Numerical extraction of electric field distribution from thermal pulse method based on Monte Carlo simulation

Abstract

Thermal-pulse method is a powerful tool for measuring space charge distributions in polymer films. The data analysis for thermal-pulse method involves the Fredholm integral equation of the first kind, which requires an appropriate numerical procedure to obtain a solution. Various numerical techniques, including scale transformation and regulation method, are proposed. Of those numerical methods, the scale transformation (ST) is the simplest and the most widely used method. However, it presents a high spatial resolution only near the sample surface. Monte Carlo (MC) method is one of the recently proposed ways to solve the equation numerically and has been successfully applied to the analysis of laser intensity modulation method data, which also involves the Fredholm integral equation of the first kind. In this paper we attempt to analyze thermal-pulse data in frequency domain with the MC method and discuss its effectiveness based on some numerical simulations. The simulation results indicate that the electric field profiles can be effectively extracted by the MC method. The computed profiles by the MC method consist well with the supposed distributions in the entire thickness of the sample, while the profiles reconstructed by the ST method fit very well to the supposed one at the vicinity of the target surface and distort sharply along the direction of the thermal pulse propagation in the sample bulk. On the other hand, the oscillations in the computed results by the MC method could deteriorate its accuracy in this study. The influence of noise level on the analysis based on the MC method is also tested by the use of the simulated data. The results show that the computed profiles would become more fluctuant as the noise level increases. This problem can be solved by selecting a larger value of tolerance during the singular value decomposition procedure. Thus, the value of tolerance is considered to be one of the key parameters in this algorithm, which is actually hard to determine. Additionally, the experimental data obtained from a polypropylene film under applied electric field are analyzed to illustrate the feasibility of MC method to be applied to the thermal-pulse experimental data. The results also show that the spatial accuracy by the MC method in the entire sample thickness is higher than by the ST method, which verifies that the MC method is more suitable for detecting the electric field distribution in the deep bulk of the sample. Owing to noise and error, the accuracy of MC calculation depends on the chosen tolerance value, which is now considered to be an obstacle in applying this method to the practical thermal-pulse measurement.