A method is provided for bonding a first substrate carrying a semiconductor device layer on its front surface to a second substrate. The method comprises producing the semiconductor device layer on the front surface of the first substrate, depositing a first metal bonding layer or a stack of metal layers on the first substrate, on top of the semiconductor device layer, depositing a second metal bonding layer or a stack of metal layers on the front surface of the second substrate, depositing a metal stress-compensation layer on the back side of the second substrate, thereafter establishing a metal bond between the first and second substrate, by bringing the first and second metal bonding layers or stacks of layers into mutual contact under conditions of mechanical pressure and temperature suitable for obtaining the metal bond, and removing the first substrate.