A back contact solar cell structure having a light receiving frontside and a metallized backside of on-cell patterned base and emitter metallization electrically connected to base and emitter regions on a back contact solar cell semiconductor substrate. A backplane laminate layer made of resin and fibers and having a coefficient of thermal expansion relatively matched to the back contact solar cell semiconductor substrate is attached to the on-cell base and emitter metallization and to portions of the back contact solar cell semiconductor substrate not covered by the on-cell base and emitter metallization.