Effect of Bi on the Tensile and Viscoplastic Behavior of Sn-Ag-Cu-Bi Alloys Used for Microelectronics Applications

Abstract

Sn-Ag-Cu-Bi (SAC-Bi) alloys are gaining popularity as a potential replacement for current lead-free solder alloys in microelectronic packages. In this study, the tensile and viscoplastic behaviors of eight SAC-Bi alloys with 0, 1 wt.%, 2 wt.%, and 3 wt.% Bi content were investigated. The samples of these eight alloys were cast, aged at room temperature, 75 °C and 125 °C, and tensile-tested at rates of 0.1/s, 0.01/s, and 0.001/s in ambient and elevated temperature environments to facilitate the quantification of viscoplasticity using the Anand viscoplastic model. The Anand parameters of all eight alloys in the as-cast and aged conditions were determined. Tensile strength was found to increase with the addition of Bi. Additionally, alloys containing 2 and 3 wt.% Bi showed a 5 to 10% increase in tensile strength after isothermal aging of 90 days at 125 °C. On the contrary, the tensile strength of alloys with up to 1 wt.% Bi decreased by 22 to 48% after such aging. Using a Scanning Electron Microscope (SEM) and energy dispersive spectroscopy (EDS), the microstructure of the alloys was characterized. The aging-induced property changes in the samples were correlated to strengthening by Bi solute atoms for alloys with 1 wt.% Bi and the formation of Bi precipitation for alloys with 2 wt.% and 3 wt.% Bi.

1. Introduction

Lead-free alloys such as Sn-3.0Ag-0.5Cu (SAC305) and Sn-4.0Ag-0.5Cu (SAC405) are widely used as solder materials because of their adequate properties and reliability [1,2,3,4,5,6,7]. However, with applications such as 5G and high-performance computing (HPC) imposing increased thermomechanical loading on solder joints, there is a pressing need to develop alloys with better mechanical properties and reliability. Bi-doped SAC alloys offer enhanced properties, making them an attractive alternative to SAC305 and SAC405. Jian et al. investigated Bi-doped alloys such as SAC-Q (Sn-4.0Ag-0.5Cu-3.0Bi) and SAC-R (Sn-0.5Cu-3.0Bi), revealing that while SAC305 exhibited significantly reduced fatigue life after 1000 h of aging, Bi-doped SAC alloys showed less change in fatigue life [8]. A comparative investigation of the fatigue reliability of SAC305 and eutectic Sn-Bi alloys by Cai et al. showed a superior fatigue strength of the eutectic Sn-Bi alloy [9]. Haq et al. showed that for the same number of cycles, the stress level for fatigue failure is 50% higher in SAC405-Bi alloy with 3 wt.% Bi compared with SAC405 with 1 wt.% Bi [10]. Lall et al. reported a 5 to 15% higher tensile strength in SAC405-3.0Bi solder compared with SAC305 across a large spectrum of strain rates ranging from 1 to 75 s⁻¹ and temperatures of −65 °C to 200 °C [11]. Belhadi et al. showed SAC 305 doped with 3 wt.% Bi has a shear strength 15 to 20% higher than SAC305 [12], and a 20 to 40% increase in tensile strength was reported on doping SAC405 with up to 3% Bi [13]. It was also reported that a doping of 3 wt.% Bi in SAC405 increases the hardness of the alloy by 37% and improves the creep strength significantly [14]. Various other material properties of SAC-Bi alloys have also been studied. Ahsan et al. reported that adding 1% and 2% Bi to SAC305 increased the modulus and ultimate tensile strength, but these properties decreased with aging and thermal exposure [15]. Maalekian et al. investigated Sn-0.6Ag-0.7Cu-Bi alloys with varying Bi content from 0 to 1, 1.5, 3, and 6 wt.% and reported a lowered melting temperature by 15 °C on the addition of 6 wt.% Bi, higher hardness and tensile strength, and improved wettability for alloys with higher Bi content [16]. Improvement in wettability on Cu pads was also reported by Yang et al. [17]. Hu et al. studied the effect of Bi addition in SAC305 on the microstructure and mechanical properties of SAC-Bi solder joints experiencing current stressing and reported that Bi addition increased nanoindentation hardness after current stressing for Bi concentrations of less than 3% [18].

As solder joints in packages are often deformed plastically under service conditions [19,20], examining properties pertaining to the plastic deformation of a solder alloy is important for assessing the reliability of these alloys. In particular, for SAC-Bi, which exhibits viscoplastic behavior when deformed [14,21,22], it is important to investigate how its mechanical behaviors vary with loading rate and quantify these viscoplastic properties using the Anand viscoplastic model to simulate their deformation behaviors in a package [23,24]. Since the microstructure and mechanical properties of solder change with time when an electronic package undergoes service conditions, it is necessary to find the Anand viscoplastic parameters not just in the unaged condition but also after high-temperature storage. Additionally, it is important to establish a structure–property correlation by identifying the microstructural causations of property changes. Various attempts have been made to determine the Anand parameters for a variety of commonly used microelectronic solder alloys. Motalab et al. reported the Anand parameters for SAC305 using uniaxial stress–strain data for various strain rates (1 × 10⁻³ s⁻¹, 1 × 10⁻⁴ s⁻¹, and 1 × 10⁻⁵ s⁻¹) and temperatures (25 °C, 50 °C, 75 °C, 100 °C, and 125 °C) as well as from creep data measured at different stresses (10 MPa, 12 Mpa, and 15 MPa) and temperatures (25 °C, 50 °C, 75 °C, 100 °C, and 125 °C) [25]. Ahmed et al. found the Anand parameters of 2 to 3% Bi-doped SAC405 solders using tensile tests performed at temperatures of 25 to 125 °C and strain rates of 1 × 10⁻³ to 1 × 10⁻⁵ s⁻¹ [21]. Basit et al. investigated the Anand parameters of various SAC solders with varying Ag content from 1 to 4 wt.% after extreme aging at 100 °C for 12 months [26]. Hassan et al. conducted uniaxial stress–strain tests at testing temperatures of 25 to 125 °C and strain rates of 1 × 10⁻³ to 1 × 10⁻⁵ for SAC405 doped with 1,2, and 3 wt.% Bi and for SAC305 and found the Anand parameters of the four alloys in unaged condition [27]. However, a comprehensive study on the viscoplastic properties and Anand parameters of SAC305 and SAC405 with varying Bi content subjected to a variety of aging conditions, including room temperature and near-service temperatures, is lacking.

In this study, the changes in tensile and viscoplastic properties over aging time were studied for the following eight solder alloys: SAC305, SAC305 + 1 wt.%Bi, SAC305 + 2 wt.%Bi, SAC305 + 3 wt.%Bi, SAC405, SAC405 + 1 wt.%Bi, SAC405 + 2 wt.%Bi, and SAC405 + 3 wt.%Bi. These alloys were subjected to tensile testing at three temperatures, with each temperature tested at three constant strain rates. From the obtained stress–strain behaviors, the Anand parameters of all eight alloys were found in their as-cast (unaged) condition as well as in the aged conditions. The variation in tensile and viscoplastic behavior with Bi doping was also studied, and the changes in microstructure caused by Bi were revealed.

2. Materials and Methods

2.1. Sample Preparation

Ingots of eight solder alloys, i.e., SAC305, SAC305 + 1 wt.%Bi, SAC305 + 2 wt.%Bi, SAC305 + 3 wt.%Bi, SAC405, SAC405 + 1 wt.%Bi, SAC405 + 2 wt.%Bi, SAC405 + 3 wt.%Bi (ACCURUS SCIENTIFIC Co., Ltd., Tainan City, East District, Taiwan), were cleaned and melted in their respective inert crucibles. Tensile testing samples of each alloy were prepared by vacuum casting, where a glass tube with an inner dimension of 1 mm × 2 mm was connected at one end to a vacuum pump and dipped in a crucible containing molten solder at the other end. The low pressure created by the vacuum pump pulled the molten solder into the tube [28], which was immediately removed from the crucible and quenched in a water bath. The solidified samples were then removed from the tube and polished to 1200 grit size to remove any stress concentrator. The samples of 50 mm length and cross-sectional dimensions of 1 mm × 2 mm were then ready for the aging experiment and subsequent testing. In total, 300 samples were casted for each alloy. Non-standard sample geometry was chosen in this study to mimic the dimensions and microstructures of solder joints used in a real package.

2.2. Aging Experiment

The casted specimens of all alloys were subjected to isothermal aging in ambient atmosphere in convectional thermal chambers. The aging experiment was conducted at room temperature (25 °C) as well as elevated temperatures of 75 °C and 125 °C. These three temperatures were chosen as they cover a wide range of typical service temperatures for solders in commercial-, industrial-, and military-grade packages [29]. There were three aging durations for each aging temperature, i.e., 30, 60, and 90 days. This choice of aging duration facilitated the comparison of the calculated Anand parameters for 90 days of aging with other investigations [22] and helped find Anand parameters for intermediate aging durations. The aging matrix is shown in

Table 1. Aging matrix.

Temp./Time	0 Day (As-Cast)	30 Days	60 Days	90 Days
25 °C	X	X	X	X
75 °C		X	X	X
125 °C		X	X	X

“X” as a check mark to indicate these are the conditions of the experiment.

.

2.3. Tensile Testing

The specimens in the as-cast and aged conditions were tensile-tested at three different temperatures, i.e., 25 °C, 90 °C, and 145 °C, using a Shimadzu AGS-X tensile tester (Kyoto, Japan) with an attached environmental chamber. As there is no specific ASTM or JEDEC standard for determining Anand parameters, the measurement followed procedures reported in the literature [28]. Specifically, for each of these temperatures, constant strain rate tests were conducted at 0.1/s, 0.01/s, and 0.001/s. The testing matrix used for the tensile testing is shown in

Table 2. Testing matrix.

Temp./Strain Rate	0.1/s	0.01/s	0.001/s
25 °C	X	X	X
90 °C	X	X	X
145 °C	X	X	X

. For each of the nine testing temperature and strain rate combinations, three repeatable stress–strain plots were obtained.

2.4. Calculation of Anand Parameters

The Anand viscoplastic constitutive model is described by a stress equation, a flow equation, and an evolution equation [22]. Equations (1)–(9) were derived by Motalab et al. to calculate Anand parameters [25].

For uniaxial loading, the stress equation is expressed as:

$$\sigma =cs;c<1$$

(1)

where s is an internal variable while c ($\dot{{\epsilon }_p},T$) is a function of the plastic strain rate ($\dot{{\epsilon }_p}$) and absolute temperature. c is given by:

$$c=\mathrm{c}\left(\dot{{\epsilon }_p},T\right)=\frac{1}{\xi }{\sinh }^{-1}\left\{{\left[\frac{\dot{{\epsilon }_p}}{A}{e}^{\left(\frac{Q}{RT}\right)}\right]}^m\right\}$$

(2)

where ξ is the multiplier of stress, A is the pre-exponential factor, Q is the activation energy, R is the universal gas constant, and m is the strain rate sensitivity. Using Equations (1) and (2), the stress equation is written as:

$$\sigma =\frac{s}{\xi }{\sinh }^{-1}\left\{{\left[\frac{\dot{{\epsilon }_p}}{A}{\mathrm{e}}^{\left(\frac{Q}{RT}\right)}\right]}^m\right\}$$

(3)

Rearranging the stress equation gives the flow equation:

$${\dot{\epsilon }}_p=\mathrm{A}{e}^{-\left(\frac{Q}{RT}\right)}{\left[\sinh \left(\xi \frac{\sigma }{\mathrm{s}}\right)\right]}^{\frac{1}{m}}$$

(4)

The internal variable s(h,${\epsilon }_p$) can be expressed as a function of h($\sigma ,s,T$) and ${\epsilon }_p.$

$$s=\mathrm{h}\left(\sigma ,s,T\right).{\epsilon }_p$$

(5)

where h is a term for the dynamic hardening and recovery process and ${\epsilon }_p$ is plastic strain. S can be differentiated to obtain evolution equation as follows:

$$\dot{s}=\left[h_0{\left(1-\frac{\mathrm{s}}{s^{\ast }}\right)}^a\sin \left(1-\frac{\mathrm{s}}{{\mathrm{s}}^{\ast }}\right)\right]{\dot{\epsilon }}_p;a>1$$

(6)

where h₀ is an Anand parameter called the hardening constant, a is called the strain rate sensitivity parameter of hardening, and s* is:

$${\mathrm{s}}^{\ast }=\widehat{s}{\left[\frac{{\dot{\epsilon }}_p}{A}\mathrm{e}\left(\frac{Q}{RT}\right)\right]}^n$$

(7)

where $\widehat{s}$ is a parameter and a coefficient and n is a parameter for the strain rate sensitivity of the saturation value of deformation resistance. Using Equation (7) in Equation (6) and integrating yields the final evolution equation for s as:

$$s=\widehat{s}{\left[\frac{{\dot{\epsilon }}_p}{A}{\mathrm{e}}^{\left(\frac{Q}{RT}\right)}\right]}^n-{\left[{\left(\widehat{s}{\left[\frac{{\dot{\epsilon }}_p}{A}{\mathrm{e}}^{\left(\frac{Q}{RT}\right)}\right]}^n-s_0\right)}^{\left(1-a\right)}+\left(a-1\right)\left\{{\mathrm{h}}_0{\left(\widehat{s}{\left[\frac{{\dot{\epsilon }}_p}{A}{\mathrm{e}}^{\left(\frac{Q}{RT}\right)}\right]}^n\right)}^{-a}\right\}{\epsilon }_p\right]}^{\frac{1}{1-\mathrm{a}}}$$

(8)

Substitution of the integrated evolution Equation (8) into the flow Equation (4) results in an expression relating the strain rate to the strain, stress, and temperature:

$${\dot{\epsilon }}_p=A{\mathrm{e}}^{-\left(\frac{Q}{RT}\right)}{\left[\sinh \left\{\xi \sigma {\left(\widehat{s}{\left[\frac{{\dot{\epsilon }}_p}{A}{\mathrm{e}}^{\left(\frac{Q}{RT}\right)}\right]}^n-{\left[\begin{array}{c}{\left(\widehat{s}{\left[\frac{{\dot{\epsilon }}_p}{A}{\mathrm{e}}^{\left(\frac{Q}{RT}\right)}\right]}^n-s_0\right)}^{\left(1-a\right)}\\ +\left(a-1\right)\left\{{\mathrm{h}}_0{\left(\widehat{s}{\left[\frac{{\dot{\epsilon }}_p}{A}{\mathrm{e}}^{\left(\frac{Q}{RT}\right)}\right]}^n\right)}^{-a}\right\}{\epsilon }_p\end{array}\right]}^{\frac{1}{1-\mathrm{a}}}\right)}^{-1}\right\}\right]}^{\frac{1}{m}}$$

(9)

Equation (9) includes the following nine Anand parameters: ξ, m, Q/R, A, a, h₀, s₀, $\widehat{s}$, and n. These Anand parameters were calculated using Equation (9) as it has nine unknown parameters along with four items that can be determined experimentally, i.e., strain, stress, strain rate, and testing temperature. The stress–strain data from the elevated temperature tensile tests conducted using the testing matrix discussed in Section 2.3 was fitted [30] in Equation (9) to determine the values of the nine Anand parameters, i.e., A, ξ, Q/R, m, h₀, a, s₀, $\widehat{s}$, and n.

2.5. Microstructural Investigation

Selected samples were sectioned and mounted in epoxy. The mounted samples were then polished using SiC papers, followed by diamond suspensions on napping cloth down to 1 μm particle size, and then finished with 40 nm colloidal silica to obtain a scratch-free surface. The polished samples were examined under the backscattered mode of a ZEISS Ultra 55 Field Emission Scanning Electron Microscope (SEM) equipped (Jena, Germany) with energy dispersive spectroscopy (EDS) to reveal and identify the various phases present. The size and distribution of phases were correlated with the effect of aging, Bi content, and observed property changes in order to establish the structure–property relationship.

3. Results

3.1. Tensile and Viscoplastic Behavior

In Figure 1, three repeatable stress–strain curves, labeled 1, 2, and 3, are plotted for each of the nine temperature–strain rate combinations for the as-cast SAC305 alloy. Three sets of Anand parameters were calculated based on these overlapping stress–strain curves, as shown in

Table 3. Anand parameters of as-cast SAC305 calculated using each of the three overlapping curves.

SAC305	Sample 1	Sample 2	Sample 3	Average	S	RSD
s0	32.85	32.69	32.78	32.77	0.08	0.24
Q/R	9068.00	9050.00	9046.00	9054.67	11.72	0.13
A	2995.10	2947.00	2965.30	2969.13	24.28	0.82
ξ	4.00	4.00	4.00	4.00	0.00	0.00
m	0.29	0.29	0.28	0.29	0.01	2.01
h0	183,010.00	183,010.00	182,980.00	183,000.00	17.32	0.01
$\widehat{s}$	40.80	40.20	41.00	40.67	0.42	1.02
n	0.01	0.01	0.01	0.01	0.00	2.14
a	1.75	1.75	1.74	1.75	0.01	0.33

. The averages of the parameters, along with their corresponding standard deviations (Ss) and relative standard deviations (RSDs), are also provided in the table, demonstrating the repeatability of the measurement. Similar levels of deviations, i.e., less than 3% for m and n and less than 1% for all the other parameters, were found for all the other alloys across all aging conditions.

For all alloys in their as-cast conditions and after an isothermal aging of 90 days at 125 °C, three overlapping stress–strain plots are plotted in Figure 2 for each aging and testing condition. As evident from the plots, all solder alloys show loading rate-dependent deformation behavior or viscoplasticity. When deformed at higher strain rates, all alloys show higher strength than deformation at slower strain rates. As expected, a higher testing temperature results in lower strength. Moreover, the SAC305, SAC305 + 1 wt.%Bi, SAC405, and SAC405 + 1 wt.%Bi alloys show significantly reduced tensile strength after aging. On the contrary, alloys containing more than 2 wt.% Bi, i.e., SAC305 + 2 wt.%Bi, SAC305 + 3 wt.%Bi, SAC405 + 2 wt.%Bi, and SAC405 + 3 wt.%Bi, show increased strengths after aging. This indicates that doping SAC305 and SAC405 alloys with 2 to 3 wt.% Bi could lead to improved mechanical performance in these alloys, particularly after high-temperature storage.

3.2. Anand Parameters

The Anand parameters of all the alloys in the nine aging conditions and the as-cast condition were calculated using the methodology discussed in Section 2.4. The values of the parameters are listed in

Table 4. Anand parameters of SAC305 in all aging conditions.

SAC305	As-Cast	30 d, 25 °C	30 d, 75 °C	30 d, 125 °C	60 d, 25 °C	60 d, 75 °C	60 d, 125 °C	90 d, 25 °C	90 d, 75 °C	90 d, 125 °C
s0	32.77	30.11	27.35	24.22	24.87	23.21	19.78	21.12	18.18	14.56
Q/R	9055	9017	9042	9030	9050	9022	9028	9072	9015	9030
A	2969.1	3055.1	3274.5	3502.3	3287.4	3465.7	3847.3	3596.5	3943.6	4175.2
ξ	4	4	4	4	4	4	4	4	4	4
m	0.29	0.28	0.25	0.24	0.21	0.20	0.18	0.16	0.15	0.12
h0	183,000	181,150	180,000	173,000	163,100	179,200	145,100	100,050	80,000	71,100
$\widehat{s}$	40.7	39.3	38.9	37.6	33.5	32.1	28.2	26.4	23.4	21.3
n	0.01	0.01	0.0085	0.0081	0.007	0.0059	0.0048	0.0019	0.0014	0.0009
a	1.75	1.76	1.79	1.82	1.83	1.87	1.91	1.92	1.94	1.97

,

Table 5. Anand parameters of SAC305 + 1 wt.%Bi in all aging conditions.

SAC305 + 1 wt.%Bi	As-Cast	30 d, 25 °C	30 d, 75 °C	30 d, 125 °C	60 d, 25 °C	60 d, 75 °C	60 d, 125 °C	90 d, 25 °C	90 d, 75 °C	90 d, 125 °C
s0	22.81	22.74	22.70	22.67	22.63	22.48	22.32	22.20	22.10	22.0
Q/R	9640	9644	9657	9648	9650	9649	9663	9648	9654	9650
A	3851.2	3864.1	3871.0	3873.7	3886.2	3896.4	3911.0	3942.5	3976.1	3997.8
ξ	6	6	6	6	6	6	6	6	6	6
m	0.34	0.34	0.34	0.34	0.33	0.32	0.32	0.32	0.31	0.30
h0	155,100	154,450	154,375	154,360	152,910	152,050	151,275	148,750	148,000	147,760
$\widehat{s}$	38.1	38.0	37.8	37.7	37.2	37.1	36.8	36.3	36.2	36.0
n	0.0085	0.0085	0.0083	0.0083	0.0081	0.008	0.008	0.0075	0.0074	0.0073
a	1.82	1.83	1.83	1.84	1.83	1.84	1.84	1.85	1.85	1.85

,

Table 6. Anand parameters of SAC305 + 2 wt.%Bi in all aging conditions.

SAC305 + 2 wt.%Bi	As-Cast	30 d, 25 °C	30 d, 75 °C	30 d, 125 °C	60 d, 25 °C	60 d, 75 °C	60 d, 125 °C	90 d, 25 °C	90 d, 75 °C	90 d, 125 °C
s0	27.31	27.33	27.66	28.1	28.1	28.2	28.6	28.7	28.9	29.1
Q/R	10,450	10,452	10,463	10,466	10,481	10,487	10,457	10,459	10,455	10,450
A	5021.6	5008.7	5010.5	4989.5	4985.1	4967.2	4957.5	4934.5	4928.5	4914.6
ξ	6	6	6	6	6	6	6	6	6	6
m	0.38	0.41	0.42	0.44	0.45	0.47	0.47	0.48	0.49	0.5
h0	110,000	112,150	11,325	114,520	114,750	115,000	116,400	117,100	117,900	120,000
$\widehat{s}$	32.5	32.7	32.8	33.2	33.3	33.5	33.7	34.0	34.4	35.0
n	0.007	0.008	0.008	0.009	0.01	0.011	0.012	0.013	0.014	0.015
a	1.88	1.87	1.86	1.85	1.86	1.85	1.83	1.82	1.81	1.80

,

Table 7. Anand parameters of SAC305 + 3 wt.%Bi in all aging conditions.

SAC305 + 3 wt.%Bi	As-Cast	30 d, 25 °C	30 d, 75 °C	30 d, 125 °C	60 d, 25 °C	60 d, 75 °C	60 d, 125 °C	90 d, 25 °C	90 d, 75 °C	90 d, 125 °C
s0	18.33	18.55	18.45	18.71	18.62	18.81	18.88	18.91	19.10	19.15
Q/R	11,520	11,520	11,520	11,548	11,565	11,538	11,544	11,530	11,548	11,540
A	6521.4	6515.2	6512.3	6507.2	6500.2	6498.3	6488.3	6475.6	6466.7	6450.1
ξ	6	6	6	6	6	6	6	6	6	6
m	0.40	0.41	0.42	0.43	0.43	0.47	0.48	0.49	0.53	0.55
h0	75,000	76,125	76,875	77,654	78,450	79,350	80,100	80,760	81,520	82,525
$\widehat{s}$	33.8	33.8	33.9	33.8	34.4	34.6	34.8	35.1	35.4	35.6
n	0.005	0.006	0.006	0.006	0.007	0.007	0.008	0.009	0.009	0.01
a	2	1.98	1.97	1.96	1.96	1.95	1.94	1.93	1.92	1.91

,

Table 8. Anand parameters of SAC405 in all aging conditions.

SAC405	As-Cast	30 d, 25 °C	30 d, 75 °C	30 d, 125 °C	60 d, 25 °C	60 d, 75 °C	60 d, 125 °C	90 d, 25 °C	90 d, 75 °C	90 d, 125 °C
s0	34.43	30.20	28.40	25.60	25.20	23.59	20.15	21.20	18.85	15.33
Q/R	9265	9258	9277	9282	9259	9260	9268	9272	9266	9263
A	2879.1	2990.5	3210.4	3455.5	3215.5	3392.4	3789.1	3522.5	3886.6	4110.5
ξ	4	4	4	4	4	4	4	4	4	4
m	0.3	0.28	0.26	0.25	0.23	0.2	0.19	0.18	0.16	0.14
h0	190,150	188,100	186,000	175,100	164,000	182,000	150,200	110,000	82,000	76,000
$\widehat{s}$	41.9	40.1	39.8	38.2	34.5	33.6	29.4	27.7	24.4	22.2
n	0.012	0.011	0.0094	0.0085	0.0075	0.0066	0.0054	0.0028	0.0019	0.001
a	1.72	1.75	1.78	1.81	1.82	1.86	1.89	1.90	1.93	1.96

,

Table 9. Anand parameters of SAC405 + 1 wt.%Bi in all aging conditions.

SAC405 + 1 wt.%Bi	As-Cast	30 d, 25 °C	30 d, 75 °C	30 d, 125 °C	60 d, 25 °C	60 d, 75 °C	60 d, 125 °C	90 d, 25 °C	90 d, 75 °C	90 d, 125 °C
s0	24.21	24.18	24.15	24.10	24.05	23.95	23.83	23.78	23.62	23.50
Q/R	9750	9743	9758	9746	9745	9754	9756	9749	9742	9746
A	3746.3	3753.7	3768.4	3780.1	3797.2	3823.5	3842.3	3868.4	3883.5	3915.1
ξ	6	6	6	6	6	6	6	6	6	6
m	0.36	0.36	0.35	0.35	0.34	0.33	0.32	0.32	0.31	0.31
h0	165,050	164,250	164,110	163,250	160,000	158,550	157,300	155,000	154,000	153,400
$\widehat{s}$	39.6	39.5	39.3	39.3	39.3	39.1	38.8	38.6	38.4	38.3
n	0.0095	0.0094	0.0093	0.0092	0.009	0.0088	0.0085	0.0083	0.008	0.0079
a	1.78	1.8	1.81	1.82	1.82	1.83	1.85	1.85	1.87	1.89

,

Table 10. Anand parameters of SAC405 + 2 wt.%Bi in all aging conditions.

SAC405 + 2 wt.%Bi	As-Cast	30 d, 25 °C	30 d, 75 °C	30 d, 125 °C	60 d, 25 °C	60 d, 75 °C	60 d, 125 °C	90 d, 25 °C	90 d, 75 °C	90 d, 125 °C
s0	27.30	27.30	27.60	28.00	28.20	28.40	28.60	28.70	28.90	29.00
Q/R	10,425	10,450	10,460	10,460	10,471	10,485	10,452	10,458	10,454	10,442
A	4885.5	4865.5	4854.5	4842.5	4832.5	4825.5	4815.5	4812.2	4810.5	4800.5
ξ	6	6	6	6	6	6	6	6	6	6
m	0.4	0.43	0.45	0.47	0.49	0.50	0.52	0.52	0.54	0.55
h0	120,000	122,120	122,650	122,770	127,470	128,100	128,850	131,450	132,450	133,100
$\widehat{s}$	32.5	32.9	33.3	33.6	34.2	34.6	35.1	35.7	36.0	36.2
n	0.009	0.0092	0.0094	0.0096	0.0098	0.011	0.013	0.015	0.017	0.018
a	1.8	1.79	1.78	1.76	1.75	1.74	1.73	1.72	1.71	1.70

and

Table 11. Anand parameters of SAC405 + 3 wt.%Bi in all aging conditions.

SAC405 + 3 wt.%Bi	As-Cast	30 d, 25 °C	30 d, 75 °C	30 d, 125 °C	60 d, 25 °C	60 d, 75 °C	60 d, 125 °C	90 d, 25 °C	90 d, 75 °C	90 d, 125 °C
s0	20.15	20.55	20.68	20.98	21.16	21.33	21.64	21.85	21.95	22.05
Q/R	11,900	11,900	11,896	11,899	11,865	11,936	11,954	11,997	11,985	11,968
A	6150.2	6147.5	6140.5	6133.6	6135.6	6125.6	6115.3	6087.9	6064.5	6050.3
ξ	6	6	6	6	6	6	6	6	6	6
m	0.42	0.43	0.44	0.46	0.47	0.48	0.5	0.52	0.54	0.56
h0	80,000	80,541	80,780	80,990	81,450	81,650	81,950	83,500	83,654	83,840
$\widehat{s}$	35.54	35.65	35.75	35.8	36.1	36.33	36.45	36.77	37	37.4
n	0.006	0.007	0.007	0.007	0.008	0.008	0.009	0.01	0.011	0.012
a	1.98	1.96	1.95	1.94	1.94	1.92	1.91	1.91	1.9	1.88

, where the parameters for SAC305 and SAC405 with no Bi addition are shown in Table 4 and Table 8, respectively.

3.3. Microstructure

Several phases were observed in backscattered electron (BSE) SEM images, and EDS was used for phase identification [31]. In Figure 3, for the SAC305 + 3 wt.%Bi sample aged for 90 days at 125 °C, the backscattered electron micrograph of a region within the sample (Figure 3a) is shown along with the EDS mapping of Bi (Figure 3b), Ag (Figure 3c), and Sn (Figure 3d) for the same region. The bright phase was rich in Bi, the grey particles were rich in Ag, and the matrix was Sn-rich. Figure 3e,f show the BSE image and EDS Ag mapping of another region, where gray particles that are rich in Ag were seen scattered in the Sn-rich matrix. Correlating these results to the phase diagrams of Sn-Ag and Sn-Bi [32,33], the Ag-rich particles were identified as Ag₃Sn, the Bi-rich phase was identified as Bi precipitate, and the matrix was identified as elemental β-Sn. The phases determined from the SEM/EDS studies were consistent with literature reports of similar SAC + Bi alloys [8,34].

Figure 4 shows backscattered electron images of representative samples. In the as-cast condition, SAC305 + x wt.%Bi microstructures were found to be pseudo-eutectic [35], as shown in Figure 4a,c,e,g with primary β-Sn dendrites and Ag₃Sn intermetallic compounds (IMCs) in the interdendritic regions, while SAC405 + x wt.%Bi in the as-cast condition showed microstructures with Ag₃Sn IMC dispersed in the β-Sn matrix, as shown in Figure 4i,k,m,o. After subjecting the alloys to isothermal aging for 90 days at 125 °C, it was observed that IMCs coarsen in all alloys, but the coarsening is suppressed in 2 to 3 wt.% Bi-containing alloys, as shown in Figure 4b,d,f,h,j,l,n,p. Suppressed IMC kinetics is attributed to the ability of Bi to retard IMC growth kinetics [35]. The coarsening of IMCs is expected to reduce the strength of the alloys as the ability of IMC particles to strengthen the matrix is inversely proportional to the spacing between particles [36,37]. On the other hand, for the SAC305 + 2 wt.%Bi, SAC305 + 3 wt.%Bi, SAC405 + 2 wt.%Bi, and SAC405 + 3 wt.%Bi alloys, the matrix showed the presence of Bi precipitates after aging, as shown in Figure 4f,h,n,p, which is expected to significantly increase tensile strength because of precipitation strengthening.

4. Discussion

To obtain a sample with a microstructure resembling that of a reflowed solder joint, it is important to attain a cooling rate comparable to that of reflow soldering during the casting of the samples, particularly in the beginning of the solidification process. The JEDEC standard J-STD-020F recommends a cooling rate of less than 6 °C/s for the beginning of temperature ramp-down for reflow soldering [38]. To verify that the cooling rate of the solder sample cast using the method outlined in Section 2.1 resembles that in reflow soldering, an analysis of the heat transfer problem was conducted. For simplification, the glass tube was modeled as a cylinder with an inner radius of r_i and an outer radius of r_o (Figure 5). The solder sample, with length l, was initially assumed to be at a uniform temperature equal to the melting temperature, T_m, while the temperature of the surrounding water bath was constantly maintained at T_w. As the sample was cooled by water, assuming the temperature in the solder remains uniform, a simple lumped system analysis was applied to model the temperature change of the solder over time, T(t). Heat transfer through the tube can be modeled as one dimensional, with the temperature of the tube depending only on the radial direction (r). In the heat transfer analysis, the temperatures on the inner and outer surfaces of the cylinder were assumed to match those of the solder and the water bath, i.e., T(t) and T_w, respectively. This assumption neglects the thermal resistance between the solder and the inner surface of the cylinder, as well as between the outer surface and the water.

The molten solder and glass assembly was quenched in water immediately after it was introduced into the glass tube and began to solidify. An energy balance on the solder was established for a differential time interval dt. The energy lost by the solder during this interval dt is described by Equation (10) [39]:

$$dQ=-m.c.dT$$

(10)

where m represents the mass of the solder, c is the specific heat capacity of the solder, and dT is the differential temperature drop in the solder during dt. The energy loss by the solder is equivalent to the heat transferred through the glass tube. The heat transferred by a cylindrical tube over time dt is given by Equation (11) [40]:

$$dQ=\frac{T\left(t\right)-T_w}{\frac{\ln (r_0/r_i)}{2\pi kl}}dt$$

(11)

where k is the thermal conductivity of the glass tube, l is the length of the cast solder sample, r_i and r₀ are the inner and outer radii of the glass tube, T_w is the temperature of water bath, and T(t) represents the temperature of the solder at any time t. Utilizing Equations (10) and (11), Equation (12) is derived as:

$$-m.c.dT=\frac{T-T_w}{\frac{\mathrm{l}\mathrm{n}(r_0/r_i)}{2\pi kl}}dt$$

(12)

Equation (12) can be rearranged to obtain Equation (13) as follows:

$$\frac{dT}{T-T_w}=-\frac{dt}{\frac{mcln(r_0/r_i)}{2\pi kl}}$$

(13)

By integrating from t = 0, at which T = T_m, to any time t, at which T = T(t), the following equations can be obtained:

$$\underset{T_m}{\overset{T}{\int }}\frac{dT}{T-T_w}={\int }_0^t-\frac{dt}{\frac{mcln(r_0/r_i)}{2\pi kl}}$$

(14)

$$\ln \frac{T\left(t\right)-T_w}{T_m-T_w}=-\frac{2\pi kl}{mcln(r_0/r_i)}t$$

(15)

Equation (15) can be re-written as follows to describe the normalized temperature change in the solder over time:

$$\frac{T\left(t\right)-T_w}{T_m-T_w}=e^{-bt}$$

(16)

where b is defined as:

$$b=\frac{2\pi kl}{mcln(r_0/r_i)}$$

(17)

Values of the constants used in Equation (16) for calculating the solder temperature are as follows: sample length (l) of 50 mm, inner radius (r_i) of 1.5 mm, outer radius (r_o) of 7.5 mm, thermal conductivity of glass (k) of 1.15 W/mK, density of solder of 7.49 g/cm³ (for calculating m), specific heat capacity of solder (c) of 0.232 J/gK, and water bath temperature of 25 °C, and the melting temperatures of solder (T_m) used in this study are between 220 °C and 230 °C. The temperature versus time plot is shown in Figure 6 for T_m = 220 °C. For all solders, the cooling rate in the beginning 20 s of ramp-down was found to be between 3.5 °C/s and 3.7 °C/s, which is comparable to the cooling rate used in the solder reflow process. This analysis confirms that the cooling rate experienced by the samples is comparable to the cooling rate in a typical solder reflow process, ensuring that the microstructures and thus the properties of the samples are similar to the solder joints used in applications.

Tensile tests conducted at both ambient and elevated temperatures on the eight alloys for all aging conditions demonstrate the consistent viscoplastic behavior of SAC-Bi alloys. A tensile test conducted at higher strain rates results in increased tensile strength across all alloy compositions and at all three testing temperatures, consistent with the observations by Hassan et al. [27]. In their as-cast conditions, all eight alloys exhibit similar tensile strength across all combinations of strain rates and testing temperatures, as shown in Figure 2a,c,e,g,i,k,m,o. As aging progresses, the effect of Bi doping in SAC305 and SAC405 becomes evident. Ninety days of isothermal aging at 125 °C significantly reduced the tensile strength of SAC305 and SAC405 alloys, as shown in Figure 2b,j. This reduction in the strength of SAC305 and SAC405 with aging is attributed to the coarsening of IMCs, resulting in increased interparticle spacing and less impedance of dislocation movement [41]. A similar, though less pronounced, reduction in tensile strength after aging is observed in the SAC305 + 1 wt.%Bi and SAC405 + 1 wt.%Bi alloys, as shown in Figure 2d,l. This can be attributed to solid solution strengthening [42] by Bi solute atoms, which lessens the decrease in tensile strength compared with that observed in the SAC305 and SAC405 alloys. Adding 2 wt.% Bi and 3 wt.%Bi to either SAC305 or SAC405 results in retained or slightly increased tensile strength after aging, as shown in Figure 2f,h,n,p. Since Bi has limited solubility in SAC305 and SAC405 [43], precipitates of Bi are expected to form in the alloy matrix for any composition that has 2 wt.% or more Bi. Bi precipitates develop progressively with aging because of the non-equilibrium solidification in reflowed solder joints [43]. The observed improvement in tensile strength with high-temperature storage is thus attributed to precipitation strengthening by Bi. The Anand parameters of SAC-Bi alloys containing 1, 2, and 3% Bi in the as-cast condition revealed in this study have the same order of magnitude as those found by Hassan et al. [27]. The viscoplastic behaviors of the SAC-Bi alloys and their change due to aging must be considered when simulating the behaviors of solder joints. The Anand parameters calculated for SAC-Bi alloys in aged conditions are a novel contribution of this study that provides essential inputs for these models. Apart from components made using conventional techniques such as reflow, additively manufactured components are gaining increasing importance in the semiconductor industry because of advantages such as their free form factor and shape, easier handling, less material wastage, and sequential approach for multilayer packages [44] for various important applications [45]. Therefore, future studies could also investigate the viscoplasticity of materials for additively manufactured components.

5. Conclusions

A detailed study was conducted to investigate the effect of Bi doping on the tensile and viscoplastic behaviors of SAC305 and SAC405 solder alloys. Eight alloys including SAC305, SAC305 + 1 wt.%Bi, SAC305 + 2 wt.%Bi, SAC305 + 3 wt.%Bi, SAC405, SAC405 + 1 wt.%Bi, SAC405 + 2 wt.%Bi, and SAC405 + 3 wt.%Bi were cast, aged at three different temperatures for up to 90 days, and tensile-tested at ambient and elevated temperatures at three different constant strain rates. Heat transfer analysis was performed to confirm that the cooling rate experienced by the samples is similar to that of a typical solder reflow process, ensuring that the microstructures of the samples closely resemble those of solder joints used in practical applications. Microstructural analyses were carried out to discuss microstructural causations of these property changes. The following conclusions are drawn from the results:

• When up to 1 wt.% Bi was added to SAC alloys, it existed as solute atoms in the alloy matrix. As aging progressed, SAC305, SAC305 + 1 wt.%Bi, SAC405, and SAC405 + 1 wt.%Bi alloys experienced a reduction in strength. The reduction was less pronounced in SAC305 + 1 wt.%Bi and SAC405 + 1 wt.%Bi because of solution strengthening by Bi solutes. However, the effect from solid solution strengthening was not sufficient to counteract the reduction in strength by 21 to 43% due to aging-induced coarsening of the IMCs.
• When 2 to 3 wt.% Bi was added to SAC alloys, the Bi exceeded the alloy’s solubility, and precipitates formed progressively with aging. The strength of SAC305 + 2 wt.%Bi, SAC305 + 3 wt.%Bi, SAC405 + 2 wt.%Bi, and SAC405 + 3 wt.%Bi increased after aging by around 6 to 10%, attributed to the formation of Bi precipitates.
• Anand viscoplastic parameters for all eight alloys in both the as-cast and nine aging conditions were obtained, which will enable the modeling of these SAC-Bi alloys as solder joints for advanced packaging applications.
• The results reveal the important role of Bi in aging-induced changes in microstructure and mechanical properties. The new findings of this study include revealing the evolution of SAC-Bi microstructures, particularly the precipitation of Bi with aging in SAC doped with 2 to 3% Bi, and the calculation of Anand parameters of SAC-Bi alloys in various aging durations.

Future work will entail applying the obtained Anand parameters in finite element analysis (FEA) to investigate stress and reliability at the packaging level. Parametric studies by FEA will also be carried out to investigate the Anand model efficiency with statistical outputs. Additional aging conditions will be studied. Future studies could also investigate the viscoplasticity of materials for additively manufactured components.