We have employed state-of-the-art cross-correlation noise spectroscopy to study carrier dynamics in silicon heterojunction solar cells, complimented by SENTARUS simulations of the same devices. These cells were composed of a light absorbing n-doped crystalline silicon layer contacted by passivating layers of i-a-Si:H and doped a-Si:H electrode layers. The method provided a two-orders-of-magnitude improved sensitivity and allowed to resolution of three additional contributions to noise in addition to 1/f noise. We have observed shot noise with Fano factor close to unity. We have also observed a peculiar generation-recombination term, which presents only under light illumination with energy above 2 eV and thus reflects light absorption and carrier trapping in the a-Si:H layers. A second, low-frequency generation-recombination term was detected at temperatures below 100 K. We argue that it appears because the process of charge carrier transfer across i-a-Si:H occurs via an intermediate defect limited by tunneling above about 100 K and a thermally assisted process below this temperature. We also discuss the spatial selectivity of noise spectroscopy, namely the tendency of the method to amplify noise contributions from the most resistive element of the cell. Indeed, in our case, all three terms are linked to the passivating i-a-Si:H layer.