We study the kink effect and the subsequent noise enhancement in short-channel InAlAs/InGaAs high electron mobility transistors by means of Monte Carlo simulations. The origin of this effect and the associated increase of noise are explained in terms of microscopic quantities provided by the simulations. The results show that holes, generated by impact ionization at the drain side of the channel, tend to pile up under the source side of the gate due to the attracting potential caused by the surface charge at the recess and, mostly, by the gate potential. Due to this pile up of positive charge, the potential barrier controlling the current through the channel is lowered, so that the channel is further opened and the drain current increases. Impact ionization processes jointly with hole recombination lead to fluctuations of the positive charge in the channel, which are strongly coupled to the drain-current fluctuations by the high transconductance of the device. Thus the kink effect is found to originate an important increase in the noise of the drain current, with a characteristic cutoff frequency related to the impact ionization rate and the hole recombination time. Additionally, the holes reaching the gate electrode lead to the appearance of shot noise in the gate current.