A method for fabricating a semiconductor device, and a semiconductor device made with the method are described. In the method, a cavity is formed in a substrate, a first epitaxy process is performed under a pressure higher than 65 torr to form a buffer layer in the cavity, and a second epitaxy process is performed to form a semiconductor compound layer on the buffer layer in the cavity. In the semiconductor device, the ratio (S/Y) of the thickness S of the buffer layer on a lower sidewall of the cavity to the thickness Y of the buffer layer at the bottom of the cavity ranges from 0.6 to 0.8.