Mean electrostatic potential measurements by transmission electron holography of nanospheres

• Main Author: Wang, Young-Chung
• Format: Dissertation
• Language: English
• Published: ProQuest Dissertations & Theses 01-01-1997
• Subjects: Materials science
• ISBN: 9780591496994; 0591496992

This research describes the use of transmission electron holography as a quantitative tool to study electron refraction. Electron holography enables recovery of the electron phase from the specimen's exit-face wavefunction. The phase shift is the product of the electron-optical refractive index and the specimen thickness. The refractive index is related to the specimen's electrostatic potential and varies with composition and structure. The basic question being addressed by this research focuses on the magnitude of phase modulation imposed on the high-energy electron wave by a thin specimen. Spherical nanoparticles of amorphous Si and polystyrene are used as model specimens, so the effect of specimen thickness on the phase shift of the electron wave can be separated from the intrinsic refractive properties of the specimen. A recursive 4-parameter $\chi$-squared minimization routine was developed to determine the sphere center $\rm(x\sb{o},\ y\sb{o}),$ radius $\rm(R\sb{o}),$ and mean inner potential $\rm(\Phi\sb{o})$ at each pixel in the phase image. The results can be averaged to define a single characteristic $\rm\Phi\sb{o}$ value with good precision due to the large number of pixels $({\sim}10\sp4).$ Averaging $\rm\Phi\sb{o}$ data derived from 12 different PS phase images gives a value of $\rm\Phi\sb{o}\sp{PS}=8.4\pm0.2$ V. The possible sources of errors in the measurement include: (i) the reconstruction/analysis procedure; (ii) specimen charging; (iii) the presence of a surface layer; (iv) radiation damage; and (v) phase resolution. Parallel analysis of ten nanospheres of amorphous Si leads to a value of $\rm\Phi\sb{o}\ \sp{a-Si}=11.9\pm0.3$V. Similar studies of crystalline Si nanospheres, which are subject to greater error due to faceting and dynamical scattering, leads to $\rm\Phi\sb{o}\sp{c-Si}=12.1\pm0.4$V. These results are in good agreement with recent first-principles calculations by Kim, Zuo, and Spence.