Prognostication of Solder-Joint Reliability of 0.4mm and 0.5mm Pitch BGAs Subjected to Mechanical Shocks up to 10,000G Pradeep Lall, Kalyan Dornala, Junchao Wei Auburn University NSF-CAVE3 Electronics Research Center Department of Mechanical Engineering Auburn, AL 36849 Tele:(334)844-3424 E-mail:
[email protected]
Ryan Lowe
Jason Foley
ARA Associates 7921 Shaffer Pkwy Littleton, CO 80127
Air Force Research Lab, Eglin, FL 32542
Abstract— Due to the reduced size and geometry constraints imposed on electronics in various applications there has been tremendous need for use of very fine pitch surface mount electronics. Fine pitch BGAs of 0.4mm and 0.5mm pitch are finding applications in military and defense applications. Fine pitch BGA electronics in aerospace applications they may be subjected to high-g levels in the neighborhood of 10,000g of mechanical shock during normal operation. Survivability and design envelope of fine pitch semiconductor packages under highg mechanical shock is unknown. In addition, the efficacy of the traditional supplemental restraint mechanisms such as underfills in mitigating the risk of interconnect failure under 10,000g mechanical shock, is not available. A circular board with an annular ring typical of projectile applications has been designed with fine pitch daisy chained packages. Packages studied have package interconnects in the range of 84-360 I/O. Two configurations of the test board have been studied including nonunderfilled, and underfilled assemblies. Full-field strain on the board assembly has been measured and the strain histories at the corner of the component locations extracted. The change in the resistance of the second-level interconnects has been monitored during the shock event using high speed data acquisition system. Resistance spectroscopy in conjunction with Kalman Filter has been used to identify the onset of failure and prognosticate remaining useful life. Keywords- Fine-Pitch BGA, Mechanical Shock, High Strain Rate, Reliability, Kalman Filter, Prognostics
I.
INTRODUCTION
Electronics in aerospace and missile systems may be subjected to high-acceleration levels during normal operation. Commercial electronics components which are increasingly used in missile applications may be subjected to g-levels upwards of 10,000g with the expectation of continued reliable operation. Military systems have longer lifetimes in the
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neighborhood of 20-40 years and higher reliability requirements compared to consumer electronics. In order to use the latest consumer electronics technologies in current and next generation military systems – there is need for tools and techniques for determining the survivability and operating envelopes of electronic components originally designed for office benign applications for use instead in harsh environments of military systems. Survivability of electronics in consumer applications is often ascertained using the JEDEC Test Standard JESD22-B111. The test standard prescribes the application of a 1500g, 0.5ms shock pulse to the board assembly. The test board for the JESD22-B111 shock test has 15 components in a 3x5 component-array configuration on a 132 mm x 77 mm test board [JEDEC 2003]. The test method widely used to assess the board level drop reliability of components for handheld electronic products. However, the correlation of the test results from the JEDEC Test Board with the component’s shock survivability in an actual product is weak. Product designs, board construction, board size, board thickness, and component layout design rules vary between manufacturers and thus the product design influence on the component survivability is quite pronounced. In this paper, a test board of the form-factor of the end application has been designed for assessment of the survivability of fine pitch consumer electronics components in harsh environment applications. Previously, Digital Image Correlation (DIC) has been widely used in a full field measurement by industry and researchers. [Zhou 2001, Yogel 2001, Zhang 2005, Xu 2006] have studied the stresses in solder interconnects of BGA packages under thermal loading with DIC technique. Lall [2005, 2007, 2008, 2012] and Tian [2005] have measured deformation gradients and full field displacement in electronics subjected to drop and shock using digital image
correlation. The use of 3D-DIC has the advantage of providing full-field strain and displacement data. The new test board is circular annular ring in shape with an outside diameter of 110mm and an inside diameter of 36mm. Two sets of test boards have been subjected to 5,000g shock pulses of 0.25ms width, and 10,000g shock pulses of 0.2ms width respectively. Explicit finite element models have been used to study both the strain and displacement response of the test assemblies at the board center and the package corners. Modal analysis has been used to characterize the mode shapes of the test board. High speed imaging along with 3D digital image correlation has been used to study the full-field transient strain and displacement distributions at the package corners on both the one component board and the four component board assemblies. All the components have been monitored in-situ for resistive opens using high-speed data acquisition system. This study’s acquisition of full-field displacement and strain data with high speed imaging to study transient mode shapes, use of explicit finite element models to capture the transient dynamic response of the board assemblies with 0.4mm pitch components, and use of high speed data acquisition for in-situ damage monitoring of all the components at high g-levels of 10,000g is new. Kalman filter models have been used for the assessment of remaining useful life of the components. II.
TEST VEHICLE
36mm. The BGA packages are assembled on the board such a way that they are equally spaced from each other and from edges of the board. The test vehicle assembly without any package reinforcements (Bare TV) is shown in Figure 2 and with Lord Thermoset ME531 underfill reinforced assembly in Figure 3. The PCB has NSMD pads and the BGAs have leadfree SAC305 solder joints. Details of various package attributes including the body size, ball pitch and I/O count etc., are shown in Table 1 and Table 2 below.
Figure 2: Test Vehicle - Packages without any reinforcement (Bare TV)
In this study, circular boards assembled with five different BGA packages CVBGA360, CVBGA97, CTBGA132, CTBGA84 and CTBGA228 have been tested at 5,000G and 10,000G shock levels to characterize the transient dynamic behavior and monitor the resistance changes. CVBGA360 and CVBGA97 are 0.4mm pitch packages while the CTBGA132, CTBGA84 and CTBGA228 are all 0.5mm pitch packages.
Figure 3: Test Vehicle - Packages reinforced with underfill Thermoset ME531 Table 1: Package Attributes For CVBGA360, CTBGA84, AND CTBGA228 Package Attributes
Figure 1: PCB design with the package footprints and traces The PCB was designed in an open source software called FreePCB. In order to mimic the construction of a functional test board, the test assembly board is designed as an eight layer PCB with cross hatched copper pattern. A computer graphic of the board design is shown in Figure 1. The outer diameter of the test board is 110mm and inner ring diameter is
Package
CVBGA360
CTBGA84
CTBGA228
Location on Board Body Size I/O Count Ball Pitch
P7 10mm 360 0.4mm 23x23 Perimeter 0.25mm NSMD(Board) SMD(Package)
P8 7mm 84 0.5mm 12x12 Perimeter 0.3mm NSMD(Board) SMD(Package)
P9 12mm 228 0.5mm 22x22 Perimeter 0.3mm NSMD(Board) SMD(Package)
Matrix Ball Diameter Substrate Pad
Table 2: Package Attributes for CVBGA132 AND CTBGA97 Package Attributes (continued) Package
CVBGA132
CTBGA97
Location on Board Body Size I/O Count Ball Pitch Matrix Ball Diameter
P11 8mm 132 0.5mm 14x14 Perimeter 0.3mm NSMD(Board) SMD(Package)
P12 5mm 97 0.4mm 10x10 Full Array 0.25mm NSMD(Board) SMD(Package)
Substrate Pad
III.
EXPERIMENTAL SETUP
A. Drop Test The drop test was setup as per the layout shown in Figure 4. The test vehicle is mounted on a dual mass shock amplifier (DMSA) with the help of four 18-8 steel half inch standoffs. The test boards including the non-underfilled and underfilled were tested under 5000g-0.25ms and 10,000g-0.2ms test conditions on a Lansmont Model 23 Shock Tower. To attain shock levels of 10,000G’s a dual mass shock amplifier (DMSA) is employed. The test setup with the DMSA on the drop tower is shown in Figure 5.
Figure 6: Acceleration pulse for 5,000g shock
Figure 7: Acceleration pulse for 10,000g shock Figure 4: Drop Test Layout
Figure 5: Test Vehicle Mounted on the DMSA of Shock Tower
An accelerometer of sensitivity 0.103 mV/g was used to measure the acceleration levels of the shock event. Drop heights for 5,000g and 10,000g levels were 24.4inches and 37.5 inches respectively. The acceleration pulses for the shock events of 5,000g and 10,000g test conditions were shown in Figure 6 and Figure 7 respectively. All packages were in-situ monitored for continuity using high speed data acquisition system. In order to measure the full field strain and displacement of the test board 3D DIC has been performed. The test boards were speckle coated and the transient dynamic shock event was captured using high speed camera at 15,000fps. B. Resistance Spectroscopy Resistance measurements were taken between each drop and continuity of all the packages is monitored in-situ during the drop using the high speed data acquisition system. A singlepole double-throw relay switch-circuit shown in Figure was used to switch between the two circuits.
Figure 8: Single pole double throw relay switch circuit The experimental setup for a resistance spectroscopy (RS) measurement is similar to a continuity measurement, but utilizes additional equipment to detect very small changes in resistance that the continuity equipment does not have adequate resolution to detect. RS measurements are capable of detecting changes in resistance as small as a milli-ohm well before the traditional definition of failure and therefore contain prognostic value. A detailed diagram of the RS measurement setup is shown in Figure 6. Capacitors C1 and C2 help eliminate stray inductances from wires running between the test board and measurement equipment. Resistors R1, R2, and R3 are used to balance the bridge. The single pole double throw relay has a small but non-negligible resistance that must be balanced out by specifying an appropriate value of resistor R3. Unlike traditional bridges, an AC voltage source drives this bridge, resulting in a sinusoidal output whose amplitude and phase shift are proportional to the resistance of the package. The lock-in amplifier performs the phase sensitive detection which effectively increases the resolution of the RS measurement compared to the continuity measurement.
based on the measured output voltage from the bridge follows closely to that of a traditional Wheatstone bridge [Wheeler 2004], but must now incorporate impedances into the calculation. The general impedance bridge equation becomes: (1) Z3 Z1 − ZPKG Z2 Vout , AC = Vin , AC ( Z2 + Z3 )( Z1 + Z4 ) Where Z1 is the combined impedance of R1 and C1, and similarly for Z2. Impedances Z3 and ZPKG are simply resistive impedances and therefore reduce to the value of resistor R3 and the daisy chained resistance of the package respectively (i.e. Z3=R3, ZPKG=RPKG). In a perfectly balanced bridge the numerator cancels out and the output voltage is zero. The resistance of the package can be solved for algebraically: (2) V Z Z − Vout ,AC ( Z2 Z1 + Z3 Z1 ) Z PKG = in ,AC 3 1 Vout ,AC ( Z2 + Z3 ) + Vin ,AC Z 2 Table 3: Discrete component values used in resistance spectroscopy AC Wheatstone bridge Component Value R1,R3 10Ω R2 Variable resistor(Balanced with RPKG ) Initial RPKG Package Resistance 1.02-1.55Ω C1,C2 10 nF Vin,AC 5.06 VRMS at 95 kHz The resistance values used in the wheat stone bridge circuitry are shown in Table 3. Initial resistances of all the packages except CVBGA360 were in the neighborhood of 1.02Ω to 1.05Ω, and CVBGA360 was around 1.45Ω to 1.55Ω. C. Digital Image Correlation Digital Image correlation (DIC) has been employed to calculate the full field displacement and strain. A spray painted board with random speckle patterns as shown in Figure 7 was used to track the displacements of the deformed images with respect to the undeformed reference image. The high speed video at 15,000 fps from the shock test has been used to track the motion of the speckles before, during and after the shock event.
Figure 6: Resistance spectroscopy measurement setup. A differential output from the bridge is input into the lock-in amplifier for phase sensitive detection. Magnitude and phase data are recorded with the data logger. The outputs from the lock-in amplifier, the magnitude and phase shift of the signal Vout,AC, are recorded using a data logger. Calculating the change in resistance of the package
Figure 7: Digital image correlation principle
The two-camera configuration has been used to measure both the in-plane and out-of-plane deformation. The set of images extracted from the high speed video were processed in a DIC software for 3D measurement of displacements and strains. Previously, the feasibility of DIC for 3D measurement of displacements during the transient shock events has been demonstrated by [Lall 2007, 2008, 2012]. The undeformed referred to as the original image and deformed images versus time have been captured using the high speed cameras (Figure 10). Since a single pixel is not a unique signature of a point hence a neighboring pixels are used. The collection of pixels is called a subset. Uniqueness of the pattern has been assured by using a non-repetitive random high-contrast speckle pattern. A subset of pixels around a reference pixel O in the reference image has been compared with the subset corresponding to pixels in the deformed image using a predefined correlation function to describe the difference of the two digital sub images. Deformation of the subset during transient deformation has been accomplished through displacement mapping using a subset shape function. The subset has been stepped through the image to measure the displacement of the complete board assembly. An algorithm based on the mutual correlation coefficient or other statistical functions are used to correlate the change in a reference pixel in the original image and the corresponding reference pixel in the deformed image. The high speed cameras have been mounted on rigid tripod mounts to prevent movement of the cameras during the shock event relative to the shock tower or relative to each other. IV.
The model with underfill on the test board is shown in Figure 9 and the transient dynamic model is shown in Figure 10. Rigid floor has been modeled with R3D4 elements. A reference node has been placed behind the rigid wall for application of constraints. Node to surface contact has been used for impact between the shock table and the floor. An event length of 5ms after impact has been modeled. Time history has been monitored at a time period of 0.1ms at the corner solder joints of all BGAs in the test assembly.
Figure 9: An underfilled model of the package
ABAQUS-EXPLICIT FE-MODELING
Finite element explicit modeling was performed in ABAQUS explicit for both the reinforced and unreinforced test boards. The PCB was modeled with S4R elements, packages with C3D8R and the solder interconnects were modeled as Timoshenko beam elements of type B31. A bare test board model is shown in Figure 8.
Figure 8: Finite element model of unreinforced TV
Figure 10: Transient dynamic model of the circular board with drop base and rigid floor
Figure 11: Bare TV out of plane deflection at 5000g shock
Transient dynamic analysis of the shock event was performed in ABAQUS Explicit. Figure 11 shows the out of plane deflection of unreinforced bare TV under 5000g and Figure 12 shows the out of plane deflection at 10000g. The peak displacement for 5000g is 1.79mm and for 10000g is 3.1mm. The models for underfilled packages have been used to extract the out-of-plane deformation and solder joint strain values.
Figure 15: Corner solder interconnect strains at different shock levels for CTBGA228 of unreinforced bare test vehicle
Figure 12: Bare TV out of plane deflection at 10000g shock
Figure 16: Corner solder interconnect strains at different shock levels for CVBGA97 of unreinforced bare test vehicle
Figure 13: Corner solder interconnect strains at different shock levels for CTBGA84 of unreinforced bare test vehicle
Figure 17: Corner solder interconnect strains at different shock levels for CVBGA360 of unreinforced bare test vehicle Solder joint strain at the corner interconnects of each package have been extracted from model results at different shock levels. The plots shown in Figure 13 to Figure 17 compare the solder joint strains of unreinforced bare TV at 5000g and 10000g. The average corner solder joint strains for all the packages at 5000g is in the neighborhood of 1750µ. At 10000g shock the corner solder join strains averages to 2300µ for all the packages. Figure 14: Corner solder interconnect strains at different shock levels for CTBGA132 of unreinforced bare test vehicle
V.
MODAL ANALYSIS
Finite element modal analysis has been performed for both unreinforced and reinforced test vehicle to characterize the natural frequencies and mode shapes. This includes the mode shapes and natural frequencies of unreinforced bare TV and ME531 underfilled board models. Figure 16 shows the first five mode shapes of unreinforced bare TV with mode 1 being the dominant factor in the transient dynamic deformation. Mode 3 and mode 4 are identical as the testboard is in a symmetrical circular shape. Figure 21: Mode 5 for unreinforced bare testboard
Figure 18: Mode 1 for unreinforced bare testboard
Figure 22: Mode1 for ME531 underfill reinforced packages
Figure 19: Mode 2 for unreinforced bare testboard
Figure 23: Mode 2 for ME531 underfill reinforced packages
Figure 20: Mode 3 and Mode 4 for unreinforced bare testboard
Figure 24: Mode 3 and Mode 4 for ME531 underfill reinforced packages
Figure 25: Mode 5 for ME531 underfill reinforced packages Table 4: Comparison of Natural Frequencies for Bare TV and Underfilled TV Natural Frequency values extracted from modal analysis Natural Frequency
Bare TV
Underfill ME531
Mode 1 Mode 2 Mode 3 Mode 4 Mode 5
857.36Hz 887.86Hz 1011.9Hz 1013.8Hz 1356.9Hz
856.37Hz 887.56Hz 1011.4Hz 1013.5Hz 1358.0Hz
Figure 27: Out of plane displacement contour of ME531 underfill reinforced TV at 5000g
The mode shapes for the ME531 underfill reinforced packages are shown in Figure 18-Figure 21. A comparison between the natural frequencies of the bare TV and underfilled TV is shown in Table 4. VI.
HIGH-SPEED IMAGING BASED DIC MEASUREMENTS
Full field strain and displacement analysis of unreinforced and reinforced test assemblies at various shock levels was performed using high-speed imaging in conjunction with 3DDIC. Figure 26 shows the out-of-plane displacement of unreinforced TV under 5000g shock and Figure 27 shows the out-of-plane displacement of ME531 underfilled TV under 5000g shock. The maximum out of plane displacement of the bare test vehicle at 5000g shock was 2.27mm and for underfilled TV was 2.15mm.
Figure 28: Out of plane displacement contour of bare TV at 10000g.
Figure 29: Out of plane displacement contour of ME531 underfill reinforced TV at 10000g Figure 26: Out of plane displacement contour of bare TV at 5000g.
Figure 28 shows the out of plane displacement of unreinforced bare TV at 10000g shock. Figure 29 shows the out-of-plane
displacement of the underfilled TV at 10,000g. The displacement contours have been captured just after the impact in both the cases. The maximum out of plane displacement for unreinforced bare TV was 2.92mm and for ME531 underfill reinforced TV was 3.01mm PCB Strains The in plane pcb-x and pcb-y strains near the corner interconnects of all the packages have been extracted from the DIC analysis. In each case the corner location plotted is the solder joint with the maximum value of strain. Figure 30 and Figure 31 show the x and y strains near corner interconnects of the packages of bare TV at 5000g shock. The maximum pcb-x and pcb-y strains observed at this condition was in the neighborhood of 5000µ and 4600µ, respectively. Similarly the pcb x and y strains of the underfilled TV at 5000g shock were extracted. From Figure 32 and Figure 33 peak values of 4800µ and 5100µ in the x and y direction respectively were observed in the underfilled case.
Figure 30: Unreinforced bare test board PCB-X strains near corner interconnects at 5000g.
Figure 31: Unreinforced bare test board PCB-Y strains near corner interconnects at 5000g
Figure 32: ME531 underfill reinforced test board PCB-X strains near corner interconnects at 5000g.
Figure 33: ME531 underfill reinforced test board PCB-Y strains near corner interconnects at 5000g.
Figure 34: Unreinforced bare testboard PCB-X strains near corner interconnects at 10000g.
each case the corner location plotted is the solder joint with the maximum value of strain. Figure 34 and Figure 35 show the pcb-x and pcb-y strains near the package corners at 10000g for unreinforced bare TV. Peak values of 6700µ and 7800µ of x and y strains respectively were observed. From Figure 36 and Figure 37 peak values of pcb x and y strains for the underfilled Tv at 10000g were in the neighborhood of 6000µ and 4100µ respectively. VII. KALMAN FILTER FRAMEWORK
Figure 35: Unreinforced bare testboard PCB-Y strains near corner interconnects at 10000g
System damage state estimation in the presence of measurement noise and process noise has been achieved using the Kalman Filter (KF). Previously, the Kalman Filter has been used in guidance and tracking applications [Kalman 1960, Zarchan 2000]. System state has been described in state space form using the measurement of the feature vector, velocity of feature vector change and the acceleration of the feature vector change. System state at each future time has been computed based on the state space at preceding time step, system dynamics matrix, control vector, control matrix, measurement matrix, measured vector, process noise and measurement noise. Figure 38 represents the data-flow through the system, where uk is the control vector or input for the system, wk is process noise, xk is the state space vector at the kth time step, H is the measurement matrix and vk is the measurement noise, zk the measured state, T is a time delay, and Φk is the system dynamics matrix. vk
wk uk
B
xk
+
Φk
Figure 36: ME531 underfilled testboard PCB-X strains near corner interconnects at 10000g.
zk H
+
T
Figure 38: Graphical state space representation of a system The equivalent Kalman Filter equation for state space representation is in the presence of process noise and measurement noise is: xˆ k = Φ k xˆ k −1+ Bk u k −1+ K k (z k − H k Φ k xˆ k −1−H k Bk u k −1 ) z k = Hx k + v k
(3) (4)
Where xˆ k is the Kalman Filter estimate of system-state at time kth time step, and x k is the actual system state at the kth timestep, B k is the control vector. The Kalman gain has been computed and updated at each time-step, while the filter is operating from the Riccati equations. The Ricatti equations can be represented in matrix form as: M k = Φ k Pk −1 Φ Tk + Q k T
b Figure 37: ME531 underfilled testboard PCB-Y strains near corner interconnects at 10000g. Full field strains were extracted at higher shock load levels of 10000g for both the unreinforced TV and underfilled TV. In
(5) (6)
MkH HM k H T + R k (7) Pk = (1 − K k H)M k Where Mk is the covariance of errors in state estimates before update, Φk is the fundamental matrix which represents the system dynamics, Qk is the discrete process noise matrix, Kk is the Kalman gain, H is the measurement matrix, and Pk is Kk =
the covariance matrix representing errors in the state estimate after an update. Rk is the process noise matrix and has been used as a device for telling the filter that we know that filter’s model of the real world is not precise. The diagonal elements of Pk represent variance of the true state minus the estimated state. Mk is sometimes referred to as the a priori covariance matrix, and Pk may be referred to as the posterior covariance matrix. Since the feature vector used for prognostication of the system health is not a constant or a straight line, therefore the zeroth and first order systems were ruled out and a second order system was used for representation of system state evolution with progression of underlying damage. The choice of the second order filter was also influenced by the general observation that feature vectors evolve non-linearly and generally accelerate towards the end of life. The rate of evolution of a second order system can be represented as follows: (8) ⎧x ⎫ ⎛ 0 1 0 ⎞⎧ x ⎫ ⎧ x ⎫ ⎟⎪ ⎪ ⎪ ⎪ ⎜ ⎪ ⎪ ⎨x ⎬ = [F]⎨x ⎬ = ⎜ 0 0 1 ⎟⎨x ⎬ ⎪x⎪ ⎜ 0 0 0 ⎟⎪x ⎪ ⎪x⎪ ⎠⎩ ⎭ ⎩ ⎭ ⎝ ⎩ ⎭ The fundamental matrix has been computed from the Taylor series expansion of the system dynamics matrix, F, as follows: Φ (t ) = e Ft = I + Ft +
(Ft )2 + ... + (Ft )n
+ ...
(9)
2! n! ⎛1 0 0⎞ ⎛0 1 0⎞ ⎛0 0 1⎞ 2 ⎜ ⎟ ⎜ ⎟ ⎜ ⎟t Φ (t ) = ⎜ 0 1 0 ⎟ + ⎜ 0 0 1 ⎟ t + ⎜ 0 0 0 ⎟ ⎜ 0 0 1 ⎟ ⎜ 0 0 0 ⎟ ⎜ 0 0 0 ⎟ 2! ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ 2 ⎛ 1 Ts 0.5Ts ⎞ ⎟ ⎜ Ts ⎟ Φ (t ) = ⎜ 0 1 ⎜0 0 1 ⎟⎠ ⎝ A model based on the accrued plastic work in interconnects of the system has not been used because the inputs to the system are not always known or measurable and cannot be assumed to always be constant or known in advance. Therefore, the feature vector based on resistance spectroscopy has been related to the underlying plastic work and its evolution used for prognostication of system state and residual life. The first and second derivatives of the feature vector based on resistance spectroscopy have been computed to estimate the state of the feature vector at future time-steps. The
The uncertainty of each prediction was quantified using the posterior error covariance. The extrapolation of the estimated state into the future to determine the RUL was accomplished by using the state evolution equation to iteratively solve the intersection of a quadratic equation with the critical resistance threshold. The parameters are estimated from the Kalman filter. The filtering and prediction algorithm is summarized below. Algorithm: Filtering and RUL prediction 1. Initialize variables at time step t = 0 2. Project state at the next time step, x k = Φ k x k −1+ w k 3. Calculate error covariance before update, M k = Φ k Pk −1 Φ Tk + Q k 4. Calculate Kalman gain, K k = M k H T (HM k H T + R k )−1 5. Take measurement, z k = Hx k + v k 6. Update estimate with measurement, xˆ k = Φ k xˆ k −1+ Bk u k −1+ K k (z k − HΦ k xˆ k −1−HBk u k −1 )
7. Calculate error covariance after measurement update, Pk = (1 − K k H )M k 8. Extrapolate feature vector to threshold value, x k + n = Φ k + n x k + n −1+ w k + n 9. Report predicted RUL (and uncertainty) 10. Iterate to step 2 for next measurement (k = k +1) VIII. RUL PREDICTION Resistance measurements were performed for each test condition between each drops for all the components. The resistance readings of the package CVBGA97 of the bare TV under 5000g shock condition is shown in Figure 39. There is a slight increase of resistance during the initial 10 drops and decrement after 10 drops can be seen. As the number of drops were increased the resistance maintained the slight increment trend up to 30 drops and a steep increase can be seen after 30 drops. The remaining useful life (RUL) of the bare TV package under 5000g shock is shown in Figure 40.
T
system state vector is represented as x k = ⎣x x x ⎦ , where x is the interconnect resistance of the daisy chained package, x is the ramp rate of the interconnect resistance, and x is the second derivative with respect to time of the interconnect resistance. The state vector evolution is represented as follows: ⎧x k +1 ⎫ ⎛ 1 Ts ⎪ ⎪ ⎜ ⎨x k +1 ⎬ = ⎜ 0 1 ⎪x ⎪ ⎜ 0 0 ⎩ k +1 ⎭ ⎝
0.5Ts2 ⎞⎧ x k ⎫ ⎟⎪ ⎪ Ts ⎟⎨ x k ⎬ 1 ⎟⎠⎪⎩x k ⎪⎭
(10)
Figure 39: CVBGA97 resistance trend over the drop and shock at 5000g
Figure 40: Remaining useful life prediction for CVBGA97 under 5000g shock
Figure 41: CVBGA97 resistance trend over the shock event of 10000g
Figure 42: Remaining useful life prediction for CVBGA97 under 5000g shock
Figure 43: ME531 underfill reinforced CVBGA97 package resistance trend under 5000g shock
Figure 44: ME531 underfill reinforced CVBGA97 package remaining useful life prediction
Figure 45: ME531 underfill reinforced CVBGA97 package resistance trend under 10000g shock
the peak strains near corner interconnects compared to the non underfilled boards. Resistance spectroscopy in conjuction with Kalman filter has been used to predict the onset of failure and prognosticate the remaining useful life. ACKNOWLEDGMENT The research presented in this paper has been supported by NSF Center for Advanced Vehicle and Extreme Environment Electronics (CAVE3) consortium-members. REFERENCES [1]
[2]
Figure 46: ME531 underfill reinforced CVBGA97 package remaining useful life prediction under 10000g shock. The resistance readings of the package CVBGA97 of underfill reinforced TV under 10000g shock condition is shown in Figure 41. A very slight increase in the resistance is seen up to 10 drops and steep increase in the resistance can be seen after 10 drops. The remaining useful life (RUL) of the bare TV package under 10000g shock is shown in Figure 42. The ME531 underfilled boards were also monitored for resistance change during the 5000g and 1000g shock events. From Figure 43, we can see the resistance vs drop trend of underfilled CVBGA97 package under 5000g shock. There has been not so significant increase in the resistance up to 16 drops and the slope started to increase at a slow rate after 16 drops. Remaining useful life prediction of underfilled CVBGA97 package under 5000g shock is shown in Figure 44. In case of 10000g shock of the underfill reinforced TV a trend similar to that of 5000g shock was observed until 15 drops but a steep increase of the resistance can be seen after 15 drops. This can be seen from the Figure 45. Remaining useful life prediction for this test condition is plotted and shown in Figure 46. IX.
[3]
[4]
[5]
[6]
[7]
[8]
[9]
CONCLUSIONS
High speed 3D-DIC measurements along with explicit finite element modeling has been used to study the transient dynamic behavior and characterize the in plane strain and out of plane deflection. From the modeling results solder joint strains were extracted for both 5,000g and 10,000g bare TV shocks. At 10,000g shock the peak strains in the corner interconnects of the packages averaged about 2300µ and in case of 5,000g it is 1750µ. The out of plane deflection contours from the modeling results were also extracted and a good correlation with respect to the 3D-DIC contours was observed. The PCB-X and PCB-Y Strains near the corner interconnects of the packages were extracted from 3D-DIC measurements. An average peak strain increase about 2000µ was observed in both PCB-X and PCB-Y strains when the boards were tested at 10000g compared to 5000g shock. Underfill reinforcing the packages shows a slight decrease in
[10]
[11]
[12]
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