INTRODUCTION
Several focused studies investigated aging and
creep/stress relaxation behavior of currently popu-
lar lead-free Sn-based solders.
1–9
Aging is a signif-
icant process that contributes to microstructural
evolution within the solder and solder/substrate in-
terface intermetallic-layer growth. Coarsening of
the intermetallic particles within the solder occurs
during aging and thermomechanical fatigue
(TMF),
2,3,10
but microstructural coarsening is not
observed in TMF,
11
though it occurs with isothermal
aging. There is no direct evidence that Ag
3
Sn parti-
cles contribute to damage accumulation.
5,12
The in-
terface intermetallic-layer growth during TMF is
comparable to that in static aging.
13
Although this
layer is hard and brittle, the fracture that precedes
TMF failure does not occur in this layer or its inter-
face with Sn. The fracture is usually within the sol-
der in a region near the intermetallic compound
(IMC) interface.
14
Creep studies on Sn-Ag solders have shown that
aging affects the secondary creep rate.
2,3
Because of
the highly heterogeneous nature of the solder joint,
creep deformation is typically inhomogeneous.
15
Creep can occur in Sn-based solder joints during the
dwell periods of the thermal excursions encountered
in service. Even the lowest temperature experienced
during service is a high homologous temperature for
Sn-based solders. The predominant creep-damage
phenomena are shear banding, grain-boundary slid-
ing, and grain-boundary decohesion, which are also
observed during TMF.
14,16
Stresses that exist in the
solder joints do not completely relax even during
dwell at the highest temperature experienced dur-
ing service because of the constraints present in the
joint.
9
Damage accumulation under isothermal reverse
straining with large strain amplitudes is very simi-
lar to the damage resulting from TMF.
17,18
Surface-
relief effects that occur under both conditions ulti-
mately develop into cracks that lead to failure of the
joint. Because stresses do not relax during TMF hold
times, it appears that isothermal creep and re-
versed-shear straining contribute to the processes
that cause TMF damage. Residual-mechanical prop-
erties deteriorate during the first few hundred TMF
cycles and then stabilize without further deteriora-
tion for several hundred more cycles.
19
Such behav-
ior is very similar to that of thermal spalling in ce-
ramics, where crack propagation by linking of
microcracks is the controlling factor more than
Journal of ELECTRONIC MATERIALS, Vol. 31, No. 11, 2002 Special Issue Paper
Modeling Thermomechanical Fatigue Behavior
of Sn-Ag Solder Joints
J.G. LEE,
1
A. TELANG,
1
K.N. SUBRAMANIAN,
1,2
and T.R. BIELER
1
1.—Department of Chemical Engineering and Materials Science, Michigan State University, East
Lansing, MI 48824-1226. 2.—E-mail: subraman@egr.msu.edu.
Stresses that develop because of the coefficient of thermal expansion (CTE)
mismatch between solder and substrate/components contribute to thermome-
chanical fatigue (TMF) of the solder joints. However, the relative importance of
several processes that contribute to damage accumulation and its role in af-
fecting the reliability of the solder joints are far from being understood. Aging,
creep/stress relaxation, and stress/strain reversals are some of the important
processes. These processes are affected by service conditions, such as the tem-
perature extremes experienced, rates of heating and cooling, dwell times at the
extreme temperatures, and so on. In addition, the elastic and plastic aniso-
tropy of tin could also contribute to the damage accumulation during TMF of
Sn-based solders. This preliminary effort to model TMF in Sn-Ag solder joints
will consider the role of each of these parameters, with significant emphasis on
the anisotropic-elastic behavior of Sn grains.
Key words: Thermomechanical fatigue, Sn-Ag, solder joints
(Received February 13, 2002; accepted May 28, 2002)
1152

Modeling Thermomechanical Fatigue Behavior of Sn-Ag
Solder Joints 1153
crack nucleation.
20
With crack propagation by link-
ing microcracks as a possible mechanism for TMF
failure, the current investigation focuses on how
cracks may nucleate due to the anisotropic nature of
Sn grains.
ANISOTROPY OF Sn SINGLE CRYSTAL
Tin exists as white tin having a body-centered-
tetragonal structure with a c/a ratio of 0.546. Figure
1 provides a schematic of a Sn unit cell along with
lattice parameters. This structure exhibits signifi-
cant anisotropy in its elastic and thermal-expansion
characteristics. Slip in tin occurs along the planes
and directions listed in Table I at the critical-re-
solved shear stresses given.
21
Acoustic emission that
results from bending of tin is usually termed “tin
crying.” However, the plastic strain that can be ac-
commodated by twinning is typically limited. The
twin plane and twin directions in Sn are {301}^ 03&.
Twinning is usually observed only when slip is not
favorable or sufficient, such as at high strain rates
or low temperatures. Thus, slip may be the preferred
mode of deformation at high temperature and low
strain rates encountered in TMF. In addition, the
elastic constant, coefficient of thermal expansion
(CTE), and hardness values for both the Cu sub-
strate and the Cu
6
Sn
5
intermetallic are important,
and polycrystal values of these parameters are pro-
vided in Table II, along with the single-crystal val-
ues for Sn in the ^a& and ^c& directions. There are
four sets of elastic constants for single-crystal Sn
tabulated by Simmons and Wang,
23
listed in Table
1
III. Because these sets differed significantly, values
given in the third column, which are also provided
in the text by Nye,
24
were used in this analysis.
Using the single-crystal values of CTE and elastic
compliances, the CTE and Young’s modulus (E)
along several chosen directions were calculated and
are presented in Table IV.
ROLE OF Sn-ANISOTROPY ON
THERMOMECHANICAL-FATIGUE
DAMAGE ACCUMULATION
Because the predominant mode of damage accu-
mulation and failure caused by TMF is by grain-
boundary sliding/relief and grain-boundary separa-
tion, this preliminary effort will estimate the elastic
stresses that could develop without plastic deforma-
tion during thermal excursions as a result of
anisotropy in each Sn grain. The calculated elastic
stresses provide an upper bound on possible stresses
because plastic deformation would result in lower
values. Several possible cases are considered to elu-
cidate the implications of Sn anisotropy on the be-
haviors observed in solder joints caused by TMF.
Case 1: Sn Grains Present at the Free Surface
of the Solder Joint That Contribute to Surface
Relief
The strains that develop because of CTE mis-
matches between polycrystalline tin and copper dur-
ing TMF for a temperature excursion of about 165°C
will be about 0.001. However, under such conditions,
the damage caused by TMF begins to develop on the
free surface of the solder joint in about 100 cycles.
Consequently, the strains caused by CTE mis-
matches between adjacent Sn grains could be signif-
icantly larger. To verify this hypothesis, a eutectic
Sn-Ag bulk-solder specimen was aged at 180°C for
180 h to produce a large-grained sample. The grains
present in this sample were about 100–300 mm in
diameter. When this sample was Thermomechanical
fatigued for 20 cycles (12,500 sec at 215°C, heated
in about 50 sec to 150°C for 1,200 sec, and cooled in
about 500 sec), no identifiable surface damage could
be noticed. However, the surface-relief effects that
developed after 100 TMF cycles can be observed by
comparing Fig. 2a and b. The crystallographic orien-
tations of grains 1, 2, and 3, indicated in Fig. 2b,
were obtained from the map in Fig. 2c with an hkl™
orientation mapping system on a Camscan 44FE
scanning electron microscope. Using the orienta-
tions for these three grains, the CTE and E values
Fig. 1. Schematic of single-crystal b-Sn (body-centered-tetragonal
structure) with a 5 5.832 and c 5 3.182 (c/a 5 0.546).
21
Table I. Properties of Single-Crystal b-Sn with Respect to Different Crystal Directions
Slip Slip Twinning Twinning
Metal Plane Direction t
CRSS
(MPa) Plane Direction
(100) [001] 1.863
(110) [001] 1.275
b-Sn (white) (101) [10 ] 1.569 (301) [ 01]
(121) [10 ] 1.667
(100) [011] (?) —
1
31