Double aspect ratio trapping

A semiconductor structure comprising:

• a semiconductor substrate portion comprising a first semiconductor material having a first lattice constant;
• a plurality of alternating first semiconductor-containing pillar structures and second semiconductor-containing pillar structures, wherein each first semiconductor-containing pillar structure comprises a second semiconductor material having a second lattice constant that is greater than said first lattice extending upwards from a surface of said semiconductor substrate portion, and wherein each second semiconductor-containing pillar structure comprises a third semiconductor material having a third lattice constant that is greater than said first lattice constant extending upwards from another surface of said semiconductor substrate portion;
• and
• a dielectric spacer laterally separating each first semiconductor-containing pillar structure from each second semiconductor-containing pillar structure, wherein each of said second semiconductor-containing pillar structures has a width that is different from a width of each of said first semiconductor-containing pillar structures.