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MODELING OF KERF-LOSS FOR SILICON WAFER

SLICING USING WIRE-EDM TECHNOLOGY

Sachin Prajapati1, Smaranika Tripathy

2

1,2Mechanical Department , NIT Kurukshetra, (India)

ABSTRACT

In this paper, modeling of the kerf profile is developed to predict the nature of the equation of the kerf profile in

Wire Electrical Discharge Machining (WEDM) of molybdenum wire of 180µm, this technology is used in

Photovoltaic industry. The model strained with experimental results conducted using L-8 orthogonal array by

considering the input parameters such as current, duty cycle and wire speed at 2 different levels. The

mathematical relation between the kerf width, slicing rate and process parameters is also established by the

regression analysis method. Predicted values of the kerf width profile using the MATLAB and regression

analysis, were compared with the experimental values and their closeness with the experimental values. The

predicted values resulting into an equation as a function of control parameters are very close to the

experimental results obtained .The polycrystalline silicon wafers form the base material for the solar cells. To

enhance the productivity and minimize the kerf loss the modeling of the profile of kerf has been done to analyze

the effect of control parameters.

Keywords: Kerf Loss, Regression Analysis ,Silicon Ingot, WEDM (Wire-Electric Discharge

Machining)

I. INTRODUCTION

The photovoltaic (PV) industry requires slicing of large diameter silicon ingots into ultrathin wafers at a

minimum kerf loss and subsurface damage .Silicon being the most widely used substrate material for

photovoltaic industries. The various properties of silicon is enlisted in the Table 1. As the semiconductor

industry requires the cutting of silicon ingots into wafers, the slicing of large, ultra thin wafers is one of the main

technologies to prevent wastage. Recently, apart from conventional inner diameter (ID) blade and multi-wire

saw methods, wire electrical discharge machining (WEDM), which has no cutting force, has been introduced to

this area and low resistance silicon may be sliced by WEDM.[1]

Micro-EDM is considered as one of the most promising methods in terms of size and precision. It has advantage

over other fabrication processes, such as LIGA (a photo-lithography method), laser, ultrasonic, ion beam etc.,

because of its economical advantage. Micro-machining techniques such as micro WEDM do not require very

expensive setup. The cutting force is comparatively low, which makes the WEDM an important process to

manufacture precise, intricate and miniature features on mechanical components. Also the majority of other

unconventional processes are slow and limited in planar geometries.The existing methods had higher kerf loss

so an alternative method solution was adopted.[4]

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Table 1- The properties of polycrystalline silicon illustrated in this table.

Density 2330 kg m-3

Young’s Modulus 47GPa

Mineral Hardness 6.5(no units)

Electrical Resistivity 10-3

Ω m

Thermal Conductivity 150W m-1

K-1

Coefficient of Linear Expansion 2.6 *10-6

K-1

Reflectivity 28%

The earlier conventional methods were the inner diameter (ID) blade and multi-wire saw methods which is

shown in figures 1.1 & 1.2 respectively.

Fig. 1.1 The inner diameter (ID) blade method

Fig. 1.2 Multi-wire saw methods

II. PRINCIPLES OF WEDM

WEDM is a widely accepted non-tradition material removal process. The material removal mechanism of

WEDM is the same as that of electrical discharge machining. It has been widely accepted that the metal removal

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mechanism in EDM is predominantly a thermal effect in nature. The basic principle behind EDM process is a

series of electric sparks between the work piece and wire electrode. The electrical discharging process generates

a tremendous amount of heat causing melting or even evaporation in the local surface layers on both wire-

electrode and work piece sides. The heat also causes vaporization of the dielectric fluid and induces high-

pressure waves, which wash out the molten and/or vaporized metal into pieces from the work piece.

Continuously injected dielectric fluid then carries the droplets of metal away. WEDM is considered as a unique

adaptation of the conventional EDM process. However, WEDM utilizes a continuously traveling wire electrode

made of thin copper, brass or tungsten material, which is capable of achieving very small corner radii. It is

desirable that the wire electrode and work piece both be electrically conductive.[3]

III. EXPERIMENTAL WORK

3.1 Experimental Design

The parametric experiments were conducted apart from the theoretical analysis for analyzing the affect of the

response factors. The wire- EDM slicing of Si ingots experimental study has been observed to consider three

control parameters which are Current, Duty Cycle and Wire Speed. The appropriate selection of these factors is

represented in Table2. The experiments conducted basically aims at improving the slicing rate (larger the better)

and profiling of kerf which are the response factors. In order to understand the effect of control parameters, a

design of experiment is required. The L-8 orthogonal array under Taguchi design of experiment (2-levels and 3-

factors) is taken for analysis using the software Minitab 16.[7]

Table 2 - L-8 Orthogonal array (2-levels and 3-factors)

Experiment No. Current Duty Cycle Wire Speed Slicing

Rate(mm/min)

Average Kerf

Width(microns)

1 1 1 1 0.21 213.37

2 1 1 2 0.28 221.73

3 1 2 1 0.17 226.38

4 1 2 2 0.26 243.98

5 2 1 1 0.72 209.7

6 2 1 2 0.93 223.15

7 2 2 1 0.74 228.23

8 2 2 2 1.21 242.6

*This value of the average kerf width is that of the middle location of the cut i.e. the 17

th location (Article 3.3).A

total of 8 experiments were conducted with 4 replications. The analysis was carried out by dividing the

individual cut into 35 locations along the height of cut necessary for the profiling of the kerf.

3.2. Experimental Setup

In the entire experiment the wire-EDM machine is used for the silicon ingot slicing. This is a wire-EDM

machine of CONCORD wire-EDM. The machine has four basic elements which are physically separated and

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connected to each other according to the setup. The four basic elements are Stabilizer, Controller, Work table

and Dielectric fluid tank (deionized water with a certain amount of a particular gel). The figure below

represents the experimental setup.

Fig. 2 The experimental setup of wire-EDM

In figure 2 the experimental setup is represented. The polysilicon work piece is mounted on the work table, the

molybdenum wire moves from upper guide to lower guide. Along with wire guides the dielectric nozzles are

there for the flushing proacess.

3.2.1 Controller

To perform the machining operation, the commands are given through the controller to the machine and this

process can be done in two steps: (1) Make 2-D drawing of tool travel path. (2) Import the 2-D drawing in the

CNC extension software. (3) give the suitable parameters through the CNC software (wherein the cad file of the

drawing is converted into (.NC file, which is similar to the code of .NC file.)

Thus, after the parameters are given to the machine the machining operation is started. There is a limited range

of parameters which can be varied current, wire speed, voltage, pulse-on Time, pulse-off Time, group-on,

group-off etc. The following figure (3.1) represents the window on the controller screen where the parameters

can be varied.

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In figure 2, the remaining element of the wire-EDM contains the work table, wire feed mechanism, digital

motion indicator and servo mechanism. The servo mechanism in the machine is same as other type of wire-

EDM but the wire feed mechanism is different. This wire-EDM contains molybdenum wire feed mechanism

which deals with different wire diameters (50 to 250 micrometers). In this kind of wire feed mechanism the

same wire is used repetitively through rolling on the drum but after some duration of the machining the wire has

to be changed. The digital motion indicator gives the co-ordinates of the tool position.

3.3. Experimental Procedure

The aim of the experiment is to understand the optimized parameters for wire- EDM slicing of silicon ingot and

kerf profiling equations. This work mainly involves cutting the silicon ingot over a height of 75mm and a depth

of 5mm to produce thin wafers of thickness 150-170 µm.

A total number of 32 cuts for generating 16 wafers along with the individual wafer given a wire movement of

395 µm

The shorter depth of 5 mm is sufficient to represent the slicing rate over the entire depth of 75mm as the slicing

speed remains more or less the same for the entire depth of the wafer. [2]

The kerf width was measured by a Rapid-I Microscope and analyzed at 35 locations .The slicing time was

measured during the cutting operation on the controller screen. Below are the images of the silicon wafers.

The slicing rate is calculated by the below mentioned equation –

Slicing Speed = Length of cut / Slicing time (Equation 1)

Fig. 3.1 shows the window on the

controller screen wherein the

process parameters can be

changed according to the

experimental conditions.

Process

parameters

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In the above equation, the unit of slicing speed is taken in mm/min. The time was noted with the help of a stop

watch and the time was also observed on the screen of the controller.

Fig. 3.2 Height of cut Fig 3.3 the cuts corresponding to eight experiments

4. RESULTS AND DISCUSSIONS

4.1 Analysis of Slicing Speed

In the Figure 4.1, represents the main effects of current, wire speed and duty cycle. Current parameter is more

effective for the slicing speed rather than wire speed and duty cycle. Wire speed is mild affecting parameter for

the slicing speed. In the experiment the current has two levels (1& 5 Amp). The plot as shown below represents

the variation of slicing speed with the energy parameter. The energy parameter basically represents the amount

of energy given for the material removal in ‘mJ ‘. It’s a product of Voltage (v), Current (Amp) and Ton (µs).

Energy parameter (β) = Voltage (V) * Current (I)* Ton(mJ) (Equation 2)

Fig. 4.1 Main effect Plots for means

75 mm

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Fig. 4.2 Main effects Plot for S/N ratios

The above plot (Fig 4.1&4.2) of slicing speed vs. energy parameter (β) consist the plots at two levels of wire

speed at 10 Hz and 50 Hz. It is very clear from the plot that at each value of energy (β) the value of slicing speed

corresponding to wire speed 50 Hz is nearly 1.5 times of the values at wire speed 10 Hz. From β=2.45 to β= 3.5

, the rise in the slicing speed is 70%.

Table 3 -The corresponding energy values illustrated in the given table

Experiment no. Energy ( mJ) Experiment no. Energy (mJ)

1 0.7 2 0.7

3 2.45 4 2.45

5 3.5 6 3.5

7 12.25 8 12.25

The plot below represents the Signal-to-Noise ratio of the control factors. For the larger slicing rate the current

parameter should be greater i.e. level 2 (5 Amp) , wire speed parameter should be greater i.e. level 2(50 Hz) and

there is not much effect of the duty cycle in the analysis of slicing rate.

Figure 4.3 Plot of slicing speed vs. energy parameter (β) at different wire speed levels.

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SLICING RATE = (- 0.239 + 0.168 CURRENT + 0.00221 DUTY CYCLE + 0.00524 WIRE SPEED)

mm/mm (Equation 3)

From the analysis of slicing rate data a regression equation is shown. The equation’s fitment parameter value

(R2= 93.9%) and R

2 (Adj) = 89.3%

4.2 Analysis of Profile of Kerf Loss

Profiling of the kerf loss varies with respect to the control parameters i.e current, duty cycle and wire speed etc.

The kerf width varies along the height of cut which shows that highest kerf width is observed in the middle

portion of wire guides followed by the top and bottom portion. The main effects plot of kerf width for means

represents that the duty cycle is the most effective parameter when compared to the rest, while wire speed has a

Fig. 5.1 Main effects plots for means

mild effect and the current has the least effect on the variation of kerf. The main effects of plot is shown in

figures 5.1 & 5.2

Fig. 5.1 Main effects plots for means

Fig. 5.2 Main effects plots for S/N ratios

After the Taguchi design analysis through Minitab, the effect of a single parameter is studied while keeping the

remaining two parameters as constant.

4.3 Modeling of Kerf Profile

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Using the Taguchi design regression analysis, the linear model equation of the kerf width is expressed in terms

of the process parameters and a function of height. To observe the effect of variation of height on kerf width, 35

locations are chosen .The regression equation is modeled at the ith

location as:-

K.Wi = Ki+ C1i*Current + C2i*Duty Cycle + C3i* Wire Speed (Equation 4)

Where, K is a function of height, C1,C2&C3 are the coefficients of current, duty cycle and wire speed etc as a

function of height. These coefficients of the process parameters are curve fitted to study the nature of C1, C2 &

C3 as well as K using MATLAB.

The regression analysis is done for each individual location through the modeled equation. It is observed that the

individual location is a function of the process parameters i.e. current, duty cycle and wire speed. The

coefficients of current, duty cycle and wire speed as well as the constant K, are observed to be varying as a

function of height. To study the nature of these terms, curve fitting is then done to estimate the varying nature of

these terms as a function of height using MATLAB.[5]

The curve fitted equations of C1,C2, C3 & K represents different functions as shown below:-

K represents the Fourier series with 8 terms which had the fitment parameter of (R2=83.35%) done by fitting

the data values using MATLAB.

K (h) =

Fitment parameter (R

2) = 83.35%

Fig. 6.1 shows the fitment curve and the residuals plot for the constant K

C1 is the coefficient of current which represents the sum of sines with 8 terms which had the fitment parameter

of (R2=97.17%) done by fitting the data values using MATLAB.

C1 (h)

178.5-0.0532*cos(0.169*h)+2.438*sin(0.169*h)-3.14*cos(0.169*2*h)

+0.1232*sin(0.169*2*h)+0.5516*cos(0.169*3*h)+0.8374*sin(0.169*3*h) +1.296*cos(0.169*4*h) +

0.1359*sin(0.169*4*h)-0.04352*cos(0.169*5*h) -0.006171*sin(0.169*5*h) -2.865*cos(0.169*6*h) +

0.5369*sin(0.169*6*h) -4.76*cos(0.169*7*h) – 0.714*sin(0.169*7*h) -0.6093*cos(0.169*8*h)

+1.402*sin(0.169*8*h) (Equation 5)

= 0.59*sin (0.57*h-4.6) + 0.8*sin(0.45*h-4.8)+0.66*sin(0.3*h-3.5)+0.5*sin(h+5.27)+0.75*sin(0.18*h-

3.45)+0.21*sin(1.23*h-0.06)+0.43*sin(0.86*h+5.87)+0.54*sin(0.72*h-11.96) (Equation 6)

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Fitment parameter (R2) = 97.17%

Fig. 6.2 shows the fitment curve and residuals plot for the coefficient of current (C1) versus

height(h)

C2 is the coefficient of duty cycle which represents the sum of sines with 8 terms which had the fitment

parameter of (R2= 95.66%) done by fitting data values using MATLAB.

C2(h) =

Fitment parameter (R2) = 95.66%

Fig. 6.3 shows the fitment curve and residuals plot for the coefficient of duty cycle (C2) versus

height(h)

C3 is the coefficient of wire speed which represents the sum of sines with 8 terms which had the fitment

parameter of (R2= 96.44%) done by fitting data values using MATLAB.

C3(h) =

Fitment parameter (R2) = 96.44%

1.264*sin(0.06*h-0.7)+0.66*sin(0.1*h+1.05)+0.05*sin(0.22*h-

0.21)+0.067*sin(1.16*h+2)+1.73*sin(0.5*h-4.6)+0.018*sin(0.7*h+3.5)+0.033*sin(h+0.157)

+1.73*sin(0.5*h+4.8) (Equation 7)

0.26*sin(0.025*h+1.23) + 0.033*sin(0.1035*h+3.66) +1.505*sin(1.212*h+3.6) + 0.0406*sin(0.0578*h-

0.293) + 0.7818*sin(1.194*h-5.187) +0.8066*sin(1.23*h+6.122) + 0.036*sin(0.447*h+5.873) +

0.03527*sin(0.96*h-2.03) (Equation 8)

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Fig . 6.4 shows the fitment curve and residuals plot for coefficient of wire speed (C3) versus

height (h)

4.4 Final Estimated Equation Of Kerf Width

From modeled equation,

K.W. = K (h) + C1 (h)*Current + C2 (h)*Duty cycle + C3 (h)* wire speed (Equation 9)

The modeled profile of the kerf is been compared to the experimental measurements of the kerf width as shown

below at low energy parameter β=0.7mJ with a standard deviation of 7.8 µm. Comparison between Experiment

no. 1&8

Fig. 7.1 Modeled and Experimental plots for experiment 1

The kerf width analysis through modeling and experimentally for the highest energy parameter β=12.25mJ is

shown below with a calculated standard deviation of 11.29 µm.

KW (in

microns)

Height (mm)

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Fig. 7.2 Modeled and Experimental plots for experiment 8

V. CONFIRMATION EXPERIMENT

For the validation of the equation of the Kerf Width some confirmation experiments are performed taking two

sets of interpolated and extrapolated control parameters (Current, Duty cycle, Wire speed) with two replications.

For each set of the control parameters the table is shown below with corresponding standard deviations.[6]

Table 4 - Below are the plots of Kerf Width vs. height(h) for the above mentioned parameters

which represent the validation of the modeled equation of the Kerf Width

Serial no. Type Current (Amp) Duty cycle (%) Wire speed (Hz) Standard deviation (µm)

1 Interpolation 2 60 42 9.4

2 Interpolation 3 70 33 10.1

3 Extrapolation 2 40 10 10

4 Extrapolation 6 90 50 35.5

KW (in

microns)

Height (mm)

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Fig. 8.1 Fig. 8.2

Fig. 8.3 Fig. 8.4

The plots for the confirmation experiments at different parameters (1) and (2) are the plots for first two set of

interpolated parameters and (3) and (4) are for next two set of extrapolated parameters as mentioned in Table 4.

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VI. CONCLUSION

In this experimental work, modeling of kerf profiling on silicon ingot was carried out. Kerf width and slicing

rate were selected as response variables. The experiments were performed on molybdenum wire-EDM with wire

diameter of 180µm. The control parameters i.e. Current, Duty cycle and Wire speed for the silicon ingot slicing

were taken throughout the experiment.

The following concluding remarks were drawn.

Profiling of kerf loss is the main focus of the experiment. The Kerf width varies along the height of the cut

and becomes maximum at the middle position.

Kerf width of a cut at a particular location also varies with the control parameters. In this experiment, the

modeled equation of the kerf width at a particular value of height is a linear model equation in terms of

Current, Duty cycle and Wire speed which is predicted with the fitment parameter in the range R2> 80% .

From the Taguchi Design analysis for kerf width, it can be observed that the Duty cycle parameter had the

highest effect and current had the least effect on the Kerf width.

It was observed in the slicing rate analysis, the Current parameter had the highest effect and the Duty cycle

had the least effect.

At different level of wire speed (10&50 Hz) the slicing rate corresponding to each energy value (β) was

larger at the higher wire speed i.e. 50 Hz.

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REFERENCES

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[2] Groover, M. P. 2007.Fundamentals of Modern Manufacturing.Materials, Processes and Systems.Third

Edition. Singapore: John Wiley & Sons (Asia) Pte Ltd.

[3] Kalpakjian, S. &Schmid , S. R. 2006. Manufacturing Engineering &Technology.Fifth Edition. Singapore:

Prentice Hall, Pearson Education South Asia Pte Ltd.

[4] N. Mohri, H. Yamada, K. Furutani, T. Narikiyo, and T. Magara, \System identificationof wire electrical

discharge machining," CIRP Annals-Manufacturing Technology, vol. 47, no. 1, pp. 173176, 1998.

[5] Dongre, G.G.; Vesvikar, C.; Singh, R.K.; Joshi, S.S. (2010) Efficient dicing of silicon ingots for

photovoltaic applications. 35th IEEE Photovoltaic Specialists Conference (PVSC), 20–25 June 2010,

Hawaii.

[6] Dongre,_Singh,_Joshi,2012,ResponseSurface analysis of silicing of silicon ingots with focus on

photovoltaic application

[7] Luo, Y.F.; Chen, C.G.; Tong, Z.F. (1992) Investigation of silicon wafering by wire EDM. Journal of

Materials Science, 27: 5805–5810.