The schematic of the energy band gap figure of the graded optical band gap (E-g(opt)) in p-i-n layer in na-Si: H solar cells was given in the paper. The intrinsic hydrogenated nanoamorphous silicon( na-Si: H) thin films with the graded band gap as a function of depth through the films were prepared by varying the processing power, gas pressure, gas composition, and etc., We have carried out a investigation of the relationships between the E-g(opt) with the crystallization ratio (Xc) and the E-g(opt) with the nanocrystalline grain size ( D) in na-Si: H thin films grown by PECVD on glass substrates through XRD, Raman scattering, transmission. The E-g(opt) increase with the decreases of the crystallization ratio (Xc) and the nanocrystalline grain size ( D). The hydrogen dilution ratio is found to increase basically both the crystallization ratio ( Xc) and the nanocrystalline grain size ( D). Two relationships in na-Si: H are discussed by the etching effect of atomic hydrogen in the framework of the growth mechanism and the quantum size effect (QSE). (C) 2005 Springer Science + Business Media, Inc.