Dispersive Hopping Transport from an Exponential Energy Distribution of Sites

With use of Monte Carlo simulation techniques, it is shown that an exponential energy distribution of hopping sites gives rise to dispersive transport which is not experimentally distinguishable from multiple trapping. At low temperatures, the dispersive parameter $\alpha$ is equal to $\frac{T}{T_0}$. At high temperatures, the power-law approximation fails exactly as found for multiple trapping. These results show conclusively that hopping does give rise to dispersion and depending upon the hopping distribution function can be observed in a macroscopic system.