Anand Viscoplastic Constitutive Model Research Articles

Prediction of mechanical properties and fatigue life of nanosilver slurry in chip interconnection

This article investigates the failure mode and mechanism of copper pillar solder joints in temperature cycling experiments, focusing on a Cu/nano Ag/Cu solder joint structure. The hot pressing bonding condition at 300 °C with insulation for 10 s is chosen for the experiments. Based on the life test results, the thermal cycling fatigue life of the nanosilver solder joint is determined to be 2050 cycles. To gain further insights, finite element software ANSYS is employed to simulate nanosilver solder joints in flip chips, revealing the stress–strain distribution within the solder joints. The simulation utilizes the Anand viscoplastic constitutive model for the solder joint, providing a reasonable representation of the stress–strain behavior under thermal cycling load. Notably, the simulation highlights that the maximum stress and strain occur in the contact area between the solder joint and the copper column. To enhance accuracy, the calculation equation is refined using relevant experience, resulting in a prediction of the thermal fatigue life of nanosilver solder joints. This prediction aligns closely with the experimental results. The research outcomes not only contribute valuable insights into the behavior of nanosilver solder but also serve as a reference for its application in electronic packaging.

Solder die attach lifetime characterization of SOT-227 power MOSFET module in a 3-phase inverter under power cycling

Abstract This study aims to assess the power cycling lifetime of the solder die attach of the silicon power metal-oxide-semiconductor field-effect transistor modules in an SOT-227 package in a 3-phase bridge inverter. This goal is achieved through a loose one-way coupling framework that incorporates a thermal computational fluid dynamics model for temperature estimation and a transient thermal-mechanical finite element model that accounts for the time-dependent viscoplastic behavior of the solder die attach through the Anand viscoplastic constitutive model for thermal-mechanical responses assessment. To facilitate an accurate prediction of the solder die attach lifetime during power cycling, a physical lifetime prediction model is constructed through the strain-based Coffin-Manson Eq. together with the experimental lifetime data and the corresponding calculated equivalent viscoplastic strain increments. Furthermore, parametric study via the coupling framework is conducted to examine the effect of cooling, operating, and structural parameters on the solder die attach lifetime, and also to identify the most crucial design parameters. At last, experimental design using a Taguchi method is conducted to seek the optimal level combination of design parameters for enhanced power cycling lifetime of the solder die attach.

Characterization of Rate-Dependent Constitutive Behavior of Copper Free-Air Ball and Its Use for Wire Bonding Process Simulation

Copper (Cu) wire bond technology is an increasingly popular alternative to gold (Au) wire bond in microelectronic devices due to its superior electrical performance and low cost. Cu wires are also approximately 25% more thermally conductive than gold wires, resulting in better heat dissipation. At present, validated constitutive models for the strain rate and temperature-dependent behavior of Cu free-air ball (FAB) appear to be largely missing in the literature. The lack of reliable constitutive models for the Cu FAB has hampered the modeling of the wire bonding process and the ability to assess risk of fracture in ultralow-k dielectric stacks. The challenge to FAB characterization is primarily due to the difficulty in performing mechanical tests on spherical FAB of micrometer size. To address this challenge, we describe a custom-built microscale tester and carry out compression tests on the FAB in this paper. The Anand viscoplastic constitutive model is developed for Cu FAB through an inverse modeling procedure. In the inverse procedure, constitutive model parameter values are iterated through an automated optimization procedure, until the load–displacement response matches the experimentally observed response. Using the estimated Anand model parameters, a finite-element analysis of the impact and ulatrasonic vibration stages of wire bonding process is carried out, and the resulting dielectric fracture risk is analyzed.

High strain rate constitutive behavior of SAC105 and SAC305 leadfree solder during operation at high temperature

Industry migration to leadfree solders has resulted in a proliferation of a wide variety of solder alloy compositions. The most popular amongst these are the Sn–Ag–Cu family of alloys like SAC105 and SAC305. Electronics subjected to shock and vibration may experience strain rates of 1–100/s. Electronic product may often be exposed to high temperature during storage, operation and handling in addition to high strain rate transient dynamic loads during drop-impact, shock and vibration. Properties of leadfree solder alloys at high strain rates at low and high temperatures experienced by the solder joint during typical mechanical shock events are scarce. Previous studies have showed the effect of high strain rates and thermal aging on the mechanical properties of leadfree alloys including elastic modulus and the ultimate tensile strength. The ANAND viscoplastic constitutive model has been widely used to describe the inelastic deformation behavior of solders in electronic components. In this study, SAC105 and SAC305 leadfree alloys have been tested at strain rates of 10, 35, 50 and 75/s at various operating temperatures of 50°C, 75°C, 100°C and 125°C. Full-field strain in the specimen have been measured using high speed imaging at frame rates up to 75,000fps in combination with digital image correlation. The cross-head velocity has been measured prior-to, during, and after deformation to ensure the constancy of cross-head velocity. Stress–strain curves have been plotted over a wide range of strain rates and temperatures. Experimental data for the pristine specimen has been fit to the ANAND's viscoplastic model.

Maximum entropy fracture model and its use for predicting cyclic hysteresis in Sn3.8Ag0.7Cu and Sn3.0Ag0.5 solder alloys

Appropriate constitutive, damage accumulation and fracture models are critical to accurate life predictions. In this study, we utilize the maximum entropy fracture model (MEFM) to predict and validate cyclic hysteresis in Sn3.8Ag0.7Cu and Sn3.0Ag0.5 solder alloys through a damage enhanced Anand viscoplasticity model. MEFM is a single-parameter, information theory inspired model that aims to provide the best estimate for accumulated damage at a material point in ductile solids in the absence of detailed microstructural information. Using the developed model, we predict the load drop during cyclic fatigue testing of the two chosen alloys. A custom-built microscale mechanical tester was utilized to carryout isothermal cyclic fatigue tests on specially designed assemblies. The resultant relationship between load drop and accumulated inelastic dissipation was used to extract the geometry and temperature-independent damage accumulation parameter of the maximum entropy fracture model for each alloy. The damage accumulation relationship is input into the Anand viscoplastic constitutive model, allowing prediction of the stress–strain hysteresis and cyclic load drop. The damage accumulation model is validated by comparing predicted and measured load drops after 55 and 85 cycles respectively for Sn3.8Ag0.7Cu and Sn3.0Ag0.5 solder alloys. The predictions agreed to within 10% and 20% of the experimental observations respectively for the two alloys. The damage enhanced Anand model developed in this study will enable the tracking of crack fronts during finite element simulations of fatigue crack initiation and propagation in complex solder joint geometries.

A Comparison of the Creep Behavior of Joint-Scale SAC105 and SAC305 Solder Alloys

In this paper, the creep behavior of Sn98.5Ag1.0 Cu0.5 (SAC105) solder alloy is experimentally characterized and compared with that of Sn96.5Ag3.0Cu0.5 (SAC305). Both solder alloys were characterized at joint-scale ( ~ 180 μm thickness) under conditions of shear. In terms of motivation, SAC105 is more cost effective than SAC305 due to its lower silver content, however, it is known to exhibit inferior reliability under stimuli which induce thermal fatigue. The objective of this paper is to quantify the behavior of SAC105 when subjected to creep loading at different temperatures. To this end, the parameters of an Anand viscoplastic constitutive model are derived for thermally preconditioned SAC105 from a series of creep tests under varying constant shear stresses (5 to 15 MPa), constant shear strain rates [1E-6 (1/s) to 1E-2 (1/s)] and temperatures (20 to 100 °C). The predictions of the Anand model are compared graphically with the experimental data to illustrate goodness-of-fit, and the data is found to be tightly bound to the Anand predictions. An extensive comparison is made of the creep behaviors of the two SAC alloys. The microstructure of both alloys is investigated and found to consist of β-Sn dendrites with precipitates of Ag3Sn and Cu6Sn5 in the interdendritic region. SAC305 is noted to have more Ag3Sn precipitates and smaller tin dendrites than SAC105, which are the primary reasons for its superior creep resistance. From a practical perspective, SAC105 is found to be significantly less creep resistant than SAC305. SAC105 is, however, preferable to SAC305 for applications which may experience high strain rate stimuli (e.g., portable electronic devices) as it undergoes plastic flow at lower stress levels. SAC305 is superior for applications which feature thermomechanical fatigue (e.g., desktop computers and servers) as it accumulates less strain than SAC105. The Anand model parameters presented here could, however, enable practitioners to determine the suitability of the lower cost SAC105 alloy for applications which induce thermal fatigue.

Constitutive Modeling of Joint-Scale SAC305 Solder Shear Samples

In this paper, the creep behavior of lead-free hypo-eutectic Sn96.5Ag3.0Cu0.5 (SAC305) solder alloy is evaluated. A series of creep tests at different stress/temperature and strain rate/temperature pairs are conducted on joint-scale solder samples under shear. Stress-strain data is reported for constant stress (15-30 MPa) and constant shear strain rate (1E-6-1E-2 s-1) tests at temperatures of 20°C, 50 °C, 75°C, and 100°C. The quantitative data gained from the tests is used to fit an Anand viscoplastic constitutive model. The quality of the model fit and the intrinsic variability of the test specimens are also assessed.

Constitutive Models for Intermediate- and High-Strain Rate Flow Behavior of Sn3.8Ag0.7Cu and Sn1.0Ag0.5Cu Solder Alloys

In much of the existing research, SnAgCu solder alloys are characterized at low strain rates, typically in the 10-6 to 1 s-1 range. In this paper, we report experimental results and constitutive models for two popular SnAgCu solder alloys at intermediate and high strain rates, ranging from 10-2 to 103 s-1 at room temperature. These experiments were performed using two different experimental setups: a MTS 810 uniaxial compression tester, and a split-Hopkinson pressure bar. In conjunction with our previous work at lower strain rates (10-6 to 10-3 s-1), these results yield the plastic flow response of these solders over nine decades of strain rate, and demonstrate a remarkably consistent relationship between the yield stress and the strain rate over the entire nine decades. We also develop the Anand viscoplastic constitutive model, and demonstrate that fit parameters for the low-strain rate regime can be extrapolated to accurately predict the experimental response at high strain rates. Thus, the model presented here proffers the capability of modeling solder deformation under a wide range of loading conditions using most commercially available finite element (FE) programs. To illustrate the validity of the model parameters, we develop idealized FE models together with cohesive zone failure descriptions at the interface between the solder and the intermetallic compound. We demonstrate that when used in conjunction with appropriate failure models, the constitutive model developed here accurately captures the empirically observed shift in failure modes from bulk failure to interfacial failure under tensile loading at higher strain rates.

Thermomechanical Reliability Study of Flip Chip Solder Bumps: Using Laser Ultrasound Technique and Finite Element Method

Current techniques for nondestructive quality evaluation of solder bumps in electronic packages are either incapable of detecting solder bump cracks, or unsuitable for in-line inspection due to high cost and low throughput. As an alternative, a solder bump inspection system is being developed at Georgia Institute of Technology using laser ultrasound and interferometric techniques. This system uses a pulsed Nd:YAG laser to induce ultrasound in electronic packages in the thermoelastic regime; it then measures the transient out-of-plane displacement responses on the package surfaces using laser interferometric technique. The quality of solder bumps in electronic packages is evaluated by analyzing the transient responses. This paper presents a systematic study on thermomechanical reliability of flip chip solder bumps using laser ultrasound-interferometric inspection technique and finite element (FE) method. The correlation between the failure parameter extracted from FE simulation for evaluating solder bump reliability and quality degradation characterization of solder bumps through noncontact, nondestructive laser ultrasound testing has also been investigated. Accelerated thermal cycling (ATC) tests were performed in two phases on flip chip package (FCP) test vehicles with 63Sn37Pb solder bumps. In phase I, four boards were thermal cycled up to 70 cycles. Every ten cycles, the boards were taken out of the chamber and FCPs on each board were tested for detecting presence of cracks using resistance and laser ultrasound testing methods. These measurements were repeated every 10 cycles and stopped after 70 cycles. Laser ultrasound testing results show that starting from 10 cycles, testing values began to increase gradually until 50 cycles when there was a sharp jump (through crack verified at 50 cycles with cross section). Cross section was done only after 70 cycles, and the results show that solder bumps at the corners had through cracks, while solder bumps at the center had partial cracks. Phase II study was a refinement of phase I study. In phase II study, seven boards were thermal cycled starting from 27 cycles to 56 cycles at an increment of approximate five cycles. After every five cycles, only one board was pulled out and tested in order to track crack initialization and propagation in solder bumps. Smaller thermal cycle increments were used in phase II to help determine when cracks initiated and propagated. It was shown that laser ultrasound technique could nondestructively track solder bump crack propagation due to thermal fatigue. The Anand's viscoplastic constitutive model was used in FE simulation to describe the inelastic deformation behavior of solder bumps in thermal cycling. A 3-D FE model was implemented using ANSYS on the same FCP as used in the ATC testing. The stress-strain results were extracted from FE modeling and the inelastic strain energy density (SED) increment per cycle calculated from the critical solder bump was used as a failure parameter. In this paper, it was demonstrated that there is a good correlation between the inelastic SED increment extracted from FE simulation and experimental results from nondestructive laser ultrasound testing.

Constitutive and Aging Behavior of Sn3.0Ag0.5Cu Solder Alloy

We describe double-lap shear experiments on Sn3.0Ag0.5Cu solder alloy, from which fits to Anand's viscoplastic constitutive model, power-law creep model, and to time-hardening primary-secondary creep model are derived. Results of monotonic tests for strain rates ranging from 4.02E-6 to 2.40E-3 s-1, and creep response at stress levels ranging from 19.5 to 45.6 MPa are reported. Both types of tests were conducted at temperatures of 25degC, 75degC , and 125degC. Following an earlier study where Anand model and time hardening creep parameters for Sn3.8Ag0.7Cu and Sn1.0Ag0.5Cu solder alloys were reported, here we report power law model parameters so as to enable a comparison between all three alloys. Primary creep in Sn3.0Ag0.5Cu solder alloy is shown to be significant and are considered in addition to secondary creep and monotonic behavior. Aging influence on behavior is also shown to be significant. On the basis of experimental data, the following four aspects are discussed: 1) difference between testing on bulk versus joint specimen; 2) consistency between the creep and monotonic behaviors; 3) comparison against behaviors of Sn1.0Ag0.5Cu and Sn3.8Ag0.7Cu alloys as well as aganist Sn40Pb, 62Sn36Pb2Ag and 96.5Sn3.5Ag alloys; and 4) comparison of Sn3.0Ag0.5Cu and Sn3.8Ag0.7Cu relative to their aging response.