Carrier-selective contacts have become a prominent path forward towards efficient crystalline silicon (c-Si) photovoltaics. Among the proposed contacting materials, organic materials may offer simplified and low-cost processing compared with typical vacuum deposition techniques. Here, branched polyethyleneimine (b-PEI) is presented as an electron-transport layer (ETL) for c-Si solar cells. The incorporation of b-PEI interlayer between c-Si(n) and Al leads to a low contact resistivity of 24 mΩ cm2. Silicon heterojunction solar cell integrated with b-PEI is demonstrated achieving a power conversion efficiency of 19.4%, which improves the benchmark efficiency of a c-Si solar cell with an organic ETL. This electron-selectivity of b-PEI is attributed to its Lewis basicity, i.e., electron donating ability, promoting favorable band bending at the c-Si surface for electron transport. Moreover, several other Lewis base polymers perform as efficient ETLs in organic/c-Si hybrid devices, indicating Lewis basicity could be a guideline for future organic ETLs design.