This paper characterizes the trade-offs between the information and energy transmission rates, the decoding error probability, and the energy outage probability in simultaneous information and energy transmission over an additive white Gaussian noise channel. The results in this paper take into account the impact of energy harvester (EH) non-linearities on the harvested energy. The analysis is carried out in the finite block-length regime with finite constellations. Improved converse and achievability bounds that account for the EH non-linearities are presented.