Modulation of electrical contact properties at the hole-selective contact represents a critical challenge for enhancing the efficiency of silicon heterojunction (SHJ) solar cells, particularly due to the complex carrier transport in the induced p-n junction at the p-layer/TCO interface. In this work, we systematically investigate the carrier transport behavior within the hole contact stack by employing TCAD numerical simulations. Specifically, both the majority- and minority-carrier analyzing models are built, based on the typical transfer length method (TLM) and cox and strack method (CSM) architectures. Our findings reveal that the activation energy (E_a,p) of p-layer is a decisive parameter governing the carrier transport dynamics. A lower E_a,p (e.g., 100 meV) significantly reduces the hole transport barrier at the p-layer/TCO interface, promoting dominant band-to-band tunneling (B2BT) or dangling-bond-assisted trap-assisted tunneling (TAT-DBS), while simultaneously optimizing band bending at the i-a-Si:H/c-Si interface to improve hole collection efficiency. These synergistic effects not only significantly reduce the contact resistivity but also suppress the parasitic electron current under high forward bias, thereby maintaining excellent carrier selectivity over a wide voltage range. From an optical perspective, a lower E_a,p broadens the selection window for transparent conductive oxide (TCO) materials, as it enables the use of TCO films with lower carrier concentration, thereby effectively reducing parasitic absorption. This study clarifies the carrier transport mechanism at the hole-selective contact and establishes key material design criteria, providing crucial theoretical guidance and practical strategies for the interface engineering and performance optimization of next-generation high-efficiency SHJ solar cells, as supported by experimental trends in recent high-efficiency devices.