The invention relates to a method for manufacturing a contact arrangement (10) between a microelectronic component (11) and a carrier substrate (12) and to an assembly unit (24) manufactured by this method, whereby thermal energy required in the connecting areas is achieved by exposing the back of the component to laser energy, a mechanical connecting contact (23) is formed between opposing connecting surfaces (17, 18) of the component and the carrier substrate, and at least one electrically conducting connecting contact (22) is formed between terminal faces (13, 15) of the carrier substrate and of the component arranged at an angle to one another by t least partially melting solder material, whereby the assembly unit manufactured by this method has at least one contact arrangement.