Analytical solutions and expressions of the propagator for Bloch equations

In this paper, we present analytical solutions to the Bloch equations. After solving the secular equation for the eigenvalues, derived from the Bloch equations, analytical solutions for the temporal evolution of the magnetization vector are obtained at arbitrary initial conditions. Subsequently, explicit analytical expressions of the propagator for the Bloch equations and optical Bloch equations are obtained. Compared to the results of existing analytical studies, the present results are more succinct and rigorous, and they can predict the behavior of the propagator in different regions of parameter spaces. The analytical solutions to the propagator can be directly used in composite laser-pulse spectroscopy.

A Direct Method to Extract Transient Sub-Gap Density of State (DOS) Based on Dual Gate Pulse Spectroscopy

Sub-gap density of states (DOS) is a key parameter to impact the electrical characteristics of semiconductor materials-based transistors in integrated circuits. Previously, spectroscopy methodologies for DOS extractions include the static methods, temperature dependent spectroscopy and photonic spectroscopy. However, they might involve lots of assumptions, calculations, temperature or optical impacts into the intrinsic distribution of DOS along the bandgap of the materials. A direct and simpler method is developed to extract the DOS distribution from amorphous oxide-based thin-film transistors (TFTs) based on Dual gate pulse spectroscopy (GPS), introducing less extrinsic factors such as temperature and laborious numerical mathematical analysis than conventional methods. From this direct measurement, the sub-gap DOS distribution shows a peak value on the band-gap edge and in the order of 1017–1021/(cm3·eV), which is consistent with the previous results. The results could be described with the model involving both Gaussian and exponential components. This tool is useful as a diagnostics for the electrical properties of oxide materials and this study will benefit their modeling and improvement of the electrical properties and thus broaden their applications.