A semiconductor chip includes a semiconductor body having a lower side with a lower chip metallization applied thereto. A first contact metallization layer is produced on the lower chip metallization. A second contact metallization layer is produced on a metal surface of a substrate. The semiconductor chip and the substrate are pressed onto one another for a pressing time so that the first and second contact metallization layers bear directly and extensively on one another. During the pressing time, the first contact metallization layer is kept continuously at temperatures which are lower than the melting temperature of the first contact metallization layer. The second contact metallization layer is kept continuously at temperatures which are lower than the melting temperature of the second contact metallization layer during the pressing time. After the pressing together, the first and second contact metallization layers have a total thickness less than 1000 nm.