The invention relates to a method of manufacturing a semiconductor device (10) with a semiconductor body (1) which is provided with at least one semiconductor element, wherein on the surface of the semiconductor body (1) a mesa- shaped semiconductor region (2) is formed, a masking layer (3) is deposited over the mesa-shaped semiconductor region (2), a part (3A) of the masking layer (3) is removed that borders a side surface of the mesa-shaped semiconductor region (2) near its top and an electrically conducting connection region (4) is formed on the resulting structure forming a contact for the mesa-shaped semiconductor region (2). According to the invention after removal of said part (3A) of the masking layer (3) but before formation of the...