The high-energy charge transport of electrons and holes in GaAs single photon avalanche diodes with multiplication region widths of 55 nm to 500 nm is investigated by means of the full-band Monte Carlo technique incorporating computationally efficient full-band phonon scattering rates. Compared to previous works, the solution of the Boltzmann transport equation and the incorporation of the full-band structure put the evaluation of the breakdown probability, the time to avalanche breakdown, and the jitter on deeper theoretical grounds. As a main result, the breakdown probability exhibits a steeper rise versus reverse bias for smaller multiplicator sizes. The time to avalanche breakdown and jitter decrease for smaller multiplicator widths. V