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This picture is from here (A and B letters are irrelevant for this question). A chip-and-pin card like Visa Electron has a contact pad like this on its face side:

enter image description here

Underneath the contact pad is the chip which has electrical connection with the contact pad. The pictures I found so far suggest that it's a single module - the chip is mechanically united with the contact pad and is then installed into a plastic card.

The contact pad is perhaps ten millimeter wide and ten millimeters long and so much larger than the chip surface. When a card is being bent the contact pad also bends and this most likely causes the chip casing to bend which causes mechanical stress of the chip. Mechanically stressing a chip doesn't sound like a good idea.

How is this problem addressed? Does merging a large contact pad with a smaller chip into a single module make the whole assembly more reliable or more fault-prone?

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mechanically, you're nearly right – think of it as top-bottom:

Place the contact pads upside down on a plane surface. Take a bit of (relatively elastic) glue and fix the die onto the center of the contact pad's back. Then use an automatic bonding machine to weld small wires from contact pads to die, with a bit of a "curve". That way, your die gets a bit of mechanical "freedom" from the pads.

Then, go ahead and bend your card. The hardest part to bend is actually the contact pads, the rest is soft plastic. Hence, the deformation at the center of the contacts isn't that bad.

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