The schematic of the energy band gap figure of the graded optical band gap (Egopt) 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 Egopt with the crystallization ratio (Xc) and the Egopt with the nanocrystalline grain size (D) in na-Si:H thin films grown by PECVD on glass substrates through XRD, Raman scattering, transmission. The Egopt 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).