Modeling of Wire EDM slicing process for Silicon

Transcription

1 Modeling of Wire EDM slicing process for Silicon Kamlesh Joshi 1, Gaurav Sharma 2, Ganesh Dongre 3, Suhas S. Joshi 4* 1,2,3,4 Department of Mechanical Engineering, Indian Institute of Technology Bombay, Mumbai, joshi.kamleshmt@gmail.com, 2 gsharma993@gmail.com, 3 dongreganesh1978@gmail.com, 4* ssjoshi@iitb.ac.in Abstract Wire-EDM is an emerging technology for Si ingot slicing with minimum kerf- loss and crack-free surface. In this work, a mathematical model has been developed using dielectric-ingot material properties, heat transfer equations and steady state heat source characteristics to predict temperature profile, melt radius and erosion rate for the ingot and its dependence on voltage, current, wire diameter and pulse on-time have been considered. Modeling of plasma for different phases like ignition phase, heating phase and removal phase has been done and the concept of mean free path (MFP) of electron is used to obtain the temperature profile at plasma-anode interface. The erosion rate predicted using the model has been found to be greater than experimental values. However, with a consideration of plasma flushing efficiency, corrected erosion rate matched well with experimental values. Keywords:Kerf-loss, mean free path, melt radius, erosion rate 1 Introduction Silicon wafers are the most commonly used substrate materials for the production ofmicroelectronic components[1]. Wire EDM process has been used to cut silicon ingots. The process does not apply any cutting force on ingots unlike ID saw and wire saw,and gives highly finished, crack-free surface, irrespective of the size of the ingot [2]. A lot of work has been done to model the conventional EDM process. Jilani and Pandey[4] studied the effect of EDM input parameters, such as pulse duration, pulseenergy and material properties on metal removal and melt shape using a two-dimensional heat transfer model. Singh and Ghosh[5]showed thedifference in material removal in EDM due to short and long pulses and calculated the melt depth. In case of wire-edm, Banerjee [6] developed a modelto prevent wire breakage. Luo [7]evaluated the energy distribution of high-speed WEDM as a function of wire speed, wire diameter, and cutting width to obtain machining conditions for high-speed cutting. Saha [8] used an FEA based approach to model the heat distribution along the wire cross section to identify the parameters responsible for wire breakage. Dhanik and Joshi [9] formulated a comprehensive plasma model for a single electro spark in micro-edm. Das and Joshi [10] developed a model for wire temperature distribution using the clustered sparks. In the present model, various parameters like wire diameter, power supplied, properties of ingot, plasma characteristics and pulse on-time have been used in the evaluation of temperature distribution of ingot, melt radius and consequently the erosion rates for ingot. At present there is no such model that incorporates all these attributes. 2 Modeling The erosion in wire-edm is caused due to sparks generated between wire and work-piece while conversion of dielectric into a ionized gas of high temperature. The spark generation can be divided into three stages namely ignition or breakdown phase, heating phase and removal phase. During ignition phase a strong electric field is generated at the micro-peak of the cathode surface due to presence of electrons and ions. Collision of liquid particles in the inter-electrode gap with the emitted electrons results in heating and formation of a micro-vapor bubble at the micro-peaks surface. The further expansion of the bubble leads to breakdown and formation of a sustainable spark [17]. While in heating phase heating of cathode and anode surface takes place by the fraction of energy transferred from plasma. In the subsequent phase, material removal takes place by electro-thermal [4, 18] or electromechanical mechanisms [19]. At the end of the pulseon-time, the vapor bubble implodes suddenly and ejects debris particle. In this section, a plasma model is developed considering the variation of thermo-physical property of de-ionized water at high temperature and heat input to anode is calculated via plasma-sheath analysis. 2.1 Modeling of breakdown phase In wire-edm, the pulse on-time is usually of the order of µs, in which, the breakdown phase duration is of the order of around 200 ns,so 309-1

2 Modeling of Wire EDM slicing process for Silicon accurate calculations of breakdown phaseis an important aspect. As mentioned before, this phase comprises of thermal heating of liquid at the asperities (micro-peaks) and the growth of bubble to form a vapor bubble at micro-peaks. The plasma channel development occurs followed by three stages namely pre-breakdown phase, nucleation phase and bubble growth phase. In pre-breakdown phase emission of electrons from cathode starts and forms the pre-breakdown current j. In nucleation phase, nucleation of plasma bubble occurs due to emitted electrons at surface micro peaks. The nucleation temperature can be calculated from the relation between the nucleation temperature (T nuc ) and electric field (E p ) given as: λ Ne 2σ 16πσ T 3 2 / kt sat 3 exp r 3 ( ) 2 ( ) 2 t πm kt T Tsat ρ h fg Tsat Tnuc cp( l) X ρl + ρm dt 1 = 0 je p T0 Tsat HereN- number of molecules per unit volume, λ- heat of vaporization per molecule, σ-surface tension, m-mass of one molecule, P-external pressure,p v - pressure in bubble, T sat - saturation temperature, ρ v - densityof bubble, Cp(l)-liquid phase heat capacity and ρ l is liquid density [9]. In the growth phase, active growth of the nucleated bubble is achieved when the density of water vapor reaches2.99 kg/m 3 [8]. Figure1 shows growthof anucleated bubble. (1) Figure1 Bubble abridged the inter-electrode gap and fully developed plasma channel During the bubble expansion, continuous heating of the water vapor takes place,thereby the state of bubble keeps on changes with time. To take this in to account, the variation in thermo-physical properties of the dielectric during expansion of the bubble towards anode, an energy balance equation is required.it is given by, ρ T p C ( T ) dt = Ejτ av p growth Tnuc (2) where, ρ av average density during propagation and growth time is ratio of inter electrode gap to electron drift velocity [14]. The equation (2)gives the plasmatemperature. 2.2 Modeling of heating phase In this phase, interaction between the anode (workpiece) and plasma is considered which will further help in modeling of the removal phase.at the elevated temperature, the mechanism of heat transfer is radiation and particle bombardment.the properties of water vapor change drastically at high temperatures because of its ionization into various ions and neutral particles. The power towards the anode due to charged particle bombardment and radiations energy is given by [16] =2 + (3) where, R P (µm) is radius of plasma channel, e is net flux of charged particles and T e is plasma electron temperature. The net flux e is given by: = + 2 /2,, + /2 4 where, n p, m and T p are particle density, mass and temperature in plasma, respectively for ions and electrons and J thermo is current due to electron emission from anode. The plasma radius is calculated as: = (5) Here,I (A)is current and (µs) is pulse on-time. In this section, modeling of plasma channel was done to get the value of net flux going to anode ( P anode ), which is further used to predict temperature profile of the work-piece and hence the erosion rate. 2.3 Modeling for Erosion rate In this section, temperature at plasma-anode interface is evaluated and then temperature distribution in anode (work-piece) with the help of energy balance equation. The process is assumed to be a single discharge phenomenon around the semi-circular periphery of the wire. The wire is considered to be half way inside the work-piece as shown in Figure 2(a) Due to micro peaks, type of material and dielectric, conditionof emission is satisfied by electric field enhancement. Therefore, a constant β (Voltage/Gap), called field enhancement factor is multiplied to the original electric field to get the enhancement

3 In this model, Mo wire is taken as cathode and Si as work-piece. Kildemo et al.[17] showed that the number of sparks at different location on the wire depend on the field enhancement factor () of the wire which in our case is coming around At the top of the wire, the number of sparks will be maximum and assumed to decrease along the wire length from top to bottom. For = 44.50, no. of sparks comes 90 [17]. For modeling of erosion rate along the length, we considered variation of sparks along the wire (Figure 2(b)). The number of sparks at the top of the wire has been taken 20 % more than the bottom. The wire of length 75 mm has been divided in 16 elements Plasma-anode interface temperature: As the ingot is in the water, it has initial temperature T W. The mean free path (MFP) is the average distance travelled by a moving particle between successive impacts. MFP of electron in ingot is given by [18]: = (6) where, σsiis conductivity, n si is electron density and v f is drift velocity of Si.A small slice of ingot with 3*MFP asthickness has been taken as electrons and ions will lose their energy after traveling this distance [18].Entire energy will be used to increase the temperature of this strip. Therefore, the plasma-interface temperature can be calculated as: = (7) where, C P is heat capacity and n i is no of sparks along the length for i th element (i= 1-16). Above equation will give the interface temperature Temperature profile for the anode:as the interface temperature of the anode is high, temperature of the remaining anode will increase due to conduction. But as convection is also taking place to dielectric (water) from both the top surface, the gradient of the conduction will decrease as we move along the anode length. Eventually, at some point, when the temperature of the ingot becomes same as, no further convection and conduction takes place and temperature will remain only. Some part of energy will be taken away by the eroded material also ( P anode ). P anode = P convection + P latent heat + P conduction (8) =2h + +, (9) There are two unknowns in the above equation T and r. Using recursion, T can be calculated for different values of r. In the direction along wire height (Fig. 2), the temperature profile can be assumed to be same as there is no heat generation within the volume of the anode. (b) (a) Figure 2Wire EDM process showing wire and ingot (a) Top View, (b) Front View 2.4Modeling of removal phase In this work, circular contours for the temperature profile have been assumed. With increasing r, the temperature along the radius length decreases. There comes aradius for which temperature becomes same as melting point of silicon i.e K. It is called melt depth which can be calculated for different values of voltage, current and pulse on-time. As the wire has been divided in 16 elements of 4.7 mm each, different melt radius and depths will occur. The interface temperature will decrease down the length of wire. Therefore, crate radius/depth also decreases. Total erosion rate will be a sum of erosion rates of all the 16 elements. Here, erosion rate (ER) has been considered (mm 2 /min) to be given by. ERi= πri +2ri +2ri / T +T (10) Total ER = (11) Finally, a program was written in Matlab to solve the equations of the model and simulations were performed for different machining parameters. 3. RESULTS AND ANALYSIS In this section, results of simulation for different machining parameters are discussed. In Fig. 3, variation of plasma and plasma-ingot interface temperature with current has been given for the top surface of the ingot. With an increase in current, both plasma and plasmaingot interface temperature increases. A similar trend was found for voltage and on time because as the input energy (V*I*T ON ) increases the temperature increases

4 Modeling of Wire EDM slicing process for Silicon Here, other parameters are T ON =24µs, T OFF =10µs, V=80 V and diameter of Mo wire was taken to be 100µm. fairly matches with the published experimental results[fig. 6and 7]. To verify the erosion rate eight experiments were conducted on wire-edm machine.it is observed that the theoretical ER was larger than experimental. This is possibly due to re-deposition of some eroded material (Fig. 8).The average PFEwas calculated for all the experiments and it comes out to be 25%. A corrected ER was obtained by multiplying theoretical ER with the average PFE. Fig. 9 shows that corrected ER is closer in value to experimental ER. Figure3Temperaturevariations with current. Melt depth was calculated for various voltages, currents, pulse on-time and wire diameter.a variation of erosion depth and erosion rate of the top sample part of the ingot is given in Fig. 4and5 respectively. Results predict that with an increase in voltage, current and pulse on-time, the erosion depth and erosion rate increase while they decrease with the wire diameter. Figure 6 Work-piece temperature distribution from literature [19]. Figure 4 Variation of erosion depth with current. Figure 7 Temperature distribution from model. Table 1 Experimental and Theoretical Erosion rate. Figure 5 Variation of erosion rate with current. 4. MODEL VERIFICATION To verify the work-piece temperature profile, modelresults were compared with the literature data for steel [19].A comparison of results shows that the trend 5. CONCLUSION In this work, wire EDM process was modeled by taking the work done by Dhanik and Joshi [9] as a basic model. It was observed from the model that as the voltage, current and pulse on time were increased, 309-4

5 theincrease in plasma temperature, interface temperature, erosion depth and erosion ratetakes place. This was happening due to the fact that as we increase these input parameters,increasein input power takes place which ultimately increases the plasma energy. Also, the effect of wire diameter was studied on erosion rate and it was observed that with the use of bigger wires the erosion rate was getting decrease. As increase in wire diameter causes more surface area on the ingotfor bombardment of ions and electrons. So same amount of energy gets transferred to bigger surface of the ingot causing decrease in interface temperature. Due to this erosion rate decreases. Figure 8 ER from experimental and model results. Figure 9 ER (from model, experimental and corrected) in different experiments 6. REFRENCES 1. Madan A (2007),"Flexible solar cells and stable highefficiency four-terminal solar cells using thin silicon technology". Mater Manuf Process 22(4): Yan, M.T. and Chien, H.T (2006), Monitoring and control of the micro wire-edm process, International Journal of Machine Tools & Manufacture. Vol. 47, No 1, pp Erden, A., Arync, F. and Kogmen, M. (2005), "Comparison of mathematical models for electric discharge machining", Journal of Materials Processing and Manufacturing Science, Vol. 4, No 2, pp Jilani, S. T. and Pandey, P.C. (1982), Analysis and modeling of EDM parameters Precision engineering Butterworth & Co (Publishers) Lmt, pp Singh, A. and Ghosh, A. (1999), A thermo-electric model of material removal during electric discharge machining, International Journal of Machine Tools & Manufacture, Vol. 39, pp Banerjee S, Prasad BV, Mishra PK (1993) "A simple model to estimate the thermal loads on an EDM wire electrode". J Mater Process Technol 39: Luo YF, (1995), "An energy-distribution strategy in fast-cutting wire" EDM. J Mater Process Technol 55: Saha S, et al. (2005),"Finite element modeling and optimization to prevent wire breakage in electrodischarge machining". Mech ResCommun 31: Dhanik S, Joshi SS (2005),"Modeling of a single resistance capacitance pulse discharge in micro-electro discharge machinin"g. ASME J ManufSciEng 127: Saradindu Das, Suhas S. Joshi (2010), "Modeling of spark erosion rate in microwire-edm", Int J AdvManuf Technol,48: , Beroual, A.(1993), Electronic and gaseous processes in the pre-breakdown phenomena of dielectric liquids, Journal of Applied Physics, Vol. 73, pp Hockenberry, T. O. and Williams, E. M. (1967), Dynamic Evolution of events accompanying the lowvoltage discharge employed in EDM, IEEE Transactions on Industry and General Applications, v 3, n 4, pp , Dijck, F.V. and Snoeys, R.(1971), Investigation of electro discharge machining operations by means of thermo-mathematical model, Annals of CIRP, Vol. 20, No.1, pp Willimas, E.M. (1952), Theory of electric spark machining, AIEE Transactions, Vol. 71, pp Fox., R. W. and McDonald, A. T. (1994), Introduction to Fluid Mechanics, 4 th edition, John Willey & Sons. 16. Roth, J. R. (1995), Industrial plasma engineering, Bristol, Institute of Physics Publication. 17.Kildemo M et al. (2003)"Breakdown and field emission conditioning of Cu, Mo, and W". Phys Rev ST Accel Beams 7, Kalajahi M. et al. (2013), Experimental and finite element analysis of EDM process and investigation of material removal rate by response surface methodology" Int. Journal of Adv. Manu. Vol 69, Issue 1-4, pp