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We investigated the tunneling of graphene/insulator/metal heterojunctions by revising the Tsu-Esaki model of Fowler-Nordheim tunneling and direct tunneling current. Notably, the revised equations for both tunneling currents are proportional to V 3 , which originates from the linear dispersion of graphene. We developed a simulation tool by adopting revised tunneling equations using MATLAB. Thereafter, we optimized the device performance of the field-emission barristor by engineering the barrier height and thickness to improve the delay time, cut-off frequency, and power-delay product.

Semiconductors have long been perceived as a prerequisite for solid-state transistors. Although switching principles for nanometer-scale devices have emerged based on the deployment of two-dimensional (2D) van der Waals heterostructures, tunneling and ballistic currents through short channels are difficult to control, and semiconducting channel materials remain indispensable for practical switching. In this study, we report a semiconductor-less solid-state electronic device that exhibits an industry-applicable switching of the ballistic current. This device modulates the field emission barrier height across the graphene-hexagonal boron nitride interface with I ON /I OFF of 10 6 obtained from the transfer curves and adjustable intrinsic gain up to 4, and exhibits unprecedented current stability in temperature range of 15-400 K. The vertical device operation can be optimized with the capacitive coupling in the device geometry. The semiconductor-less switching resolves the long-standing issue of temperature-dependent device performance, thereby extending the potential of 2D van der Waals devices to applications in extreme environments.