Semiconductor wafers are polished by a material-removing polishing process A, on both sides of the wafer, using an abrasive-free polishing pad, and a polishing agent which contains abrasive; and a material-removing polishing process B, on at least one side of the wafer, using a polishing pad with a microstructured surface containing no materials which contact the wafer which are harder than the semiconductor material, and a polishing agent is added which has a pH≧ to 10 and contains no substances with abrasive action. Preferred is a method for producing a semiconductor wafer, comprising the following ordered steps: separating a semiconductor single crystal into wafers; simultaneously processing both sides of the wafer by chip-removing processing; polishing the wafer, comprising a polishing process A and a polishing process B; and CMP of one side of the wafer, removing