The disclosed technology generally relates to semiconductor wafer bonding, and more particularly to direct bonding by contacting surfaces of the semiconductor wafers. In one aspect, a method for bonding a first semiconductor substrate to a second semiconductor substrate by direct bonding is described. The substrates are both provided on their contact surfaces with a dielectric layer, followed by a CMP step for reducing the roughness of the dielectric layer. Then a layer of SiCN is deposited onto the dielectric layer, followed by a CMP step which reduces the roughness of the SiCN layer to the order of 1 tenth of a nanometer. Then the substrates are subjected to a pre-bond annealing step and then bonded by direct bonding, possibly preceded by one or more pre-treatments of the contact surfaces, and followed by a post-bond annealing step, at a temperature of less than or equal to 250° C. It has been found that the bond strength is excellent, even at the above named annealing temperatures, which are lower than presently known in the art.