We propose a mechanism which can lead to shot-noise enhancement when electronic transport is controlled by tunneling. Numerical simulations performed for a single barrier heterostructure made with ${\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}/\mathrm{A}\mathrm{l}}_{0.25}{\mathrm{Ga}}_{0.75}\mathrm{As}$ at $300\mathrm{K}$ evidence an increase of the Fano factor up to a value of $7$ at intermediate bias voltages significantly larger than the thermal value $KT/e$ in the region of positive differential resistance. The positive feedback between space charge and single electron tunneling probability is ultimately responsible for the super-Poissonian pulse distribution so found.