Factorial design and design of experiments for developing novel lead free solder alloy with Sn, Cu and Ni

Inherent toxicity makes lead a banned material in solder alloy making process. Lead-tin alloy was a favorable alloy used for soldering in electronic packaging manufacturers. As a result of the ban on lead, electronics package industries were looking for novel lead free alloys which can substitute the conventional Sn-Pb alloy. Many alloys were discovered by the scientists. None of them were able to substitute the Sn-Pb alloy and become the market leader. In this paper a new composition with Sn, Cu and Ni is made to analyze which can potentially replace the lead containing solder alloy. Using the design of experiments method, the optimized composition of Cu and Ni is predicted. The full factorial design of experiments with two replications is used to find the optimized composition. Melting temperature, contact angle and hardness were taken as the critical output parameters. Results obtained shows that the optimum composition of Cu and Ni are 1 and 1% by wt.


Introduction
Soldering is a metallurgical joining method without melting the parent metals [1]. Soldering has varied application in the electronics package manufacturing industry. The solder gives electrical and mechanical continuity in the electronic packages [2]. Sn-Pb was the most widely used solder material due to its good solderability. Soldering process has a long history. Only few realized the fact that soldering has been used by human beings thousands of years before. The recovered jewelry from the preserved burial sites found by the archeologists throws light about the soldering process used during olden times. Au-Cu, Ag-Cu and Pb-Cu were the alloys used in those times. The Romans introduced Sn-Pb alloy long back. Sn-Pb (63Sn-37Pb) was extensively used in the modern electronics industry. Due to the inherent toxicity of the lead, it is banned from alloy making [1][2][3]. Various environmental legislations came to existence to ban lead in alloy making. Waste of Electrical and Electronic Equipment (WEEE), Restrictions on Hazardous Substances (RoHS) by European Union (EU) are examples [4]. Many countries also followed the same path. Therefore electronic industries shifted to lead free solder alloys. Need for new lead free alloys which can replace the Sn-Pb alloy aroused. Researchers around the world started searching for new lead free solder alloy. The desirable qualities of new alloys are low melting point, good hardness, low contact angle, low cost, availability etc. Many compositions were discovered as a replacement for Sn-Pb alloy. Some major compositions include Sn-Bi-Ag [5], Sn-Bi [6], Sn-Zn [7], Sn-Ag-Cu [8,9], Sn-Cu [7], Sn-Zn-Bi [5], Sn-Cu-Ni [10,11], Sn-Cu-Bi [12].
SAC (Sn-Cu-Ag) alloys were having good acceptance (e.g. SAC305 and SAC405. But the amount of silver adds the cost of the alloy. Some of the SAC alloys incur huge patent costs also. In this paper new composition of lead free solder alloy is developed with Sn, Cu and Ni. The full factorial design of experiments with two replications is used to find the proper combination. Assuming a location dispersion model, dispersion effects tests were conducted and presented with two level factorial experiments [13].
Here the melting temperature, hardness and the contact angle are taken as critical output parameters. The criteria for the optimized composition are, the melting point should be low, hardness should be high and the contact angle should be minimum.

Design of experiments (DoE) and full factorial design
Design of experiments is a methodology proposed by Robert Fischer in 1935. This methodology is used to design any job that plans to explain the variations under conditions. There are hypothesis to reflect this variations. The change in one or more independent variables is generally hypothesized to result in a change in one or more dependent variables. The method also identifies control variables that must be kept constant, to avoid the external factors to affect the results. The main concerns in the DoE are the reliability, replicability and validity. In this paper, with the aid of design of experiments, the optimum composition of new lead free solder alloy is predicted. This new composition contains Sn, Cu and Ni. Full factorial and fractional factorial designs at 2 and 3 levels are the most commonly used experiments designs in the manufacturing industry field. Factorial designs help the researcher to analyze the joint effect of the design or process parameters on an output or response. A factorial design can be full factorial or fractional factorial. This paper discusses the full factorial design at level 2. When the number of process parameters is less than or equal to four, full factorial design is a good choice. This is done at early stage of experiment work. For studying k factors at 2 levels, number of experiments required is 2 k . The response is almost linear over the range of the factor settings selected. This is one of the assumptions in this analysis [14].

New lead free solder alloy
The aim of this project is to find a new lead free solder alloy with Tin (Sn), Copper (Cu) and Nickel (Ni). The Sn is considered to be the base metal. Small amount of Cu and Ni is added to make the required alloy. With the addition of Cu and Ni, the melting temperature and contact angle is expected to be decreased. The hardness of the alloy is expected to be increased. This analysis has to be done prior to our experiments. An optimum composition of Cu and Ni is studied and tried to predict so that the melting point and contact angle is lower. This alloy should exhibit good hardness properties.

Design of experiments
The experiment was run with two factors (F), which is Cu & Ni composition and two levels (L), which is 0.5% and 1% by wt. for Cu, 0.5% and 1% by wt. for Ni. 8 runs were conducted with 2 replications, as per the formula:(L) F , (2) 2 = 4 Â 2 replications = 8. Three responses were recorded as output out of each run, Melting temperature, Contact Angle & Hardness. It is shown in the Table 1.

Factorial regression: melting temp(C) versus Cu, Ni
Factorial regression of melting temperature versus Cu and Ni were conducted. The analysis of variance is shown in the Table 2. The model summary is tabulated in the Table 3. The coded coefficients details are shown in the Table 4.  The optimized response from the analysis is shown in the Tables 11 and 12. The prediction of the optimized composition is shown in the Table 13 and Table 14.
It can be found that the composition of Cu is 1% and of Ni is 1% by wt.

Main effect plots
The mean response of the level factors can be represented in the main effect plots. This is done by connections made by the lines. It can be interpreted that there is no main effect if horizontal line is present in the diagram. Little deflection from the horizontal direction means that it will significantly affect the response. Lines with higher slope give the information that the magnitude of the main effect is higher. The effect can be defined as the variations in melting temperature, hardness and the contact angle when the factor changes from one level to another level.
Calculations are done at minimum and maximum values of each factor [15,16]. The information about the direction of the effect (i.e. Increase or decrease in the average response value) is obtained from the sign of the main effect plot. The strength of the effect is obtained from the magnitude [17]. The main effect diagrams give vital information about the information about the factor influence in the properties like melting temperature, hardness and the contact angle of SCN110. The main effect plots for melting temperature, hardness and contact angle is given in the Figures 1, 2 and 3.

Interaction plots
The behaviors of one variable which is depending on the value of another variable is better understood by interaction plots. An interaction plot displays the levels  of one variable on the X axis and has a separate line for the means of each level of the other variable. The Y axis is the dependent variable. The interaction effects are analysed in the regression analysis, ANOVA and DOE. The influence of one factor and a continuous response with the value of the second factor can be identified from the interaction plots [18]. The lines in the diagram can be used to interpret how the relation between the factor and the response are affected. If there are parallel lines, it means that there is no interaction. Non-parallel lines in the diagram interprets that there is interaction occurring. The strength of the interaction is proportional to number of non-parallel lines. Interaction plot for hardness, contact angle and melting temperature is shown in the Figures 4, 5 and 6. It can be interpreted that the influence of these factors are present.

Conclusion
Lead cannot be used in solder making process because of its inherent toxicity. New lead free solder alloys are made which can replace the Sn-Pb alloy. This paper, using design of experiments (DoE) checks the use of Sn, Cu and Ni to make a new lead free solder alloy. By design experiments it has been found that, the selected parameters are the most impacting factors for response. The ANOVA evidently shows with its p-values having less than 0.05 that Cu and Ni composition in the alloy is having significant impact in the Melting temperature, Contact Angle and Hardness. The R 2 values of the regression equation is calculated to be more than 95% which denotes that model is best and