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The transport of photogenerated minority carriers (photocarriers) across the heterointerface of amorphous silicon (a-Si) and crystalline silicon (c-Si) in a-Si/c-Si heterostructure solar cell is shown in this work to critically depend on the non-Maxwellian energy distribution function of those carriers impinging on the heterointerface. A theoretical model is presented that integrates the effect of the high electric field inversion region upon energy distribution function of the impinging carriers with the transmission probability of those carriers across the heterointerface. The transport of the photocarriers across the high electric field inversion region is simulated by the full solution of the Boltzmann transport equation by Monte Carlo technique while the transmission probability of carriers across the heterointerface is calculated through the percolation path technique. The results are discussed under two different condition of band bending; strongly inverted and weakly inverted c-Si surface. The results comparing different conditions of band bending show that the energy distribution of the carriers impinging on the heterointerface is non-Maxwellian and the integrated photocarrier collection increases with the strength of the inversion field since the carrier population is weighted towards higher energy where the transmission probability through the barrier is higher. Thus we demonstrate that hot carriers play an important role in heterostructure cell operation.