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lead-free solders, the linear acceleration at high temperature (t). A nonlinear
has been assumed. curve fit of the temperature cycling data
Other acceleration models. It should of the ceramic ball grid array (CBGA),
be emphasized that the linear acceleration, chip scale package (CSP), and thin small The constants A, B, and C are shown in
x o = αx T , is only one form of acceleration. outline package (TSOP) on a PCB at Table 1 for three SMDs and test conditions.
There are many other accelerations,e.g., η various temperature ranges such as Linear acceleration factor for
≠ 1 and . More reliability 0 60ºC, 0 100ºC, and -25 125ºC, Sn3Ag0.5Cu in terms of frequency
tests should be performed for a variety of Pan et al., [8] obtained the following and maximum temperature. For
IC packages and temperature cycling l i ne a r a c c e l e r at i o n f a c t or f or Sn3Ag0.5Cu, some of the researchers
conditions to establish the suitable Sn3Ag0.5Cu: still use the classical Norris-Lanzberg
acceleration model [5]. acceleration model, i.e., in terms of
the cyclic frequency and maximum
Acceleration factors temperature during thermal cycling. For
To determine α (the acceleration where t t and t o are the dwell time at PBGA, flip-chip plastic ball grid array
factor), you need an acceleration high temperature, ∆T t and ∆T o are (fc-PBGA), CBGA, CSP, quad flat pack
model, which has been discussed in the the temperature range (in degrees
previous section. How do you choose Celsius) during thermal cycling, and
an acceleration model? The answer is T max , t and T max , o are the maximum
tests and failure mechanisms, which are (peak) temperatures (in degrees Kelvin)
discussed below. at tained during ther mal cycling,
Well-known linear acceleration respectively under testing conditions and
factor for SnPb based on frequency under operating conditions. It should be
and maximum temperature. For SnPb noted that the effect of dwell time on the
solder joints, the following Norris- acceleration factor is (t t /t o ). Because t o
Landzberg linear acceleration factor (operating dwell) is usually longer than
(Equation (2.68) of [4]), has been t t (testing dwell), that means that for a
frequently used: positive power, (t t /t o ) is a deceleration
factor. This is just like the effect of (f o /
f t ) in the classical Norris-Landzberg
equation; usually f t (testing frequency) is
larger than f o (operating frequency). Table 2: The constants a, b, and c for various lead-
free solders in the linear acceleration factor based on
In this equation, T T , f T , ΔT T , and T o , As an example based on the above frequency and mean temperature.
f o , ΔT o , are the maximum temperature discussion, consider the test conditions
during cycling (in degrees Kelvin), the are: 0 100ºC with the dwell time at (QFP), flip-chip, etc. with test conditions
temperature cycling frequency, and the high temperature = 15 minutes and the such as ∆T = 135ºC and ∆T = 180ºC, Lall
temperature range (in degrees Celsius), operating conditions are: 20 70ºC et al., [10] obtained the following linear
respectively, at the testing conditions with the dwell time at high temperature acceleration factor for Sn3Ag0.5Cu:
and at operating conditions. For SnPb = 720 m i nut e s. T he n t he l i ne a r
solders, q = 1/3, and c = 1.9 ~ 2.0 have acceleration factor is:
been used.
Linear acceleration factor for
Sn3Ag0.5Cu in terms of dwell time For example, in the thermal cycling
and maximum temperature. For t e s t o f t he f a n - o ut l e a d - f r e e
Sn3Ag0.5Cu, Pan et al., [8] proposed a For other surface mount devices (SMDs) (Sn3Ag0.5Cu) package of the 10mm x
modification of the classical Norris- and test conditions, Miremadi, et al., [9] 10mm chip, the test conditions are -40
Landzberg equation by replacing the obtained the following linear acceleration 85ºC with 24 cycles per day, and we
cyclic frequency (f) with the dwell time factor with Sn3Ag0.5Cu solder alloy: know that the product can survive 280
cycles. However, we also need to know if
this value of 280 cycles is sufficient to
meet the 5-year operating condition
given by 20 60ºC with 1 cycle per day
(see the calculations below).

The product with SAC305 will survive
13.79 x 280 cycles per day = 3861 ÷ 365 =
10.5 years > 5 years.
Linear acceleration factor for
Table 1: The constants A, B, and C for Sn3Ag0.5Cu tested in various SMDs and conditions in the linear Sn3Ag0.5Cu and other lead-free
acceleration factor based on dwell-time and maximum temperature.

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