One-dimensional particle transmission in a statistically distributed potential field

In this study, wave functions are used to analyze the transmission of micro-scale particles throughout a sequence of one-dimensional potential barriers. This model can be used to simulate the motion of particles through a crystalline or non-crystalline thin film. Our focus is on the configuration of barriers which can be characterized by their heights, widths and lengths, and on their effects on the transmission probability. As a common phenomenon in crystalline structure, the resonant transmission can be found at classical forbidden energy levels and they form some energy bands. We further investigate the effects of voids and impurities on the transmission of particles by introducing variations to barrier heights. Results indicate that transmission can be weakened or reinforced by the presence of impurities or voids. In order to study more realistic structures, a statistical approach is introduced for us to imitate more variations on the barrier heights. This scheme allows us to study the transmission of particles through amorphous-like thin film. The quantitative results show that resonant energy bands can be significantly reduced by the irregular structures inside an amorphous-like film due to the destructive interference among waves.