Abstract: A connection structure between lead frames and a base plate of aluminum nitride, to be applied as a connection structure between components of a semiconductor apparatus, has a base plate made of a sintered body of aluminum nitride on which a semiconductor device is to be mounted. The lead frames are made of iron alloy containing nickel in 29 wt. % and cobalt in 17 wt. %. A silver solder is used for joining the base plate and the lead frames. A surface of the lead frame to be joined to the base plate is clad with a stress relief layer of oxygen-free copper of a high plastic deformability to relieve, by its plastic deformation, a thermal stress caused by a difference between a thermal expansion coefficient of the aluminum nitride base plate and that of the lead frame in a cooling process at the time of soldering. Preferably, only a portion of each lead frame to be joined to the base plate comprises an inner layer of an iron alloy containing 29 wt. % of nickel and 17 wt.