Heterogeneous semiconductor device substrates with high quality epitaxy

A method comprising:

• forming a mask layer over a substrate;
• patterning the mask layer to expose portions of the substrate;
• etching the substrate by using the patterned mask layer as an etch mask to form a plurality of pyramid protrusions at a top surface of the substrate, wherein a top surface of one of the plurality of pyramid protrusions has a (100) crystal orientation;
• removing the patterned mask layer;
• forming a first epitaxial layer over and in contact with the plurality of pyramid protrusions of the substrate, wherein the first epitaxial layer is a single piece of continuous material;
• forming a second epitaxial layer over the first epitaxial layer, wherein the second epitaxial layer is a single piece of continuous material, and the first epitaxial layer is in contact with the substrate and the second epitaxial layer;
• and
• forming a transistor over and partially embedded in the second epitaxial layer.

A method comprising:

• forming a mask layer over a substrate;
• forming a plurality of holes in the mask layer to expose the substrate, wherein a diameter of each of the holes is less than about 100 nm, and the diameter of each of the holes of the mask layer is substantially equal to a minimum width of a portion of the mask layer directly between adjacent two of the holes of the mask layer;
• etching the substrate by using the mask layer as an etch mask such that a plurality of recesses are formed in the substrate;
• forming a first epitaxial layer over the substrate and filling the recesses;
• and
• forming a second epitaxial layer over the first epitaxial layer.