A charge carrier drifts along a line of trap sites labelled
PHYSICS · Subjective · Fermi University Physics · Mathematical Methods for Physics · Probability, statistics and stochastic methods · Probability, statistics and stochastic methods
Error, Chance and the Machine, Ch Random walks and Markov chains
Problem
A charge carrier drifts along a line of trap sites labelled 0,1,…,10, hopping right with probability p=0.45 and left with probability q=1−p=0.55 at each step. Site 0 is a recombination centre and site 10 is a collecting electrode; the walk stops on reaching either. The carrier starts at site 5. Find the probability that the carrier reaches the collecting electrode (site 10) before recombining (site 0).