The Urysohn identity and dimension of manifolds

Abstract

A unique fabrication technique of Ge 1Àx C x nanocrystal (NC) assemblies with high-density (>10 11 dots/cm 2 ) and small diameter (<10 nm) on a Si(100) substrate has been investigated. In this method, a bio-nanoprocess with proteins ''ferritin'' and solid-source molecular beam epitaxy (MBE) with an arc-plasma gun were adopted. For the MBE growth of Ge 1Àx C x NCs, a Si thin film ''nanomask'' was developed. The MBE-grown Ge 1Àx C x NCs were obtained up to the substitutional C content x ¼ 3:2%. From analyses of field emission scanning electron microscope, transmission electron microscope, the Ge 1Àx C x (x ¼ 1:5%) NC assemblies of very small diameter 7:3 AE 3 nm and high-density more than 1 Â 10 11 dots/cm 2 were revealed. In the photoluminescence (PL) spectra measured at 7 K, a PL peak of around 1.3 mm was obtained due to the quantum confinement effect.