The topology of hopping in the energy domain of systems with rapidly decaying density of states

Phenomenological transport models of disordered systems often provide useful tools for experimental analysis and device engineering but provide limited insight into the microscopic detail underlying the transport mechanism and its effect on the macroscopic properties of the process. To address this deficiency from the stand point of the widely employed hopping models, we use Monte Carlo simulations to dissect the transport process for hopping systems that have rapidly decaying density of states into their statistical constituents to attain a clear and quantitative representation of the process. Through this analysis we show that while the transport energy concept provides valid intuition regarding charge carrier propagation in the energy domain of such systems, caution is needed when using it in quantitative calculations and in the deduction of system attributes such as the transport activation energy and mobility. To this end, we present an analytic approach for calculating the energy distributions of sites which charge carriers hop to when propagating in the system. It in turn provides more insight regarding the physics determining the carrier target energy distributions characteristics and holds the potential to serve as an ancillary tool for approximating system properties such as the system mobility and Peltier coefficient in a physically transparent and accurate way.