US 20130275096A1
(19) United States
(12) Patent Application Publication (10) Pub. No.: US 2013/0275096 A1
(43) Pub. Date:
Yoshimura et al.
(54)
SOLDER JOINT FATIGUE LIFE PREDICTION
(57)
Oct. 17, 2013
ABSTRACT
METHOD
(71) Applicant: INTERNATIONAL BUSINESS
MACHINES CORPORATION, (U S)
(72) Inventors: Akifumi Yoshimura, Tokyo (JP); Keishi
Okamoto, KanagaWa (JP)
(21) App1.No.: 13/801,162
(22)
Filed:
Mar. 13, 2013
(30)
Foreign Application Priority Data
Apr. 16, 2012
(JP) ............................ .. JP2012093407
Publication Classi?cation
(51)
Int. Cl.
(52)
US. Cl.
(2006.01)
G06F17/50
CPC ................................ .. G06F 17/5018 (2013.01)
USPC
............................................................ ..
703/2
A solder joint fatigue life predicting method includes: estab
lishing a maximum temperature, a minimum temperature,
and a temperature cycle frequency in a ?eld environment;
establishing a maximum temperature, a minimum tempera
ture, and a temperature cycle frequency in a laboratory envi
ronment for accelerated testing; implementing the acceler
ated testing to measure test fatigue life until failure of the
product; determining exponents for the ramp rate and dWell
time in a novel acceleration factor equation Which is repre
sented using the ramp rates and dWell times of the ?eld
environment and the laboratory environment from pro?le
data of the temperature cycle in the ?eld environment, from
pro?le data of the temperature cycle in the laboratory envi
ronment, and from test fatigue life data, and calculating an
acceleration factor by plugging these exponents into the
acceleration factor equation; and calculating ?eld fatigue life
of the product from the calculated acceleration factor and
measured test fatigue life.
3.43
3.43
003041435324
E 3.44
g
3.42
g
g
y = 0.0310(435255
3.4
g
y = 00313135203
i 3.33
+ DWELL: SMINUTES
335-
3.34
0
+ DWELL: 10 MINUTES
+ DWELL: 20 MINUTES
,
I
I
I
0.5
1
1-5
2
[X-AXIS] NOHHALIZED RAMP RATE
2.5
Patent Application Publication
Oct. 17, 2013 Sheet 1 0f 9
US 2013/0275096 A1
FIG. 1
2.0 CYCLE/HR
(°C)TEMPRATURE
75
0=00
2.6 CYCLE/HR
o='15
0='30
0=45
TIME (HOURS)
1='oo
1=15
1=30
Patent Application Publication
Oct. 17, 2013 Sheet 2 of9
FIG. 2
ZOO
SET USAGE CONDITIONS
FOR PRODUCT
1
SET CONDITIONS FOR
ACCELERATED TEST
1
IMPLEMENT
ACCELERATED TEST
1
DETERMINE
ACCELERATION FACTOR
1
PREDICT FATIGUE
LIFE OF PRODUCT
US 2013/0275096 A1
Patent Application Publication
Oct. 17, 2013 Sheet 4 of9
US 2013/0275096 A1
FIG . 4
TEMPERATURE CYCLE PRoFILE
-—— Tmax -15°C
+ FAST
(TEM“PRA1TU)E
+ sLow
‘
Tmin +10°C
‘T
5'00
H—)
90% FIT T0
1000
1500
TIME (SECONDS)
STRAIGHT LINE
DETERMINE RAMP RATE
FROM Tmin+10°C/TmaX-15°C
2000
Patent Application Publication
Oct. 17, 2013 Sheet 5 0f 9
US 2013/0275096 A1
FIG. 5
TEMPERATTRE CYCLE PROFILE
HIGH
TEMPERATURE
UMELL
HIGH
TEMPERATURE
———— Max -15°C
%
+ FAST
%
+ sLow
———— Tlnin +10°C
-100
.
500
Low- 1
TEMBEFEIHURE
LOW
TEMPERATURE
DWELL
.
.
1000
1500
TIME (SECONDS)
2000
Patent Application Publication
Oct. 17, 2013 Sheet 6 0f 9
US 2013/0275096 A1
FIG. 6
N50) FATIGUE LIFE
3.50E+03
3.00E+03
2.50E+03
[(LFNyCAT-IYSFLGXOEUIT)S]
2.00E+03
1.50E+03
+ DWELL: 5 MINUTES
+ DWELL: 10 MINUTES
—I— DWELL: 20 MINUTES
5.00E+02
0.50E+00
0
30
40
50
B0
[X-AXIS] RAMP HATE PEI/MINUTE)
70
B0
90
Patent Application Publication
Oct. 17, 2013 Sheet 7 0f 9
US 2013/0275096 A1
FIG. 7
NORMALIZED mam FATIGUE LIFE
3.49
3.45
y = -0.0804x+3.5324
E 3.44
g
3.42
%
g
y = -0.081BX+3.52B5
3.4
g
y = -0.0B18x3.5203
i 3.39
+ WELL: 5 MINUTES
+ DWELL: 20 MINUTES
3.34
o
I
l
I
I
0.5
1
1.5
2
[X-AXIS] NOHMALIZED RAMP RATE
2.5
Patent Application Publication
Oct. 17, 2013 Sheet 8 0f 9
US 2013/0275096 A1
FIG. 8
M50) FATIGUE LIFE
9.50503
y 7 3032.5><-°-°222
3.00m
H
x
i
A
F
H
+
I-I-I
A
Q 2.50E+03-
a
EQ
H
I
1 y=
2El23.3x
-0022s
-
l P2485“ coma
'
2.00E+03-
E
g
1.50E+03
1; 1.00503
—
+ RISING RAMP HATE: 82.5“C/MINUTES
+ RISING RAMP HATE: 1B.5°C/MINUTES
+ RISING HAMP HATE: 6.B°C/MINUTES
5-0050?
0
|
|
|
|
5
10
15
20
[x-AXIS] DWELL TIME (MINUTES)
25
Patent Application Publication
Oct. 17, 2013 Sheet 9 0f 9
US 2013/0275096 A1
FIG. 9
NORMALIZED N(50) FATIGUE LIFE
3.48
3 4B
y = -0.0228x+3.450B
358Wm:.52:%i.
a 42
a 38
_
y = -0.024BXE|.3953
3 34
0.2
0.4
0.6
0.8
1.2
[X-AXIS] NORMALIZED DWELL TIME
+ RISING RAMP RATE: 82.5°C/MINUTES
—I— RISING RAMP RATE: 16.5°C/MINUTES
—i— RISING RAMP RATE: B.E°CIMINUTES
1.4
Oct. 17, 2013
US 2013/0275096 A1
SOLDER JOINT FATIGUE LIFE PREDICTION
METHOD
BACKGROUND
[0001]
[0002]
1.Technical Field
The present invention relates to predicting the
[0008] Also, methods for predicting the fatigue life of a
solder joint have been proposed in Which the crack groWth
rate of the solder joint is determined and used. These fatigue
life prediction methods have been disclosed in the folloWing
patent literature:
1. Japanese Laid-open Patent Publication No. 2005- 14801 6
fatigue life of a solder joint, and more speci?cally to a method
for predicting the fatigue life of a solder joint using acceler
2. Japanese Laid-open Patent Publication No. 2008-2869
ated testing.
[0003] 2. BackgroundArt
[0004] The Modi?ed Co?in-Manson (Norris-LandZberg)
3. Japanese Laid-open Patent Publication No. 2012-18107
SUMMARY
Equation is the most commonly used method for predicting
electrical component solder joint fatigue life. This equation is
[0009]
expressed as folloWs.
predicting the fatigue life of a solder joint in a product joined
An aspect of the present invention is a method for
by soldering, the method including the steps of: establishing
a maximum temperature Tmax??eld, a minimum temperature
Equation 1
Tml-njeld, and a temperature cycle frequency F?eld in a ?eld
(Equation 1)
environment of the product; establishing a maximum tem
perature Tmaxilab, a minimum temperature THU-"Jab, and a
temperature cycle frequency F 1a b in a laboratory environment
for accelerated testing of the product; implementing the
[0005] In Equation 1, the acceleration factor (AF) is a num
ber representing the degree to Which results from accelerated
testing are accelerated relative to the ?eld environment. The
index “?eld” represents the ?eld environment on the market,
and “lab” represents the laboratory environment. AT?eZd and
ATM, are the difference betWeen the Tm“ (maximum tem
perature) and the Tm.” (minimum temperature) in a tempera
ture cycle test repeating high and loW temperatures. F is the
frequency of the temperature cycle (representing the number
of rising temperature and falling temperature cycles Within a
given period of time), F?e id is the temperature cycle frequency
in the ?eld environment, and PM is the temperature cycle
frequency in the laboratory environment. Tmax??eld is the
maximum temperature in the ?eld environment, and Tmaxilab
is the maximum temperature in the laboratory environment.
E, is the activation energy, and R is the Boltzmann Constant.
[0006] The activation energy E, is a value (constant) deter
mined from experimental results. The value used for 5Sn
95Pb solder is usually 0.123 eV in fatigue life estimates. The
Boltzmann Constant R is 8.6159><10_5 eV/k (physical con
stant). The exponent n for AT (AT?eZd and ATM) is a value
accelerated testing of the product to measure a test fatigue life
NM, until failure of the product; determining exponent ml for
the ramp rate and exponent m2 for the dWell time in Equation
2 beloW, Which is represented using the ramp rate Ramp ?eld
and the dWell time DWell?e 1d of the ?eld environment, and the
ramp rate Ramp lab and the dWell time DWellZab of the labo
ratory environment from the pro?le data of a temperature
cycle using the established maximum temperature Tm axje 1d,
the minimum temperature Tml-n??eld, and the temperature
cycle frequency F?eld of the ?eld environment, from the pro
?le data of a temperature cycle using the established maxi
mum temperature Tmax Jab, the minimum temperature Tm,-L
1a b, and the temperature cycle frequency F 1a b of the laboratory
environment, and from the measured data of the test fatigue
life NM, and calculating an acceleration factor AF by plug
ging the determined exponents ml and m2 into Equation 2;
and calculating a ?eld fatigue life N?eld of the product from
the calculated acceleration factor AF and the test fatigue life
Nlab (N?eZd:AF XNZGZJ)’
Equation 2
(constant) determined from experimental results, With n:1.9
used for 5Sn-95Pb solder, and n:2.1 used for Pb-free solder.
The exponent m for F (F?eld and Flak) is a value (constant)
AF : [AT?eld
1*” X [ Ramp/72M
1''“ X
ATM;
Ramplab
determined using Norris-Landsberg testing, Where m:1/3. In
(Equation 2)
E
l
l
Dwell?eld m2 X ?lmgj?mgq]
accelerated testing, the AT, F and Tmax for the ?eld environ
ment (?eld) and the laboratory environment (lab) are knoWn,
Dwelllab
and can be used in the calculation along With the constants to
predict the fatigue life in the ?eld environment (?eld) from
experimental results. For example, When the test fatigue life
of an experimental solder joint is 3,000 cycles, and the accel
eration factor AF derived from the Modi?ed Co?in-Manson
Equation is 4.5, the folloWing fatigue life is estimated for the
?eld environment of the market: 3,000 cycles><4.5 (accelera
tion factor):13,500 cycles.
[0007]
The fatigue life of the solder is predicted using ?nite
element analysis, and the strain energy density is used as one
of the parameters in predicting the fatigue life of the solder.
ATIQbITmQXJQb- TminAlab
n: Constant Determined By Solder
Ea: Activation Energy
R: BoltZmann Constant
The acceleration factor modeled and calculated in the ?nite
[0010]
element analysis is in harmony With actual experimental
rate” is the rate at Which the temperature rises to a high
temperature or falls to a loW temperature (unit: ° C./hour), and
results.
As understood by those skilled in the art, “ramp
US 2013/0275096 A1
“dwell time” is the retention time at a predetermined high
temperature or loW temperature (unit: hours).
[0011] In an embodiment, the step for calculating the accel
eration factor AF further includes, When determining the
exponent ml for the term of the ramp rates Ramp?e 1d and
Oct. 17,2013
[0018] In an embodiment, When it has been determined in
the determination of a correlation betWeen the test fatigue life
NM, and the ramp rate during a falling loW temperature
RampDoWnZab that there is no correlation, ml 17:0 and [Ramp
DoWn?eZd/RampDoWnZabY"lbIl for [RampDoWn?eZd/Ramp
Ramp 1a b, determining Whether or not the size of the ramp rate
Downzaljmlb constituting another portion of the ramp rate
RampUpZab and the ramp rate RampDoWnZab for a rising tem
perature and a falling temperature in the temperature cycle of
term [Ramp?eZd/Ramp Zab]'"1.
the laboratory environment for the ramp rate Ramp 1a b are the
[0019] In an embodiment, When it has been determined in
the determination of a correlation betWeen the test fatigue life
same or different.
NM, and the ramp rate during a falling loW temperature
[0012]
RampDoWnZab that there is a correlation, a linear function
representing a normalized test fatigue life NM, using a nor
In an embodiment, When it has been determined that
the size of the ramp rate RampUp 1a b and the ramp rate Ramp
DoWnZab for a rising temperature and a falling temperature in
the temperature cycle of the laboratory environment are the
same, a function is derived representing the test fatigue life
NM, using a ramp rate Ramplab corresponding to a ramp rate
RampUpZab or RampDoWnZab for a rising or falling tempera
ture, and a correlation is determined betWeen the test fatigue
life NM, and the ramp rate Ramplab.
[0013] In an embodiment, When it has been determined in
the determination of a correlation betWeen the test fatigue life
NM, and the ramp rate Ramplab that there is no correlation,
m1:0, and the ramp rate term [Ramp?eld/ Ramp 1a b]’"1:1.
[0014] In an embodiment, When it has been determined in
the determination of a correlation betWeen the test fatigue life
NM and the ramp rate Ramplab that there is a correlation, a
linear function representing a normalized test fatigue life NM,
using a normalized ramp rate Ramplab is derived from the
function representing the test fatigue life NM, using the ramp
rate Ramplab, ml is determined from the slope of the linear
function, and the ramp rate term [Ramp?eld/Ramplab]’”l is
calculated.
[0015] In an embodiment, When it has been determined that
the size of the ramp rate RampUpZab and the ramp rate Ramp
DoWnZab for a rising temperature and a falling temperature in
the temperature cycle of the laboratory environment are dif
ferent, a function is derived representing the test fatigue life
malized ramp rate during a falling loW temperature Ramp
DoWnZab is derived from a function representing the test
fatigue life NM, using the ramp rate during a falling loW
temperature RampDoWnZab, mlb is determined for [Ramp
DoWri?eZd/RampDoWnZab]'"1b constituting another portion of
the ramp rate term [Ramp?ezd/Ramplab]’”l from the slope of
the linear function, and [RampDoWn?eZd/RampDoWnZab]'"1b
is calculated.
[0020] In an embodiment, the step for calculating the accel
eration factor AF further includes, When determining the
exponent m2 for the term of the dWell times DWell?eZd and
DWellZab, determining Whether or not a dWell time DWell_
Highlab and a dWell time DWell_LOWZab for a high tempera
ture and a loW temperature in the laboratory environment for
the dWell time DWellZab are the same or different.
[0021]
In an embodiment, When it has been determined that
the dWell time DWell_HighZab and the dWell time DWell_
LOWZab for a high temperature and a loW temperature in the
laboratory environment are the same, a function is derived
representing the test fatigue life NM, using a dWell time
DWellZab corresponding to the DWell_HighZab or the DWell_
LOWZab for a high temperature or a loW temperature, and a
correlation is derived betWeen the test fatigue life NM and the
dWell time DWellZab.
[0022] In an embodiment, When it has been determined in
the determination of a correlation betWeen the test fatigue life
NM, using the ramp rate RampUpZab during a rising high
NM, and the dWell time DWellZab that there is no correlation,
temperature and the correlation is determined betWeen the
test fatigue life NM, and the ramp rate RampUp 1a b during a
rising high temperature, and a function is derived represent
m2:0 and the dWell time term [DWell?eZd/DWellZab]’"2:1.
ing the test fatigue life NM, using the ramp rate RampDoWnZab
during a falling loW temperature and the correlation is deter
mined betWeen the test fatigue life NM, and the ramp rate
RampDoWnZab during a falling loW temperature.
[0023] In an embodiment, When it has been determined in
the determination of a correlation betWeen the test fatigue life
NM and the dWell time DWellZab that there is a correlation, a
linear function representing a normalized test fatigue life NM,
using a normalized dWell rate DWellZab is derived from the
NM, and the ramp rate during a rising high temperature Ram
pUpZab that there is no correlation, mMIO and [RampUp?eZd/
RampUp 1a b]’"1“:1 for [RampUp?eZd/ RampUp 1a b]’"l“ consti
tuting a portion of the ramp rate term [Ramp?eld/Ramplab]’"l.
function representing the test fatigue life NM, using the dWell
time DWellZab, m2 is determined from the slope of the linear
function, and the dWell time term [DWell?eZd/DWelllab]’”2 is
calculated.
[0024] In an embodiment, When it has been determined that
the dWell times DWell_HighZab and the DWell_LOWZab for a
high temperature and a loW temperature in the laboratory
[0017] In an embodiment, When it has been determined in
the determination of a correlation betWeen the test fatigue life
the test fatigue life NM, using the dWell time DWell_HighZab
[0016] In an embodiment, When it has been determined in
the determination of a correlation betWeen the test fatigue life
environment are different, a function is derived representing
ramp rate during a rising high temperature RampUpZab is
for a high temperature and the correlation is determined
betWeen the test fatigue life NM, and the dWell time DWell_
Highlab for a high temperature, and a function is derived
representing the test fatigue life NM, using the dWell time
derived from a function representing the test fatigue life NM,
DWell_LOWZab for a loW temperature and a correlation is
using the ramp rate during a rising high temperature RampU
p My“ from the slope of the linear function, and [Ramp
determined betWeen the test fatigue life NM and the dWell
time DWell_LOWZab for a loW temperature.
[0025] In an embodiment, When it has been determined in
the determination of a correlation betWeen the test fatigue life
Up?eZd/RampUpZab]'"1“ is calculated.
NM, and the dWell time at high temperature DWell_HighZab
NM, and the ramp rate during a rising high temperature Ram
pUpZab that there is a correlation, a linear function represent
ing a normalized test fatigue life NM, using a normalized
p lab, mm is determined for [RampUp?eZd/RampUpZab]'"1“
constituting a portion of the ramp rate term [Ramp?eZd/Ram
US 2013/0275096 A1
Oct. 17,2013
that there is no correlation, m2a:0 and [Dwell_High?eZd/
Equation 3; and calculating a ?eld fatigue life N?eld of the
Dwell_HighZab]’"2“:l for [Dwell_High?eZa/DwelLHighZab]
product from the calculated acceleration factor AF and the
m2“ constituting a portion of the dwell time term [Dwell?eld/
test fatigue life NW, (N?eZfAFxNZa 1,).
DwellZab]’"2.
[0026] In an embodiment, when it has been determined in
the determination of a correlation between the test fatigue life
Equation 3
(Equation 3)
NM and the dwell time at high temperature Dwell_HighZab
ATM,
that there is a correlation, a linear function representing a
normalized test fatigue life NM, using a normalized dwell
time at a high temperature Dwell_HighZab is derived from the
Ramplab
Tmm. ?eld m3
Dwelllab
E
1
1
*i[
**************
ii]
X e R Tmaxjeld Tmax’lab
Tminhzb
function representing the test fatigue life NM, using the dwell
time at a high temperature Dwell_HighZab, m2a is determined
for [Dwell_High?eZd/Dwell_HighZab]m2“ constituting a por
tion of the dwell time term [Dwell?eld/Dwelllal,]'"2 from the
slope of the linear function, and [Dwell_High?eZd/Dwell_
Highlab]’"2a is calculated.
[0027] In an embodiment, when it has been determined in
the determination of a correlation between the test fatigue life
NM, and the dwell time at low temperature Dwell_Low 1a b that
there is no correlation, m2b:0 and [Dwell_Low?eZd/Dwell_
ATlab: Tmaxilab_ TminAlab
n: Constant Determined By Solder
Ea: Activation Energy
R: Boltzmann Constant
Lowla b]’”2l7 :1 for [Dwell_Low?eZd/DwelLLowZab]"'217 consti
tu2ting a portion of the dwell time term [Dwell?eld/Dwelllab]
BRIEF DESCRIPTION OF THE DRAWINGS
[0028] In an embodiment, when it has been determined in
the determination of a correlation between the test fatigue life
[0030] FIG. 1 is a graph showing pro?les of temperature
cycles at two different frequencies.
[0031] FIG. 2 is a ?owchart schematically illustrating a
method for predicting a solder joint fatigue life according to
NM and the dwell time at low temperature Dwell_LowZab that
there is a correlation, a linear function representing a normal
ized test fatigue life NM, using a normalized dwell time at a
an embodiment of the present invention.
low temperature Dwell_LowZab is derived from the function
representing the test fatigue life NM, using the dwell time at a
low temperature Dwell_LowZab, m2b is determined for
in Step 240 of the method shown in FIG. 2.
[Dwell_Low?eZa/Dwell_LowZab]’"2b, constituting another
portion of the dwell time term [Dwell?eld/Dwelllal,]'"2l7 from
the slope of the linear function, and [Dwell_Low?eZd/Dwell_
Lowlal,]'"2l7 is calculated.
[0029] A further aspect of the present invention is a method
for predicting the fatigue life of a solder joint in a product
joined by soldering, the method comprising the steps of:
establishing a maximum temperature Tmaxjeld, a minimum
temperature Tml-n??eld, and a temperature cycle frequency
F?eld in a ?eld environment of the product; establishing a
maximum temperature Tmaxilab, a minimum temperature
Tminilab, and a temperature cycle frequency PM in a labora
tory environment for accelerated testing of the product;
implementing the accelerated testing of the product to mea
sure a test fatigue life NM, until failure of the product; deter
mining exponent ml for the ramp rate, exponent m2 for the
dwell time, and exponent m2 for the minimum temperature in
Equation 3 below, which is represented using the ramp rate
[0032]
[0033]
FIG. 3 is a ?owchart showing processing performed
FIG. 4 is a graph showing pro?les of temperature
cycles related to ramp rate.
[0034]
FIG. 5 is a graph showing pro?les of temperature
cycles related to dwell time.
[0035] FIG. 6 is a graph showing a function representing
test fatigue life using a ramp rate.
[0036] FIG. 7 is a graph showing a linear function repre
senting normalized test fatigue life using a normalized ramp
rate.
[0037] FIG. 8 is a graph showing a function representing
test fatigue life using a dwell time.
[0038] FIG. 9 is a graph showing a linear function repre
senting normalized test fatigue life using a normalized dwell
time.
DETAILED DESCRIPTION
Technical Problems
[0039]
In the commonly used Modi?ed Cof?n-Manson
Equation, the acceleration factor AF is a function of the tem
Ramp?ezd and the dwell time Dwell?eld of the ?eld environ
perature cycle frequency F. Because of the relationship to the
ment, and the ramp rate Ramp 1a b and the dwell time Dwell 1a b
temperature cycle frequency F 1a b for a laboratory environ
ment in the denominator, m is 1/3 and a positive value. Thus,
the value for the acceleration factor AF is smaller at a faster
of the laboratory environment from the pro?le data of a tem
perature cycle using the established maximum temperature
Tmax??eld, the minimum temperature Tml-n??eld, and the tem
perature cycle frequency F?eld of the ?eld environment, from
the pro?le data of a temperature cycle using the established
maximum temperature Tmax Jab, the minimum temperature
temperature cycle with a greater PM, value, and the value for
the acceleration factor AF is larger at a slower temperature
cycle with a smaller F 1a b value relative to a longer fatigue life.
Therefore, the fatigue life is shorter.
Tml-nilab, and the temperature cycle frequency PM, of the
[0040]
laboratory environment, and from the measured data of the
test fatigue life NM, and calculating an acceleration factor AF
by plugging the determined exponents m1, m2 and m3 into
the oven conditions were JEDEC JESD 22-Al 04 Condition G
However, an experiment was conducted in which
(—45/l25° C.) as shown in FIG. 1. In other words, the Tm,”
(minimum temperature) was —45° C., the Tmax (maximum
Oct. 17, 2013
US 2013/0275096 A1
temperature) was 1250 C., and SoakMode2 Was used. Under
these conditions, the temperature cycle frequencies are 2
cycles per hour (see 110 in FIG. 1) and 2.6 cycles per hour
(see 120 in FIG. 1), With the holding time at Tm.” and Tmax
being a minimum of ?ve minutes. As a result, the fatigue life
Was 20% faster, that is, shorter, at 2.6 cycles per hour, Which
is the sloWer temperature cycle frequency. In the calculation
performed using the Modi?ed Co?in-Manson Equation, 2
cycles per hour, Which is the faster temperature cycle fre
quency, had a larger acceleration factorAF than 2.6 cycles per
hour, Which is the sloWer temperature cycle frequency, and
the fatigue life Was 9% shorter. Thus, the experimental results
demonstrated that the fatigue life prediction for the solder
joint of the product using the Modi?ed Co?in-Manson Equa
tion Was not accurate.
[0041]
The acceleration factor modeled and calculated in
the ?nite element analysis is in harmony With actual experi
mental results, but a model has to be created in the ?nite
element analysis simulation for each product shape to be
tested. The results depend entirely on the equation represent
ing the model, hoW the model is created, the boundary con
ditions, and the incorporated parameters. In other Words, it is
not generaliZed, and a simple fatigue life prediction method
cannot be obtained. A solder joint fatigue life prediction
method using the crack groWth rate of the solder joint is also
not a simple fatigue life prediction method because the crack
groWth rates have to be determined and used individually.
[0042] The present invention realiZes a simple method that
is able to predict the fatigue life of a solder joint in a product.
[0050]
Maximum PoWer of Product
[0051] Air FloW Rate During Cooling
[0052]
Next, the conditions for the accelerated testing are
established (Step 220).
[0053] The conditions for the accelerated testing include
the maximum temperature Tmaxilab, the minimum tempera
ture Tml-Llab, and the temperature cycle frequency PM, in the
laboratory environment for accelerated testing of the product.
For example, the accelerated testing can be performed under
the JEDEC JESD 22-A104 Condition G (—45/125o C.) as
shoWn in FIG. 1. In other Words, the Tm.” (minimum tempera
ture) is —45° C., the Tmax (maximum temperature) is 1250 C.,
and SoakMode2 is used. Under these conditions, the tempera
ture cycle frequencies are 2 cycles per hour (see 110 in FIG.
1) and 2.6 cycles per hour (see 120 in FIG. 1), With the dWell
time (holding time) at Tm,” and Tmax being a minimum of ?ve
minutes. Thus, the maximum temperature Tmax lab is estab
lished at 1250 C., the minimum temperature Tm; 1a b is estab
lished at —45° C., and the temperature cycle frequencies PM
are established at 2 cycles per hour and 2.6 cycles per hour.
[0054] Next, the accelerated testing is implemented under
the established conditions (Step 230). The accelerated testing
is implemented, and the test fatigue life Nlab is measured until
failure of the product. If the test fatigue life NM, can be
measured in the accelerated testing by accelerating the failure
of the product using the temperature load of the temperature
cycle, an actual experiment does not have to be conducted. An
experiment simulation able to faithfully reproduce an experi
Solution to Problems
[0043]
The folloWing is an explanation of the present inven
tion With reference to a preferred embodiment of the present
invention. HoWever, the present embodiment does not limit
the present invention in the scope of the claims. Also, all
combinations of characteristics explained in the embodiment
are not necessarily required in the technical solution of the
present invention. The present invention can be embodied in
many different Ways, and the present invention should not be
interpreted as being limited to the content of the embodiment
described beloW. In the explanation of the embodiment of the
present invention, identical con?gurational units and con
ment can be employed.
[0055]
Next, the acceleration factor is determined using a
novel acceleration factor equation (Step 240). The novel
acceleration factor equation can be either Equation 2 or Equa
tion 3. An acceleration factor can be determined using either
Equation 2 or Equation 3.
Equation 2
AT 12
T”
Ramp“;
?gurational elements are denoted using the same reference
signs.
[0044]
m1
(Equation 2)
“=1 ATM;f”) l RamplabM] X
m2
,,,,,,,,,,,,,,, ,if
X e R [Tmaxjeld Tmax’lab]
Dwelllab
FIG. 2 is a ?owchart schematically illustrating a
method 200 for predicting a solder joint fatigue life according
to an embodiment of the present invention. First, the ?eld
conditions of the solder-j oined product are established (Step
210). The ?eld conditions of the product include the maxi
mum temperature Tmaxje 1d, the minimum temperature Tmi,L
?e 1d, and the temperature cycle frequency F?e 1d under the ?eld
conditions of the product. These can be established by simply
using the speci?cations of the product When available. At a
minimum, the folloWing items are usually provided in the
speci?cations of a product.
[0045] Number of Years Under Product Warranty
[0046] PoWer ON Time (PoWer ON Time Guarantee)
[0047]
ON/OFF Cycle (Number of Product ON/OFF
Cycles)
[0048] Minimum/ Maximum Operating Environment
Temperatures (Installation Environment of the Product)
[0049] Minimum/ Maximum Product Temperatures
[0056] As for Equation 2, exponent ml for the ramp rate
term [Ramp?eld/Ramplab]’"l and exponent m2 for the dWell
time term [DWell?eZa/DWellZab]'"2, Which are represented
using the ramp rate Ramp?ezd and the dWell time DWell?eZd of
the ?eld environment, and the ramp rate Ramplab and the
dWell time DWellZab of the laboratory environment, are deter
mined from the pro?le data of the temperature cycle using the
established maximum temperature Tmax??eld, the minimum
temperature Tml-njeld, and the temperature cycle frequency
F?eld of the ?eld environment established in Step 210, from
the pro?le data of the temperature cycle using the established
maximum temperature Tmaxilab, of minimum temperature
THU-"Jab, and the temperature cycle frequency PM of the
laboratory environment established in Step 220, and from the
test fatigue life NM, measured in Step 230, and the accelera
tion factor AF is calculated by plugging the determined expo
nents ml and m2 into Equation 2.
Oct. 17, 2013
US 2013/0275096 A1
the product and its application, the dwell time for the ?eld
Equation 3
AF
environment is Dwell_High?e1dIDWell_Low?eZd:Dwell?eZd,
AT?eld ’” [Ramp?dd )ml
_[ ATM, ]
Ramplab
Tmm?eld m3
.
Dwell?eld '“2
[ Dwelllab ]
(Equation 3)
J] **************ii]
E
X e R Tmaxjeld Tmax’lab
Tminlab
[0057] As for Equation 3, exponent ml for the ramp rate
term [Ramp?eZd/Ramp Zab]'"1, exponent m2 for the dwell time
term [Dwell?eld/Dwelllaby?, and exponent m3 for the mini
mum temperature term [Tml-njeld/Tml-Lla?m, which are rep
resented using the ramp rate Ramp?eld, the dwell time Dwell
?eld, and the minimum temperature Tml-n??eld of the ?eld
environment, and the ramp rate Ramplab, the dwell time
Dwell lab, and the minimum temperature Tml-Llab of the labo
ratory environment, are determined from the pro?le data of
the temperature cycle using the established maximum tem
or Dwell?eld:[(40000/3000)—(0.5*2)]/2z6. 17 hours. When
the minimum temperature Tmin??eld and the maximum tem
perature Tmax??eld for the ?eld environment of the product are
—10° C. and 105° C., and the siZes of the ramp rates Ramp
Up?eld and RampDown?eZd during rising and falling tempera
tures are the same, the ramp rate for the ?eld environment is
RampUp?e ZfRampDown?e ZfRamp?e id, or Ramp?e Zd:
[105—(—10)]/30z3.83° C./minute. In this way, the dwell times
Dwell_High?eZd and Dwell_Low?eZd and the ramp rates Ram
pUp?eZd and RampDown?eZd for the ?eld environment can be
obtained whether the high-temperature and low-temperature
dwell times and the rising temperature and falling tempera
ture ramp rates are the same or different.
[0061] A temperature cycle pro?le for the laboratory envi
ronment can be obtained from the data in the following way.
In FIG. 4 and FIG. 5, a temperature cycle pro?le for the
laboratory environment is represented in a graph using tem
perature Tmax??eld, the minimum temperature Tml-n??eld, and
perature and time data. The graphs in FIG. 4 and FIG. 5
the temperature cycle frequency F?el d of the ?eld environment
established in Step 210, from the pro?le data of the tempera
ture cycle using the established maximum temperature Tmax
Jab, the minimum temperature Tml-nilab, and the temperature
represent the relationship between temperature and time by
linking the temperature (° C.) and the time (seconds) when the
temperature cycle frequency is 2.6 cycles/hour (FAST) and
when the temperature cycle frequency is 2 cycles/hour
(SLOW). A single temperature cycle is shown in FIG. 4 and
FIG. 5, but a single cycle is enough to determine the tempera
cycle frequency PM, of the laboratory environment estab
lished in Step 220, and from the measured data of the test
fatigue life NM, established in Step 230, and an acceleration
factorAF is calculated by plugging the determined exponents
m1, m2 and m3 into Equation 3.
[0058] Next, the fatigue life of the product is estimated
(Step 250). The fatigue life of the product is estimated by
calculating the ?eld fatigue life N?eld of the product from the
acceleration factor AF calculated using Equation 2 or Equa
tion 3, and from the measured test fatigue life NM,
(N?eZd:AF><NZab) The fatigue life of the solder joint estimated
in this way does not depend on the temperature cycle fre
quency as in the Modi?ed Co?in-Manson Equation, but is
derived in a newly devised way from the ramp rate and the
dwell time or from the ramp rate, the dwell time and the
minimum temperature. As a result, the fatigue life is more
accurately re?ected in accelerated testing, and matches
experimental results more closely than the Modi?ed Co?in
Manson Equation.
[0059] FIG. 3 is a ?owchart showing processing 300 per
formed in Step 240 of the method 200. First, the temperature
ture cycle pro?le because the same cycle is repeated. FIG. 4
and FIG. 5 show examples of temperature cycle pro?le data
for two different temperature cycles, but the temperature
cycle pro?le data can also be determined using a single tem
perature cycle frequency. When determined using a single
temperature cycle frequency, various temperature cycle pro
?les can be obtained by varying the ramp rate and dwell time.
[0062] Next, the temperature cycle pro?le is divided (Step
315), and the ramp rate term and the dwell time term are
processed. Because the ramp rates and dwell times for the
?eld environment have already been explained, the ramp rates
and dwell times for the laboratory environment will now be
explained. The ramp rates for the laboratory environment
include the rising temperature and falling temperature ramp
rates RampUpZab and RampDownZab in the temperature cycle.
The ramp rates for the laboratory environment can be deter
mined from the temperature rate (unit: ° C./hour) for the
portion of the relationship of the temperature and the time
cycle pro?les are acquired (Step 310). The temperature cycle
pro?les, which represent the relationship between tempera
when the temperature is rising or falling which is a 90% ?t
with a straight line, or from the temperature rate (unit: °
C./hour) for a rising or falling temperature between the maxi
ture and time, include the temperature cycle pro?le for the
?eld environment and the temperature cycle pro?le for the
mum temperature Tmax ‘lb-15° C. and the minimum tempera
ture Tml-Lla b+10° C. In FIG. 4, the falling temperature ramp
laboratory environment. The temperature cycle pro?le data
rate RampDownZab is determined from the temperature rate
(unit: ° C./hour) for the portion which is a 90% ?t with a
straight line, and the rising temperature ramp rate RampUp 1a b
is determined from the temperature rate (unit: ° C./hour)
for the ?eld environment is obtained from the maximum
temperature Tmax??eld, minimum temperature Tml-n??eld, and
the temperature cycle frequency F?eld, and the temperature
cycle pro?le data for the laboratory environment is obtained
from the maximum temperature Tmaxilab, minimum tempera
ture Tml-Llab, and the temperature cycle frequency Flak.
[0060] A temperature cycle pro?le for the ?eld environ
ment can be obtained from the data in the following way.
When there are 3,000 ON/OFF cycles over 40,000 hours, the
power ON time is calculated as 40,000/3,000z13.3 hours/
cycle, and the time per cycle is 13.3 hours. When the rising
temperature and falling temperature times are 30 minutes
each and the retention time at the high temperature and the
low temperature are the same based on the characteristics of
between the maximum temperature Tmax Jab-15° C. and the
minimum temperature T minila b+10° C.
[0063] The dwell times for the laboratory environment
include high-temperature and low-temperature dwell times
Dwell_HighZab and Dwell_LowZab. In dwell times for the
laboratory environment, the high-temperature dwell time
Dwell_HighZab can be the time the temperature is held
between the maximum temperature Tmaxilab and the maxi
mum temperature TmaLZab—15° C., and the low-temperature
dwell time Dwell_LowZab can be the time the temperature is
held between the minimum temperature Tml-Llab and the
Oct. 17, 2013
US 2013/0275096 A1
denotes the ramp rate. As shown in FIG. 6, the fatigue life
minimum temperature TmaLZab+10° C. For example, when
the maximum temperature Tmaxilab is 125° C., the high-tem
perature dwell time Dwell_HighZab is the time the product is
N(50) becomes smaller or shorter as the ramp rate becomes
faster or larger.
held at a temperature between 110° C. (125-15° C.) and 125°
C. When the minimum temperature Tml-Llab is —45° C., the
[0067] Next, the correlation with fatigue life is determined
(Step 332). In this determination, the derived functions are
low-temperature dwell time Dwell_LowZab is the time the
used. As shown in FIG. 6, the three derived functions are
product is held at a temperature between —35° C. (—45+10°
C.) and —45° C. As shown in FIG. 5, the high-temperature and
ramp rate. If the three derived functions are different or the
low-temperature dwell times Dwell_HighZab and Dwell_
Lowlab are determined from the temperature cycle pro?les.
[0064]
When the ramp rate term shown on the left in FIG. 3
is processed, it is ?rst determined whether the sizes of the
rising temperature and falling temperature ramp rates Ram
pUpZab and RampDownZab are the same or different (Step
similar, and indicate the correlation between fatigue life and
ramp rates do not change the fatigue life N(50) by more than
5% in the entire ramp rate range, it can be determined that
there is no correlation between fatigue life and ramp rate. In
this situation, the process advances to Step 334, where ml:0
for the ramp rate term [Ramp?el d/Ramp 1a l,]’"1 in Equation 2 or
Equation 3, and [Ramp?eld/ Rampla b]’"1:1. Afterwards, the
320). In this determination, it is determined whether the sizes
process advances to Step 390, and [Ramp?ela/Ramplab]'"l:l
of these ramp rates RampUp 1a b and RampDownZab are differ
ent by 20% or more. If not, they are deemed to be the same.
tion 2 or Equation 3.
The faster or larger ramp rate is used as the reference, and it is
determined by comparing 20% of the size to the difference
between the sizes of both ramp rates.
[0065] Next, when it has been determined that the sizes of
the rising temperature and falling temperature ramp rates
is used in the novel acceleration function equation of Equa
[0068] When it has been determined in Step 332 that there
is a correlation between the fatigue life and the ramp rate, the
process advances to Step 336 where the ramp rate term is
calculated. In the calculation of the ramp rate term, a linear
function representing a normalized fatigue life N(50) using a
normalized ramp rate is derived from a function representing
RampUpZab and RampDownZab are the same, the process
advances to Step 330, and the correlation between the ramp
rate and the fatigue life is calculated. In this calculation, the
temperature cycle pro?le data is used to derive a function
the three fatigue lives N(50) derived in Step 330 (in the
representing the test fatigue life NM, using at least three
in Table 2 below are used.
calculation of the correlation between the ramp rate and the
fatigue life) using the ramp rate. In this derivation, the loga
rithms of the data in Table 1 are taken, and the values shown
different ramp rates for at least three different dwell times.
For example, the three different dwell times may be the same
at the hi gh-temperature end, the low-temperature end, or both
ends, and may be 5 minutes, 10 minutes and 20 minutes. The
TABLE 2
Normalized N(50) Fatigue Life
three different ramp rates at these dwell times may be the
same for a rising temperature, a falling temperature, or both.
These may be 82.5° C./minute, 16.5° C./minute and 6.6°
Dwell Time
0.69897
1
1.30103
C./minute during a rising temperature. The results shown in
Table 1 below were obtained when nine different combina
tions of these dwell times and ramp rates were applied to
Rising
Ramp
1.916454
1.217484
3.378245
3.434904
3.370086
3.427662
3.363315
3.421146
Rate
0.819544
3.466319
3.45943
3.452926
fatigue life N(50) at which 50% of the products in the accel
erated testing failed. A fatigue life N(50) at which 50% of the
products in the accelerated testing fail is used as the test
[0069]
fatigue life NM, so as to take into account the implementation
the vertical axis denoting the normalized fatigue life N(50)
time of the accelerated testing. However, the test fatigue life
NM, is not limited to fatigue life N(50). If the implementation
time of the accelerated testing is not taken into account, any
and the horizontal axis denoting the normalized ramp rate, the
linear functions shown in FIG. 7 are derived. The resulting
fatigue life N(P) at which 50% or more of the products in the
accelerated testing fail can be used. Here, 50sPs100 because
50% or more of the products have to fail in the accelerated
testing in order to obtain a test fatigue life NM, that is reliable
TABLE 1
RampUpZab:RampDownZafRampZab, ml is obtained from
the resulting slope, and the ramp rate term [Ramp?eZd/Ram
term [Ramp?ezd/Ramplab]’”l is plugged into the novel accel
eration factor equation in Equation 2 or Equation 3.
N(5 0) Fatigue Life
Dwell Time Minutes
82.5
16.5
6.6
slopes of the three linear functions are a coe?icient of variable
x. The average of the three slopes is taken as the slope of the
linear
function.
Because
the
ramp
rate
is
plal,]’"l is calculated. A value obtained in the manner
described above is used as Ramp?eld, and a value obtained in
the accelerated testing is used as Ramplab. Afterwards, the
process advances to Step 390, and the calculated ramp rate
and accurate.
Rising
Ramp Rate
(° C./min.)
When numerical values in Table 2 are graphed with
[0070]
5
10
20
2389
2722
2926
2345
2677
2880
2308
2637
2837
When it has been determined in Step 320 that the
sizes of the rising temperature and falling temperature ramp
rates are different, the process advances to Step 340 or Step
350. In Step 340, the correlation between the ramp rate and
the fatigue life during high-temperature rising is calculated.
In Step 350, the correlation between the ramp rate and the
fatigue life during low-temperature falling is calculated.
[0066] The functions shown in FIG. 6 were derived by
plotting the data in Table 1 on a graph in which the vertical
axis denotes the fatigue life N(50) and the horizontal axis
These calculations are performed in the same way as the
calculations in Step 330. However, the data for the ramp rate
is data for the ramp rate during high-temperature rising or
Oct. 17, 2013
US 2013/0275096 A1
M117 '
data for the ramp rate during low -temperature falling. Data is
pUpZab
obtained as shown in Table 1, and as shown in FIG. 6, func
to the novel acceleration factor equation of Equation 2 or
tions are derived representing the fatigue life N(50) using the
Equation 3.
or [RampDown?eZd/RampDownZab]
is applied
ramp rate during high-temperature rising or the ramp rate
[0073]
during low-temperature falling.
3 is processed, it is ?rst determined whether the high-tem
[0071] Next, the correlations with the fatigue life are deter
mined (Step 342 and Step 352). These determinations are
performed in the same way as the determination in Step 332.
If the three functions derived in Step 340 or Step 350 are
similar, the correlation with the fatigue life can be deter
mined. If the three derived functions are different or the ramp
rates do not change the fatigue life N(50) by more than 5% in
When the dwell time term shown on the right in FIG.
perature and low-temperature dwell times are the same or
different (Step 325). In this determination, it is determined
whether the dwell times Dwell_HighZab and Dwell_LowZab
are different by 20% or more. If not, they are deemed to be the
same. The longer dwell time is used as the reference, and it is
determined by comparing 20% of the longer time to the
difference between both dwell times.
the entire ramp rate range, it can be determined that there is no
[0074] Next, when it has been determined that the high
temperature and low-temperature dwell times Dwell_HighZab
correlation between fatigue life and ramp rate. In this situa
and Dwell_Low 1a b are the same, the process advances to Step
tion, the process advances to Step 344 and Step 354, where
360, and the correlation between the dwell time and the
fatigue life is calculated. In this calculation, the temperature
cycle pro?le data is used to derive a function representing the
test fatigue life Nlab using at least three different dwell times
mla:0 for [RampUp?eld/RampUplabyy'la, which is a portion
of ramp rate term [Ramp?eld/Ramplab]’"l in Equation 2 or
Equation 3, and [RampUp?eZd/RampUpZab]mlaIl. Alterna
tively, ml f0 for [RampDown?eZd/RampDownZab]’"lb, which
is a portion of ramp rate term [Ramp?eld/Ramplab]ml in Equa
tion 2 or Equation 3, and [RampDown?eZa/RampDownZab]
mlbIl. Afterwards, the process advances to Step 390, and
[RampUp?eZd/RampUpZab]mlaIl or [RampDown?eZd/Ramp
Downzab]’"lb:l is used in the novel acceleration function
equation of Equation 2 or Equation 3.
[0072] When it has been determined in Step 342 that there
is a correlation between the fatigue life and the high-tempera
ture rising ramp rate, the process advances to Step 346 where
the high-temperature rising ramp rate term is calculated.
for at least three different ramp rates. For example, the three
different ramp rates may be the same for a rising temperature,
a falling temperature, or both. These may be 825° C./minute,
16.5o C./minute and 66° C./minute during a rising tempera
ture. The three different dwell times at these ramp rates may
be the same at the hi gh-temperature end, the low-temperature
end, or both ends, and may be 5 minutes, 10 minutes and 20
minutes. The results shown in Table 1 above were obtained
when nine different combinations of these dwell times and
ramp rates were applied to fatigue life N(50) at which 50% of
the products in the accelerated testing failed. The functions
shown in FIG. 8 are derived when the data in Table 1 is
When it has been determined in Step 352 that there is a
graphed with the vertical axis denoting the fatigue life N(50)
correlation between the fatigue life and the low-temperature
falling ramp rate, the process advances to Step 356 where the
low-temperature falling ramp rate term is calculated. The
calculation for the high-temperature rising ramp rate term and
the calculation for the low-temperature falling ramp rate term
and the horizontal axis denoting the dwell time.
[0075] Next, the correlation with fatigue life is determined
(Step 362). In this determination, the derived functions are
used. As shown in FIG. 8, the three derived functions are
similar, and indicate the correlation between fatigue life and
are performed in the same way as the calculation in Step 336.
ramp rate. If the three derived functions are different or the
A linear function expressing a normalized fatigue life N(50)
using a normalized high-temperature rising ramp rate is
derived from a function representing the three fatigue lives
N(50) derived in Step 340 (in the calculation of the correla
tion between the high-temperature rising ramp rate and the
dwell times do not change the fatigue life N(50) by more than
fatigue life) using the high-temperature rising ramp rate,
determining, from the slope of the derived linear function,
mm for [RampUp?eZa/RampUpZab]’"1“, which is one portion
of the ramp rate term [Ramp?eld/Ramplab]'"l, and [Ramp
Up?eZd/RampUpZab]'"1“ is calculated. A value obtained in the
manner described above is used for RampUp?eZd, and a value
obtained in accelerated testing is used for RampUpZab. A
linear function expressing a normalized fatigue life N(50)
using a normalized low-temperature falling ramp rate is
derived from a function representing the three fatigue lives
N(50) derived in Step 350 (in the calculation of the correla
tion between the low-temperature falling ramp rate and the
5% in the entire dwell time range, it can be determined that
there is no correlation between fatigue life and dwell time. In
this situation, the process advances to Step 364, where m2:0
for the dwell time term [Dwell?eZa/Dwel11Gb]m2 in Equation 2
or Equation 3, and [Dwell?eld/Dwelllaby?? . Afterwards, the
process advances to Step 390, and [Dwell?eld-Dwelllab]'"2:l
is used in the novel acceleration function equation of Equa
tion 2 or Equation 3.
[0076] When it has been determined in Step 362 that there
is a correlation between the fatigue life and the dwell time, the
process advances to Step 366 where the dwell time term is
calculated. In the calculation of the dwell time term, a linear
function representing a normalized fatigue life N(50) using a
normalized dwell time is derived from a function representing
the three fatigue lives N(50) derived in Step 360 (in the
calculation of the correlation between the dwell time and the
fatigue life) using the low-temperature falling ramp rate,
fatigue life) using the dwell time. In this derivation, the loga
determining, from the slope of the derived linear function,
mlb for [RampDown?eZd/RampDownZab]’"lb, which is one
portion of the ramp rate term [Ramp?eld/Ramplab]'"l, and
[RampDown?eZd/RampDownZab]'"lb is calculated. A value
rithms of the data in Table 1 are taken, and the values shown
in Table 2 below are used. When numerical values in Table 2
are graphed with the vertical axis denoting the normalized
obtained in the manner described above is used for Ramp
malized dwell time, the linear functions shown in FIG. 9 are
derived. The resulting slopes of the three linear functions are
a coe?icient of variable x. The average of the three slopes is
taken as the slope of the linear function. Because the dwell
Down?eld, and a value obtained in accelerated testing is used
for RampDownZab. Afterwards, the process advances to Step
390, and the calculated ramp rate term [RampUp?eZd/Ram
fatigue life N(50) and the horizontal axis denoting the nor
US 2013/0275096 A1
time is Dwell_Highlab:Dwell_LowZab:DwellZab, m2 is
obtained from the resulting slope, and the dwell time term
[Dwell?eZd/Dwel11Gb]m2 is calculated. A value obtained in the
manner described above is used as Dwell?eld, and a value
obtained in the accelerated testing is used as Dwell lab. After
Oct. 17,2013
used for Dwell_High?eZd, and a value obtained in accelerated
testing is used for Dwell_HighZab. A linear function express
ing a normalized fatigue life N(50) using a normalized low
temperature dwell time is derived from a function represent
ing the three fatigue lives N(50) derived in Step 380 (in the
wards, the process advances to Step 390, and the calculated
calculation of the correlation between the low-temperature
dwell time term [Dwell?eZd/Dwelllab]'"2 is plugged into the
novel acceleration factor equation in Equation 2 or Equation
dwell time and the fatigue life) using the low-temperature
dwell time, determining, from the slope of the derived linear
3
function, m2b for [Dwell_Low?eZa/Dwell_LowZab]’"2b, which
[0077] When it has been determined in Step 325 that the
high-temperature and low-temperature dwell times are differ
ent, the process advances to Step 370 or Step 380. In Step 370,
the correlation between the high-temperature dwell time and
the fatigue life is calculated. In Step 380, the correlation
between the low-temperature dwell time and the fatigue life is
is one portion of the dwell time term [Dwell?eZd/DwellZab]'"2,
Dwell_Low?eZd, and a value obtained in accelerated testing is
used for Dwell_LowZab. Afterwards, the process advances to
Step 390, and the calculated dwell time term [Dwell_High
calculated. These calculations are performed in the same way
?eZa/Dwell_HighZab]’"2“ or [Dwell_Low?eZa/Dwell_LowZab]
as the calculations in Step 360. However, the data for the
dwell time is data for the high-temperature dwell time or data
for the low-temperature dwell time. Data is obtained as shown
in Table l, and as shown in FIG. 8, functions are derived
M21’ is applied to the novel acceleration factor equation of
Equation 2 or Equation 3.
representing the fatigue life N(50) using the hi gh-temperature
dwell time or the low-temperature dwell time.
[0078] Next, the correlations with the fatigue life are deter
mined (Step 372 and Step 382). These determinations are
performed in the same way as the determination in Step 362.
If the three functions derived in Step 370 or Step 380 are
similar, the correlation with the fatigue life can be deter
mined. If the three derived functions are different or the dwell
times do not change the fatigue life N(50) by more than 5% in
the entire dwell time range, it can be determined that there is
no correlation between fatigue life and dwell time. In this
situation, the process advances to Step 374 and Step 384,
where m2a:0 for [Dwell_High?eZd/Dwell_HighZab]"'2",
which is a portion of dwell time term [Dwell_High?eZd/
Dwell_HighZab]'"2 in Equation 2 or Equation 3, and [Dwell_
High?eZd/DwelLHighZab]m2“:l. Alternatively, m2b:0 for
[Dwell_Low?eZd/Dwell_LowZab]’"2b, which is a portion of
dwell time term [Dwell?eZd/Dwelllab]’”2 in Equation 2 or
Equation 3, and [Dwell_Low?eZd/Dwell_LowZab]'"ZZ’II.
Afterwards, the process advances to Step 390, and [Dwell_
High?eZd/DwelLHighZab]’"2“:l or [Dwell_Low?Zed/Dwell_
Lowlab]'"2b:l is used in the novel acceleration function equa
tion of Equation 2 or Equation 3.
[0079] When it has been determined in Step 372 that there
is a correlation between the fatigue life and the high-tempera
ture dwell time, the process advances to Step 376 where the
high-temperature dwell time term is calculated. When it has
been determined in Step 382 that there is a correlation
between the fatigue life and the low-temperature dwell time,
the process advances to Step 386 where the low-temperature
dwell time term is calculated. The calculation for the high
temperature dwell time term and the calculation for the low
temperature dwell time term are performed in the same way
as the calculation in Step 366. A linear function expressing a
normaliZed fatigue life N(50) using a normaliZed high-tem
perature dwell time is derived from a function representing
the three fatigue lives N(50) derived in Step 370 (in the
calculation of the correlation between the high-temperature
dwell time and the fatigue life) using the high-temperature
dwell time, determining, from the slope of the derived linear
and [Dwell_Low?eZd/DwelLLowlab]’”2l7 is calculated. A
value obtained in the manner described above is used for
[0080]
Afterwards, in Step 390, the values of the ramp rate
term and the dwell time term corresponding to the calcula
tions are plugged into the novel acceleration factor equation
of Equation 2 or Equation 3, and the acceleration factor AF is
calculated. The product of the acceleration factor AF calcu
lated in process 300 of FIG. 3 and the fatigue life N(50) is
determined to calculate the ?eld fatigue life of the product,
and the fatigue life of the product is predicted as shown in
Step 250 of FIG. 2.
[0081] A minimum temperature term [Tminjezd/Tminizab]
"'3 is included in the novel acceleration factor equation of
Equation 3. The minimum temperature term is incorporated
so as to take into account the effect of the minimum tempera
ture on the fatigue life of a solder joint in the same manner as
the ramp rate and dwell time. The value for the minimum
temperature can be determined in the same way the values for
the ramp rate term and the dwell time term were determined
in FIG. 3.
[0082] The present invention was explained using an
embodiment, but the technical scope of the present invention
is not limited to the embodiment described above. Various
changes and improvements can be added to the embodiment,
and embodiments with these changes and improvements are
included within the technical scope of the present invention.
What is claimed is:
1. A method for predicting the fatigue life of a solder joint
in a product joined by soldering, the method comprising the
steps of:
establishing a maximum temperature Tmax??eld, a mini
mum temperature Tml-njeld, and a temperature cycle
frequency F?eld in a ?eld environment of the product;
establishing a maximum temperature Tmaxilab, a minimum
temperature Tml-nilab, and a temperature cycle frequency
PM, in a laboratory environment for accelerated testing
of the product;
implementing the accelerated testing of the product to
measure a test fatigue life Nlab until failure of the prod
uct;
determining exponent ml for the ramp rate and exponent
m2 for the dwell time in Equation 1 below, which is
represented using the ramp rate Ramp?e 1d and the dwell
time Dwell?ezd of the ?eld environment, and the ramp
function, m2a for [Dwell_High?eZd/Dwell_HighZab]"'2",
rate Ramp 1a b and the dwell time Dwelllab of the labora
which is one portion of the dwell time term [Dwell?eld/
tory environment from pro?le data of a temperature
DwellZab]’"2, and [Dwell_High?eZd/Dwell_Highlab]m2“ is cal
cycle using the established maximum temperature
Tmax??eld, the minimum temperature Tml-n??eld, and the
culated. A value obtained in the manner described above is
US 2013/0275096 A1
Oct. 17,2013
temperature cycle frequency F?eld of the ?eld environ
ment, from pro?le data of a temperature cycle using the
established maximum temperature Tmaxilab, the mini
mum temperature Tminilab, and the temperature cycle
frequency PM, of the laboratory environment, and from
measured data of the test fatigue life NM, and calculat
ing an acceleration factor AF by plugging determined
exponents ml and m2 into Equation 1;
p la h during a rising high temperature, and deriving a function
representing the test fatigue life NM, using the ramp rate
RampDoWnZab during a falling loW temperature and deter
mining a correlation betWeen the test fatigue life NM, and the
ramp rate RampDoWnZab during a falling loW temperature.
7. The method of claim 6, Wherein, When it has been deter
mined in the determination of a correlation betWeen the test
Equation 1
(Equation 1)
ATlab
the test fatigue life NM, using the ramp rate RampUpZab dur
ing a rising high temperature and determining a correlation
betWeen the test fatigue life NM, and the ramp rate RampU
Ramplab
fatigue life NM, and the ramp rate during a rising high tem
perature RampUpZab that there is no correlation, mMIO and
[RampUp?eZd/RampUpZab]mlaIl for [RampUp?eZd/RampU
p la b]’"l“ constituting a portion of the ramp rate term
[Ramp?eld/Ramplab]m l -
8. The method of claim 6, Wherein, When it has been deter
mined in the determination of a correlation betWeen the test
fatigue life NM, and the ramp rate during a rising high tem
ATM? :Tmaxilab_ Tminilab
n: Constant Determined By Solder
perature RampUpZab that there is a correlation, a linear func
tion representing a normaliZed test fatigue life Nlab using a
normaliZed ramp rate during a rising high temperature Ram
pUpZab is derived from the function representing the test
Ea: Activation Energy
fatigue life NM, using the ramp rate during a rising high
R: Boltzmann Constant
temperature RampUp 1a b, m1 a is determined for [RampUp?eZd/
and calculating a ?eld fatigue life N?eld of the product from
RampUplaljmla constituting a portion of the ramp rate term
the calculated acceleration factor AF and the test fatigue
[Ramp?eld/Ramplab]’"l from the slope of the linear function,
and [RampUp?eZa/RampUpZabY'l“ is calculated.
life Nlab (N?eZd:AFXNZab)'
2. The method of claim 1, Wherein the step for calculating
the acceleration factor AF further comprises, When determin
ing the exponent ml for the term of the ramp rates Ramp?eld
and Ramplab, determining Whether or not the siZe of a ramp
rate RampUpZab and a ramp rate RampDoWnZab for a rising
temperature and a falling temperature in the temperature
cycle of the laboratory environment for the ramp rate Ramp la b
are the same or different.
3. The method of claim 2, further comprising, When it has
been determined that the siZe of the ramp rate RampUp 1a b and
the ramp rate RampDoWnZab for a rising temperature and a
falling temperature in the temperature cycle of the laboratory
environment are the same, deriving a function representing
the test fatigue life Nlab using a ramp rate Ramp la b corre
sponding to the ramp rate RampUp 1a b or the ramp rate Ramp
DoWnZab for a rising or falling temperature, and determining a
correlation betWeen the test fatigue life NM, and the ramp rate
Ramplab'
4. The method of claim 3, Wherein, When it has been deter
mined in the determination of a correlation betWeen the test
fatigue life NM and the ramp rate Ramplab that there is no
correlation, ml:0, and the ramp rate term [Ramp?eZd/Ram
plab]ml:l'
5. The method of claim 3, Wherein, When it has been deter
mined in the determination of a correlation betWeen the test
fatigue life NM and the ramp rate Ramp la b that there is a
correlation, a linear function representing a normaliZed test
fatigue life Nlab using a normaliZed ramp rate Ramp la b is
derived from the function representing the test fatigue life
NM, using the ramp rate Ramp 1a b, m1 is determined from the
slope of the linear function, and the ramp rate term [Ramp?eld/
Ramplalj'"l is calculated.
9. The method of claim 6, Wherein, When it has been deter
mined in the determination of a correlation betWeen the test
fatigue life NM and the ramp rate during a falling loW tem
perature RampDoWnZab that there is no correlation, mlb:0
and [RampDoWn?eZd/RampDoWnZab]'"lbIl for [RampDoWn
?eM/RampDoWnZabYMb constituting another portion of the
ramp rate term [Ramp?eld/Ramplab]'"l.
10. The method of claim 6, Wherein, When it has been
determined in the determination of a correlation betWeen the
test fatigue life NM, and the ramp rate during a falling loW
temperature RampDoWnZab that there is a correlation, a linear
function representing a normaliZed test fatigue life NM, using
a normalized ramp rate during a falling loW temperature
RampDoWnZab is derived from the function representing the
test fatigue life NM, using the ramp rate during a falling loW
temperature RampDoWnZab, mlb is determined for [Ramp
DoWri?eZd/RampDoWnZab]'"1b constituting another portion of
the ramp rate term [Ramp?ezd/Ramplab]’”l from the slope of
the linear function, and [RampDoWn?eZd/RampDoWnZab]'"1b
is calculated.
11. The method of claim 1, Wherein the step for calculating
the acceleration factor AF further comprises, When determin
ing the exponent m2 for the term of the dWell times DWell?eZd
and DWellZab, determining Whether or not a dWell time
DWell_HighZab and a dWell time DWell_LOWZab for a high
temperature and a loW temperature in the laboratory environ
ment for the dWell time DWellZab are the same or different.
12. The method of claim 11, further comprising, When it
has been determined that the dWell time DWell_HighZab and
the dWell time DWell_LOWZab for a high temperature and a loW
temperature in the laboratory environment are the same,
6. The method of claim 2, further comprising, When it has
deriving a function representing the test fatigue life Nlab using
been determined that the siZe of the ramp rate RampUp 1a b and
the ramp rate RampDoWnZab for a rising temperature and a
a dWell time DWellZab corresponding to the dWell time DWell_
Highlab or the dWell DWell_LOWZab for a high temperature or
falling temperature in the temperature cycle of the laboratory
a loW temperature, and determining a correlation betWeen the
environment are different, deriving a function representing
test fatigue life NM, and the dWell time DWellZab.
Oct. 17, 2013
US 2013/0275096 A1
13. The method of claim 12, wherein, When it has been
maliZed dWell time at a loW temperature DWell_LOWZab is
determined in the determination of a correlation betWeen the
derived from the function representing the test fatigue life
test fatigue life NM, and the dWell time DWellZab that there is
no correlation, m2:0 and the dWell time term [DWell?eZd/
NM, using the dWell time at a loW temperature DWell_LOWZa ,
DWellZab]'"2:1.
14. The method of claim 12, Wherein, When it has been
determined in the determination of a correlation betWeen the
test fatigue life NM, and the dWell time DWellZab that there is
a correlation, a linear function representing a normalized test
fatigue life NM, using a normaliZed dWell rate DWellZab is
derived from the function representing the test fatigue life
NM, using the dWell time DWellZab, m2 is determined from the
slope of the linear function, and the dWell time term [DWell
?eld/Dwelllaljm2 is calculated.
15. The method of claim 11, further comprising, When it
has been determined that the dWell times DWell_HighZab and
the DWell_LOWZab for a high temperature and a loW tempera
ture in the laboratory environment are different, deriving a
function representing the test fatigue life NM, using the dWell
time DWell_HighZab for a high temperature and determining a
correlation betWeen the test fatigue life NM and the dWell
time DWell_HighZab for a high temperature, and deriving a
function representing the test fatigue life Nlab using the dWell
time DWell_LOWZab for a loW temperature and determining a
correlation betWeen the test fatigue life NM, and the dWell
time DWell_LOWZab for a loW temperature.
16. The method of claim 15, Wherein, When it has been
determined in the determination of a correlation betWeen the
test fatigue life NM and the dWell time at high temperature
DWell_HighZab that there is no correlation, m2a:0 and
[DWell_High?eZd/DWell_HighZab]'"2“:1 for [DWell_High?eZd/
m2b is determined for [DWell_LOW?eZd/DWell_LOWZab1m b
constituting another portion of the dWell time term [DWell/
DWell?eZd/DWellZabY" from the slope of the linear function,
and [DWell_LoW eM/DWelLLoWZab]"'217 is calculated.
20. A method flgr predicting the fatigue life of a solder joint
in a product joined by soldering, the method comprising the
steps of:
establishing a maximum temperature Tmax??eld, a mini
mum temperature Tmin??eld, and a temperature cycle
frequency F?eld in a ?eld environment of the product;
establishing a maximum temperature Tmax Jab, a mini
mum temperature Tml-nilab, and a temperature cycle fre
quency PM, in a laboratory environment for accelerated
testing of the product;
implementing the accelerated testing of the product to
measure a test fatigue life Nlab until failure of the prod
uct;
determining exponent ml for the ramp rate, exponent m2
for the dWell time, and exponent m3 for the minimum
temperature in Equation 2 beloW, Which is represented
using the ramp rate Ramp?eld and the dWell time DWell
?e 1d of the ?eld environment, and the ramp rate Ramp lab
and the dWell time DWellZab of the laboratory environ
ment from pro?le data of a temperature cycle using the
established maximum temperature Tmax??eld, the mini
mum temperature Tml-njeld, and the temperature cycle
frequency F?eld of the ?eld environment, from pro?le
data of a temperature cycle using the established maxi
DWell_HighZab]'"2“ constituting a portion of the dWell time
mum temperature Tmax Jab, the minimum temperature
term [DWell?eZa/DWellZabY”.
laboratory environment, and from the measured data of
the test fatigue life NM, and calculating an acceleration
factor AF by plugging the determined exponents ml, m2
and m3 into Equation 2;
17. The method of claim 15, Wherein, When it has been
determined in the determination of a correlation betWeen the
test fatigue life NM, and the dWell time at high temperature
DWell_HighZab that there is a correlation, a linear function
representing a normaliZed test fatigue life NM, using a nor
maliZed dWell time at a high temperature DWell_HighZab is
THU-"Jab, and the temperature cycle frequency PM of the
Equation 2
derived from the function representing the test fatigue life
NM, using the dWell time at a high temperature DWell_
Highlab, m2a is determined for [DWell_High?eZd/DWell_
Highlaljmza constituting a portion of the dWell time term
[DWell?eZd/DWel11Gb]m2 from the slope of the linear function,
and [DWell_High?eZa/DWell_HighZab]’”2‘1 is calculated.
(Equation 2)
ATM,
Ramplab
Dwelllab
Tmm. ?eld m3
E
1
1
*i[
**************
ii]
X e R Tmaxjeld Tmax’lab
Tminhzb
18. The method of claim 15, Wherein, When it has been
determined in the determination of a correlation betWeen the
test fatigue life NM, and the dWell time at loW temperature
DWell_LOWZab that there is no correlation, m2b:0 and
[DWell_LOW?eZa/DWell_LOWZab]m2b:l for [DWell_LOW?eZd/
DWell_LoWZab]’"2l7 constituting a portion of the dWell time
term [DWell?eZa/DWellZabY”.
19. The method of claim 15 Wherein, When it has been
determined in the determination of a correlation betWeen the
minilab
n: Constant Determined By Solder
Ea: Activation Energy
R: Boltzmann Constant
and calculating a ?eld fatigue life N?eld of the product from
test fatigue life NM and the dWell time at loW temperature
the calculated acceleration factorAF and the test fatigue
DWell_LOWZab that there is a correlation, a linear function
representing a normaliZed test fatigue life Nlab using a nor
life Nlab (N?eZd:AFXNZab)'
*
*
*
*
*