Mechanical and package stress is the damage caused by force and deformation: strain forced into joints when materials of different expansion heat and cool, residual stress in deposited films, pressure from moisture in a plastic package during soldering, the stresses of bonding, and the vibration and shock of use. This page covers thermal-mismatch fatigue of solder joints, film stress and wafer bow, moisture-induced cracking, wire-bond failures, vibration and drop. The heat path and the temperature itself are on the Thermal Stress page, the statistics of lifetime are on the Failure Rate and the Bathtub Curve page, and the wear-out of metal lines belongs to other pages of this folder.

1. Why It Happens

Trigger: Temperature swings of an assembly whose parts expand by different amounts (TI; Lei Li et al.); moisture taken up by the plastic package that is then heated quickly in solder reflow (TI; Monolithic Power); vibration and impact of the board (Steinberg tutorial; Shao et al.); stress left in a deposited film (University Wafer); and excessive thermal treatment or wrong parameters in wire bonding (EE Semi).
Mechanism, thermal cycling: The difference of the expansion coefficients forces a shear strain into the joint, $Δ γ = F (L_{D} / h) Δ α Δ T$ , so a joint far from the neutral point of the package or a thin joint is strained most (background knowledge). The solder deforms by plasticity (Lei Li et al.) and creep, whose energy density is the damage measure of the Darveaux model (Shan Li et al.); the plastic strain accumulates in each cycle until failure, and the crack starts at a local discontinuity such as the stress concentration near the solder and pad interface (Vasudevan and Fan) and spreads along the interface between the intermetallic layer and the coarsened solder (Lei Li et al.). If the whole 5 per cent of an assumed geometry were plastic, the SAC305 fit would give only about 114 cycles (computed).
Mechanism, moisture: The hygroscopic moulding compound absorbs water; at reflow the water vaporises, the internal pressure delaminates the package and in severe cases cracks it, the popcorn effect (TI; Monolithic Power). The saturation pressure of water rises from 0.23 $MPa$ at 125 $^{\circ} C$ to 4.69 $MPa$ at 260 $^{\circ} C$ (computed), so the peak temperature of the reflow matters as much as the moisture content.
Mechanism, wire bonds: Ball bonds lift by Kirkendall voiding, by intermetallic spiking (Devaney mechanism) or by too much intermetallic formed under thermal stress; the neck of a gold ball breaks if the grain structure became bamboo-like through excess thermal treatment; the heel of an aluminium wedge breaks from wrong parameters, wrong looping or delamination of the lead finger; silicon under the pad cracks (cratering) from wrong parameters or too much probing (EE Semi). In power cycling the aluminium wires also age by fatigue from the mismatch with silicon (Thermal Stress page).
Mechanism, vibration and shock: The board bends, the relative displacement strains the leads and joints, and the life falls with the displacement to a power of 6.4 for component lead wires (Steinberg tutorial). In a drop the reciprocating bending of the board strains the outer balls of the array (Shao et al.).
What sets the rate: For solder cycling the temperature range (exponent 1.9 to 2.65), the cycling frequency or dwell, the maximum temperature ( $E_{a} / k_{B}$ from 1414 to 2185 $K$ ) and the geometry through $L_{D} / h$ (Accendo; Vasudevan and Fan; the geometry is background knowledge); for moisture the body thickness, the time out of the bag and the peak reflow temperature (Monolithic Power); for bonds the temperature and time at temperature (EE Semi); for vibration the displacement; for drop the peak acceleration, the pulse width and the strain at the corner balls (Shao et al.); for film stress the curvature, as $1/ R$ (University Wafer).
Failure criterion: A crack through the joint, seen in a daisy chain as a transient resistance above 100 $Ω$ for more than 1 $μ s$ and then a static value above 1000 $Ω$ (Shao et al.); a delaminated or cracked package; a lifted or broken bond (EE Semi); and for a film or wafer a bow or a crack that the process cannot tolerate, a limit that the sources do not give.

2. Where to Look

Location: In a ball-grid array the outer balls of the array and above all the corner balls, where the cracks start in the solder and run close to the intermetallic layer, and the joints near the centre of the board, where the strain is largest (Shao et al.); for cycling fatigue also the joints farthest from the neutral point (background knowledge). In a wire-bonded chip look at the ball bond on the pad, the neck of the ball, the heel of the aluminium wedge, the middle of the span and the silicon under the pad (EE Semi). In a plastic package look at the interfaces between the compound and the die pad or lead frame (background knowledge). On a wafer the whole surface shows the film stress as bow.
Signature: Resistance spikes in a daisy chain that become permanent, with static failure after about 100 transient failures in the drop test (Shao et al.). A rising $V_{C E s a t}$ or thermal resistance in a power module points to bond wires or base-plate solder (Thermal Stress page). A failure that appears after reflow or after a long time out of the bag points to moisture (my reading, from TI). A wafer that bows more after a deposition step has a film stress that follows $1/ R$ (University Wafer). Failures that cluster at the corners or at the centre of the board point to a mechanical cause (Shao et al.).
Confirm with: A cross-section shows the crack path in the solder or along the intermetallic layer (Shao et al. found it close to the layer). Continuous monitoring of the daisy-chain resistance with a threshold of 100 $Ω$ for 1 $μ s$ finds transient opens (Shao et al.). A profilometer measures the wafer curvature (University Wafer). Acoustic microscopy shows delamination, and pull or shear tests show the strength of the bonds (background knowledge). Interim readings during temperature cycling show the drift (Thermal Stress page).
Look-alikes: A midspan wire break comes from corrosion, nicks or electrical overstress and not from vibration, and a lifted wedge bond can come from corrosion of the pad or lead finger (EE Semi). Cratering can come from too much probing as well as from bonding parameters (EE Semi). The crack path does not separate cycling fatigue from impact: a fatigue crack starts at a stress concentration near the solder and pad interface and in the review of Lei Li et al. spreads along the boundary between the intermetallic layer and the coarsened solder (Vasudevan and Fan; Lei Li et al.), and the drop cracks of Shao et al. were also close to the intermetallic layer, so the loading history and the failure statistics are better evidence (my reading). A rising thermal resistance can come from the die attach and not from the base-plate solder (Thermal Stress page).

3. Prevention

Design: Shorten the distance from the neutral point and raise the joint height, since the strain is proportional to $L_{D} / h$ (background knowledge). Choose the package for the moisture class and the reflow temperature that the line uses (Monolithic Power). On the board the allowable displacement grows with the board thickness and falls with the component length, the position factor and the component constant (Steinberg tutorial), so a thicker board, shorter components and a well-supported position all help. Keep the temperature range of the product small, since the life falls with it to the power of about 2 for solder (Accendo; RF Essentials).
Material and process: Lead-free solder SAC305 has an exponent close to that of tin-lead (RF Essentials; Accendo). Keep the thermal treatment in bonding low enough to avoid too much intermetallic and a bamboo grain structure, set the bond parameters and the loop correctly and limit the probing of the pads (EE Semi). Keep the peak body temperature of reflow within the classification of the package (Monolithic Power). Manual rework with an iron below 360 $^{\circ} C$ and the package surface below its peak temperature (Monolithic Power).
Operation: Observe the floor life of the moisture class, store the bags at or below 30 $^{\circ} C$ and 40 to 85 per cent relative humidity for 3 years (6 years for the extended shelf life, or one year from delivery), keep opened parts in a cabinet below 25 $^{\circ} C$ and 10 per cent relative humidity, and bake as the standard requires, for instance 125 $^{\circ} C$ for 48 $h$ if the floor life is exceeded or unknown (Monolithic Power). Avoid shocks in handling.
Screening and test: Temperature cycling, with the acceleration factor of the Norris-Landzberg row used to turn the test cycles into field cycles (the sign of its frequency term is discussed in the first question below); board-level drop with the half-sine pulses of 1500 $g$ and 0.5 $ms$ and up (Shao et al.); vibration with the displacement limit of Steinberg (Steinberg tutorial); and classification of the moisture level to J-STD-020 (Monolithic Power).

Thermomechanical Strain and Film Stress

Name	Formula	Related Formulae	Variables/Constants
Thermal mismatch strain and stress	$ε_{m} = (α_{1} - α_{2}) Δ T$	$σ = \frac{E}{1 - ν} ε_{m}$	$ε_{m} : s t r ain t ha t tw o b o n d e d ma t er ia l s w o u l d d i f f er b y i f t h ey w er e f r ee$ $α_{1} an d α_{2} : t h e i r e x p an s i o n coe f f i c i e n t s$ $Δ T : t e m p er a t u r e c han g e$ $E an d ν : Y o u n g^{'} s m o d u l u s an d P o i sso n r a t i o o f t h e co n s t r ain e d l a y er, t h e s t r ess f or m h o l d s f or a t hin l a y er f u l l y co n s t r ain e d b y a t hi c k s u b s t r a t e (ba c k g r o u n d k n o w l e d g e), e x p an s i o n coe f f i c i e n t s f r o m t h e p o w er - e l ec t r o ni cs p a p er : s i l i co n 4.1, co pp er 17 an d a l u mini u m 24 ppm/K, T I an d L e i L i e t a l . : t h e mi s ma t c h o f t h e e x p an s i o n coe f f i c i e n t s p u t s t h er ma l s t r ess an d s t r ain in t o t h e j o in t s, an d t h er ma l cy c l in g t h e n l e a d s t o f ai l u r e$ $(co m p u t e d : f or Δ T = 100 K co pp er o n s i l i co n g i v es 0.129 p er ce n t an d a l u mini u m o n s i l i co n 0.199 p er ce n t, ab o u t 0.20 p er ce n t a s o n t h e T h er ma l S t r ess p a g e; t h e mi s ma t c h i s a f r ee s t r ain, an d t h e s t r ain a c t u a l l y f or ce d in t o a j o in t d e p e n d s o n t h e g eo m e t r y, see t h e n e x t r o w)$
Shear strain of a solder joint in thermal cycling	$Δ γ = F \frac{L _{D}}{h} Δ α Δ T$	$Δ α = α_{p a c k a g e} - α_{b o a r d}$ $N_{f} = \frac{1}{2} (\frac{Δ γ}{2 ε _{f}^{'}})^{1/ c} \propto Δ γ^{- n}, n = - \frac{1}{c}$ $c = - 0.442 - 6 \times 1 0^{- 4} T_{s} + 1.74 \times 1 0^{- 2} ln (1 + f)$	$Δ γ : cy c l i c s h e a r s t r ain r an g e o f t h e j o in t$ $L_{D} : d i s t an ce f r o m t h e n e u t r a l p o in t o f t h e p a c k a g e t o t h e j o in t, l a r g es t a t t h e cor n er$ $h : h e i g h t o f t h e j o in t$ $F : e m p i r i c a l f a c t or o f or d er 1$ $N_{f} : cy c l es t o f ai l u r e$ $ε_{f}^{'} : f a t i g u e d u c t i l i t y coe f f i c i e n t$ $c : f a t i g u e d u c t i l i t y e x p o n e n t (n e g a t i v e)$ $n : l i f e e x p o n e n t$ $T_{s} : m e an cy c l i c so l d er t e m p er a t u r e in^{\circ} C$ $(co m p u t e d : t h e e x p o n e n t g i v es c = - 0.397 an d n = 2.52 f or t h e A T L A S c a se, a s in t ha t p a p er, an d c = - 0.459 an d n = 2.18 f or a ss u m e d T_{s} = 60^{\circ} C an d f = 2 p er d a y, c l ose t o t h e 1.96 o f S A C 305 in t h e C o f f in - M an so n r o w; w i t h a ss u m e d n u mb er s L_{D} = 5 mm, h = 0.1 mm, Δ α = 10 ppm/K, Δ T = 100 K an d F = 1 t h e s t r ain t er m i s Δ γ = 0.05, t ha t i s 5 p er ce n t; ha l v in g t h e j o in t h e i g h t d o u b l es t h e s t r ain)$
Film stress from wafer curvature (Stoney)	$σ_{f} = \frac{E _{s} t _{s}^{2}}{6 ( 1 - ν _{s} ) t _{f}} (\frac{1}{R _{f}} - \frac{1}{R _{i}})$	$M_{s} = \frac{E _{s}}{1 - ν _{s}}$ $s = \frac{r ^{2}}{2 R}$	$σ_{f} : a v er a g e f i l m s t r ess$ $E_{s} an d ν_{s} : Y o u n g^{'} s m o d u l u s an d P o i sso n r a t i o o f t h e s u b s t r a t e$ $t_{s} an d t_{f} : s u b s t r a t e an d f i l m t hi c k n ess$ $R_{i} an d R_{f} : r a d i u s o f c u r v a t u r e o f t h e s u b s t r a t e b e f or e an d a f t er d e p os i t i o n$ $M_{s} : bia x ia l m o d u l u s (t h e so u r ce g i v es E_{s} an d ν_{s} se p a r a t e l y)$ $s : s a g i tt a o f a w a f er o f r a d i u s r b e n t t o t h e r a d i u s R (ba c k g r o u n d k n o w l e d g e), U ni v er s i t y W a f er : t h e e q u a t i o n i s m os t a ppl i c ab l e w h e n t h e f i l m i s m u c h t hinn er t han t h e s u b s t r a t e, an d t hi c k er f i l m s, m u l t i l a y er s, s t r o n g l y ani so t r o p i c s u b s t r a t es or l a r g e d e f or ma t i o n s n ee d f u r t h er m o d e l s, t h e p a g e d oes n o t s a y w hi c h s i g n o f t h e c u r v a t u r e c han g e m e an s t e n s i l e s t r ess$ $(co m p u t e d w i t h a ss u m e d n u mb er s f or a s i l i co n w a f er, E_{s} = 130 GPa, ν_{s} = 0.28, t_{s} = 725 μ m, t_{f} = 1 μ m an d R_{i} in f ini t e : M_{s} = 180.6 GPa an d R_{f} = 100 m g i v e 158 MPa; t h e s am e w a f er w i t h r = 100 mm ha s a b o w o f 50 μ m; a t R_{f} = 50 m t h e s t r ess i s 316 MPa an d a t 300 m i t i s 53 MPa, b ec a u se t h e s t r ess i s p r o p or t i o na l t o 1/ R)$

Solder Fatigue

Name	Formula	Related Formulae	Variables/Constants
Coffin-Manson relation for solder	$N_{f} = C Δ ε_{p}^{- n}$ $N_{f} = 0.32 γ_{p}^{- 1.96}$	$\frac{N _{1}}{N _{2}} = (\frac{Δ ε _{2}}{Δ ε _{1}})^{n}$ $ε_{a} = \frac{σ _{f}^{'}}{E} (2 N_{i})^{b} + ε_{f}^{'} (2 N_{i})^{c}$	$N_{f} : cy c l es t o f ai l u r e$ $C : f a t i g u e d u c t i l i t y coe f f i c i e n t$ $Δ ε_{p} : pl a s t i c s t r ain r an g e p er cy c l e$ $n : f a t i g u e e x p o n e n t$ $γ_{p} : pl a s t i c s h e a r s t r ain r an g e, R F E sse n t ia l s : n i s 1.5 t o 2.5 f or so l d er, an d C i s ab o u t 0.32 w i t h n ab o u t 1.96 f or S A C 305, so t h e seco n d f or m u l a i s t h e S A C 305 c a se, S c hmi t z e t a l . : t h e l a s t r e l a t e d f or m u l a, t h e C o f f in - M an so n - B a s q u in e q u a t i o n, a dd s t h e B a s q u in e l a s t i c t er m t o t h e C o f f in - M an so n pl a s t i c t er m, w i t h ε_{a} : t o t a l s t r ain am pl i t u d e$ $σ_{f}^{'} : f a t i g u e s t r e n g t h coe f f i c i e n t$ $E : Y o u n g^{'} s m o d u l u s$ $N_{i} : cy c l es t o cr a c k ini t ia t i o n$ $b : f a t i g u e s t r e n g t h (B a s q u in) e x p o n e n t$ $ε_{f}^{'} : f a t i g u e d u c t i l i t y coe f f i c i e n t an d c : f a t i g u e d u c t i l i t y (C o f f in - M an so n) e x p o n e n t, t h e e l a s t i c t er m g o v er n s t h e hi g h - cy c l e r e g im e an d t h e pl a s t i c t er m t h e l o w - cy c l e r e g im e, L e i L i e t a l . w r i t e t h e C o f f in - M an so n p a r t a s Δ ε /2 = C N_{f}^{k} w i t h t h e s t r ain am pl i t u d e o n t h e l e f t an d g i v e n o v a l u es o f C or k$ $(co m p u t e d : ha l v in g t h e s t r ain m u l t i pl i es t h e l i f e b y 2.83, 3.89 an d 5.66 f or n = 1.5, 1.96 an d 2.5; t h e S A C 305 f or m g i v es 2660 cy c l es a t γ_{p} = 0.01 an d 29 cy c l es a t γ_{p} = 0.1, w hi c h i s a f i t an d n o t a m e a s u r e m e n t o n a p a r t i c u l a r j o in t)$
Energy-based fatigue life (Darveaux)	$N_{0} = K_{1} Δ W^{K_{2}}$ $\frac{d a}{d N} = K_{3} Δ W^{K_{4}}$	$N_{f} = N_{0} + \frac{a}{d a / d N}$ $Δ W_{a v e} = \frac{\sum _{i} Δ W _{i} V _{i}}{\sum _{i} V _{i}}$	$Δ W : v o l u m e - a v er a g e d in e l a s t i c (cr ee p) e n er g y d e n s i t y a cc u m u l a t e d p er cy c l e$ $N_{0} : cy c l es t o cr a c k ini t ia t i o n$ $a : cr a c k d i s t an ce t o b e cr osse d u n t i l t h e j o in t se p a r a t es, t ak e n a s t h e so l d er d iam e t er a t t h e p a c k a g e - s i d e or b o a r d - s i d e in t er f a ce, d a / d N : cr a c k g r o w t h p er cy c l e$ $N_{f} : cy c l es t o f ai l u r e, K_{1} t o K_{4} : co n s t an t s o f t h e so l d er j o in t$ $Δ W_{i} : in cr e m e n t o f t h e cr ee p e n er g y d e n s i t y p er cy c l e in e l e m e n t i$ $V_{i} : v o l u m e o f e l e m e n t i, S han L i e t a l . : t h e a v er a g e i s t ak e n o v er tw o l a y er s o f so l d er e l e m e n t s, e a c h 25 μ m t hi c k, n e a r t h e p a c k a g e an d t h e b o a r d s i d es, an d f or S A C 405 f r o m D a r v e a ux (2000) t h ey q u o t e K_{1} = 11.6 cy c l es p er M P a^{K_{2}}, K_{2} = - 1.52, K_{3} = 7.71 \times 1 0^{- 9} mm p er cy c l e p er M P a^{K_{4}} an d K_{4} = 0.98 (t h e s u mma r y g a r b l e d t h e s u p er scr i pt s), L ima y e e t a l . : f or W L C S P S n A g C u j o in t s a p o w er l a w o f t h e cr a c k a r e a g r o w t h p er cy c l e in t h e e n er g y d e n s i t y, w i t h an e x p o n e n t o f 0.95 t o 1.05 f or e n er g y d e n s i t i es o f 1 t o 5 MPa, w hi c h a g r ees w i t h K_{4}, f r o m a cr ee p - o n l y so l d er m o d e l an d t o b e u se d w i t h c a u t i o n o u t s i d e t h e r an g e, t h e i r co n s t an t s a r e in a t ab l e t ha t w a s n o t r e a d, V a s u d e v an an d F an : t h ey l i s t t h e m o d e l o f S y e d (a cc u m u l a t e d cr ee p s t r ain e n er g y d e n s i t y) an d t h e ana l y t i c a l m o d e l o f C l ec h w i t h o u t e q u a t i o n s an d s a y t ha t f ini t e - e l e m e n t m o d e l s ha d l imi t e d s u ccess in p r e d i c t in g a cce l er a t i o n f a c t or s, t h e s u m o f t h e tw o s t a g es i s t h e f or m o f S han L i e t a l .$ $(co m p u t e d w i t h t h e q u o t e d S A C 405 co n s t an t s : f or e n er g y d e n s i t i es o f 1 an d 5 MPa N_{0} = 11.6 an d 1.0 cy c l es an d d a / d N = 7.7 \times 1 0^{- 9} an d 3.7 \times 1 0^{- 8} mm p er cy c l e, so f or an a ss u m e d a = 0.5 mm t h e g r o w t h s t a g e w o u l d t ak e 6.5 \times 1 0^{7} an d 1.3 \times 1 0^{7} cy c l es; t h ese l i v es a r e n o t p h y s i c a l f or so l d er j o in t s, so t h e co n s t an t s or t h e i r u ni t s a r e p r o bab l y g a r b l e d in t h e s u mma r y (m y r e a d in g), an d t h e p a g e d oes n o t u se t h e m t o g i v e a l i f e)$
Norris-Landzberg acceleration factor	$A F = \frac{N _{f i e l d}}{N _{t es t}} = (\frac{Δ T _{t es t}}{Δ T _{f i e l d}})^{n} (\frac{f _{f i e l d}}{f _{t es t}})^{m} exp [\frac{E _{a}}{k _{B}} (\frac{1}{T _{ma x, f i e l d}} - \frac{1}{T _{ma x, t es t}})]$	$A F_{C M} = (\frac{Δ T _{t es t}}{Δ T _{f i e l d}})^{a} (\frac{f _{t es t}}{f _{f i e l d}})^{b} e^{c (1/ T_{f i e l d} - 1/ T_{t es t})}$	$A F : r a t i o o f t h e cy c l es t o f ai l u r e in t h e f i e l d an d in t h e t es t$ $Δ T : t e m p er a t u r e r an g e o f t h e cy c l e$ $f : cy c l in g f r e q u e n cy$ $T_{ma x} : ma x im u m t e m p er a t u r e in K$ $E_{a} : a c t i v a t i o n e n er g y$ $k_{B} : B o l t z mann co n s t an t 8.617 \times 1 0^{- 5} eV/K$ $m an d n : f i tt e d e x p o n e n t s, t h e f i r s t f or m u l a u ses t h e p h y s i c a l s i g n, in w hi c h a l o w er f r e q u e n cy (l o n g er d w e l l) r e d u ces t h e cy c l es t o f ai l u r e (ba c k g r o u n d k n o w l e d g e, see t h e f i r s t q u es t i o n b e l o w), t h e seco n d f or m u l a i s t h e f or m p r in t e d b y R F E sse n t ia l s w i t h a ab o u t 2.0 an d b ab o u t 0.33 an d an u n s p ec i f i e d c, A cce n d o p r in t s t h e f r e q u e n cy r a t i o a s (f_{f i e l d} / f_{t es t})^{- m} an d t h e r an g e r a t i o a s (Δ T_{f i e l d} /Δ T_{t es t})^{- n}, an d t h e p a g e s t a t es t ha t E_{a} / k_{B} i s 1414 (u ni t s n o t s t a t e d), f or S n P b e u t ec t i c so l d er m = 1/3 an d n = 1.9, an d A cce n d o s a y s t ha t a r ece n t p a p er f in d s t h e s am e v a l u es f or S A C, t h e E C T C 2008 p a p er g i v es m = 1/3, n = 1.9 an d E_{a} / k_{B} = 1414 f or t h e or i g ina l, m = 0.136, n = 2.65 an d E_{a} / k_{B} = 2185 f or P an e t a l .^{'} s S n A g C u f i t, an d m = 0.33, n = 1.9 an d E_{a} / k_{B} = 1414 f or i t s o w n l e a d - f r ee m o d e l, w i t h a m e an er r or o f 5.8 p er ce n t o v er 17 d a t a se t s, a g ain s t 60.66 p er ce n t f or P an e t a l ., w hi c h i t c a l l s r e a so nab l e b e l o w an a cce l er a t i o n f a c t or o f 3.5$ $(co m p u t e d f or t h e R F E sse n t ia l s e x am pl e, a t es t o f - 40 t o 125^{\circ} C a t 2 cy c l es p er h o u r (Δ T = 165 K) an d a f i e l d o f 0 t o 60^{\circ} C a t 1 cy c l e p er d a y (Δ T = 60 K) : w i t h t h e p h y s i c a l s i g n an d 1414 K t h e f a c t or s a r e 6.83 f or t h e r an g e, 0.275 f or t h e f r e q u e n cy an d 2.00 f or t h e A r r h e ni u s t er m, so A F = 3.76 an d 3000 t es t cy c l es s t an d f or 11300 f i e l d cy c l es, ab o u t 31 y e a r s; w i t h P a n^{'} s co n s t an t s A F = 25.2 an d 75500 cy c l es; w i t h t h e f r e q u e n cy s i g n r e v er se d A F = 49.7 an d 149000 cy c l es; R F E sse n t ia l s s t a t es ab o u t 85000 cy c l es, w hi c h a r e v er se d s i g n w i t h a r an g e e x p o n e n t o f 2.0, a f r e q u e n cy e x p o n e n t o f 0.33 an d n o A r r h e ni u s t er m r e p r o d u ces a t 81400; E_{a} i s 0.122 eV f or 1414 K an d 0.188 eV f or 2185 K)$

Package Moisture and Wire Bonds

Name	Formula	Related Formulae	Variables/Constants
Moisture uptake of a plastic package	$\frac{\partial c}{\partial t} = D \frac{\partial ^{2} c}{\partial x ^{2}}$ $D = D_{0} e^{- E_{D} / (k_{B} T)}$	$\frac{M ( t )}{M _{\infty}} \approx 1 - \frac{8}{π ^{2}} e^{- π^{2} D t / h^{2}}$ $t \propto \frac{h ^{2}}{D}$	$c : m o i s t u r e co n ce n t r a t i o n in t h e m o u l d in g co m p o u n d$ $D : d i f f u s i o n coe f f i c i e n t$ $D_{0} : p r e - f a c t or$ $E_{D} : a c t i v a t i o n e n er g y o f d i f f u s i o n$ $k_{B} : B o l t z mann co n s t an t 8.617 \times 1 0^{- 5} eV/K, M (t) an d M_{\infty} : ab sor b e d m o i s t u r e a t t im e t an d a t s a t u r a t i o n$ $h : t hi c k n ess o f a pl a t e t ha t ab sor b s t h r o ug h b o t h f a ces, t h e l a t e - t im e f or m o f t h e ser i es so l u t i o n i s ba c k g r o u n d k n o w l e d g e, T I an d M o n o l i t hi c P o w er : t h e h y g r osco p i c pl a s t i c e n c a p s u l an t ab sor b s m o i s t u r e, w hi c h c an v a p or i se in r e f l o w, an d t h e f l oor l i f e o u t o f t h e ba g a t 30^{\circ} C an d 60 p er ce n t r e l a t i v e h u mi d i t y i s u n l imi t e d f or M S L 1, 1 yr f or M S L 2, 4 w ee k s f or 2 a, 168 h f or 3, 72 h f or 4, 48 h f or 5, 24 h f or 5 a, an d a bak e b e f or e u se f or M S L 6 (M o n o l i t hi c P o w er g i v es M S L 1 a t 30^{\circ} C an d 85 p er ce n t), n o so u r ce g i v es a d i f f u s i o n coe f f i c i e n t$ $(co m p u t e d : t h e t im e t o r e a c h a g i v e n f r a c t i o n o f s a t u r a t i o n g r o w s w i t h t h e s q u a r e o f t h e t hi c k n ess, so d o u b l in g t h e b o d y t hi c k n ess m u l t i pl i es i t b y 4; t h e 125^{\circ} C bak e t im es o f J - S T D - 033 f or M S L 3 a f t er m or e t han 72 h o f e x cess e x p os u r e r i se f r o m 4 h a t 0.5 t o 0.8 mm t o 48 h a t 2.0 t o 4.5 mm, a r a t i o o f 12 a g ain s t 25 f or a s q u a r e l a w a t a ss u m e d ban d mi d p o in t s, so t h e ban d e d t ab l es a r e n o t a s q u a r e l a w)$
Vapour pressure at reflow	$p_{v} \leq p_{s a t} (T_{p})$ $F = p_{v} A_{d}$	$T_{p} \leq T_{c l a ss}$	$p_{v} : p r ess u r e o f t h e m o i s t u r e in a v o i d or d e l amina t e d g a p a t t h e r e f l o w t e m p er a t u r e$ $p_{s a t} : s a t u r a t i o n p r ess u r e o f w a t er a t t h e p e ak b o d y t e m p er a t u r e T_{p}, so t ha t p_{s a t} i s an u pp er b o u n d o n p_{v} (m y r e a d in g)$ $F : f or ce o n t h e d e l amina t e d a r e a A_{d}, w hi c h cr a c k s t h e co m p o u n d w h e n i t e x cee d s t h e s t r e n g t h o f t h e pl a s t i c o v er t h e d i e p a d (ba c k g r o u n d k n o w l e d g e)$ $T_{c l a ss} : c l a ss i f i c a t i o n t e m p er a t u r e o f t h e p a c k a g e, M o n o l i t hi c P o w er T ab l e 2 an d 3 o f J - S T D - 020 : t h e p e ak t e m p er a t u r e f or l e a d - f r ee i s 260^{\circ} C f or b o d i es b e l o w 1.6 mm, f or 1.6 t o 2.5 mm i t i s 260, 250 an d 245^{\circ} C f or v o l u m es b e l o w 350, 350 t o 2000 an d ab o v e 2000 m m^{3}, f or b o d i es ab o v e 2.5 mm i t i s 250, 245 an d 245^{\circ} C, an d f or t in - l e a d i t i s 235 or 220^{\circ} C b e l o w 2.5 mm an d 220^{\circ} C ab o v e$ $T I : a c l a ss i f i c a t i o n t e m p er a t u r e o f 220 t o 225^{\circ} C a pp e a r s o n l y in a l ab e l l in g co n t e x t, T I an d M o n o l i t hi c P o w er : v a p or i s a t i o n in r e f l o w cr e a t es in t er na l s t r ess t ha t d e l amina t es t h e p a c k a g e an d in se v er e c a ses cr a c k s i t (p o p cor n e f f ec t)$ $(co m p u t e d w i t h s t e am p r o p er t i es f r o m I A P W S - I F 97 : t h e s a t u r a t i o n p r ess u r e o f w a t er i s 0.232 MPa a t 125^{\circ} C, 0.476 MPa a t 150, 2.32 a t 220, 3.06 a t 235, 3.65 a t 245, 3.98 a t 250 an d 4.69 MPa a t 260^{\circ} C; t h e r e a l p r ess u r e in a p a c k a g e i s l o w er b ec a u se t h e m o i s t u r e i s l imi t e d t o t h e am o u n t ab sor b e d an d i s n o t f r ee l i q u i d w a t er, so t h e v a l u es g i v e t h e t e m p er a t u r e d e p e n d e n ce an d n o t t h e s t r ess)$
Bake time scaling with temperature	$\frac{t _{1}}{t _{2}} = exp [\frac{E _{D}}{k _{B}} (\frac{1}{T _{1}} - \frac{1}{T _{2}})]$	$E_{D} = k_{B} \frac{l n ( t _{1} / t _{2} )}{1/ T _{1} - 1/ T _{2}}$	$t_{1} an d t_{2} : bak e t im es n ee d e d a t t h e ab so l u t e t e m p er a t u r es T_{1} an d T_{2} w i t h T_{1} b e l o w T_{2}$ $E_{D} : a pp a r e n t a c t i v a t i o n e n er g y o f d r y in g$ $k_{B} : B o l t z mann co n s t an t 8.617 \times 1 0^{- 5} eV/K, t h e r e l a t i o n a ss u m es t ha t t h e bak e t im e i s se t b y d i f f u s i o n a l o n e an d i s m y co n s t r u c t i o n f r o m t h e t ab l es, M o n o l i t hi c P o w er T ab l e 5 : a f t er e x p os u r e b ey o n d t h e f l oor l i f e b y m or e t han 72 h a b o d y o f 2.0 t o 4.5 mm i s bak e d 48 h a t 125^{\circ} C or 10 d a y s a t 40^{\circ} C an d b e l o w 5 p er ce n t r e l a t i v e h u mi d i t y, b o d i es b e l o w 1.4 mm a t M S L 2 n ee d n o bak e (N o t e 4), t a p e, r ee l an d t u b es m u s t n o t e x cee d 40^{\circ} C, an d r e w or k in s t r u c t i o n s g i v e 125^{\circ} C f or 48 h i f t h e f l oor l i f e i s e x cee d e d or u nk n o w n, T I T ab l e 4 (d e f a u l t bak e b e f or e d r y - p a c k) : a b o d y o f a t m os t 1.4 mm a t M S L 2 n ee d s 7 h a t 125^{\circ} C or 3 h a t 150^{\circ} C$ $(co m p u t e d : t h e 40 an d 125^{\circ} C p ai r g i v es E_{D} = 0.20 eV (2360 K) an d t h e 125 an d 150^{\circ} C p ai r g i v es 0.49 eV (5710 K); t h e tw o d i f f er b ec a u se t h e t ab l es ser v e d i f f er e n t p u r p oses an d a r e w r i tt e n a s s a f e se tt in g s an d n o t a s m e a s u r e d d i f f u s i o n t im es)$
Intermetallic growth at a wire bond	$x^{2} = k_{x} t$ $k_{x} = k_{0} e^{- Q / (k_{B} T)}$	$\frac{t _{1}}{t _{2}} = exp [\frac{Q}{k _{B}} (\frac{1}{T _{1}} - \frac{1}{T _{2}})]$	$x : t hi c k n ess o f t h e in t er m e t a l l i c l a y er a t t h e b o n d in t er f a ce$ $t : t im e a t t e m p er a t u r e$ $k_{x} : p a r ab o l i c g r o w t h co n s t an t$ $k_{0} : p r e - f a c t or$ $Q : a c t i v a t i o n e n er g y o f t h e g r o w t h$ $k_{B} : B o l t z mann co n s t an t 8.617 \times 1 0^{- 5} eV/K$ $t_{1} an d t_{2} : t im es t o r e a c h t h e s am e t hi c k n ess a t T_{1} b e l o w T_{2}, t h e p a r ab o l i c l a w i s ba c k g r o u n d k n o w l e d g e an d E E S e mi g i v es n o n u mb er s, E E S e mi : ba l l b o n d l i f t in g c an co m e f r o m K i r k e n d a l l v o i d in g, f r o m in t er m e t a l l i c s p ik in g b y t h e D e v an ey m ec hani s m or f r o m e x cess i v e t h er ma l s t r ess t ha t f or m s t oo m u c h in t er m e t a l l i c, an d a b r e ak a t t h e n ec k o f a g o l d ba l l c an co m e f r o m a bamb oo g r ain s t r u c t u r e c a u se d b y e x cess i v e t h er ma l t r e a t m e n t$ $(co m p u t e d w i t h an a ss u m e d Q o f 1.0 eV : g o in g f r o m 150 t o 175^{\circ} C s h or t e n s t h e t im e t o t h e s am e t hi c k n ess b y a f a c t or o f 4.6, an d a f o u r f o l d t im e g i v es a l a y er tw i ce a s t hi c k)$

Vibration and Shock

Name	Formula	Related Formulae	Variables/Constants
Allowable board displacement under random vibration (Steinberg)	$Z_{3 σ} = \frac{0.00022 B}{C h r L}$ $\frac{N _{2}}{N _{1}} = (\frac{Z _{1}}{Z _{2}})^{b}$	$Z_{3 σ} = 3 Z_{1 σ}$ $Z_{s in e, 0 - p} \approx 2 Z_{1 σ}$	$Z_{3 σ} : a l l o w ab l e 3 σ r e l a t i v e d i s pl a ce m e n t o f t h e b o a r d f or ab o u t 20 mi l l i o n cy c l es, in in c h es$ $B : l e n g t h o f t h e b o a r d e d g e p a r a l l e l t o t h e co m p o n e n t in in$ $L : l e n g t h o f t h e co m p o n e n t in in$ $h : b o a r d t hi c k n ess in in$ $r : r e l a t i v e p os i t i o n f a c t or o f t h e co m p o n e n t o n t h e b o a r d, 1.0, 0.707 or 0.50$ $C : co n s t an t f or t h e co m p o n e n t t y p e, 0.75 t o 2.25$ $b : e x p o n e n t o f t h e d i s pl a ce m e n t - l i f e r e l a t i o n, 6.4 f or co m p o n e n t l e a d w i r es o f a p r in t e d b o a r d (t h e so u r ce g i v es t h e v a l u e an d n o t t h e nam e o f t h e r e l a t i o n)$ $N : cy c l es t o f ai l u r e a t t h e d i s pl a ce m e n t Z, t h e d i s pl a ce m e n t f or m u l a i s t h e r eco n s t r u c t e d E q . 1 o f t h e so u r ce, c h ec k e d t h er e a g ain s t an a pp e n d i x v a l u e o f 0.0081 in, t h e so u r ce g i v es 1 σ = 0.00068 in an d 3 σ = 0.00204 in f or an 8.8 g r m s in p u t, an d s ug g es t s t ha t s in e an d r an d o m d ama g e a r e ab o u t e q u a l w h e n t h e s in e z er o - t o - p e ak am pl i t u d e i s ab o u t t h e 2 σ r an d o m am pl i t u d e$ $(co m p u t e d w i t h a ss u m e d n u mb er s : B = 6 in, L = 1 in, h = 0.062 in, r = 1.0 an d C = 1.0 g i v e 0.0213 in, t ha t i s 0.54 mm; w i t h b = 6.4 a d o u b l in g o f t h e d i s pl a ce m e n t c u t s t h e l i f e b y a f a c t or o f 84 an d an in cr e a se o f 20 p er ce n t c u t s i t b y a f a c t or o f 3.2)$
Cumulative damage over several stress levels (Miner)	$D = \sum_{i} \frac{n _{i}}{N _{i}}, D = 1 at failure$	$n_{1 σ} : n_{2 σ} : n_{3 σ} \approx 68.3 : 27.2 : 4.3$	$D : a cc u m u l a t e d d ama g e$ $n_{i} : cy c l es a ppl i e d a t l e v e l i$ $N_{i} : cy c l es t o f ai l u r e a t t ha t l e v e l, t h e r u l e an d t h e f ai l u r e a t D = 1 a r e ba c k g r o u n d k n o w l e d g e, t h e r a t i o i s t h e s ha r e o f a G a u ss ian s i g na l b e tw ee n 0 an d 1 σ, 1 an d 2 σ an d 2 an d 3 σ (co m p u t e d, t h e so u r ce d oes n o t g i v e t h e s ha r es), S t e inb er g^{'} s m e t h o d u ses t h e l e v e l s 1 σ, 2 σ an d 3 σ, an d t h e so u r ce s t a t es t ha t f or a R a y l e i g h d i s t r ib u t i o n ab o u t 1.1 p er ce n t o f t h e ab so l u t e p e ak s e x cee d 3 σ (a s r e a d, a p oss ib l e mi s p r in t), t h e s am e r u l e a ppl i es t o t h er ma l cy c l es o f d i f f er e n t r an g e, f or w hi c h t h e N or r i s - L an d z b er g an d C o f f in - M an so n r o w s g i v e N$ $(co m p u t e d w i t h a ss u m e d n u mb er s : 1 \times 1 0^{5} cy c l es a t a l e v e l w i t h N = 1 \times 1 0^{6} an d 1 \times 1 0^{8} cy c l es a t a l e v e l w i t h N = 5 \times 1 0^{8} g i v e D = 0.1 + 0.2 = 0.3, so 70 p er ce n t o f t h e l i f e r e main s; a G a u ss ian s i g na l e x cee d s 3 σ f or 0.27 p er ce n t o f t h e t im e)$
Half-sine shock pulse and its drop equivalent	$A (t) = A_{0} sin \frac{π t}{t _{w}}, Δ v = \frac{2}{π} A_{0} t_{w}$	$h_{e q} = \frac{Δ v ^{2}}{2 g}$	$A_{0} : p e ak a cce l er a t i o n$ $t_{w} : p u l se w i d t h$ $Δ v : v e l oc i t y c han g e o f t h e p u l se$ $h_{e q} : f r ee - f a l l h e i g h t w i t h t h e s am e im p a c t s p ee d i f t h e b o a r d d oes n o t r e b o u n d (m y d er i v a t i o n, r e b o u n d w o u l d r ai se t h e v e l oc i t y c han g e)$ $g : 9.807 m/ s^{2}, S ha o e t a l . : t h e t es t f o l l o w s J E S D 22 - B 111 f or han d h e l d p r o d u c t s an d u ses t h e ha l f - s in e p u l ses B o f 1500 g an d 0.5 ms, G o f 2000 g an d 0.4 ms, an d H o f 2900 g an d 0.3 ms (t h e p u l se t ab l e i s a tt r ib u t e d t o J E S D 22 - B 110), a ppl i e d b y t h e I n p u t - G m e t h o d o n an im p a c t t es t s t an d, so a f r ee d r o p w a s n o t ma d e$ $(co m p u t e d : B g i v es 4.68 m/s an d 1.12 m, G g i v es 4.99 m/s an d 1.27 m, an d H g i v es 5.43 m/s an d 1.50 m)$
Stress-life relation and failure criteria in a drop test	$l g N = a + b l g σ_{ma x}$	$l g σ_{ma x} = a + b l g N$ $R_{c hain} > 100 Ω for > 1 μ s \Rightarrow transient$ $R_{c hain} > 1000 Ω \Rightarrow static$	$N : d r o p s t o f ai l u r e$ $σ_{ma x} : ma x im u m s t r ess or s t r ain o f t h e j o in t (t h e u ni t s a r e n o t c l e a r in t h e s u mma r y)$ $a an d b : f i tt e d co n s t an t s, t h e f i r s t f or m i s a s g i v e n in t h e f e t c h - t oo l s u mma r y an d t h e seco n d i s t h e o t h er w a y r o u n d (m y a l t er na t i v e r e a d in g, see t h e q u es t i o n o n t h e d i r ec t i o n o f t h e f i t), S ha o e t a l . f or S n 63 P b 37 j o in t s o f a 21 mm P B G A w i t h 36 ba l l s o f 0.5 mm o n a 180 b y 160 b y 2 mm b o a r d : a = 1.7 an d b = - 0.2173 f or t h e t r an s i e n t f i t, a = 1.526 an d b = - 0.1381 f or t h e s t a t i c f i t, an d a s t r ain - e n er g y f i t w i t h a = 5.234 an d b = - 0.4474, a t r an s i e n t f ai l u r e i s a c hain r es i s t an ce ab o v e 100 Ω f or m or e t han 1 μ s an d a s t a t i c f ai l u r e i s ab o v e 1000 Ω, f ai l u r es l i e main l y a t t h e o u t er so l d er ba l l s an d in p a r t i c u l a r t h e cor n er ba l l s, t h e cr a c k s s t a r t in t h e so l d er an d r u n c l ose t o t h e in t er m e t a l l i c l a y er, t h e s t r ain i s l a r g es t n e a r t h e b o a r d ce n t r e, an d t h e so u r ce s t a t es t ha t s t a t i c f ai l u r e occ u r s a f t er ab o u t 100 t r an s i e n t f ai l u r es, ab o u t 12 b o a r d s w er e u se d$ $(co m p u t e d : w i t h t h e f or m a s r e a d, a r i se o f t h e s t r ess b y 10 p er ce n t c han g es t h e l i f e b y o n l y 2 p er ce n t (t r an s i e n t co n s t an t s) or 1.3 p er ce n t (s t a t i c), s in ce 1.1 r ai se d t o - 0.2173 i s 0.980 an d t o - 0.1381 i s 0.987; t h e s t r ain s o f b o a r d 036 a t co n d i t i o n B (3948.3 mi cr os t r ain, f i r s t s t a t i c f ai l u r e a t 116 d r o p s) an d b o a r d 033 a t G (3071.4 mi cr os t r ain, 148 d r o p s) p u t in t o t h e f i t s a s r e a d g i v e 167 an d 176 d r o p s w i t h t h e t r an s i e n t co n s t an t s an d 72 an d 75 w i t h t h e s t a t i c o n es, w hi c h d o n o t r e p r o d u ce t h e o b ser v a t i o n s; r e a d t h e o t h er w a y r o u n d, t h e l i f e g oes a s t h e s t r ess t o t h e p o w er - 4.6 (t r an s i e n t) or - 7.2 (s t a t i c))$

Important Questions

Ques: Which sign does the frequency term of the Norris-Landzberg factor have, and how many field cycles do 3000 test cycles stand for?

Accendo prints $(f_{f i e l d} / f_{t es t})^{- m}$ and RF Essentials prints $(f_{t es t} / f_{f i e l d})^{b}$ , which are the same sense, with a lower field frequency lengthening the life in cycles. Accendo also records a notation error in one paper and reader comments about inverted ratios. I use the opposite sign, because longer dwell at the hot end gives more creep per cycle and so fewer cycles (background knowledge). For the RF Essentials example the range term is 6.83, the frequency term 0.275 and the Arrhenius term 2.00 for 1414 $K$ , so 3000 test cycles stand for 11300 field cycles, about 31 years at one cycle per day (computed). The printed sense gives 149000 cycles, and RF Essentials states about 85000. I regard 11300 as more likely, but I could not check the original paper. Reference: Accendo Reliability, ‘Norris-Landzberg solder joint fatigue’ (author and date not read) (fetch-tool summary; reader comments there say some sources invert the ratios); RF Essentials glossary, ‘Coffin-Manson equation’ (fetch-tool summary; its acceleration-factor example is quoted as read); A. Vasudevan (Intel) and X. Fan (Lamar University), ‘An Acceleration Model for Lead-Free (SAC) Solder Joint Reliability under Thermal Cycling’, IEEE Electronic Components and Technology Conference (ECTC) 2008, pp. 139-145, file ‘Fan 2008_13 ECTC_3’ on the Lamar University publication list (fetch-tool summary; the equations were garbled and reconstructed there).

Ques: Is the exponent of the temperature range 1.9, 2.0, 2.65 or 1.96 for lead-free solder?

Accendo and Vasudevan and Fan give 1.9, RF Essentials gives 2.0, Pan et al. fitted 2.65 for SnAgCu, and the Coffin-Manson fit for SAC305 has 1.96 on the strain and not on the range, which is the same only while strain is proportional to the range. For the example range ratio of 2.75 the factors are 6.83, 7.56, 14.6 and 7.26 (computed). The ECTC paper reports a mean error of 5.8 per cent over 17 data sets for its lead-free model with 1.9 and 60.66 per cent for Pan et al., which it calls reasonable only below an acceleration factor of 3.5. That comparison comes from the authors of the competing model. I regard 1.9 to 2.0 as more likely for a general estimate (my reading). Reference: Accendo Reliability, ‘Norris-Landzberg solder joint fatigue’ (author and date not read) (fetch-tool summary; reader comments there say some sources invert the ratios); RF Essentials glossary, ‘Coffin-Manson equation’ (fetch-tool summary; its acceleration-factor example is quoted as read); A. Vasudevan (Intel) and X. Fan (Lamar University), ‘An Acceleration Model for Lead-Free (SAC) Solder Joint Reliability under Thermal Cycling’, IEEE Electronic Components and Technology Conference (ECTC) 2008, pp. 139-145, file ‘Fan 2008_13 ECTC_3’ on the Lamar University publication list (fetch-tool summary; the equations were garbled and reconstructed there).

Ques: The Thermal Stress page found an exponent of 4.5 for power modules, so is the exponent of solder joints 2 or 4.5?

The Thermal Stress page computed 4.48 from two module cases, a swing of 14 $K$ with about $5 \times 1 0^{8}$ cycles and 56 $K$ with about $1 \times 1 0^{6}$ , and noted that they differ in mean temperature and cycle time. The solder-fatigue sources here give 1.9 to 2.65 for a joint and no source gives an exponent for bond wires or base-plate solder in a module. For a fourfold range the life changes by a factor of 498 with 4.48 and 16 with 2 (computed), a gap of 31. The two numbers describe different structures, wire bonds and large-area solder against small ball joints, and a fit through two points is not a material constant. I would not carry either to the other structure, and would fit the structure itself (my reading). Reference: Thermal Stress page of this vault (its power-electronics paper, arXiv:1607.01578); RF Essentials glossary, ‘Coffin-Manson equation’ (fetch-tool summary; its acceleration-factor example is quoted as read); Accendo Reliability, ‘Norris-Landzberg solder joint fatigue’ (author and date not read) (fetch-tool summary; reader comments there say some sources invert the ratios).

Ques: At which temperature should the vapour pressure in a package be judged: 260, 245 or the 220 to 225 degrees Celsius of the TI table?

The saturation pressure of water is 4.69 $MPa$ at 260 $^{\circ} C$ , 3.65 $MPa$ at 245 $^{\circ} C$ and 2.32 $MPa$ at 220 $^{\circ} C$ (computed with IAPWS-IF97), so the choice changes the pressure by a factor of 2.0. TI mentions 220 to 225 $^{\circ} C$ only as a classification temperature in a labelling context. The J-STD-020 tables in the Monolithic Power note give the peak body temperature by thickness and volume: 260 $^{\circ} C$ for lead-free bodies below 1.6 $mm$ , 245 to 260 $^{\circ} C$ up to 2.5 $mm$ , and 220 or 235 $^{\circ} C$ for tin-lead. I regard the peak body temperature of the actual package size and solder as the right one (my reading), and the saturation value as an upper bound, since absorbed moisture is not free liquid water. Reference: Texas Instruments application report SNOA550 on moisture sensitivity (title and date not read) (fetch-tool summary); Monolithic Power Systems technical note on moisture sensitivity, April 2024, tables of IPC/JEDEC J-STD-020 and J-STD-033 (fetch-tool summary); steam properties computed with IAPWS-IF97 (Python package iapws).

Ques: Is a bake needed for an MSL 2 part, and do the bake tables imply one activation energy for drying?

TI’s default bake before dry-pack is 7 $h$ at 125 $^{\circ} C$ or 3 $h$ at 150 $^{\circ} C$ for a body of at most 1.4 $mm$ at MSL 2, whereas the Monolithic Power rebake table says no bake is required for MSL 2 bodies below 1.4 $mm$ and gives 18 or 15 $h$ at 1.4 to 2.0 $mm$ . These serve different purposes, packing a part and rebaking after exposure, so I do not read them as a conflict. Treating times as Arrhenius gives 0.20 $eV$ from 125 and 40 $^{\circ} C$ (48 $h$ against 10 days) and 0.49 $eV$ from 125 and 150 $^{\circ} C$ (computed). The tables are safe settings for all packages, so I regard neither as a diffusion property. Reference: Texas Instruments application report SNOA550 on moisture sensitivity (title and date not read) (fetch-tool summary); Monolithic Power Systems technical note on moisture sensitivity, April 2024, tables of IPC/JEDEC J-STD-020 and J-STD-033 (fetch-tool summary).

Ques: Do wire bonds fail by fatigue or by intermetallic growth?

EE Semi lists lifting of the ball bond from Kirkendall voiding, Devaney spiking or too much intermetallic formed under thermal stress, and heel breaks of aluminium wedges from parameters, looping or delamination, and it does not name cycling fatigue. The Thermal Stress page, from the power-electronics paper, says that aluminium bond wires age by fatigue from the mismatch with silicon, 24 against 4.1 $ppm/K$ , which raises $V_{C E s a t}$ . I do not read these as a conflict: both occur, and I would expect intermetallic growth after long hot storage and fatigue under power cycling, with the fracture site telling them apart (background knowledge). For an assumed Q of 1.0 $eV$ , going from 150 to 175 $^{\circ} C$ shortens the growth time by 4.6 (computed). Reference: EE Semi, ‘Bonding failures’ (fetch-tool summary; no numbers); Thermal Stress page of this vault (its power-electronics paper, arXiv:1607.01578).

Ques: Which way round is the stress-life fit of the drop test: life as a function of stress or stress as a function of life?

The fetch summary of Shao et al. gives $l g N = a + b l g σ_{ma x}$ with $b$ = -0.2173 for the transient and -0.1381 for the static failures. Read that way, a 10 per cent rise of stress changes the life by only 2 and 1.3 per cent (computed), and the strains of the two example boards (3948 and 3071 microstrain) give 167 and 176 drops with the transient constants and 72 and 75 with the static ones, against 116 and 148 observed (computed). Read the other way round, the life goes as the stress to the power -4.6 or -7.2, the range of the 6.4 of Steinberg. I regard the second reading as more likely, but I could not check the paper or the units of the stress (my reading). Reference: Shao, Zhang and Chen, Electronics 2019, 8(3), 279, board-level drop reliability of PBGA packages (fetch-tool summary); Vibrationdata tutorial electronic_rd_n.pdf on vibration of electronic equipment after Steinberg (author and date not read) (fetch-tool summary; Eq. 1 was garbled and reconstructed there).

Ques: Why does doubling the displacement cut the vibration life by 84 times when doubling the strain cuts the thermal-cycling life by only about 4 times?

With $b$ = 6.4 for component lead wires the life changes by $2^{6.4}$ = 84 for a doubled displacement, and with the SAC305 exponent of 1.96 a doubled strain changes it by $2^{1.96}$ = 3.9 (computed). The exponents belong to different regimes. Steinberg’s displacement limit is set for about 20 million cycles, the elastic region of high-cycle fatigue, whereas the Coffin-Manson exponent describes the plastic region of low-cycle fatigue in solder; Schmitz et al. give the combined Coffin-Manson-Basquin equation, with the Basquin elastic term for the high-cycle regime and the Coffin-Manson plastic term for the low-cycle regime. They also concern different materials, lead wires and solder. I regard each as right for its regime and would not use one outside it (my reading). Reference: Vibrationdata tutorial electronic_rd_n.pdf on vibration of electronic equipment after Steinberg (author and date not read) (fetch-tool summary; Eq. 1 was garbled and reconstructed there); RF Essentials glossary, ‘Coffin-Manson equation’ (fetch-tool summary; its acceleration-factor example is quoted as read); S. Schmitz, G. Rollmann, H. Gottschalk and R. Krause, ‘Risk Estimation for LCF Crack Initiation’, arXiv:1302.2909 (year not stated) (fetch-tool summary).

Ques: Does the crack path tell a thermal-cycling fatigue failure from a drop failure?

A common assumption (background knowledge) is that cycling fatigue runs through the bulk of the solder and that an impact crack follows the brittle intermetallic layer. The sources do not support so clean a split. Vasudevan and Fan say that a fatigue failure begins at a local stress concentration near the solder and pad interface. Lei Li et al. say that fatigue cracks form at tin-rich phases or grain boundaries in the coarsened solder and then spread along the boundary between the intermetallic layer and the coarsened region. Shao et al. found the drop cracks close to the intermetallic layer. Both mechanisms can therefore end near the interface. The two papers on cycling describe that case directly, so they are more likely right, and the crack path alone is a weak test (my reading). Reference: A. Vasudevan (Intel) and X. Fan (Lamar University), ‘An Acceleration Model for Lead-Free (SAC) Solder Joint Reliability under Thermal Cycling’, IEEE Electronic Components and Technology Conference (ECTC) 2008, pp. 139-145, file ‘Fan 2008_13 ECTC_3’ on the Lamar University publication list (fetch-tool summary; the equations were garbled and reconstructed there); L. Li, X. Du, J. Chen and Y. Wu, ‘Thermal Fatigue Failure of Micro-Solder Joints in Electronic Packaging Devices: A Review’, Materials 17(10), 2365 (2024), DOI 10.3390/ma17102365 (fetch-tool summary; it gives the Coffin-Manson form but not the Basquin, Engelmaier or Darveaux models); Shao, Zhang and Chen, Electronics 2019, 8(3), 279, board-level drop reliability of PBGA packages (fetch-tool summary).

Ques: Can the Darveaux constants quoted for SAC405 be used?

Not as read. Shan Li et al. quote $K_{1} = 11.6$ , $K_{2} = - 1.52$ , $K_{3} = 7.71 \times 1 0^{- 9}$ and $K_{4} = 0.98$ for SAC405 from Darveaux (2000), and their summary garbled the superscripts. For energy densities of 1 and 5 $MPa$ these give 11.6 and 1.0 cycles to initiation and a growth stage of $6.5 \times 1 0^{7}$ and $1.3 \times 1 0^{7}$ cycles for an assumed 0.5 $mm$ crack (computed), far from the 1000 to 10000 cycles usual in thermal cycling tests (background knowledge). Limaye et al. fit a growth exponent of 0.95 to 1.05 for energy densities of 1 to 5 $MPa$ , which agrees with $K_{4} = 0.98$ . The exponents therefore look right, and the prefactors or their units are more likely garbled (my reading). The constants should be taken from Darveaux’s own papers before any life is computed. Reference: S. Li, Z. Huang, J. Wang (Intel Shanghai) and S. Gao (ABAQUS Shanghai), ‘Temperature Cycling Analysis of Lead-Free Solder Joints in Electronic Packaging’ (year not stated, the latest reference is from 2005) (fetch-tool summary; the superscripts were garbled and the equations follow the standard form); P. Limaye, B. Vandevelde, D. Vandepitte and B. Verlinden, ‘Crack Growth Rate Measurement and Analysis for WLCSP SnAgCu Solder Joints’, Circuits Assembly, 27 January 2006, presented at SMTA International, September 2005 (fetch-tool summary; Tables 2 and 3 are in a linked PDF that was not read).

Ques: Does the exponent of the Engelmaier model use the cycling frequency or the dwell time?

George, Osterman and Pecht say that the original 1983 exponent depended on the mean cyclic temperature and the cycling frequency, and that Engelmaier replaced the frequency by the dwell time in 1988 without explanation. Their regression for tin-based lead-free solders gave a t-statistic for the frequency 3 to 10 per cent higher than for the dwell time, so they recommend the frequency form. The ATLAS paper uses that form, $c = - 0.442 - 6 \times 1 0^{- 4} T_{s} + 1.74 \times 1 0^{- 2} ln (1 + f)$ , which gives $c = - 0.397$ for $T_{s} = - 0.5$ $^{\circ} C$ and 12 cycles per day, as in that paper, and a life exponent $n = - 1/ c = 2.52$ (computed). The frequency form is more likely the better choice for lead-free solder, on the evidence of one abstract (my reading); no dwell-time constants were found. Reference: E. George, M. Osterman and M. Pecht, ‘An evaluation of dwell time and mean cyclic temperature parameters in the Engelmaier model’, Microelectronics Reliability 55, 582-587 (2015), DOI 10.1016/S0026-2714(15)00039-6 (abstract only); Y. Li et al. (ATLAS HGTD collaboration), ‘Thermal Cycling Reliability of Hybrid Pixel Sensor Modules for The ATLAS High Granularity Timing Detector’, arXiv:2509.14045 (year not stated) (fetch-tool summary); A. Vasudevan (Intel) and X. Fan (Lamar University), ‘An Acceleration Model for Lead-Free (SAC) Solder Joint Reliability under Thermal Cycling’, IEEE Electronic Components and Technology Conference (ECTC) 2008, pp. 139-145, file ‘Fan 2008_13 ECTC_3’ on the Lamar University publication list (fetch-tool summary; the equations were garbled and reconstructed there).

Quartz 5

Explorer

Mechanical and Package Stress