The low temperature photoluminescence under bias (PLb) and the photoconductivity (PC) of a p-i-n GaInNAs/GaAs multiple quantum well sample have been investigated. Under optical excitation with photons of energy greater than the GaAs bandgap, PC and PLb results show a number of step-like increases when the sample is reverse biased. The nature of these steps, which depends upon the temperature, exciting wavelength and intensity and the number of quantum wells (QWs) in the device, is explained in terms of thermionic emission and negative charge accumulation due to the low confinement of holes in GaInNAs QWs. At high temperature, thermal escape from the wells becomes much more dominant and the steps smear out.