Exploring the cryogenic transport properties of two-dimensional electron gas in semiconductor heterostructures is always a focus of fundamental research on Si-based gate-controlled quantum devices. In this work, based on the electrical and magnetic transport characteristics of Si/SiGe heterostructure Hall-bar shaped field effect transistors (FETs) at 10 K and 1.6 K, we study the effects of electron tunneling that occurs in the heterostructure and populates the oxide/semiconductor interface on its transport properties. The initial position of dual-channel conduction is determined by the gate-controlled electrical hysteresis curves. Furthermore, we discover that there exist different tunneling mechanisms of electrons in Si quantum well under the action of gate voltage, and the electron tunneling can well explain the two drain current plateaus appearing in direct-current transfer characteristics. Combining the power-law exponent of electron mobility versus density curve and the gate-related Dingle ratio, we clarify the dominant scattering mechanism and the result can be supported by different tunneling mechanisms. Our work demonstrates the gate-depended electronic transport performance in undoped Si/SiGe heterostructure FETs, which has an implication for the development of Si/SiGe heterostructure gate-defined quantum dot quantum computation.