A method and apparatus for rapid and selective heating of materials using variable frequency RF and microwaves. The apparatus uses variable frequency solid state electronics as a microwave power source, a novel microwave heating head to couple microwave energy to the target materials and a match-up network to tune the frequency and impedance match between the microwave source and the load. An electronic and computer measurement and control system is employed to monitor and control the microwave heating process. The method teaches the use of inductive microwave coupling for thin conductive materials such as metal film and impurity doped silicon wafers. The method also teaches the use of capacitive microwave coupling for dielectric material such as glass and ceramics. The method further teaches the use of rapid and selective heating of heterostructure for bonding and sealing of mems and integrated circuits. The method and apparatus can provide ultra-high heating speed along with ultra-high heating temperatures for rapid thermal processing of semiconductors and other materials. It also allows the use of bonding materials with high melting temperature for strong bonding and sealing of mems and IC devices. The apparatus further provides for high interconnection density of integrated circuits as connections are made without the use of solder bumps.