I've found a paper that may interest you:
The quantum size effects on the surface potential of nano-crystalline silicon thin film transistors
(Available online 29 October 2009)
The impact of the grain size of nc-Si (nano-crystalline silicon) on the surface potential of doped nc-Si TFTs (thin film transistors) is discussed. Quantum size effects cause the change in both band-gap and dielectric constant of nc-Si. Numerical calculation of the surface potential in nc-Si TFTs shows that the diameter of nc-Si has a larger effect on the surface potential of nc-Si TFTs. The results demonstrate that, for medium size (7 ~ 50 nm), the change in the band-gap of nc-Si should be considered, whereas, for small size (< 7 nm), the change in the dielectric constant of nc-Si should be considered. A simplified surface potential equation for nc-Si TFTs under strong inversion condition is proposed, and shows good agreement with the original equation via numerical calculation.