy, the smaller the effective area (A), the higher the energy density will be. So, hollow electrodes will have a higher spark energy density compared to block electrodes. In addition, the equation for the material removal rate (MRR) is as follows:

$$\mathrm{MRR}=\mathrm{k}{\displaystyle \frac{{\mathrm{E}}_{\mathrm{s}}}{{\mathrm{T}}_{\mathrm{p}}}}$$

where T_p = pulse time duration and k = coefficient related to parameters such as polarity, electrode, dielectric, flushing condition, etc. In our case, everything is identical except the effective machining area, so for both hollow and block electrodes, the MRR is proportional to Es. As the 0.04″ wall thickness has the highest energy spark density, it will have the highest MRR [44,45].

From Figure 20, it can be observed that there is an increase in the MRR values with the reduction in the wall thickness of hollow electrodes. The values of the MRR are 36.098, 48.012, 68.529, and 111.419 mm³/min for the block electrode and the 0.12″-, 0.08″-, and 0.04″-thick hollow electrodes, respectively. In the case of the 0.04″-thick hollow electrode, the MRR is around 3 times more than for the solid block electrode, approximately 2.5 times more than for the 0.12″-thick hollow electrode, and around 1.5 times more than for the 0.08″-thick hollow electrode. During machining with square block electrodes, the area of the silicon workpiece melts and vaporizes, which is equal to the bottom surface area of block electrodes. However, for hollow electrodes, only the wall thickness area caused sparking over the silicon workpiece and was responsible for machining. As a result, the hollow electrode cut through a biscuit-shaped block equal to the inner cross-section of the hollow electrode, while leaving a square through slot on the silicon workpiece. This significantly reduces the sparking surface area and thus the energy consumption during machining. As a result, the energy per area of the lower-thickness electrode will be higher than that of block electrode and higher-wall-thickness hollow electrode. As a result of that, the 0.04″-thick hollow electrode depicts a higher MRR compared to the 0.12″ and 0.08″ wall thickness hollow electrodes and the solid block electrode. The portion of the workpiece that is inside the hollow electrode was dropped as a square biscuit of silicon, while for machining with a block electrode with a 1 in × 1 in cross-section, the entire material is removed in the form of small craters via continuous sparking. These crater sizes can be controlled by the selection of parameters, thus controlling the discharge energy per pulse [46]. Advanced pulse generators using a Resistance–Capacitance-type (RC) pulse generators are found to produce smaller craters due to their capability of using lesser discharge energy per pulse during machining, and can be useful for improving the dimensional accuracy of silicon in EDM [47]. However, smaller craters will create a lot of powdery debris, which must be removed from the electrode–workpiece gap, thus slowing down the machining process. This biscuit-shaped silicon produced as a result of machining using a hollow electrode can be used for another purpose, if needed, thus minimizing the wastage of silicon material.

3.2.3. Analysis of the Quality of Machined Features on Silicon

It can be seen from Figure 21 that silicon workpieces machined using block electrodes have signs of chipping on the machined square holes, especially at the exit side, compared to those machined using hollow electrodes. It is found that hollow electrodes with a 0.04″ wall thickness have the least amount of chipping at the exit side of the silicon workpiece. It has been found that with the decrease in the wall thickness of hollow electrodes, there is an improvement in the quality of the machined parts in silicon workpieces. The irregular or zagged edges and signs of chipping are more obvious in the image of machined features on the exit side, as shown in Figure 21b. The machined silicon workpiece for 0.08″ and 0.12″ can be seen in Appendix B as Figure A3.

From

Table 12. Quality of the machined parts of the workpiece with different thicknesses of hollow electrodes.

Type of Electrode	Percentage of Deviation (%) at Entry Side		Percentage of Deviation (%) at the Exit Side		Overall Percentage of Deviation (%)
	Length	Width	Length	Width
Block	3.244%	3.371%	4.544%	4.669%	3.957%
0.12″	3.085%	3.355%	3.514%	3.641%	3.399%
0.08″	3.355%	3.083%	3.498%	3.084%	3.255%
0.04″	3.095%	1.985%	2.795%	1.701%	2.394%

and Figure 22, it can be seen that the overall percentage of deviation is decreased with the reduction in the wall thickness from the block electrode (1″) to 0.12″, 0.08″, and 0.04″ wall thickness electrodes. The overall percentages of deviation (%) are 3.957, 3.399, 3.255, and 2.394 for the block electrode (1″), 0.12″, 0.08″, and 0.04″ hollow electrodes, respectively. The average percentages of deviation (%) for the length and width are 3.244, 3.085, 3.355, and 3.095 and 3.371, 3.355, 3.083, and 1.985 for the block electrode (1″), 0.12″, 0.08″, and 0.04″ hollow electrodes, respectively, at the entry side. The average percentages of deviation (%) for the length and width are 4.544, 3.514, 3.498, and 2.795 and 4.669, 3.514, 3.084, and 1.701 for the block electrode (1″), 0.12″, 0.08″, and 0.04″ hollow electrodes, respectively, at the exit side. Due to chipping at the exit side of the through hole, the percentage of deviation is higher at the exit side of the silicon workpiece compared to the entry side, especially for the block electrode. The characterization of the block electrode, the hollow electrodes of 0.12″, 0.08″, and 0.04″ wall thicknesses, and the mirror image of these electrodes on the silicon workpiece (square holes) is shown in Appendix A as

Table A2. Characterization of graphite block and hollow electrode and Silicon workpiece.

Type of Electrode	Electrode		Workpiece (Entry)		Workpiece (Exit)
	Average Length (μm)	Average Width (μm)	Average Length (μm)	Average Width (μm)	Average Length (μm)	Average Width (μm)
Block	25,463.5	25,467.73	26,289.42	26,326.31	26,620.65	26,656.71
0.12″	25,467.73	25,471.97	26,253.40	26,326.49	26,362.77	26,399.44
0.08″	25,471.97	25,467.73	26,326.49	26,252.98	26,362.98	26,253.16
0.04″	25,467.73	25,741.97	26,255.85	26,252.98	26,179.44	26,179.83

.

3.2.4. Analysis of Tool Wear Ratio

Figure 23 depicts carbon deposition on the block and hollow electrodes of various thicknesses and it can be observed that there is a very small amount of carbon deposition on those electrodes.

From Figure 24, it was observed that, with the decreased thickness of the electrode, carbon deposition on the electrode also gradually decreased. The average carbon deposition per electrode was 1.22, 0.89, and 0.845 gm for thicknesses of 0.12″, 0.08″, and 0.04″, respectively. It can be said that due to the reduction in the contact area for lower-thickness electrodes, the amount of carbon deposition is also less. The carbon deposition for the block electrode is 0.973 gm, which is slightly less than for the 0.12″-thick electrode, but greater than 0.08″- and 0.04″-thick electrodes.

4. Conclusions

This study proposes two electrode design methodologies for improving machining speed during the slotting of silicon using die-sinking EDM. The influence of arrays of electrodes and electrode leg heights, as well as the effect of solid vs. hollow electrodes with different wall thicknesses on the material removal rate, tool wear rate, dimensional accuracy, and edge surface quality of the machined features on silicon workpieces have been investigated. For the tool wear rate, carbon deposition on the surface of the tool electrode resulted in a negative tool wear rate compared to most of the studies where a positive tool wear rate was reported because of the removal of material from the tool electrode. The effect of carbon deposition on the EDM performance has also been investigated. The conclusions that can be drawn from this experimental study are as follows:

• The increased arrays of electrode legs have a positive effect on the machining time and material removal rate. With the increment in arrays of the electrode, the machining time required for each slot decreased and the material removal rate per slot increased, irrespective of the height of the electrode leg. For both cases of electrode leg heights (0.2″ and 0.3″), 6 × 4 arrays of electrodes required less time per slot and provided a higher material removal rate than the 5 × 4, 4 × 4, 3 × 4, 2 × 4, and 1 × 4 arrays of electrodes;
• For 1 × 4 and 2 × 4 arrays of electrodes, smaller electrode leg heights performed better in terms of the MRR or machining time. For the case of higher arrays of electrodes (3 × 4, 4 × 4, 5 × 4, and 6 × 4) there are no significant differences in the MRR for different electrode leg heights. It is found that with increased arrays of electrodes, the effect of the electrode’s leg height became insignificant;
• The overall quality of the machined features on the silicon workpiece became better with an increased array of electrodes due to improvements in the flushing conditions. The mirror image of the graphite electrode on the silicon workpiece for 6 × 4 arrays of electrodes is closer to the desired output than those of 5 × 4, 4 × 4, 3 × 4, 2 × 4, and 1 × 4 arrays of electrodes. For both heights, the overall quality of the features of the mirror image of the graphite electrode leg on the workpiece is nearly comparable;
• For both cases of electrode leg heights, carbon deposition per electrode has gradually decreased as the arrays of electrodes have increased. Carbon deposition per electrode leg is quite similar for different arrays of electrodes for both electrode heights. Carbon deposition also plays a critical role in determining the material removal rate and edge quality of the machined features. The higher the accumulation of carbon, the higher the chance of secondary sparking, thus resulting in chipping and zagged edges of machined features on silicon;
• Careful electrode array design, considering the flow direction of dielectric fluid and selecting an ideal number of channels in between electrode arrays and leg heights of the electrodes, can increase both the machining speed (i.e., productivity) and feature quality (i.e., dimensional accuracy, quality of the machined parts, and edge surface finish) of the machined features on silicon via die-sinking EDM;
• The hollow electrodes can provide a faster machining speed compared to fully solid block electrodes when machining the same through features on silicon. With the decrement in the wall thickness of the hollow electrode, there is an increase in the value of the MRR and a reduction in the required machining time to complete a slot. In terms of the MRR, the block electrode ranks the lowest when compared to the hollow electrodes with varied wall thicknesses;
• The overall quality of the machined features on the silicon workpiece became better with a decreased thickness of the electrode due to the smaller sparking area resulting in higher energy density. The mirror image of the graphite electrode on the silicon workpiece for the 0.04″-thick electrode (quality of square through holes on silicon) is better than those of the hollow electrodes with 0.08″ and 0.12″ thicknesses and the block electrode. In terms of the quality of the parts, the block electrode ranks the lowest, providing a zagged edge surface finish at the exit of machined square holes, and the 0.04″-thick hollow electrode ranks at the top, providing clear edges with minimum variations. The improved quality of the machined features using hollow electrodes is associated with less carbon deposition on the thinner walls of hollow electrodes, thus minimizing the chances of secondary sparking, i.e., arcing and short-circuiting.

5. Future Research

• The study found that 6 × 4 arrays and the 0.04″-thick wall showed the optimum results in terms of the MRR and surface quality of machined features in Silicon, which comes with some potential trade-offs. One of the major trade-offs is the higher fabrication time due to the intricate design of electrodes with 6 × 4 arrays and a 0.04″ thickness for mass production/industrial adoption, which can be easily eliminated by using high-end CNC milling;
• Furthermore, a high-flow-rate-capacity peristaltic pump can be attached to the hollow square electrode for pressure flushing to improve the flushing conditions and reduce the machining time. Vibration on the workpiece can also be used for better flushing to improve the MRR for slotting silicon in die-sinking EDM;
• From the literature review, it can be found that powder-mixed EDM generated the least surface roughness on the machined parts. So, powder-mixed EDM can be used to improve the surface finish in the future, as in the present experiments, we have seen chipping along the edge of the machined holes, especially at the exit side;
• It has been found that gluing conductive material to silicon improves the machining performance, including the surface finish, through more uniform and stable discharge, which can also be used in the future studies;
• Future studies should also focus on applying vibroacoustic diagnostics to understand whether dielectric fluid effectively removes the sludge/debris or not. By analyzing the amplitude of the vibroacoustic signals, information regarding the change in the concentration of debris at the machined zone can be identified, thus indicating the efficacy of the flushing mechanism.