Visibility of Si nanoparticles embedded in an amorphous SiO2 matrix

The visibility of a Si crystalline nanoparticle of diameter 2 nm embedded in an amorphous SiO(2) layer is evaluated quantitatively by multislice calculation. The visibility depends on the crystal orientation of the Si nanoparticle, the thickness of the amorphous SiO(2) layer and the defocus. Scherzer defocus always gives the highest visibility at any crystal orientation. The visibility is higher when the incident beam is parallel to the (111) planes and the (111) fringes are most visible. The image of a Si nanoparticle is obscured by random images from the amorphous SiO(2) layer and the Si nanoparticle becomes invisible when it is misoriented or the amorphous layer is thicker than 60 nm. The probability that a Si nanoparticle can be distinguished from the random noise of amorphous images is 89% when the thickness of the amorphous SiO(2) layer is 12 nm, but this is reduced to 21% when the layer is 48 nm thick. These quantitative results are useful when estimating the density of Si nanoparticles including invisible nanoparticles.