A method for fabricating a semiconductor device includes the steps of growing a second semiconductor layer on a first semiconductor layer which is highly doped with an impurity such as Zn and diffusing the impurity concurrently with the growing step of the second semiconductor layer from the first semiconductor layer as an impurity source to the second semiconductor layer to have a predetermined carrier concentration profile, by controlling both the diffusing speed of said impurity and the growing speed of said second semiconductor layer by changing the temperature in accordance with a predetermined sequence to have a predetermined carrier concentration profile in the second semiconductor layer.