Optimisation of thermo-fatigue reliability of solder joints in surface mount resistor assembly using Taguchi method

Finite Elements in Analysis and Design 107 (2015) 13–27

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Optimisation of thermo-fatigue reliability of solder joints in surface mount resistor assembly using Taguchi method Emeka H. Amalu a,n, N.N. Ekere a, M.T. Zarmai a, G. Takyi b a b

School of Engineering, Faculty of Science and Engineering, University of Wolverhampton, West Midlands WV1 1LY, UK Department of Mechanical Engineering, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana

art ic l e i nf o

a b s t r a c t

Article history: Received 25 April 2015 Received in revised form 29 July 2015 Accepted 19 August 2015

The effect of geometric and ambient parameters on static structural integrity of solder joints in surface mount resistor assembled on printed circuit board (PCB) is investigated to improve the thermo-fatigue reliability of the joints and components. The optimisation of resistor thickness (RT) and components standoff height (CSH) in a range of operating homologous temperature (TH) is poised to produce optimal assembly which could accumulate least strain energy density (ωacc) in resistor joints and consequently possesses longer cycles to failure (Nf). Taguchi design of experiment (DOE), L 9 (33), is used to generate nine designs and finite element modelling (FEM) is employed to simulate the responses of the assemblies to reliability influencing factors (RIFs). The Garofalo–Arrhenius constitutive creep relation is utilised to model high-temperature response of the soldered joints while the concept of signal to noise ratio and statistics are used to determine the optimal design. The results show that settings of lowest RT, highest CSH and TH of 0.86 produce optimal assembly which demonstrates potential of reducing ωacc and increasing Nf of the best design of DOE by 46.9% and 88.3%, respectively. More results show that the nature of finite element model and difference in magnitude of thermal expansion coefficient (CTE) of two bodies bonded together and which experience the same temperature change determine the degree of damage on the interface with the former being more determining.

Keywords: Solder joint reliability Resistor assembly Lead-free solder Component standoff height Homologous temperature Taguchi experimental design Finite element modelling Fatigue damage Accelerated thermal cycling

The authors propose the model DM / N ≡ DN / M =

3

1 ≤ DM / N ≡ DN / M ⟨∞ K1 × K2 { 1 ≤ K1 × K2 ⟨∞

(where: M/N, K1, K2 are isotropic materials, CTE and geometric ratio, respectively) as a quick tool to rank and compare boundary damage in a multi-isotropic-material joining. & 2015 Elsevier B.V. All rights reserved.

1. Introduction Resistors remain the key components of most electronic devices which are increasingly deployed to mission critical electronic systems. Such systems operate in sectors which include automotive, oil well-logging and aerospace. In automobiles, electronics are increasingly deployed in the under-the-hood where they serve as sensors and control devices or Electronic Control Unit (ECU). It is anticipated that increase in electronic content of vehicle in response to increasing demand on improving many automobile systems which include engine performance, transmission, steering, traction and combustion, will lead to more electronics being deployed to high-temperature zones of the automobile. Typical under-bonnet and silencer electronics experience temperature n

Corresponding author. Tel.: þ 44 1902322263. E-mail address: [email protected] (E.H. Amalu).

http://dx.doi.org/10.1016/j.finel.2015.08.004 0168-874X/& 2015 Elsevier B.V. All rights reserved.

cycling outside the “traditional” temperature range from
55/
65 °C to þ125 °C temperatures depending on drive duration, location and climate. Johnson et al. [1] reported that under-thehood electronics and specifically on-engine electronics can experience ambient temperature cycling in the range from
40 to þ150 °C. Electronics used in well-logging experiences identical temperature cycling. Watson and Castro [2] reported that electronic systems and sensors deployed in downhole drilling operations function at temperatures of about 150–175 °C and above 200 °C in deeper well drilling. Characteristic oil well operates at about 150 °C. Parmentier et al. [3] reported that 80% of oil-wells operates below 150 °C with 95% of them functioning under 175 °C ambient temperature. The search for new oil and gas in very deep reserves coupled with subsequent development and completion of highpressure-high-temperature (HPHT) wells has necessitated operations in higher-temperature ambient. Consequently, development

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E.H. Amalu et al. / Finite Elements in Analysis and Design 107 (2015) 13–27

Nomenclature A,B,C RT CSH TH SJs RIFs PCB CEMs FCOB ATC CSP SSFs TM ETs FIP L W G PW BL BT Ex,y,z

νxy,xz,yz

HATC dεcr dt

σ R u (w ) γ M,N α ∆l ∆w ∆t j n Ej Fjmin Nf

reliability influencing factors thickness of resistor component standoff height homologous temperature solder joints reliability influencing factors printed circuit board contract electronics manufacturer flip chip on board accelerated temperature cycle chip scale package static structural factors melting temperature excursion temperatures fatigue indicator parameter resistor length resistor width shortest distance between pads copper pad width PCB length PCB thickness Young's moduli (in x, y and z) Poisson ratios (in xy, xz, yz) highly accelerated temperature cycle creep strain rate von Mises effective stress universal gas constant. displacement in the vertical direction cubic expansitivity component or Material (A, B) coefficient of linear expansion change in length change in width change in thickness RIFs (designated as A, B or C) Number of level in the experiment. effect of factor j minimum value of factor j number of cycle to failure

and production of oil and gas from HPHT wells technically demand that the logging tool electronics be protected from extreme temperature and pressure which would otherwise cause conventional logging tool electronics to fail. Thus, these electronics are protected in sondes and cartridges which increase the device weight and pose a challenge to electronics manufacturing miniaturisation trend. Similar to the automotive engines, aero engines experience high volume of electronics deployment in recent years. Mechanical and hydraulic actuators in aero engine are increasingly being replaced with electronic actuators. Designing and manufacturing electronics which will operate reliably in harsh ambient demands that the design engineer has in-depth understanding of the complex relationship and interactions among electronics materials, structural integrity of electronics assembly and operating ambient temperature to ensure that system properties and functions are preserved over long operating periods. Continued reliable performance of surface mount electronic components is challenged by the miniaturisation trend in electronics manufacturing. Surface mount resistors of smaller size are being manufactured and assembled on substrates using varied

Li ECU HPHT S/N FC R103 SMCs WEEE OEMs FEA FEM IMCT TA r yi ωacc TL TT PL PT BW PWB ax,y,z Gxy,xz,yz C1, 2, 4, 4 ΔT Q T V ∆V D l w t K1 j¯i BGA Fjmax MTTF K2

factor level electronic control units high-pressure-high-temperature signal to noise ratio flip chip resistor component model 103 surface mount components waste from electrical and electronic equipment original equipment manufacturers finite element analysis finite element modelling thickness of intermetallic compound ambient temperature number of measurement value of the ith measured response accumulated strain energy density termination length termination thickness copper pad length copper pad thickness PCB width printed wire board coefficient of thermal expansions (in x, y and z) shear moduli (in xy,xz,yz) Garofalo creep parameters change in temperature activation energy absolute temperature volume of material change in volume damage on a material length width thickness CTE ratio of two materials mean of S/N ratio ball grid array maximum value of factor j mean-time-to-failure geometric ratio of two materials

component standoff height (CSH). The CSH is the height between the base of the resistor and the top of the substrate printed circuit board (PCB). It is basically the height of the solder joints in electronic assembly. With suitable CSH and right thickness of resistor, a good solder joint integrity could be achieved in a resistor assembly. Such assembly has potential to operate satisfactorily in a high-temperature and harsh ambient. In addition to miniaturisation trend, harsh operating conditions and specifically high-temperature operations has adverse effect on the reliability of solder joints in electronic devices. In earlier investigation [4] the effect of elevated temperature operations on thermo-mechanical reliability of flip chip (FC) assemblies was studied and the impact on the integrity of FC solder joints was reported. Since the integrity of solder joints in electronic assemblies depends hugely on the geometry of the joints, evaluating the integrity of solder joints in resistor R102 will provide information which could be used to improve its thermo-fatigue reliability. There are significant amount of published studies on improvement of integrity of solder joints in surface mount components (SMCs) but most of them have focused on joints made of lead based solder alloys. With lead-free solders rapidly replacing the

Resistor (Alumina)

Termination

E.H. Amalu et al. / Finite Elements in Analysis and Design 107 (2015) 13–27

15

Solder joint

Copper pad Substrate PCB Fig. 1. Resistor assembly showing solder joints and interconnect technology: (a) 3D geometry (b) Front elevation (c) Components of one end of the assembly.

former, and being deployed to operate in high-temperature and harsh environment, the need to conduct research which will provide vital information on improving the thermo-mechanical reliability of SMC assembled with lead-free solder on a substrate is needed. Current studies on lead-free solder joints and their mechanical properties include Refs. [5,6]. Liu et al. [5] investigated and compared the shear response of solder joints formed with different compositions of lead-free alloys. Their findings demonstrate that addition of Bi–Ni to SAC alloy results in higher shear strength at both the bulk solder and soldered interface in the joints. They found that increasing the Bi content significantly increased the shear strength of the joints. In their study, Yang et al. [6] among other things investigated the effect of aluminium concentration on the mechanical properties of Sn–0.7Cu lead-free solder alloy. Their findings show that increase in aluminium content increases the tensile strength and creep resistance of Sn–0.7Cu alloys. The present study is similar to the other two because it seeks to demonstrate techniques of achieving a higher lead-free solder joint strength with minimum damage during device operations. Fig. 1 shows a model of a R102 resistor assembled on a PCB using lead-free solder to form the joints. Fig. 1(a) and (b) are the 3D models while Fig. 1(c) depicts the front view of one end of the soldered joints showing the five components in the assembly. The increase in adoption and use of lead-free solder alloys in electronics assembly is in response to health concerns which led to the introduction of the European Union's Waste from Electrical and Electronic Equipment (WEEE) directive in July 2006. One challenge in continued use of lead-free solder material to form solder joints in electronics is that unlike the lead based, its mechanical properties have not been fully characterised. Some published properties of lead-free solder alloys in many studies have demonstrated marked differences which have made it difficult to compare the reliability of lead-free solder with that of lead based solder that is widely reported. Siviour et al. [7] reported that Sn–Pb solder showed a strong dependence on strain rate and temperature, whereas lead-free solders showed only a weak dependence on these parameters. On the contrary, Stam and Davitt [8] reported that reflowed lead-free solder joints did not show a better integrity than near eutectic lead-based ones even

Operating temperature (TH)

Reliability influencing factors (RIFs)

Component Reliability Thickness of resitor chip standoff (RT) height (CSH)

Fig. 2. Interaction field for key reliability influencing factors (RIFs).

though the former showed better bulk mechanical properties. In addition, they stated that although microstructural differences can be seen between them, similar failure mechanisms were observed in the joints. Consequently, the adoption and use of lead-free solders in electronics manufacturing has led to new device reliability concerns and an urgent need for a better understanding of the thermo-fatigue reliability of interconnects used in safety critical applications before the impending deadline for WEEE compliance. Both the Contract Electronics Manufacturers (CEMs) and Original Equipment Manufacturers (OEMs) are interested in information on how reliability influencing factors (RIFs) could be controlled to improve the life of interconnects in resistors made with the new lead-free materials. The interaction field for the factors considered in this investigation is represented diagrammatically in Fig. 2. The representation presents the reliability of interconnection to be central when the effects of geometric and operating ambient parameters are considered. These parameters are called RIFs in this study. Research has been on-going in this area of improving the thermo-fatigue and thermo-mechanical reliability of solder joints in SMCs assembly. Goh [9] investigated numerically the effects of critical design parameters such as die size, joint height, joint diameter, joint pitch, PCB thickness and material properties of

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E.H. Amalu et al. / Finite Elements in Analysis and Design 107 (2015) 13–27

underfill on the solder joint reliability of (flip chip on board) FCOB. He concludes that parametric (finite element analysis) FEA technique is a very cost effective tool in evaluating the solder joint reliability of FCOB assemblies and also that a useful set of assembly design guidelines can be generated from the result of his study. Recently, Ma et al. [10] investigated accelerated thermal cycling performance of solder joints in lead-free devices at a series of wide temperature ranges. Their results show that the fatigue life of lead-free packages consistently degrades with increasing accelerated temperature cycle (ATC) range. They concluded that failure mode at high-temperature is a mixture of solder joint crack and pad cratering. It was added that failure at low temperature is mainly driven by only pure solder joints fatigue failures. Ye et al. [11] demonstrated how combination of FEM and Taguchi method can be utilised to produce an optimal design capable of reducing the creep strain energy density of chip scale package (CSP) by 78.4% compared with the original design parameters. In a recent study, Wan et al. [12] reported how a mixed robust method based on three-level and experiment design (the quadric surface) and finite element analysis were used to optimise thermal fatigue reliability of FBGA package. They reported that their optimised model achieved equivalent thermal fatigue strain reduction of 48.77% when compared with the original model. The geometric parameters considered in this investigation are CSH and RT while homologous temperature (TH) is the environmental factor. The optimisation of these factors towards improving the quality of electronic assembly is poised to provide useful technical information. Technically, depending on variables which include area of bond pad on PCB and reflow profile peak temperature, the CSH of R102 is likely to vary after assembly. This study is significant because its focus is to study the thermo-fatigue reliability of solder joints in miniaturised resistor assembly and provide information on how CSH could be used to improve the thermo-fatigue life of such joint for application in mission critical systems operating in elevated temperatures. The study is vital considering the fact that at high homologous temperature of operation, the sensitivity of thermo-mechanical properties of solder alloy material to creep deformation increases and impacts the systems long time performance. It is believed that the interactions between geometric factors and the ambient temperature affect the reliability of solder joints. The assembly of a reliable system with improved service life requires better understanding of the complex interactions between assembly's parameters and operating environmental conditions. The aim of this investigation is to predict the optimal combination of the magnitude of RT, CSH, and TH which will yield high integrity assembly of R102 on PCB. It is hoped that this result will be useful to R&D engineers involved in electronics design, assembly and packaging.

interconnection can be improved through optimisation of the static structural factors. Ridout and Bailey [13] have reported that solder joints are often the cause of failure in electronic devices. The integrity of interconnection in turn depends on many static structural factors (SSFs). In earlier studies [4,13], it was identified that CSH and thickness of intermetallic compound (IMCT) in the interconnection are two key RIFs for solder bump joints in FC assembly. In this study, we extend this line of investigation to resistors assembly and identify CSH, RT and TH as the key RIFs. In the study [14], techniques and factors which produce different magnitude of CSH in assemblies of identical FC component are presented. These techniques and factors are not different in the case of resistor assembly. The magnitudes of the area of pad on PCB and reflow profile temperature are the factors which cause variation of CSH in any electronic component assembly. In this study, three set of values of RT (438 μm, 508 μm and 550 μm) are selected while 60 μm, 80 μm and 100 μm are chosen for CSH. The assembly is modelled using three values of TH of 0.81, 0.86 and 0.91. These magnitudes of RT and CSH are within the range employed by Refs. [15,16]. To extend the findings of this study to other solder and interconnect materials used in electronic assembly, the TH of the lead-free solder material is used instead of degrees centigrade temperature. It is generally known that different materials have comparable properties at the same TH. In addition, TH is a more generic index in application because it expresses the temperature of a material as a quotient of the operating ambient and melting temperature using the Kelvin scale. The TH can be expressed mathematically as in Eq. (1).

TH =

TA + 273 TM + 273

(1)

Where parameters TH , TA and TM are the homologous, ambient and melting temperatures, respectively. The SnAgCu solder alloy used in this study melts at 221 degrees centigrade temperature. Excursion temperatures (ETs) of 125 °C, 150 °C and 175 °C are selected for this investigation. These temperatures are obtainable in commercial, automotive and oil-well logging operations. Tsai et al. [17] have reported that the effect of temperature range is the most significant parameter which influences equivalent total strain range under temperature cyclic loadings. At this set of temperatures (125 °C, 150 °C and 175 °C), SnAgCu solder joints are functioning at THs of approximately 0.81, 0.86 and 0.91, respectively. These temperatures are within the creep region of solder alloy materials; and their physical behaviour becomes very sensitive to strain rate, temperature, strain hardening and softening. Table 1 presents a summary of the RIFs (designated as A, B and C) and their levels (designated as 1, 2 and 3). 2.2. Design of experiment (DoE) using the Taguchi approach

2. Research design The research paradigm and design employed in this investigation are presented in the following three sub-headings. The subSection 2.1 presents discussions on design considerations while sub-Section 2.2 details the method utilised in designing the experiments. The discussions in this section end with sub-Section 2.3 where the technique of signal-to-noise (S/N) ratio employed in the analysis of results is outlined. 2.1. Design considerations The optimal performance of electronic assemblies depends to a huge extent on the integrity of the interconnections between package and substrate; and also the interaction of the assembly materials with the operating environment. The integrity of

The importance of experimental design as a tool for engineers and scientists for use in product design and development as well as process development and improvement cannot be overstressed. Numerous researchers including [11,18–20] have successfully Table 1 Control factors and their levels. Reliability influencing factors (RIFs)

Thickness of resistor (RT) Component standoff height (CSH) Homologous temperature (TH)

Unit

Designation Level (Li), (i ¼1,2,3) 1

2

3

(μm) A (μm) B

438 60

508 80

550 100

C

0.81

0.86

0.91

E.H. Amalu et al. / Finite Elements in Analysis and Design 107 (2015) 13–27

Design point number

Accumulated creep strain energy density ωacc(J/m3)

Table 2 Taguchi experimental design: orthogonal array L9(33). Reliability influencing factors (RIFs)

1 2 3 4 5 6 7 8 9

A

B

C

1(438) 1(438) 1(438) 2(508) 2(508) 2(508) 3(550) 3(550) 3(550)

1(60) 2(80) 3(100) 1(60) 2(80) 3(100) 1(60) 2(80) 3(100)

1(0.81) 2(0.86) 3(0.91) 2(0.86) 3(0.91) 1(0.81) 3(0.91) 1(0.81) 2(0.86)

17

40 35 30 25 20 15 10 5 0 0

1

2

3

4

5

Number of temperature cycle

Fig. 3. Plot of strain energy density as a function of thermal load cycle for the nine models.

computed using the relation n

wacc = employed a number of designs which include the methods of factorial, fractional factorial and Taguchi in their experiments. The author, Montgomery [21], believes that the use of experimental designs early in the product cycle can substantially reduce development lead time and cost while leading to processes and products that perform better in the field and have higher reliability than those developed using other approaches. Thus, experimental design is employed to develop nine designs. A factorial experiment based on Taguchi design is employed in this investigation. The L9(33) orthogonal array is considered to determine which of the RIFs and levels have the highest main effect on damage of resistor solder joints. In addition, the design seeks to determine the existence of interactions among the variables as well as the contribution of the interactions to damage of the joints and other interconnection boundaries. The focus of the array is to identify the best design in the DoE that will be robust to RIFs. The Taguchi design is presented in Table 2. 2.3. Signal-to-noise ratio (S/N) The notion of signal-to-noise ratio (S/N) is an analysis tool which is useful in analysing results of numerical modelling. It is employed in this study to calculate the average effects of the RIFs. This technique couple with statistics is used to determine optimal settings of factors from the DoE design for an optimal design. The S/N can be expressed mathematically as

⎛ S = − 10 log10 ⎜⎜ N ⎝

r ∑i = 1 yi2 ⎞ ⎟

r

⎟ ⎠

∑ Δw c=s

(4)

Where c is the cycle, s is the cycle at first stabilisation of the hysteresis loop and on set of steady state secondary creep while n is the last cycle before the onset of tertiary creep. Fig. 3 shows plots of ωacc against thermal load time for the nine models representing the nine designs. In general, the figure shows that the ωacc of model 1 is the largest while that of model 9 is the lowest. It also shows that the ωacc increases as the loading progresses except for models 2, 3, 5, and 9. These models are probably within their secondary creep region with the temperature test range. It can be seen in the figure that plots M1, M6 and M8 follow the well-known creep model while the rest model seem to only show the primary and secondary creep region. It is pointed that only the secondary steady-state creep region that is used to compute the ωacc . The results of this computation are presented in Table 6 and Fig. 7. The crossing of some of the plots with the other is an indication that the factors interact and the parameters can be optimised. To adopt and use Eq. (2) in this investigation and considering that the interest is to minimise the damage in the solder joints, the concept of the smaller the better S/N ratio is implemented where the variable yi is the ωacc . Numerical analysis is not known to produce variations in measured data, thus the quantity r is assigned a unity value. The Eq. (2) may therefore be reduced to Eq. (5)

S 2 = − 10 log10ωacc N

(5)

(2)

where r is the number of measurement, yi is the value of the i th

3. Finite element modelling (FEM)

∑ri = 1 yi2

is the mean-squared deviation measured response and r (MSD). The multiplier 10 is a scale factor which has no effect on the conclusions deduced from the usage of this expression and technique. The response of the assembly to the effect of variation of the RIFs is the degree of damage of the solder joints and other component of the assembly. One parameter used to measure the damage in solder joint is the strain energy density designated as ω . The accumulation of change in ω per unit volume of the solder in the joints, per cycle of temperature loading, is known as accumulated creep strain energy density. It is designated as ωacc and could be measured in J/m3. Consequently, the creep energy dissipation per unit volume accumulated over one thermal cycle, Δω, could be expressed mathematically as: n

Δw =

∑i = 1 Δwi Δvi n

∑i = 1 Δvi

(3)

Where Δwi is the creep energy accumulated in a cycle in element i and Δvi is the volume of the element. Similarly, the ωacc can be

Finite element modelling (FEM) has been widely employed to study thermo-mechanical reliability of solder joints in SMCs which are subjected to ATCs. With reference to the objectives of this investigation, FEM method is an adequate tool and thus is applied. This section is presented in three sub-headings. These divisions are: model and methodology; materials and their properties; and applied loads and boundary conditions. 3.1. Model and methodology Nine three-dimensional Finite Element (FE) models representing the design points of the resistor assemblies are created using SolidWorks software. The parameters of the assembly and their values are presented in Table 3 and shown schematically in Fig. 4. The figure presents the assembly plan with dimensions in Fig. 4(a). In Fig. 4(b), the front of one end of the solder joint is depicted which shows in details six interface boundaries as well as the CSH and the RT. Fig. 4(c) is the whole assembly showing adequate mesh

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E.H. Amalu et al. / Finite Elements in Analysis and Design 107 (2015) 13–27

Table 3 Dimensions of the parameters used in resistor assembly. Parameter

Dimension

Resistor thickness, RT Resistor length, L Resistor width, W Termination length TL Termination thickness, TT Component standoff height, CSH Shortest distance between pads, G Copper pad length, PL Copper pad width, PW Copper pad thickness PT PCB length, BL PCB width, BW PCB thickness, BT

0.55 mm 6.21 mm 3.11 mm 0.56 mm 25.0 μm 80. 0 μm 4.45 mm 1.68 mm 3.15 mm 35.0 μm 16.0 mm 8.0 mm 1.6 mm

based on creep are used to model the behaviour of materials over a relatively long period at low strain. Consequently, many researchers have adopted creep models to capture the ratedependent plasticity of solder alloys in joints. Unfortunately, this condition of low strain over a long period cannot be simulated precisely in the control laboratory because of its high demand on time and cost. The ATC or highly accelerated temperature cycle (HATC) are used as an alternative. The flow equation of creep strain rate is given as ⎛

⎛

3.2. Materials and their properties The key materials used in mounting the resistor die on PCB are: alumina die, silver termination, copper pad, SnAgCu alloy solder, metallization layer and PCB. One essential derivative of the reactions among copper pad, metallization materials and the SnAgCu alloy solder is the intermetallic compound (IMC). However, this compound is not considered in this investigation because the effect is assumed to be relatively the same in the models and thus would not influence the findings. Moreover, the authors have extensively investigated its contribution to static structural integrity of solder joints in FC assembly in Refs. [4,22]. Table 4 presents the properties of these materials. All the materials were modelled as linear elastic and isotropic substances except the solder and PCB which are simulated using Garofalo creep models and orthotropic materials, respectively. The Garofalo creep model was employed to simulate the thermo-mechanical response of solder bump to the applied ATCs. A good number of studies which include [11,28,29] have utilised the same model in their research which are related to this study. At field service conditions, the duration of thermal cycle of solder joints is in the order of minutes and days. The TH of solder alloys in interconnects is within the creep region. Thus solder joints formed using SnAgCu alloy solder are presumed to deform primarily due to creep under this condition. Generally, constitutive relations

⎞

−C 4 ⎜ ⎟ dεcr C = C1 ⎡⎣ sin h ( C2 σ ) ⎤⎦ 3 exp⎝ T ⎠ dt

Where used in its modelling. The whole assembly is used in the modelling because it gives a better result though it takes longer time to simulate. The FE models were input into V.14.5 ANSYS' FEM software, where their static structural responses to cyclic induced thermal loads are simulated. In setting up the models for simulation, adequate meshes of different sizes are used for the components. This process involves the use of body sizing method that enables the usage of different mesh size for each component of the assembly. The element type selected by the software is SOLID186. In specific terms, the sizes of the elements of the key components: resistor die, solder joint, copper pad, terminator are 3.0  E
4, 7.5  E
5, 1.7  E
4, 1.7  E
4, respectively. These are the smallest elements that can be used for the various components in each of the nine models and achieve complete simulation run. The smallest possible element sizes are selected because the authors are aware of the effect of mesh size on simulation result. As there is no possible smaller mesh size for complete simulation run, the mesh sensitivity check did not arise in this investigation. Basically, the number of total nodes, contact elements, spring elements, solid elements and total elements in the FE model are 48717, 35952, 0, 8248 and 44200, respectively.

⎞

−Q ⎟ ⎜ dεcr C = C1 ⎡⎣ sin h ( C2 σ ) ⎤⎦ 3 exp⎝ RT ⎠ dt

dεcr , dt

(6)

σ , Q, R and T are the scalar creep strain rate, von Mises

effective stress, activation energy, universal gas constant, absolute temperature, respectively. The other symbols represent material dependent parameters. The values of the parameters C1, C2, C3 and C4 are presented in Table 5. 3.3. Load and boundary condition The nine models created using the design points are subjected to their various six complete ATCs corresponding to their TH in 25 load steps. In the study Amalu and Ekere [30], the sufficiency of at least six complete ATCs in thermal cycling reliability of lead-free solder joints is reported. The plot of temperature profiles as a function of temperature time steps for the three profiles used in this investigation is presented in Fig. 5. The temperature loading started from TH of 0.597 for the 3 ATCs, ramped up at the rate of 15 °C/min to the various ETs corresponding to the maxima THs of 0.81, 0.86 and 0.91. The assembly dwelled for 10 min in these ETs to ensure thermal equilibrium resulting in uniform temperature distribution. They were then ramped down to TH of 0.476 (corresponding to lower dwell region) at the same rate, where they also rested for 10 min. This magnitude of ramp rate is used because Aoki et al. [31] reported that the internationally accepted ramp rate of 10–15 °C per minute is required by test standard IEC60749-25 temperature cycling (JESD22-A104-B), established for evaluating the reliability of semiconductor parts and assembly printed wire boards (PWBs). It is stated that this ramp rate is widely used in the United States and Europe and in their follow up study, Aoki et al. [32] reported that they have tested ramp rates from market environment conditions at 15 °C/min (IEC standard 60749-25). It can be easily seen in Fig. 5 that the ramp rate (slope) of the ATCs are parallel to one another. A constant ramp rate has been used because different ramp rates produce different mean-time-to-failures. In the same study, Aoki et al. [32] reported that their investigation confirms that the higher the ramp rate, the shorter the failure cycle. The assembly (Fig. 4(c)) was simply supported such that the condition of the structure at the support is

at the PCB base, w = 0 and u(w) = 0.

(7)

The u(w ) , represents the displacement in the w vertical direction. A few assumptions were made to aid the simplification of the structure for analysis. These assumptions are: the assembly was at stress free state at room temperature of 22 °C which was also the starting temperature of the thermal cycle loading, the assembly is at homogeneous temperature at load steps, initial stresses which may have accumulated from reflow soldering process in the package are neglected and all contacting surfaces are assumed to be bonded with perfect adhesion.

E.H. Amalu et al. / Finite Elements in Analysis and Design 107 (2015) 13–27

19

BL

TT

PW

W

BW

L

TL

RT

*I PT

IV *

V

*

III

*

CSH

VI*

II

* BT

PL

Fig. 4. Resistor assembly showing: (a) the plan with dimensions (b) the front of one end of the solder joint with dimensions (c) the whole assembly with adequate mesh.

Table 4 Mechanical properties of materials in resistor assembly. S/No

Component

Young's modulus (GPa) Ex

1 2 3 4 5

Resistor die (Alumina) [23] Silver (Termination) [24] Copper pad [25] Sn3.9Ag0.6Cu solder [26] PCB [27]

282.7 83 129.0 43.0 27.0

Ey

27.0

C.T.E (ppm/°C) Ez

αx

22.0

6.0 18.9 17.0 23.2 14.0

αy

14.0

Poisson ratio αz

νxy

15.0

0.2222 0.37 0.34 0.30 0.17

νxz

0.2

Shear modulus (GPa) νyz

Gxy

Gxz

Gyz

0.17

115.67 30.29 48.1 16.5 27.0

22.0

27.0

20

E.H. Amalu et al. / Finite Elements in Analysis and Design 107 (2015) 13–27

4. Results and discussion

Table 5 Garofalo creep parameter value for SnAgCu solder [28,29]. C1 (1/s)

C2 (MPa)
1

C3

C4 (K)

Value

277984

0.02447

6.41

6500

Homologous temperature, (TH)

Parameter

0.95 0.85

ATC 1 ATC 2

0.75

ATC 3

0.65

The analysis of results and the discussion on the findings are done through numerous studies and evaluations. These are outlined in six parts and they include the quantification of damage on the components using the FIPs, analysis of damage magnitudes occurring in models 2 and 5 and their relationship, derivation of model to quantify and rank damage at interconnection of two isotropic materials bonded together, evaluation of main effect of the RIFs and their interactions, optimisation of the magnitude of RIFs and the comparison of the optimal design with the best design of the DoE. 4.1. Characterisation and quantification of damage on the components in the assembly

0.55 0.45 0

2000

4000

6000

8000

10000

12000

14000

16000

18000

Time step (Seconds)

Fig. 5. Plots of three temperature profiles of thermal load test conditions used in the design points.

The ωacc is used as an index to quantify the damage of the soldered joints in this investigation. The distribution of damage caused by RIFs such as the creep stain and stress are considered and presented in Fig. 6 for the components in one model. Fig. 6 (a) shows the magnitude and nature of distribution of damage in

Fig. 6. Magnitude and nature of damage in components of the resistor assembly showing: (a) Equivalent creep strain in solder joint. (b) Equivalent stress in solder joint. (c) Creep strain energy distribution in solder joint. (d) Equivalent stress in resistor die. (e) Equivalent stress in terminator. (f) Equivalent stress in copper pad.

E.H. Amalu et al. / Finite Elements in Analysis and Design 107 (2015) 13–27

4.2. Analysis of damage magnitude occurring in models 2 and 5 and their relationship The analysis of damage magnitude occurring in models 2 and 5 and the derivation of their relationship is carried out in this section. A schematic representation of the resistor assembly in normal ambient temperature is presented in Fig. 8. At elevated temperature, the PCB expands more that the resistor die. A resultant moment, Mz, is induced in the assembly which causes a curvature of magnitude ρ in the die. The curvature induces a resultant axial load on the solder joint which results in the stress (sy) causing the damage (ω). These parameters are shown in the figure. Mathematically, the curvature, strain (ε), stress along the x-axis and moment can be express as Accumulated creep strain energy density ωacc (J/m 3)

the soldered joint cause by creep strain. It can be seen that the damage concentrates at the edges of the sides of the base of the soldered joint. These are the areas of crack initiation which will propagate to the centre to cause device failure. These areas correspond to the areas of maximum stress in the resistor die and copper pad as seen in Fig. 6(d) and (f). The damage distribution caused by stress is different. The solder joint experiences maximum stress at the tip, base area of 90 degrees bend and the area in contact with the ends of the resistor thickness. These areas are shown with three black ellipses in Fig. 6(b). These areas are critical to crack initiation and need to be reinforced for increased assembly fatigue reliability. The observation in Fig. 6(b) is supported by Fig. 6(c) which shows maximum strain energy density in areas around the 90 degrees bend. In Fig. 6(d), maximum stresses are observed at the tips on the base of the die. Maximum stresses would have developed at these areas because the die was constrained from free thermal expansion and these highly stressed points form the support during its convex deflection in response to the constrained expansion. The use of materials with very low coefficient of thermal expansion to manufacture resistor chip would result in minimum expansion and thus minimal damage. As a consequence of this constrained expansion by the termination, the 90 degrees bend on the base of the U-channel termination are seen to be critical. Fig. 6(e) shows that the edge tips of this bend are more critical. These spots need to be strengthened to improve the thermo-mechanical reliability of the assembly. The pads shown in Fig. 6(f) depict two critical spots each, which coincide with the two critical edges in the U-channel terminations. They are potentially the areas of crack initiation and thus need to be reinforced. Since the solder joint is considered the most critical to failure, its ωacc is further investigated. The FIP accumulates in solder joints when components in the assembly are constrained from thermal expansion induced by applied temperature load. The constraint sets up boundary stresses at the interface of materials which have been widely reported to cause crack initiation. The values of ωacc at the various design points are taken from output of computer simulation and presented in Table 6 and Fig. 7. It can be seen in the table and figure that model 2 and model 5 have the least and highest value of damage, respectively. An analysis of a simplified free body diagram (FBD) of the simplified assembly architecture is carried out in Section 4.2 to provide an insight and explanation to this observation. The Eq. (5) was employed to convert the values of ωacc to S/N ratio. Table 7 shows the design points, their corresponding response and S/N ratio on the L 9 (33) Taguchi orthogonal array design.

21

Accumulated creep strain energy denity ωacc (J/m^3)

7.0 6.0 5.0 4.0 3.0 2.0 1.0 0.0 1

2

3

4

5

6

7

8

9

Model number Fig. 7. Accumulated creep strain energy density ( ωacc ) for the various design points (J/m3).

Table 7 Main experiment. Design point number

Factor and level

1 2 3 4 5 6 7 8 9 Average

A RT

B CSH

C TH

1 1 1 2 2 2 3 3 3

1 2 3 1 2 3 1 2 3

1 2 3 2 3 1 3 1 2

Quality/response ωacc (J/m3) S/N


13.75 47.63 11.58 7.07
17.92
16.08 1.25
17.37 30.57 3.66

4.868 0.004 0.264 0.443 7.870 6.370 0.866 7.390 0.030

Table 6 Magnitude of accumulated creep strain energy density ωacc for the design points J/m3). Homologous temperature [TH] (C)

Resistor thickness [RT] (A) 438

508

550

Component standoff height [CSH] (B) 60 0.81 0.86 0.91

80

100

60

80

4.868

100

60

6.370 0.004

100

7.390

0.443 0.264

80

0.030 7.870

0.866

22

E.H. Amalu et al. / Finite Elements in Analysis and Design 107 (2015) 13–27

y W Resistor die Z

a

b

d

c

X

Solder joint PCB

R1 X

Mz X

c

/

Fig. 8. Schematic and simplified free body diagram showing the moment and damage (ω/sy) in a resistor assembly.

Curvature, ρ =

Strain, ε = −

1 R1

(8)

C = − Cρ R1

(9)

Mz C I

(10)

Stress, σx = Eε =

Combining Eqs. (8)–(10), obtain

Curvature, ρ =

Mz 12Mz = EI EwRT3

(11)

Where I is the moment of inertia and E is the young modulus of elasticity of the die, respectively. The authors argue that the magnitude of Mz for the same value of CSH and ρ is directly proportional to the axial load which induces the stress (sy) and damage (ω) in the solder joints. Applying Eq. (11) the responses of model 2 and 5 (which have equal CSH) to the cyclic fatigue loading can be explained. The numerals 2 and 5 are used to designate the models 2 and 5 respectively. If it is assumed that the same condition of thermal load produces the same curvature, ρ, in the resistor die, then the magnitude of the moment inducing the damage can be obtained. Thus, Eq. (11) can be reduced to Eq. (12)

ρ=

Mz 2 RT3 2

=

Mz 5 RT3 5

⎛ R ⎞3 Mz5 = ⎜ T 5 ⎟ Mz2 ⎝ RT 2 ⎠

(12)

(13)

Eq. (13) establises the relationship between the moments in the two models. Since RT 5 > RT 2, then Mz5 > Mz2. Thus, damage in model 5 should be greater than the damage in model 2. A similar geometric analysis on FC warpage was carried out in a similar research by Tsai et al. [33]. The researchers employed a modified Suhir solution to evaluate the deformation/warpage of FC PBGA package subjected to thermal loading by modelling it as a spherically bent plate. They found and reported significant bending strain in the package.

4.3. Derivation of model to quantify and rank damage at interconnection of two isotropic materials bonded together The effects of FE model architecture/geometry of model and coefficient of thermal expansion (CTE) on the damage of the interconnection boundaries are evaluated to determine their contributions. The integrity of multi-material joints has been a current national and international concern because the technology for advanced joining and assembly process of multi-materials holds a key to multi-material design of components and structures. Such technology and design will provide opportunity to develop products that are able to operate under more exigent requests demanded by market and society. These include increased strength-to-weight ratio, multi-functionality, high aggressive environments and low carbon footprint. Thus, an attempt is made to evaluate the effect of geometry and CTE on a multi-material joining. The study intends to develop a mathematical model which can be helpful in ranking damage in multimaterial joining. A material body which has volume, V, and experiences temperature change, ΔT, has its co-efficient of cubic expansion, γ , express as

γ=

∆V V ∆T

(14)

where ∆V is the change in volume of the body. For a rectangular body and considering contacting interface surface, Eq. (14) maybe written as

3α=

∆l×∆w×∆t l × w × t ×∆T

(15)

where α , l , ∆l , w , ∆w , t and ∆t are the coefficient of linear expansion, length, change in length, width, change in width, thickness and change in thickness of the body, respectively. The thickness vector is orthogonal to the contacting interface surface area. At the boundary between two bonded bodies of dissimilar materials M and N, the area of contact is the same and thus equal. Since the bonded bodies experience the same change in temperature, Eq. (15) may be expressed as:

E.H. Amalu et al. / Finite Elements in Analysis and Design 107 (2015) 13–27

At the boundaries, 3 (l × w × ∆T ) =

∆l × ∆w × ∆t α×t

∀ bonded constituents

(16)

For two bonded constituents M and N, the contact area and change in temperature is the same. Thus, Eq. (16) reduces to

∆l×∆w×∆t ∝×t

= M

∆l×∆w×∆t ∝×t

23

component which has the minimum and maximum values. The result is presented in Table 8. The table shows that PCB developed minimum values of the FIPs. The stress and elastic strain on the Termination are maxima while solder observed the highest deformation. PCB is also seen to develop the maximum elastic energy.

N

4.4. Evaluation of main effect and interaction

⎛ ∆l ⎞2 ⎛ ∝ ⎞ ⎛ t ⎞ ⎛ ∆l ⎞ Thus, ⎜ M ⎟ = ⎜ M ⎟ ⎜ M ⎟ ⎜ N ⎟ ⎝ ∝N ⎠ ⎝ tN ⎠ ⎝ ∆lM ⎠ ⎝ ∆lN ⎠

(17)

All materials except PCB are assumed to be isotropic and PCB is orthotropic. For simplicity, the PCB is assumed to be isotropic and the mean of its CTEs in three directions are computed and utilised. For isotropic materials, it can be written that:

The contributions of the RIFs (RT, CSH and TH) to damage of solder joints and other components in the resistor assembly are evaluated by determining their average effect on the response in terms of S/N ratio. The Minitab14 statistical software is engaged to analyse the data presented in Table 7 to obtain the main effect and interactions of the factors. The results of this analysis are

(18)

∆l=∆w =∆t

3

t

∝

( ∝M )( tM ) N

N

⎧ 1 ≤ DM / N ≡ DN / M 〈∞ K1 × K2 ⎨ ⎩ 1 ≤ K1 × K2 〈∞

(19)

Eq. (19) is the mathematical model where DM/N is a measure of the damage at the boundaries between the two bodies M and N which are bonded together and experience the same temperature change. The numerical value of DM/N is least at “1” and the degree of damage is measured by the deviation from “1”. The higher the damage, the greater is the deviation. The value “1” is given by the condition when the same material with equal thickness are bonded together and subjected to the thermal loading. Thus K1 and K2 are equal and has value of 1. For other conditions, K1  K2 ∝ Z1. The K1 and K2 are ∝M and tM , respectively. The K1 represents tN

N

the CTE ratio while the K2 represents the geometric ratio of the two bodies. The quantity ∆ lM is proposed as an index to compare ∆ lN

and rank damage in the boundary of two bodies bonded together. This relation is a quick tool to rank boundaries in an assembly to determine the most critical. The rank of damage assesses the degradation of interface boundaries and presents a base for comparison. The higher the rank, the more susceptible is the boundary to damage. Interface with highest rank and thus experiences highest boundary stress/warpage arising from highest magnitude of differential plane surface area expansion will observe highest strain energy which will initiate crack and subsequently fatigue failure. The Eq. (19) is employed to evaluate the damage in the six interconnects (I to VI) shown in Fig. 4(b). The result of this evaluation is presented in Fig. 9. The figure shows that the boundaries between die end and termination centre (interface IV) experiences the highest magnitude of damage. To investigate this occurrence further to have a better understanding, the stress range experienced by the various components are plotted in Fig. 10. The terminations are seen to develop the highest range followed by the copper pad and the die is the third in rank. Thus, the bond between termination and die experiences the highest damage because there is no direct bond/contact between termination and the copper pad. Their interface is filled with solder which has inadvertently served as a cushion and reduces the amount of constraints between the two components. These observations have justified that the proposed relation is a quick tool to rank boundaries for damage evaluation. With reference to the mechanical properties of the constituents (Table 4) and Fig. 4, it can be observed that the effect of geometric ratio is more critical than that of CTE ratio. The assembly was evaluated using FIPs such as stress, elastic strain, elastic energy and deformation to determine the

Interconnection boundary

4.0 3.0 2.0 1.0 0.0 (I) Solder

(II)Solder

(III) Solder

(IV) Die end

(V) Die base

(VI) Copper

and

and

and copper

and

and

pad and PCB

termination

termination

centre

pad

termination

termination

base

base

Interconnet boundary

Fig. 9. Magnitude of

Stress range (MPa)

Therefore, DM / N ≡ DN / M =

∆ lM =3 ∆ lN

Rank of boundary

5.0

Thus, Eq. (17) becomes

∆ lA ∆ lB

for the boundaries.

120 100 80 60 40 20 0

Stress Range (MPa)

Component Fig. 10. Plot of stress range of the components in the resistor assembly.

Table 8 Response of components to FIPs. FIPs

Component

Stress Elastic strain Elastic energy Deformation

Minimum

Maximum

PCB PCB PCB PCB

Termination Termination PCB Solder

Table 9 S/N response and rank. Level

1 2 3 Effect Rank

Factors A

B

C

15.15
8.98 4.82 24.13 2


1.81 4.11 8.69 10.50 3


15.73 28.42
1.70 44.16 1

24

E.H. Amalu et al. / Finite Elements in Analysis and Design 107 (2015) 13–27

Main Effects Plot ( data means) for Signal-to-noise ratio ( dB)

Mean of Signal- t o- noise ratio (dB)

B, Component stand off height

A,Resist or thickness

30 20 10 0 -10 438 30

508

550

60

80

100

C, Homologous temperature

20 10 0 -10 0.81

0.86

0.91

Fig. 11. Main effect plot of thickness of resistor, component standoff height and homologous temperature.

Interaction Plot (datameans) for Signal-to-noise ratio (dB) 60

80

100

0.81

0.86

0.91 50

25 A, Resistor thickness 0

50

25 B, Componentst and off height 0

A, Resistor thickness 438 508 550 B, Component stand off height 60 80 100

C, Homologoust emperature

Fig. 12. Interaction plot of thickness of resistor, component standoff height and homologous temperature.

presented in Table 9, Figs. 11 and 12. The means of S/N ratio presented in Table 9 and plotted in Fig. 11 may be obtained using the data in Table 7 and employing Eq. (20).

ji =

1 n

n

∑ ji = 1

ji ∀ j, i

(20)

Where j which may be designated as A, B or C is the RIFs. Similarly, i which assumes values such as 1, 2 or 3 is the level. The other symbols: j¯i and n are the mean of S/N ratio and the number of level in the experiment, respectively. The sign ∀ j, i denotes that Eq. (20) is evaluated at j and i values. These means represent the factor average effects at each level. Furthermore, with reference to Table 9, the effect of a factor ( Ej ) is the observed range in its level. It can be represented as:

Ej = Fjmax − Fjmin ∀ i

(21)

where Ej , Fjmax , Fjmin are effect of factor j, maximum and minimum

value of factor j, respectively. The sign ∀ i designates that Eq. (21) is evaluated across the level. The data presented in Table 9 shows that the homologous temperature (factors C) has the highest contribution while the CSH (factor B) has the least contribution. Thus, the ambient operating temperature is found to have more effect than the geometric parameters in influencing the reliability of resistor assembly. The significance of this finding is that leadfree solder alloy compositions should be qualified for the variety of ambient temperatures they operate in. Generally, the mechanical strength of materials decreases when operating in higher homologous temperature environment where the sensitivity of their properties to plastic strain rate increases. More importantly, the results demonstrate that geometric parameters could be used to improve the thermo-mechanical reliability of surface mount resistor assembled on PCB in the current miniaturisation manufacturing trend. Fig. 11 shows that smallest RT, highest CSH and intermediate operating temperature have the highest magnitude of main effect on ωacc and could be used to control its value. The interaction plots

E.H. Amalu et al. / Finite Elements in Analysis and Design 107 (2015) 13–27

of the RIFs with one another are presented in Fig. 12. The plots show the average response at each treatment combination. The significant interaction of the factors is indicated by the lack of parallelism of the lines as they cross one another. The interaction plot between RT and CSH reveals a huge interaction among the treatment levels. It is seen that intermediate RT (508 μm) interact with lower region CSH while largest RT interact with CSH at upper region. The significance of this observation is that the geometric parameter could be used to decrease the magnitude of ωacc in the solder joints in the advance of miniaturisation manufacturing trend. The interaction plot between RT and TH demonstrate the lowest interaction among the factors. There is no observable interaction within the range investigated in this study. It could be inferred that irrespective of the thickness of resistor and operating ambient, the magnitude of change in damage of solder joint will be trivial. The interaction between CSH and TH shows a significant interaction at high TH and no observable interaction at low TH. This observation points out that the creep effect is predominant at higher operating temperature as expected. The observation also indicates that at high TH, high CSH would affect the magnitude of ωacc significantly. In other words, the thermo-mechanical reliability of solder joints operating in higher homologous temperature is very sensitive to CSH. Thus, the magnitude of CSH should be considered when designing for such ambient operations. The better impact of intermediate temperature may be explained from stress relaxation concept. The increased interaction is observed because the solder alloy is operating within higher creep region and consequently its physical properties become very sensitive to creep strain rate, temperature and strain hardening and softening. The interactions among the factors demonstrate that the CSH could be used to mitigate ωacc in the solder joints of a resistor assembly which operates in high homologous temperature. 4.5. Optimisation of reliability influencing factors (RIFs)

1.0 0.8 0.6 0.4 0.2 0.0

M2 ωacc (J/m^3) OPT A1B3C2ωacc (J/m^3)

0 2 4 Number of teperature cycle

Equivalent stress σ (MPa)

Creep energy density ω' (J/m 3)

To optimise the resistor assembly thermo-fatigue life while minimising the effect of RIFs, the absolute value of magnitude of S/ N ratio has to be maximised. The maximum value will yield the least magnitude of ωacc in the solder joints. Basically, the technique involves the selection of factor levels which produce the highest magnitude of S/N ratio. Table 9 and Fig. 11 are used for this selection. It can be easily observed in this table that the highest absolute value of the mean of S/N ratio occurred in levels 1, 3 and 2 for factors A, B and C, respectively. Based on this analysis, the optimal parameter setting is A1B3C2. Thus, for optimal design in

25

this assembly, the thickness of resistor should be 438 μm, CSH should be 100 μm, and the homologous temperature should be 0.86 (A1B3C2 ¼RT 438 μm; CSH 100 μm; TH 0.86). The significance of this result is that a resistor assembly will possess longer operating thermo-fatigue life time when structurally it has thin die thickness, high component standoff height and operating within homologous temperature of 0.86. The smallest RT will exert the least axial load on the joint while the highest CSH will allow for the maximum deflection of the resistor die. Operation at the 0.86 TH is the best because it will not support crack initiation in the solder compared to 0.81 TH. 4.6. Comparison of the optimal design with the best design point The comparison of the best design from the DoE and the optimal design are done using two damage indices named as the rate of accumulation of creep strain energy density at comparable creep region ( ω′acc ) and accumulated creep strain energy density using the hysteresis loop (ω′′acc ). The secondary steady state creep regions were identified in the output simulation results of the two models. The data are used to plot the graph presented in Fig. 13 (a) which shows the rate of accumulation of creep strain energy densities in the two models. It can be seen in the plot that the optimal design demonstrates possession of least magnitude of ω′acc at the early stage of temperature cycling. As loading progresses, the value of the two quantities becomes equal. The attainment of equal magnitude could results from stress relaxation of the solder due to operation in the same TH of 0.86. To validate this finding further, the plot of stress against strain know as hysteresis loop was carried out for the two designs. The plot is presented in Fig. 13 (b). The area of the loop represents the volumetric strain energy density dissipated per cycle loading. Therefore, the area is a measure of the damage where larger area signifies larger damage. It can be seen in the plot that the optimised design (A1B3C2) has smaller area than the best design of DoE. It can also be seen that while both designs attained also equal stress magnitude, the M2 experiences more creep strain deformation. Geometrically, it has a lower CSH than the optimum design which may explain this behaviour. The magnitudes of 'ωacc for the two designs are computed and presented in Table 10. The values demonstrate that the percentage change in ω'acc between model 2 and Optimum design and using model 2 as a reference is 46.9%. In evaluating the number of cycles to failure of the two designs, the relation proposed by Syed [29] for SnAgCu solder is employed. This relation is represented thus:

Nf = (0.0019 × ωacc )−1

(22)

60.0

M2 hysteresis loop

50.0

A1B3C2 hysteresis loop

40.0 30.0 20.0 10.0 0.0 0.000

0.020

0.040

0.060

Equivalent creep strain Fig. 13. Comparison of accumulated creep strain energy density ω of the optimal design and best design from DOE using: (a) Plot of comparable creep energy density against number of temperature cycle. (b) Plot of hysteresis loop.

26

E.H. Amalu et al. / Finite Elements in Analysis and Design 107 (2015) 13–27

Table 10 Comparison of damage and fatigue lives of the two critical designs. Model

M2 (Best design of DoE) Optimal design Life gain (%)

Factor and level

Quality/response ω'acc (J/m3) Nf (Cycles)

A RT

B CSH

C TH

1

2

2

1.13

466

1

3

2

0.60

877 88.3

Where Nf is the number of cycles to failure, ωacc is the accumulated creep strain energy dissipated per cycle. Although this relation is developed for ball grid arrays (BGA), its application in this investigation will be useful because the research seeks to evaluate the percentage gain in life of the optimal design over the best design in the DoE rather than the numerical values. The results demonstrate that optimal design has the potential of increasing the Nf of the solder joint of the best design by 88.2%.

termination base and the copper pad has absorbed significantly the stress which would have developed between termination and pad. It is proposed that the use of solder between die ends and terminations will serve as stress diffuser and mitigate the high stress developed at the interface between the two components. 1 ≤ DM / N ≡ DN / M ⟨∞ The relation DM / N ≡ DN / M = 3 K1 × K2 { devel1 ≤ K1 × K2 ⟨∞ oped for quick determination of the most critical interface boundary is dependent on ratios of CTE and thickness of components with the geometric ratio being more determining. This relation could be helpful in determining the contribution of assembly geometry as a stress riser in multi-material interconnection in an assembly. The results of this study have demonstrated that the magnitude of accumulated creep strain energy density ωacc depends on the setting of the RIFs. It also shows that the optimal design has the potential to reduce ωacc of the joint of best design from DOE by 46.9% while improving its fatigue life by 88.2%.

Acknowledgements The authors acknowledge the support of Staff of University of Wolverhampton, UK.

5. Conclusions References This paper has reported the investigation on thermo-fatigue reliability of a resistor R102 assembled on substrate printed circuit board using SnAgCu solder joints. The investigation aims to study the effect of reliability influencing factors (RIFs) which are resistor die thickness (RT), component standoff height (CSH) and operating ambient homologous temperature (TH) on mechanical integrity and reliability of lead-free solder joints and other components of the assembly. The investigation seeks to characterise the distribution of damage in the assembly whilst quantifying its magnitude. It is the focus of the study to evaluate and determine the effect of geometry of components and the coefficient of thermal expansion of the materials to magnitude of damage of interface in the assembly. In addition, this research optimises the RIFs and compares the optimal design with best design of the DoE in terms of accumulated creep strain energy density (ωacc) and fatigue life. It is found that the RIFs have main effect and also interact with one another to influence the performance of the assembly at the simulated conditions. The ambient operating temperature is found to be the most influential factor in contributing to the damage of the soldered joints while at higher operating temperature, the thickness of the resistor die is indifferent to the other two RIFs. This observation occurs because the fluidity of the joint increases and mitigates the solid state damage of the joint. It can be deduced that for assembly which will operate at high homologous temperature, the fatigue life of the assembly could be increased by using optimal CSH to assemble the chip resistor on PCB. Consequently, optimal design of resistor assembly should specify the operating homologous temperature range. Damage distribution on the components is found to concentrate at the periphery and edge of the components. For the soldered joints, increasing the thickness of these areas may mitigate inherent crack initiation and propagation. For the other components, surface treatment and design changes to eliminate edges are recommended. Although the stress range in termination is the highest followed by copper pad and then the resistor die, the interface between die end and termination was found to be the most critical to failure. The solder sandwich between the

[1] R.W. Johnson, J.L. Evans, P. Jacobsen, J.R. Thompson, M. Christopher, IEEE Transac. Electron. Packag. Manuf. 27 (3) (2004) 164–176. [2] J. Watson, G. Castro, High-temperature electronics pose design and reliability challenges, Analog Dialogue, 2012, pp. 1–7. [3] B. Parmentier, B.O. Vermesan, L. Beneteau, in: Proceedings of the International Conference on HITEN, Oxford, U.K., 2003. [4] E.H. Amalu, N.N. Ekere, J. Mater. Process. Technol. 212 (2012) 471–483. [5] Y. Liu, F. Sun, Y. Liu, X. Li, J. Mater. Sci.: Mater. Electron. 25 (6) (2014) 2627–2633. [6] L. Yang, Y. Zhang, J. Dai, Y. Jing, J. Ge, N. Zhang, Mater. Des. 67 (0) (2015) 209–216. [7] C.R. Siviour, S.M. Walley, W.G. Proud, J.E. Field, J. Phys. D: Appl. Phys. 38 (2005) 4131–4139. [8] F.A. Stam, E. Davitt, Microelectro. Reliab. 41 (2001) 1815–1822. [9] T.J. Goh, in: Proceedings of the CPMT Electronics Packaging Technology Conference, Raffles City Convention Centre, Singapore, 1998. [10] H. Ma, M. Ahmad, K.-C. Liu, in: Electronic Components and Technology Conference Las Vegas, Nevada, United States, 2010, pp. 1816–1822. [11] H. Ye, S. Xue, L. Zhang, F. Ji, W. Dai, Comput. Mater. Sci. 48 (3) (2010) 509–512. [12] Y. Wan, H. Huang, M. Pecht, IEEE Transac. Device Mater. Reliab. 15 (2) (2015) 206–213. [13] S. Ridout, C. Bailey, Fatigue Fracture Eng. Mater. Struct. 30 (5) (2007) 400–412. [14] E.H. Amalu, N.N. Ekere, Microelectron. Reliab. 52 (12) (2012) 2982–2994. [15] H. Lu, C. Bailey, M. Dusek, C. Hunt, J. Nottay, in: Proceedings of the International Symposium on Electronic Materials and Packaging, Hong Kong, China, 2000. [16] L.T. Orsini, Mechanical Engineering Department, Rensselaer Polytechnic Institute, Hartford Connecticut USA (2011), p. 1–94. [17] H.C. Tsai, W.R. Jong, H.T. Chang, J. Reinf. Plast. Compos. 28 (19) (2008) 2365–2376. [18] E.H. Amalu, N.N. Ekere, S. Mallik, Mater. Des. 32 (2011) 3189–3197. [19] L. Haslehurst, N.N. Ekere, J. Electron. Manuf. 6 (1996) 307–316. [20] G.J. Jackson, M.W. Hendriksen, R.W. Kay, M. Desmulliez, R.K. Durairaj, N. N. Ekere, Solder. Surface Mount Technol. 17 (1) (2005) 24–32. [21] D.C. Montgomery, Design and Analysis of Experiments, 8th Ed., John Wiley & Sons, Inc. (2013), p. 1–730. [22] E.H. Amalu, N.N. Ekere, Comput. Mater. Sci. 65 (2012) 470–484. [23] Z. Zhang, S. Park, K. Darbha, R.N. Master, in: Electronic Components and Technology Conference Las Vegas, Nevada, 2010, pp. 14–19. [24] B.A. Zahn, in: Electronic Components and Technology Conference San Diego CA, 2002, pp. 1475–1483. [25] T.T. Nguyen, D. Lee, J.B. Kwak, S. Park, Microelectron. Reliab. 50 (7) (2010) 1000–1006. [26] S. Stoyanov, C. Bailey, M. Desmulliez, Solder. Surface Mount Technol. 21 (1) (2009) 11–24. [27] High Performance FR-4 for Multi-layered PWB High Performance FR-4 for Multi-layered PWB Copper Clad Laminates, 17 December, 2009 [cited 2011 29th March]. Available from: 〈www.mgc.co.jp/eng/products/lm/btprint/ lineup/fr4.html〉.

E.H. Amalu et al. / Finite Elements in Analysis and Design 107 (2015) 13–27

[28] A. Schubert, in: Electronic Components and Technology Conference, New Orleans, Louisiana, USA, 2003. [29] A. Syed, in: Electronic Components and Technology Conference, Las Vegas, Nevada, USA, 2004, pp. 737–746. [30] E.H. Amalu, N.N. Ekere, Microelectron. Reliab. 53 (11) (2012) 2731–2743. [31] Y. Aoki, I. Tsujie, T. Nagai, Espec Technology Report No 25, 2007, pp. 4–13.

27

[32] Y. Aoki, I. Tsujie, T. Nagai, follow-up to Report No. 25, Espec Technology Report, 2007, pp. 1–13. [33] M.Y. Tsai, H.-Y. Chang, M. Pecht, IEEE Transac. Device Mater. Reliab. 9 (3) (2009) 419–424.