As materials are heated, they expand. The coefficient
of thermal expansion (CTE) is a measurement of that rate of
expansion. Typical units for CTE are parts per million per
degree C (ppm/C).
Silicon has a coefficient of expansion of approximately 3 ppm/C,
while the expansion of copper is 17 and the expansion of
aluminum is 23. Because of this large mismatch, silicon or
other low expansion materials cannot be bonded directly to
copper or aluminum without undergoing unacceptably high
stresses. Likewise, ceramic packages mounted on FRP boards
are likewise subjected to large mismatches in CTE. The
copper/graphite composite can act as a constraining core for FRP
Unlike most materials, graphite fibers actually contract as
they are heated. Depending upon the amount of graphite
fiber incorporated into the copper/graphite composite, CTE
values can be varied over a wide range, as shown:
The copper/graphite composite typically has a CTE between 4
and 6 ppm/C.
Below is a graph showing expansion versus temperature for a
typical 6 ppm/C copper/graphite sample. The CTE of many
materials including Cu/Invar/Cu, Cu/Mo/Cu, Kovar, and epoxy,
varies as a function of temperature due to such effects as phase
changes or glass transition temperatures. Likewise, the
CTE of the copper/graphite varies as a function of temperature.
For most applications, a linear approximation of the CTE
value works well. Because the expansion of the composite
can be varied, thermal mismatches between a die and the
composite substrate can be minimized. Die can be bonded
with soft solder or by eutectic gold-silicon or gold-tin
alloys. The reduction in thermal resistance between the
die and the substrate can be very substantial.
Please Note: The properties of the
copper/graphite composites are a function of the type and amount
of graphite fiber incorporated in the composite, as well as the
orientation of that fiber. Thus, the properties discussed
are typical for a composite reinforced with a chopped graphite
fiber oriented within the plane of the composite.