ABSTRACT
There are various specimen configurations available in the literature for characterizing the mechanical behavior of solder interconnect materials. An ideal test specimen should use a simple geometry which produces a reasonably uniform material response throughout the gage zone and minimizes the complexity of data reduction to extract material model constants. In the thermo-mechanical micro scale (TMM) test used in this study, we use a simple, notched shear specimen, based on a concept originally proposed by Iosipescu [1967] [1], which produces a reasonably uniform shear stress field throughout the solder joint [Reinikainen et al.,1998] [2].
Our modified Iosipescu specimen comprises of two oxygen free, high conductivity (OFHC) copper platens soldered together and loaded in simple shear, as in a lap-shear specimen. The solder joint in this specimen is only 180 microns wide to capture the length scale effects of functional solder interconnects. This study examines the effects of dimensional variabilities of this modified Iosipescu test setup on the shear stress and strain distributions in the solder specimen. Variabilities encountered in these specimens include: (i) fillets at the V-notches, caused by excess solder; (ii) offset between the two copper platens along the loading direction; (iii) taper of the solder joint due to lack of parallelism of the edges of the copper platens; and (iv) misalignment between the specimen centerline and loading axis of the TMM test frame due to mounting variability. Detailed parametric studies of these four dimensional variations in the TMM specimen are conducted using a simple two-dimensional finite element model for measurement of elastic-plastic-creep properties of solder materials.
INTRODUCTION & MOTIVATION
Typical field conditions seen in electronic packages include thermal cycling, mechanical cycling, vibration loading and drop, to name a few. Solder joint integrity is critical to functionality since they not only form the electrical interconnection but are also the load bearing mechanical interconnection. Hence accurate experimental methods to characterize the material response of the solder are very important. In this study we examine the accuracy of a selected mechanical test method, by examining the sensitivity of the extracted elastic-plastic stress-strain curves and constitutive creep properties to the dimensional, processing and loading variabilities of the test setup.
Past studies confirm that geometric variabilities in the test specimen such as notch angle, root depth, misalignment between the specimen centerline and the loading axis of the test setup can significantly alter the constitutive and durability properties of the solder interconnects. Most of the studies reported in the literature were conducted on monolithic Iosipescu specimens, and only a few [2] have addressed multi-component structures such as the solder specimen we have used in our study.
Fig 1: Misalignment between loading axis and specimen centerline
Fig 2: Fillet due to excessive solder volume
Fig 3: Tapered solder joint due to lack of parallelism between edges of mating copper platens
Fig 4: Offset between horizontal centerlines of mating copper platens
Our solder test specimen consists of two different copper platens soldered together, which creates opportunities for additional dimensional, processing and loading variabilities, that are examined in this paper: (i) misalignment between the specimen centerline and loading axis of the TMM test frame due to mounting variability; (ii) fillets at the V-notches, caused by excess solder; (iii) taper of the solder joint due to lack of parallelism of the edges of the copper platens; and (iv) offset between the two copper platens along the loading direction. These variabilities are schematically illustrated in Figures (1-4).
Fabricated specimens considered in the present study have a solder joint thickness of 180 |im, which is of the same length scale seen in functional solder interconnects. This is important to replicate microstructural length-scale effects that are known to exist in functional solder joints, especially for Pb-free, Sn-Ag-Cu (SAC) solders. The specimens are deformed in mechanical shear. A schematic of the test specimen considered in the 2D finite element elastic-plastic analysis is shown in Fig 5. The TMM specimen considered here consists of a thin layer of solder connecting two copper platens. The solder joint is approximately 180 microns wide, 3.0 mm long and approximately 1 mm thick. The specimen is originally 1.5 mm thick and reduced to approximately 1mm thickness using standard grinding and polishing processes. Due to this plane-stress configuration, 3D and 2D models are found to provide similar parametric sensitivities. To minimize computing time in nonlinear parametric sensitivity studies, the model considered for study here is a plane stress 2D model.
Fig 5: Schematic of TMM specimen
The main objective of this paper is to study the effects of selected dimensional variabilities of this modified Iosipescu specimen on the shear stress and strain distributions and constitutive creep properties in the solder joint, using elastic-plastic finite element analysis (FEA) and comparing them with the distributions in a nominal specimen with no geometric imperfections in it. The range of different variabilities considered for the modeling has been decided on the basis of the measured variations in different batches of our fabricated test specimens.
APPROACH
The 2-D FEA [3] model considered here consists of 8-noded 183, quadrilateral, plane-stress elements in a mapped mesh configuration. The elastic-plastic behavior is modeled with a Ramberg-Osgood model, as presented in Equation (1)
where, s is von-Mises strain, a is von-Mises stress, E is elastic Young’s modulus, K & n are the elastic-plastic Ramberg-Osgood constants for the solder considered. An image of the finite element model showing mesh, boundary conditions & loads is shown in Fig 6. The copper platen in the left is constrained in both x and y directions but the platen in the right is constrained only in x-direction and given a displacement of 90 microns in y-direction.
The mesh sensitivity of the model accuracy was studied by gradually increasing the density of mesh from the center of the specimen towards the root of the notch where stress concentrations are expected. The current mesh was found to be acceptable from the perspective of reducing the effect of the mesh, element distortion and element aspect ratio, on the accuracy of the output.
Fig 6: Meshed elastic plastic creep model
Parametric FEA studies are conducted by systematically varying the geometric parameters listed in Section 1 and shown in Figures 1-4. The effect of these variations on the accuracy of the TMM test is examined by comparing the elastic-plastic material properties (E, K, n) and secondary creep strain rate (dy/dt) extracted from these error-seeded FEA models, to those from a reference model which has the nominal geometry and loading. Secondary creep strain rate is calculated using sine-hyperbolic Garofalo secondary strain rate equation as presented in Equation (2). Rate dependent plasticity study was done for a single stress level (10 MPa) for two different temperatures 298 & 398 K. The extracted material constants are based on averages of the deformation and stress fields over the entire solder volume, since typical experimental measurement capabilities are based on similar averages. Localized averages of these constants are not investigated since they cannot be experimentally measured and are of limited value due to local microstructural inhomogeneties.
where, ds/dt = von Mises strain rate, a = von Mises stress, a = Stress constant, n = stress exponent, Q = Activation energy, R=Universal gas constant, T = Temperature in Kelvin The range of variabilities considered here for the relevant geometric parameters in this study is decided based on experience gained during fabrication & testing of TMM specimens. Misalignment between the centerlines of the specimen & test frame (shown in Figure 1) is varied up to 560 microns. Offset between the horizontal centerlines of the copper platens (shown in Figure 2) is varied up to 125 microns, based on the asymmetry check done on the copper platens. The asymmetry is inspected using an optical microscope and ESEM (Environmental Scanning Electron Microscope) imaging techniques. The taper of the joints (shown in Figure 3) is varied upto 50 microns over the length of the joint. Taper variation is inspected in the ESEM after the solder specimen is aged, ground and polished. Fillets produced at the notch of the solder joint due to overflow of excess solder (shown in Figure 4) are varied by 240 microns. These fillets can create localized stress inhomogeneties in the solder joint during the test, and cause anomalous recrystallization.
RESULTS SUMMARY & DISCUSSIONS
The variation of the extracted values for elastic shear modulus (G), with respect to previously mentioned variabilities, is evaluated. Corresponding variations in the extracted values for plastic Ramberg-Osgood model constants are also evaluated as a function of the mentioned variabilities.
Results show that the parameter that has the strongest effect on the accuracy of the extracted shear stiffness is the lateral misalignment between the specimen and test frame centerlines. The next most influential parameter is solder joint taper. The top two parameters (in descending order of severity) to affect the accuracy of the plastic constants (hardening exponent n, and strength coefficient K) are solder joint taper and fillet size at the notch root. The accuracy of the extracted plastic Ramberg-Osgood constants is therefore found to be more sensitive to the solder geometry variations than the geometric misalignment generated due to faulty positioning of the specimen with respect to the test frame. Rate dependent von Mises strain rate is found to be sensitive to the fillet of the solder joint
In general, the elastic shear stiffness (G) is found to be more sensitive than the plastic Ramberg-Osgood constants (K, n), to the geometric error seeding study here. In rate dependent model study, von Mises strain rate is found to be more sensitive than elastic & rate independent plastic parameters. This is due to the fact that plastic deformations reduce the local stress gradients caused by the various geometric errors. The results obtained from this study can be used to specify tolerance limits for the geometric attributes studied here. Finally, the results of this study can be used to calculate correction factors to improve the accuracy of the extracted material constants, based on the extent of the observed geometric variability in each specimen. These corrections will reduce the scatter usually observed in the measured results.
