Practical procedure for retrieval of quantitative phase map for two-phase interface using the transport of intensity equation

Abstract

A practical procedure for retrieving quantitative phase distribution at the interface between a thin amorphous germanium (a-Ge) film and vacuum based on the transport of intensity equation is proposed. First, small regions were selected in transmission electron microscopy (TEM) images with three different focus settings in order to avoid phase modulation due to low frequency noise. Second, the selected TEM image and its three reflected images were combined for mirror-symmetry to meet the boundary requirements. However, in this symmetrization, extra phase modulation arose due to the discontinuous nature of Fresnel fringes at the boundaries among the four parts of the combined image. Third, a corrected phase map was obtained by subtracting a linear fit to the extra phase modulation. The phase shift for a thin a-Ge film was determined to be approximately 0.5 rad, indicating that the average inner potential was 18.3 V. The validity of the present phase retrieval is discussed using simple simulations.

Assessment of off-axis and in-line electron holography for measurement of potential variations in Cu(In,Ga)Se2 thin-film solar cells

“…Two of the most common holographic techniques are off-axis EH and bright field through focus in-line EH. Both of these techniques have widely been used to characterize homogeneous and monocrystalline material systems, such as silicon-based devices (e.g., [11][12][13][14][15][16]), nitrides (e.g., [17,18]), GaAs systems (e.g., [19]), single nanoparticles (e.g., [20][21][22]), or simple interfaces (e.g., [23][24][25][26]). However, only few EH studies have been reported on more complex materials, such as the CIGS compound (e.g., [6,27,28]).…”

“…In order to overcome these issues, different approaches have been reported in literature. The subtraction of a linear background [23,26] and the selection of small sub-regions [26,40] were used to subtract low-frequency noise in phase…”