【正文】 presented in great detail in Ref.4 Discussion of Observations FEM Analysis. The temperatures at the hot and cold sides are relatively constant at approximately 160176。C and 50176。C, respectively, with an error margin of 1176。C. Due to the distance of the thermocouples to the solder joint and the difficulty in measuring the temperature at the top and bottom of the solder joint, a 3D finite element method FEM heat transfer analysis was used. An eightnode linear heat transfer brick element was utilized, and the thermocouple probe locations were used as thermal boundary conditions. The mesh sensitivity is very low in such a way that a 167% increase in the number of elements results in a % decrease in temperature. Temperature dependent between 30176。C and 220176。C, unless otherwise stated material properties used for the FEM analysis are tabulated in Table 1. The results show that thetop and bottom temperatures are 155176。C and 55176。C, thus creating a temperature gradient of 1000176。C/cm [Fig. 3]. SEMEDX Observations. The experiments are stopped at 286 h, 712 h, and 1156 h. Samples are cross sectioned and analyzed using SEM and EDX for microstructural and elemental analyses, especially at the hot and cold interfaces. The results are pared with those of isothermally annealed samples of the same stressing time. Isothermal heating took place at 55176。C and 170176。C, which is almost the same temperature as the cold and hot sides of the test vehicle. Isothermally annealed samples are manufacturedthe same way as other samples. The IMC thickness is measured using an image processing software. The software is used to identify and calculate the IMC area enclosed in a square, whose dimension is dependent on the IMC thickness. The thicker the IMC, as in the case of isothermal annealing, the bigger the square is. To reduce the waviness effect, as in the case of the hot side of thermal gradient samples, the square size is reduced to 1010
m2. The IMC thickness can be determined when the IMC area is known. A minimum of five squares are used to establish the average IMC thickness. The Cu6Sn5 IMC at both hot and cold sides for flowed .,The Cu6Sn5 IMC at both hot and cold sides for flowed [.,untested]sample is shown in Fig. 4. Nanoindentation Testing. In this study, MTS nanoindenter was used for hardness and modulus measurements, whosedetails are given in Ref. In this experiment, the hardness measurement and modulus calculation for each indentation is based on a prescribed maximum load of 250 after considering the surface area size and number of indentation that needs to be done. A larger load will produce a deeper and larger area of indentation thus limiting the number of indentations that can be done. The average indentation depth due to 250 maximum load is
m. The depth is in orders of magnitude smaller than the size of the solder joint in such a way that the measurements are not influenced by the distance from the free edge. The measurement method uses a series of load/unload cycles for an indentation. The hardness and modulus are determined using the stiffness calculated from the slope of displacement curve Fig. 10 during each unloading cycle
14. As shown in Fig. 11, at maximum load, the hardness reaches an asymptotic value, which indicates the actual hardness of the material. In Fig. 12, however, the maximum load has not caused the elastic modulus to reach an asymptotic value. The modulus is not indicative of the actual modulus,but in this experiment it provides parative moduli across the surface area of the same sample. A typical hardness measurement and elastic modulus for one row of indentation points are shown in Figs. 11 and 12, the measurement at maximum load is taken into account for this paper. For each test, the number of specimen used ranges from 2 to 4. The numerical data and statistical analysis for Figs. 11 and 12 are presented in the Appendix. The mean hardness and elastic modulus for every sample versus the distance from the hot side are plotted in Figs. 13 and 14, respectively. Numerical data for both figures are available in the Appendix. The average surface hardness [Fig. 13] from nanoindentation tests shows that the thermal gradient sample hardness increases from the hot to the cold side at a relatively constant rate. The average hardness for the asflowed samples is shown for reference, and has a value of  GPa. This value is identical to the value, which is  GPa, obtained by Ye for the SnPb solder. The average hardness for isothermal [IT] samples is relatively constant, and lower than the TG samples. Structural changes for the isothermal samples all occurred within the first test interval of 286 h.5 Discussion The two major microstructural differences observed between thermomigration and isothermal experiments are [1] the absence of Cu3Sn at both the cold and hot sides in thermomigration samples, and [2] the thinning of Cu6Sn5 layer on the hot 155176。C side in thermomigration thinning of asflowed Cu6Sn5 IMC layer at the hot side is due its disintegration to 6Cu and 5Sn atoms under thermal gradient according to Eq. [1] Cu6Sn5?6Cu + 5Sn [1] The Soret effect from thermal gradient segregates the Cu6Sn5 IMC to Sn and Curich layers, as shown in Fig. 15(a）. The Cu atoms from the Curich layer drift to the cold side under the thermal gradient force. A similar result was observed by Ding et ,24 under electromigration at 150176。C isothermal temperature. They conclude that Cu atoms from CuUBM and Cu6Sn5 dissolutions drift to bulk solder under electromigration force.6 ConclusionsThe microstructural and mechanical properties of the leadfree solder joint/copper pad interface were studied under a thermal gradient of 1000176。C/cm. The two major microstructure differences between the thermomigration and isothermal samples are the lack of Cu3Sn IMC layer at both the hot and cold sides and the th