CTE Mismatch Design in PCB Assembly

Every joint on a board is made between materials that expand at different rates. The board expands in the plane, the package expands less, the solder expands more, and the plated hole expands in a direction that the surrounding laminate does not follow. A cte mismatch is not a defect in itself; it is a permanent condition of the assembly, and the design work is to keep the resulting strain below the level that the joint and the barrel can survive.

Where the Strain Comes From

A surface mount joint is held between a component and a board that move by different amounts as the temperature changes. The difference is proportional to the distance from the neutral point of the package and to the difference in the expansion coefficients.

The strain appears as a shear in the solder. For a small package the displacement is small and the joint survives, while for a large package the displacement at the outermost joint becomes the limiting factor for the thermal cycling life.

A plated through hole sees a different mechanism. The laminate expands in the thickness direction more than the copper, so the barrel is stretched between the surface layers and the strain concentrates where the barrel meets a pad or a plane.

The Numbers That Matter

The thermal expansion coefficient of a laminate is quoted in the plane and through the thickness, and the two are different because the glass fabric restrains the material in the plane. The through thickness figure is the one that affects a plated hole.

The coefficient is not constant with temperature. Below the glass transition it is low and above it is several times higher, which is why the material choice and the process temperature are connected.

The other numbers are the package size, the stand off of the joint and the modulus of the solder. A taller joint with a larger diameter distributes the same displacement over more material and reduces the strain per unit of length.

Design Responses for Surface Mount

The first response is the solder joint itself: a taller stand off and a larger diameter reduce the strain. That is the reason for the different ball sizes on a large package and for the preference for a slightly thicker paste deposit on a large body.

The second is the package construction. A package with an interposer or a compliant layer between the die and the balls absorbs part of the displacement before it reaches the joint, and it is a standard measure for a large device.

The third is the underfill, which couples the package to the board over its whole area and removes the concentration of strain at the outer row. It is used where the package size and the thermal cycling requirement cannot be met by the joint design alone.

Design Responses for Vias

A via is improved by keeping the dielectric thickness through which it passes within the material capability. A very thick board with a small via produces a high aspect ratio and a high strain on the barrel.

The plating thickness matters because a thicker barrel carries the same strain with a lower stress. The figure should be at the top of the specification rather than the bottom for a board that will see thermal cycling.

The copper distribution also affects the barrel. A via that is connected to a large plane is restrained at that layer, so the strain concentrates at the interface between the plane and the barrel. A thermal relief or a controlled connection can reduce the concentration at the cost of the electrical performance.

Material Selection

A laminate with a lower expansion through the thickness reduces the strain on every plated hole on the board at once. That is the main argument for a high tg material with a high filler content on a board that will be thermally cycled.

The expansion above the glass transition is the figure that matters for a lead free assembly, because the board spends time above the transition during the process and the expansion rises sharply there.

The metal core construction has the opposite problem. Its base has a much higher expansion than the laminate, which puts a large strain on the dielectric interface, and that is why the dielectric layer and the bonding to the base are the reliability critical items.

Component and Assembly Factors

The package body material and the die size set the expansion that the joint has to accommodate. A large die in a small body produces a larger mismatch than the body dimensions alone would suggest.

The assembly profile affects the strain that is applied during the process as well as in service. A fast ramp produces a larger temperature difference across the assembly at any moment, and the difference is what drives the displacement.

The rework of a joint applies a local thermal cycle that is more severe than the assembly cycle. A board that is reworked several times accumulates damage that the qualification test, with its uniform cycling, does not represent.

Test and Qualification

The qualification is a thermal cycling test with a defined temperature range, a defined dwell and a defined ramp. The result depends on all three, so a test that quotes only the range cannot be compared with another.

The test vehicle should represent the worst case in the product: the largest package, the smallest via, the thickest board and the thinnest dielectric. A test on an easy vehicle demonstrates nothing about the difficult one.

The failure should be recorded with its location. A crack at the outer joint of a package and a barrel crack near a plane have different causes, and the location is what connects the failure to the design decision that should change.

Predicting and Reducing the Strain

A first estimate can be made from the geometry: the displacement between the component and the board over the temperature range, divided by the joint height, gives the shear strain. The number is approximate but it identifies the cases that need attention.

Simulation is justified for the largest and most expensive assembly, where the cost of a field failure is high. The model should be validated against a measured result on a test vehicle before it is used to make a decision.

The reduction options, in the order of cost, are a change of joint geometry, a change of package construction, an underfill and a change of laminate. Applying them in that order addresses the largest contributors before the expensive ones.

Practical Rules

Estimate the displacement at the worst case temperature, size the joint for the strain and keep the plated holes within the material capability. Qualify with a test that represents the largest package and the thinnest dielectric.

Record the material and the cycling data with the build records and the joint reliability data, and review the dimensional stability data and the derating rules when a package is qualified.

FAQ

Why do the outer joints of a large package fail first? The displacement between the package and the board grows with the distance from the neutral point, so the outermost joint sees the largest shear strain.

How does underfill help? It couples the package to the board over its whole area, so the strain is shared rather than concentrated at the outer row of joints.

What makes a plated hole fail? The laminate expands more through the thickness than the copper, so the barrel is stretched and the strain concentrates where it meets a pad or a plane.