Chapter 5: Ball Grid Array (BGA)

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1 Chapter 5: Ball Grid Array (BGA) 5.1 Development of the Models The following sequence of pictures explains schematically how the FE-model of the Ball Grid Array (BGA) was developed. Initially a single solder bump was modelled (Figure 5.1) that represented reasonably accurate the geometry and size of a real solder connection, as outlined in the specifications provided by Siemens. Note, that very small ball structures, I.e. the Al-pad passivation and other layers, have been neglected. The modelling of these is left to a future sub-model of the solder joints. The top and bottom layers of each ball are 25 micron in height, which is the recommended size for averaging interface strains [36]. 0.42mm Top and Bottom Layers, 25 micron 0.56mm 0.52mm Figure 5.1a: Solder ball dimensions Figure 5.1b: Height of solder ball

2 The solder balls were structured in 6 layers such that the top and bottom layers were 25 µ thick, whilst keeping the ratio between adjacent layers below a maximum of 6:1. Exceeding this ratio between adjacent elements can lead to errors during the running of the finite element programme. Figure 5.2: Structure of top and bottom layers of the solder balls The design of the elements is such that the solder can be divided diagonally down the middle to allow the creation of the symmetrical structure, discussed in Chapter 4. a b Ratio Between Dimensions of Adjacent Elements Eg. a:b Should Not Exceed 6:1 Figure 5.3: Detail view of elemental structure in the solder material

3 In a second step a unit cell was created, which has the moldmass, substrate and printed circuit board (PCB) layers added to the solder ball structure. All geometries/sizes of this model followed the technical specifications for the Ball Grid Array provided by Siemens. 0.5mm Moldmass 0.4,0.6,0.8mm Substrate 1.6mm PCB Figure 5.4: BGA unit cell structure

4 Thirdly, the unit cell is replicated to form a block of 34 solder balls, which represents one eighth of the BGA solder ball array (using Siemens labelling convention). Solder Ball Array Ball T Ball S Ball R Ball Q 1.27mm Ball P Ball O Printed Circuit Board Ball N Ball M Ball L Ball K Row 17 Row 18 Row 19 Row 20 Figure 5.5: Solder ball array shown on printed circuit board Figure 5.6: Detail of elemental structure on line of symmetry

5 In a fourth step a simplified unit cell is created and duplicated to form the rest of the structure, reducing computational time required during analysis. An edge cell is also added at the plane of symmetry, to avoid mis-shapen (e.g. triangular) elements. The chip is created by changing the material property in the appropriate zone to silicon. Finally, the upper layer of moldmass is extruded from the structure. Plane of Symmetry Detailed Mesh Simplified Cells Edge Symmetry Cells Figure 5.7: Detail view of mesh construction

6 The final version of the Finite Element, Ball Grid Array, model contains: 31,693 Nodes 6342 Elements (20 node quadratic brick elements with reduced integration) The overall dimensions of the model were as follows: 5mm 0.5mm 0.5mm Silicon Chip Moldmass Substrate 12.7mm PCB Solder Figure 5.8: Overall dimensions of the BGA model

7 5.2 Modelling Results The predicted lifetime of each model is based on the strain development within the solder joints during simulated temperature cycles between 398 K(125 C) and 233 K(-40 C), as discussed in Chapter 4. The process of lifetime prediction is illustrated here for the bilinear elastic-ideal plastic analysis of the 0.4mm thick substrate of the full model. The detailed results of other substrate thicknesses, model variants and material laws are included in the appendix section of the thesis. First the strain energy developed by the thermal cycling is divided by the solder ball volume, to give an average value for the whole ball: At least one discussion of creep should be provided here. energy density, e [MPa] step, N [-] ball K17 ball K18 ball K19 ball K20 ball L17 ball L18 ball L19 ball L20 ball M17 ball M18 ball M19 ball M20 ball N17 ball N18 ball N19 ball N20 ball O17 ball O18 ball O19 ball O20 ball P17 ball P18 ball P19 ball P20 ball Q17 ball Q18 ball Q19 ball Q20 ball R18 ball R19 ball R20 ball S19 ball S20 ball T20 Figure 5.9: Plastic energy density development: BGA (Ideal plasticity, whole ball averaging, 0.4mm substrate)

8 The variation in strain energy density between each row of solder balls can be observed, showing a decrease towards the centre of the array (see Figure 5.5, ball labelling): energy density, e [MPa] step, N [-] ball K20 ball L20 ball M20 ball N20 ball O20 ball P20 ball Q20 ball R20 ball S20 ball T20 Figure 5.10: Plastic energy density development: BGA (ideal plasticity, whole ball averaging, row 20) 6.00 ball K ball L19 energy density, e [MPa] ball M19 ball N19 ball O19 ball P19 ball Q19 ball R step, N [-] ball S19 Figure 5.11: Plastic energy density development: BGA (ideal plasticity, whole ball averaging, row 19)

9 6.00 ball K ball L18 energy density, e [MPa] ball M18 ball N18 ball O18 ball P ball Q step, N [-] ball R18 Figure 5.12: Plastic energy density development: BGA (ideal plasticity, whole ball averaging, row 18) 6.00 ball K17 energy density, e [MPa] ball L17 ball M17 ball N17 ball O ball P step, N [-] ball Q17 Figure 5.13: Plastic energy density development: BGA (ideal plasticity, whole ball averaging, row 17)

10 The energy density increment is then calculated for each of the eight steps in the analysis. The first step is distinguished by an extremely large increment. This is due to the fact that it consists of the cooling process, from the stress free state of reference at 456 K down to 398 K. Note that the other steps do not contain such a large increment and stay essentially at a constant level. Consequently, a certain amount of initial irreversible deformation is induced in the solder from the very beginning. This contribution is excluded within the spreadsheet data manipulation, since the objective is a lifetime assessment as a consequence of thermal cycle tests between levels 233 K and 398 K alone. increment of energy density, e [MPa] step, N [] ball K17 ball K18 ball K19 ball K20 ball L17 ball L18 ball L19 ball L20 ball M17 ball M18 ball M19 ball M20 ball N17 ball N18 ball N19 ball N20 ball O17 ball O18 ball O19 ball O20 ball P17 ball P18 ball P19 ball P20 ball Q17 ball Q18 ball Q19 ball Q20 ball R18 ball R19 ball R20 ball S19 ball S20 ball T20 Figure 5.14: Development of plastic energy density increment: BGA (ideal plasticity, whole ball averaging)

11 The energy density increments are then consolidated into four cycles, each consisting of two steps. The fact that the energy density increment between steps shows little change suggests that this will give a reasonable prediction of expected lifetime. These values are then used to calculate the number of cycles to crack initiation (N o ) and crack propagation, based on Darveaux s equations, described in Chapter 4. The first cycle is modified in the spreadsheet such that the cycle begins at 398 K, thus eliminating the very large energy density increment due to cooling down from the stress free state of 456 K. The choice of stress free temperature, however, still has an effect on the level of strain energy produced within the temperature cycles. increment of energy density, e [MPa] cycle, N [-] ball K17 ball K18 ball K19 ball K20 ball L17 ball L18 ball L19 ball L20 ball M17 ball M18 ball M19 ball M20 ball N17 ball N18 ball N19 ball N20 ball O17 ball O18 ball O19 ball O20 ball P17 ball P18 ball P19 ball P20 ball Q17 ball Q18 ball Q19 ball Q20 ball R18 ball R19 ball R20 ball S19 ball S20 ball T20 Figure 5.15: Development of plastic energy density increment by cycle: BGA (ideal plasticity, whole ball averaging)

12 The strain energy distribution in the solder balls can be examined using the ABAQUS POST processor. There are three relevant variables related to time-independent plasticity, which are: PENER: Energy dissipated by rate independent and rate dependent plasticity, per unit volume EPDDEN Total energy dissipated per unit volume in the element by rate independent and rate dependent plastic deformation PEEQ: Equivalent plastic strain, defined as ε pl t + & ε 0 0 pl dt For the 0.4mm substrate, these distributions are as follows: Figure 5.16: Side view of dissipated plastic energy, PENER, in 0.4mm substrate solder balls

13 Figure 5.17: Side view of dissipated plastic energy, EPDDEN, in 0.4mm substrate solder balls Figure 5.18: Side view of dissipated plastic energy, PEEQ, in 0.4mm substrate solder balls

14 The predicted lifetimes of the solder connections are plotted in a grid, showing the position of each ball in the structure. For clarity and in order to represent only full solder balls, the grid is shown representing one quarter of the actual structure. This is done by duplicating the results for each ball about the 45 axis of symmetry. The specification for this model has solder balls around the periphery of the structure, with no connections at the centre, hence the empty spaces in the figures below. The predicted lifetimes are shown below for the 0.4, 0.6 and 0.8mm substrates: 1400 cycles to failure, Nf k l m n o p Ball Number 19 Ball Letter q r s t Figure 5.19: BGA predicted lifetime, 0.4mm Substrate (ideal plasticity, whole ball averaging) The most strained ball (i.e. lowest cycles to failure) is predicted to be at the outside corner of the structure, which corresponds with experimental test results carried out by Siemens. Careful, this needs a ref and some evidence!

15 1400 cycles to failure, Nf k l m n o p Ball Number 19 Ball Letter q r s t Figure 5.20: BGA predicted lifetime, 0.6mm Substrate (ideal plasticity, whole ball averaging) 1400 cycles to failure, Nf k l m n o p Ball Number 19 Ball Letter q r s t Figure 5.21: BGA predicted lifetime, 0.8mm Substrate (ideal plasticity, whole ball averaging)

16 Next, time dependent creep analyses were run, with and without encapsulating moldmass, giving the following results (averaged data for 34 solder balls): Cycles To Failure (Nf) Creep No Moldmass Creep Data, Full Model 0 Ideal Plastic Data 0.4mm 0.6mm 0.8mm Substrate Thickness Figure 5.22: Sensitivity of the BGA model to the presence of encapsulating moldmass It can be seen that the presence of encapsulating moldmass appears to reduce the predicted lifetime of the BGA model. The trend of the data from the ideal elastic-plastic analysis, is different to that from the time dependent creep analyses, casting doubt on the validity of this simplification for BGA modelling.

17 Finally, in order to explore the data trends further, a model was evaluated with a 0.25mm thick substrate. In addition, the results of the averaged data from the 34 solder balls were compared to those for the most strained ball only Cycles To Failure (Nf) Creep Data, Full Model, Average of 34 Solder Balls Most Strained Ball mm 0.4mm 0.6mm 0.8mm Substrate Thickness Figure 5.23: Comparison of most strained ball with data from 34 ball average As would be expected, analysis of the most strained ball shows a lower predicted number of cycles to failure than an average of all 34 solder balls. The data trend for the most strained ball is very similar to that of the 34 ball averaged data.

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