Index
Drop Impact Test – Mechanics & Physics of Failure !
E.H. Wong, "K.M. Lim, "Norman Lee, "Simon Seah, #Cindy Hoe, #Jason Wang !
"
Institute of Microelectronics, Email:
[email protected] National University of Singapore, Department of Mechanical Engineering # Worley Advanced Analysis, Singapore
Abstract This paper deals with the mechanics and physics of boardlevel drop test with the intention of providing the fundamental understanding required to design and analyse the results of a drop test. Three finite element analyses were performed to understand the physics of failure in board-level drop impact: (i) velocity impact of a PCB - modeled as a beam; (ii) velocity impact of a PCB with centrally mounted package - modeled as a beam; (iii) velocity impact of a drop assembly – solid elements with submodeling. Parametric studies have been performed on the solid model for a number design variables: drop height, fall plate thickness, PCB length, PCB thickness, solder bump height, solder bump size, solder bump number, and impact cone diameter. Differential flexing as well as inertia has been identified as the key failure drivers. In both cases, the transverse stress, S33, is the most critical stress component. Geometrical stress concentration and intermetallics of the interconnection are critical in the impact strength of interconnection. 1.
Introduction The increasing trend of electronic product miniaturisation has resulted in greater concern for drop impact reliability of electronic components for various reasons: (i) The miniaturised products tend to be more mobile and wearable and hence are more at risk of accidental drop or impact when in used. (ii) The miniaturised product, with less materials and reduced design freedom, are less able to dissipate impact energy, hence passing much of the impact energy to the electronic components within the product. The reduced packing clearance between the components within the product further raises the risk of inter-knocking of the components during drop impact. (iii) To support product miniaturisation, electronic packages are miniaturised through finer interconnection, which are more vulnerable to drop impact. (iv) Polymeric based adhesive interconnections, gaining interest due to their ability to offer finer pitch and Pb-free interconnection, are generally more vulnerable to drop impact. (v) Propelled by raising power requirement, the ever larger and heavier external thermal solution could exert very high inertia force on the interconnections during impact. (vi) Optoelectronic module with its multi-components construction and extreme sensitivity to mis-alignment is inherently vulnerable to drop impact. The stress experienced by the electronic packages and interconnection during drop impact of a product depends on many factors. These include external factors such as drop height and the impacting object; product factors such as the
materials, stiffness, mass, the exterior shape and form of the product, as well as the packing clearance between components [1]; printed circuit board (PCB) factors such as the size and shape of PCB, the methods of attaching the PCB to the product, as well as the mass distribution of the components on the PCB; component factor such as the package construction, package size, the interconnection between the packages and the PCB. A major challenge facing the electronic packaging industry is the ability to assess the drop impact reliability of the electronic packages that are to be assembled into an end product, which can have wide difference in design, forms and shapes. There has been converging trend to test the drop impact reliability of these electronic packages using a boardlevel drop test [2-5]. While it is doubtful that such a simple test can mimic the state of loading experienced by the electronic packages in a real product, the test does provide a standard platform to evaluate the drop impact reliability of packages. This is provided if the test is appropriately designed, executed, and the results appropriately interpreted. For this, a thorough understanding of the mechanics of the test and the physics of failure is required. These are the focus of this paper 2.
Mechanics of Board Level Drop Impact Fig 1 illustrates a typical board level drop test. It consists of a PCB assembled with package/s. The PCB is attached to a metal block through connectors that allow flexing of the PCB. The entire assembly is guide-dropped from a height with the metal block landing on a material whose geometry, dimensions and properties may be adjusted to achieve the desired impulse.
PCB Connector Metal Block H
Guide Rod Impacting
Fig 1 A typical board level drop test The velocity of the assembly prior to impact, V, is related to the drop height, H, simply through conservation of mechanical energy, where g is the gravitational acceleration.
V = 2gH
eq (1)
At the instance of contact, the velocity of the bottom surface of the metal block is reduced to zero, resulting in high
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compressive stress, while the rest of the assembly are still travelling downward at velocity V (Fig 2a). The stress wave travels longitudinally upward until the velocity of the entire metal block is reduced to zero, and under compressive stress (Fig 2b). As some compressive stress wave travels up the connectors, the rest reflects at the free surface of the metal block and returns as tensile wave, together with an upward velocity (fig 2c). As the stress wave travels into the PCB, it turns predominantly into bending wave. During this time, the reflected longitudinal wave returns to the contact surface, resulting in rebounding of the entire assembly (Fig 2d).
V
σ=0
V=0 σ =-ve
3.
Finite Element Analysis Three finite element analyses were performed to gain better insight into the mechanics of drop impact and the associated physics of failure.
Compressive σ
-σ σ
V V=0
Fig 2a Initial contact
V
σ +σ σ -σ
Fig 2b Stress wave travels up to metal block V=0
Tensile σ Fig 2c Stress wave travels up to connectors
Rebound
V
V
σ
V
where ϖ is the angular frequency component of the bending wave [8]. For a beam with freely supported edges that deflects predominantly in the fundamental mode, ϖ may be equated to the fundamental frequency of vibration as ϖ = π 2 γ L2 , where L is the length of the beam [9]. The velocity of the bending wave may then be expressed as eq (6) C b = πγ L This is a fraction of the velocity of the longitudinal wave. As an illustration, the longitudinal stress wave in the metal block, usually made of steel, has a velocity of more than 5000 m/s; while the bending wave in a typical PCB, with an aspect ratio of 100, has a velocity of only 30 m/s. It would take less than 40 µs for the longitudinal wave to travel up and down a 100 mm steel block, while it would take more than 1 ms for a bending wave to travel from the edge of a 100 mm length PCB to its centre. The deflection of the PCB therefore takes place during the rebound of the drop test assembly.
Fig 2d Assembly rebound + bending wave in PCB The longitudinal stress wave in the assembly may be described simply by the following wave equation, neglecting the lateral components of motion [6-8]
CL2
∂u 2 ∂x
2
2
(x, t ) − ∂u2 (x, t ) = 0 ∂t
eq (2)
3.1 Velocity impact of a PCB - modeled as a beam The model and the z-displacement history at various points along the beam are depicted in Fig 3a & 3b respectively. Note (i) Maximum deflection along the beam occurs at almost the same time, suggesting the existence of a dominant fundamental deformation mode. This supports the argument in arriving at the bending wave velocity of eq (6). (ii) Substituting the geometrical and material properties of Fig 3a into eq (6), the bending wave velocity is obtained as Cb=10π m/s. The time taken for the bending wave to travel to the centre of the beam is computed as tm=0.5*L/Cb = 1.6 ms. This agrees remarkably well with the deflection history obtained from FEA (Fig 3b). (iii) The wavy nature of the displacement history is attributed to the high frequency components of the stress waves.
where E
z
eq (3)
ρ
is the propagation velocity of the longitudinal stress wave, E is the modulus, and ρ is the density of the material. The bending wave in the PCB, model as a beam, may be described by the following wave equation [6-8] γ
2
∂w
4
∂x 4
(x, t ) +
∂w
2
∂t 2
(x, t ) = 0
eq (4)
where γ = D ρ a ; D is the flexural modulus Eh 3 12 , h is the thickness, ρa=ρ.h is the area density. The propagation velocity of the bending wave is dependent on the frequency components of the wave as expressed in eq (5)
C b = γϖ
eq (5)
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x
V Fig 3a Model Z- displacement (mm)
CL =
L=0.1m, h=1mm, V=-1 m/s E=24 GPa, ρ=2000 kg/m3
0
x=0.05 L x=0.15 L
-0.5
x=0.25 L -1
x=0.5 L
-1.5 0
0.4
0.8
1.2
Time (ms) Fig 3b Z-displacement
1.6
Package: Lp=20 mm, h=2 mm, E=100 GPa, ρ=4000 kg/m3 Solder : Ls=1 mm, h=0.75 mm, E=30 GPa, ρ=10000 kg/m3 z x
Z- velocity (m/s)
0.5
x=0.05 L
0 -0.5
x=0.5 L
-1
x=0.25 L
-1.5
Z- acceleration (x103g)
0
0.5
1
1.5
Time (ms) Fig 4c Z-velocity Vs Time
2
4
x=0.05 L 2
x=0.25 L
0
x=0.5 L -2 0
0.05
0.1
0.15
0.2
Time (ms) Fig 4d Z-acceleration Vs Time
S1
Absolute Stress (MPa)
3.2 Velocity impact of a PCB with package - model as a beam The model, beam deflection at maximum amplitude, zdisplacement history at various points along the beam, zvelocity history, z-acceleration history, stress in interconnection at maximum downward and upward deflection are depicted in Fig 4. The following observations have been made: (i) The presence of a dominant mode is clearly evident from the near sinusoidal displacement history of the beam (Fig 4b). The period at 84 ms agree well with the fundamental frequency at 118.8 Hz obtained from modal analysis of the system. The results again validates eq(6). (ii) The high stiffness of the package has contributed to the smoother z-displacement history of the mid-point (Fig 4b). The near absence of the high frequency components is evident in the velocity history (Fig 4c). (iii) Very high acceleration (>10,000g) was observed near the ends during the initial period of impact (Fig 4d). This is not surprising as the beam, travels at 1 m/s, was brought to instant halt from the ends. (iv) The interconnection at the outer most of the package experienced the highest stress in both upward and downward deflection (Fig 4e). This is attributed to the differential flexing between the PCB and the package – usually of higher stiffness. Similar mechanism has been responsible for vibration fatigue [9]. That the outer-most interconnection experiences the maximum elongation/compression and bending is clearly shown in Fig 4e. (v) It follows from the above that packages of larger size, stiffer construction, and lower stand-off are more vulnerable to drop impact. The later is particularly vulnerable as will be demonstrated in section 3.3 (ii).
S2
40
S3
S4
S5
S axial
30
S bending, PCB S bending, IC
20 10 0 S1
S2
S3
S4
S5
Interconnection position
Absolute Stress (MPa)
V Fig 4a Model
Z- displacement (mm)
1.5 1 0.5 0 -0.5 -1 -1.5
x=0.05 L
Time (ms) 0
2
4
6
8
x=0.15 L x=0.25 L x=0.5 L
40
S axial S bending, PCB
30
S bending, IC
20 10 0 S1
S2
S3
S4
S5
Interconnection position
Fig 4b Z-displacement Vs Time
Fig 4e Absolute stress in solder interconnection at maximum upward and downward deflection
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330
Fall plate Impact cone Rigid surface Fig 5a Model
PCB Fall plate Rigid surface Abaqus Explici
Global detail solid model
Validation Abaqus Standard
Local detail model
Submodelin Global shell-beam model
Abaqus Explici
PCB Fall plate Rigid surface Fig 5b Modeling methodology
S33 (Normalised)
3.3 Velocity impact of a board level test assembly – detail modeling of the assembly. The model used was similar to that of [3] and [10] (Fig 5a). The analysis was performed using Abaqus-explicit and Abaqus-standard for the assembly and solder interconnection respectively. The global-local methodology is depicted in Fig 5b. A reduction of 3 times in degree of freedom (DOF) and more than 20X in computation effort has been achieved with the global-local technique [10]. Maximum stress has been found on the outer solder in the z-direction (S33). The accuracy of the submodeling has been validated (Fig 5c). The following parameters were investigated for its effect on the maximum z-stress on the solder. Drop height (Fig 5d, 1m), solder bump height (Fig 5e, 0.3mm), number of solder bumps per corner of package (Fig 5f, 3), thickness of fall plate (Fig 5g, 20mm), diameter of impact cone (Fig 5h, 5mm), PCB length (Fig 5i, 120mm), and PCB thickness (Fig 5j, 0.7mm). The value in the bracket indicates the nominal values used in the baseline model. For the parametric studies, only the solders were modeled with solid elements while the rest were modeled with shell and beam elements. The following observations have been made: (i) As expected, S33 increases linearly with impact velocity and with square root of drop height (Fig 5d). The earlier arrival of stress signal accompanying the higher impact velocity is agreeable with eq (5). (ii) S33 increases monotonically with decreasing bump height (Fig 5e) - in agreement with the explanation in section 3.2 (v). The near logarithmic increase in stress is particularly alarming. (iii) S33 decreases monotonically but almost asymptotically with increasing number of solder bumps (Fig 5f). That is, there is a threshold beyond which increasing the number of bumps will not lead to lower bump stress. The threshold in this case is only 7 bumps per corner of package. (iv) S33 increases monotonically and asymptotically with increasing thickness of the fall plate (Fig 5g), accompanying by earlier arrival of stress signal. The lower stress and the slower stress signal are attributed to the negative curvature developed by the thinner fall plate as the impact cone struck against the rigid surface. (v) S33 increases only very marginally with decreasing diameter of impact cone (Fig 5h). It is believed that its effect will be more significant when thinner fall plate is used. (vi) S33 increases generally with increasing PCB length (Fig 5i). However, multiple stress peaks became evident at lower PCB length due to increase presence of the high velocity components of bending stress wave. (vii) Interestingly, S33 decreases before increases with increasing PCB thickness (Fig 5j). This is in contradiction with the intuition that PCB of higher stiffness that deflects less shall experience lower stress. A detail explanation to this phenomenon will be reserved in the discussion section.
Global model
Local model
0
0
0.5
1
1.5
2
Time (ms) Fig 5c S33 stress on corner solder - Global Vs local model
S33 (normalised)
S33 (normalised)
1.5 m 1.25 m 1.0 m 0.75 m 0 0
0.5
1
Time (ms)
1.5
120 mm 90 mm
60 mm
0
2
0
0.5
S33 (normalised)
S33 (normalised)
0.2 mm 0.25 mm 0.3 mm 0.35 mm 0 0.5
1
1.5
2
2
1.5
1.6 mm 1.2 mm 1.0 mm 0
0.7 mm
0
Time (ms) Fig 5e S33 Vs solder bump height
Fig 5i S33 Vs PCB length
0.5
1
1.5
2
Time (ms) Fig 5j S33 Vs PCB thickness
S33 (normalised)
3
4.
7 10
Failure Drivers in Drop Impact Basing on the observations and analysis performed in section 3, three drivers for board-level drop impact failure of interconnections have been identified.
0.5
1
1.5
2
Time (ms) Fig 5f S33 Vs numbers of solder bump per corner 20 mm
S33 (normalised)
15 mm 10 mm 5 mm 0
0
0.5
1
2
1.5
Time (ms) Fig 5g S33 Vs fall plate thickness 7.5 mm 10 mm 12.5 mm 15 mm 0 0
0.5
Discussions
4.1
0 0
S33 (normalised)
1
Time (ms) Fig 5i S33 Vs PCB length
Fig 5d S33 Vs drop height
0
150 mm
1
1.5
Time (ms) Fig 5h S33 stress Vs impact cone diameter
2
Elongation and bending of interconnection due to differential flexing of PCB and package This failure mechanism has been identified in section 3.2 (iv) and was illustrated in Fig 4e. The maximum stress is in the z-direction (S33), which is a combination of both bending stress and axial stress. Maximum S33 occurs in the outer most interconnection at maximum deflection of PCB, when the package is located at the centre of the PCB. The downward mounting of package results in tensile stress which is more detrimental. The magnitude of stress increases with larger packages, stiffer packages, and stiffer PCB. It is particularly sensitivity to the stand-off of interconnections. Miniaturised interconnections with low stand-off are particularly vulnerable. The combined bending and axial stress reached 40 MPa in the example of section 3.2. Inertia force from electronic packages It is clear from Fig 4c in section 3.2 that the PCB adjacent to the supports could experience up to thousands of gravitational acceleration. A package mounted on the PCB near the supports could experience the same acceleration. The resultant inertia force induces both shear stress in the PCB as well as S33 stress in the interconnection, as illustrated in Fig 6. The individual interconnection will experience inertia force given by Fi=miai, where mi is the equivalent mass distributed over the interconnection.
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Fi =miai
F=ma
Fig 6 Inertia force from acceleration Using the example of section 3.2, the inertia force experienced by the interconnection adjacent to the support with mi=0.02 gm and acceleration 10,000g is 2 N. For an interconnection with cross-section of 0.4 mm2, this results in a z-axial stress of 5 MPa. In comparison, significantly lower acceleration, and hence inertia force, is experienced by the interconnection near the center of PCB. This may be estimated as a=ϖ2.δ. For the example of section 3.2 where ϖ≈745rad/s and δ≈0.0014m (Fig 4b), the acceleration is only 79g. Longitudinal stress wave from impact Besides the high inertia stress, the interconnection adjacent to the support may also experience high magnitude of longitudinal stress transmitted from the steel support. The maximum magnitude of stress, assuming a step wave form, may be estimated using eq(7) [6-8] eq (7) σ=ρCLV For solder interconnection, σ≈17 MPa. The actual stress experienced by the interconnection, with a gentle wave form, shall only be a fraction of this magnitude. 4.2 Impact strength of materials The eventual structural integrity of the interconnection depends not only on the magnitude of the driving force, but also on the impact strength of the materials. The effect of strain rate on the fracture strength of the materials has been comprehensively studied [11] and are summarised below. • High strain rate tends to promote brittle fracture through suppression of plastic deformation. • High strain rate raises the fracture toughness of ductile materials while lowers the fracture toughness of brittle materials. Two deductions follows from the above discussions: (i) Geometrical stress concentration, which is less critical in the thermal cycling fatigue analysis, will be utmost critical in the drop impact due to the suppression of plastic yielding (Fig 7). Endeavour shall be make to minimise geometrical stress concentration in the interconnection design.
(ii) The reliability of interconnections at drop impact hinges on the impact strength of brittle materials such as intermetallics. It is possible that the pad and under-bump metallurgy (UBM) that were ideal for thermal cycling may not be idea for drop impact. 4.3 Optimum PCB thickness The maximum deflection of a simply supported beam under velocity impact may be estimated by equating the bending strain energy at maximum deflection with the kinetic energy of beam before impact, leading to 2
24ρ L V eq (8) E π h This gives δ as 1.43 mm for the model of section 3.1 which agrees well with the FEA results (Fig 3b). The maximum deflection of beam is therefore inversely proportional to its thickness. Basing on the differential flexing theory, the zcomponent stress in the interconnection shall then decrease monotonically with increasing PCB thickness. But this was not the case in Fig 5j. An explanation is provided: By approximating the discrete interconnections between the PCB and package as a continuous layer of flexible material, called an elastic foundation, the extension of interconnections η may be described with the following differential equation [12]. d4η + 4λ 4 η = 0 eq (9) dx 4 δ=
(
)
14
represents the relative stiffness where λ defined as k 4D ∗ of the interconnections, k, and the effective stiffness of PCB and package, D* given by 1 D * = ∑ 1 E i I i . The extension of interconnection, and hence its axial stress, therefore depends on the relative stiffness of the interconnection and the PCB/package. Using the appropriate boundary conditions for a centrally mounted package [13], the z-component stress in the interconnection along the package has been computed for 3 thickness of PCB that undergone the same maximum deflection δ (Fig 8). It is clear that the axial stress in the outermost interconnection increases monotonically and rapidly with increasing PCB thickness. 1
S33 (normalised)
Ftensile
Fshea
0.8
PCB thickness 1.50 t
0.6
PCB thickness 1.25 t PCB thickness 1.00 t
0.4 0.2 0
-0.2
Stress concentration
-0.4 0
0.2
0.4
0.6
0.8
1
Normalised distance from center to edge of package Fig 8 S33 Vs PCB thickness – Analytical solution Fig 7 Stress concentration critical in interconnection design
A physical illustration of the interaction of the stiffness of interconnection and PCB/package is depicted in Fig 9.
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Comparing to a thick PCB, a thinner PCB with lower flexural stiffness is more ready to compromise and kink locally where the interconnection is attached, reducing the interconnection strain. PCB of high stiffness, non compromising deformation High stress
PCB of low stiffness, compromising deformation Low stress Fig 9 High stiffness Vs low stiffness PCB Considering that a thinner PCB will lead to increase deflection (eq 8), it is no surprise that an optimum PCB thickness may be found for which the interconnection stress becomes minimum, as seem in Fig 5j. This characteristic of PCB could be exploited for both the product design as well as the board level test. 5. Conclusions • The propagation speed of flexural wave in PCB, C b = πγ L , is a few orders lower than the longitudinal wave
in the steel fixture, C L = E ρ . The deflection of PCB occurs during the rebounding of the entire drop structure. • Differential flexing has been identified as the dominant failure driver for components mounted near the centre of the PCB. The z-direction stress from bending and axial stretching is the most critical stress component. The outer most interconnection of the package is most vulnerable under this failure driver. • Inertia force and longitudinal stress wave are the dominant failure drivers for components mounted near the support. Interconnection adjacent to the support may experience acceleration from tens and hundred thousands of gravitational acceleration compares to tens to hundred gravitational acceleration for interconnection mounted at the centre of the PCB. The z-direction stress from axial stretching is the most critical stress component. • The critical z-component stress has been found to increases with increasing drop height, fall plate thickness, PCB length, package stiffness, package size and decrease with increasing solder bump height, solder bump size, solder bump number, and impact cone diameter. • There is strong interaction between z-component stress and PCB thickness. An optimum PCB thickness could be found that would result in minimum z-component stress in the interconnection. • Intermetallics may be the weakest link of the interconnection structure. Interconnection with low geometrical stress concentration and high impact strength intermatallic structure is highly desirable.
Acknowledgement This work is part of the collaboration project between Institute of Microelectronics, National University of Singapore, and University of Cambridge funded by ASTAR of Singapore. References [1] S.K.W. Seah, et al., “Mechanical response of PCBs in portable electronic products during drop impact”, to be presented in EPTC 2002. [2] JEDEC Standard JESD22-B110, “Subassembly mechanical shock”, March 2001. [3] T. Sogo, et al., “Estimation of fall impact strength for BGA solder joints”, Proc. ICEP, pp. 369-373, 2001. [4] L. Zhu, “Submodeling technique for BGA reliability analysis of CSP packaging subjected to an impact loading”, Proc. IPACK, 2001. [5] I. Hirata, et al., “Drop-simulation of electronic boards mounted with CSPs”, Proc. ICEP, pp. 422-426, 2001. [6] H. Kolsky, “Stress wave propagation in solid”, Dover, NJ, 1963. [7] W. Johnson, et al., “Impact strength of materials”, Edward Arnold, 1972. [8] Graff K.F. “Wave Motion in Elastic Solids”, Oxford University Press, 1975. [9] D.S. Steingerg, “Vibration analysis for electronic equipment”, 3rd ed., John Wiley, 2000. [10] J. Wang, et al., “Modelling solder joint reliability of BGA packages subject to drop impact loading using submodelling”, Porc. Abaqus Conference, 2002. [11] M.A. Meyers, “Dynamic behavior of materials”, John Willey, 1994. [12] E. Suhir, “On a paradoxical phenomenon related to beams on elastic foundation: Could external compliant leads reduce the strength of a surface-mounted device?”, J. Applied Mechanics, 55:818, 1988. [13] P. Engel, “Structural analysis for circuit card systems subjected to bending,” JEP, 112:2, 1990.
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