Systems and methods for designing and fabricating multi-layer structures
having thermal expansion properties are provided. One embodiment of the
present invention provides a multi-layer structure. Briefly described,
one such multi-layer structure comprises a central layer, a first layer,
and a second layer. The first layer is constrained to a first side of the
central layer and has a first thickness. The first layer comprises a
first material having a first value for a thermal expansion property. The
second layer is constrained to a second side of the central layer and has
a second thickness. The second layer comprises a second material having a
second value for a thermal expansion property. The second thickness and
the second value for the thermal expansion property and the first
thickness and the first value for the thermal expansion property are such
that, upon a change in temperature, the net change in the strain energy
in the first layer and the net change in the strain energy in the second
layer are substantially equal.