Nucleation behavior of III/V crystal selectively grown inside nano-scale trenches: The influence of trench width

In the paper, we theoretically investigate a new size effect of trench width on inter-island distance in case of 3D growth mode. The comparison between blanket substrates and narrow trenches illustrates the qualitative tendency: a greater critical inter-island distance in narrower trenches in the nano-scale regime. This leads to an incomplete coalescence process inside scaled trenches, which is demonstrated by selective area growth (SAG) of InP onto patterned Si(001) substrates. This understanding is of significant importance to realize high quality hetero-epitaxy of III/V semiconductors onto large scale Si substrates by the selective growth technique for advanced field effect transistors.