The influence of barrier thickness variability on the charge transfer characteristics of an InP/InAs/InP nanowire resonant-tunneling diode is studied. The transmission probability through the diode is calculated by solving the time-dependent effective-mass Schrödinger equation with the Alternating-Direction Hybrid Implicit-Explicit (ADHIE) Finite-Difference Time-Domain (FDTD) method. This recently developed method is tailored towards multiscale problems and thus allows for a much faster evaluation of the transmission probability compared to the commonly used leapfrog FDTD method. Accurate and efficient modeling of small geometric features with the ADHIE-FDTD method now facilitates the development of a robust Monte Carlo method to assess the significant influence of the thickness of the barriers on the transmission probability and the current-voltage characteristic.