Despite several years of research into graphene electronics, sufficient on/off current ratio I-on/I-off in graphene transistors with conventional device structures has been impossible to obtain. We report on a three-terminal active device, a graphene variable-barrier "barristor" (GB), in which the key is an atomically sharp interface between graphene and hydrogenated silicon. Large modulation on the device current (on/off ratio of 10(5)) is achieved by adjusting the gate voltage to control the graphene-silicon Schottky barrier. The absence of Fermi-level pinning at the interface allows the barrier's height to be tuned to 0.2 electron volt by adjusting graphene's work function, which results in large shifts of diode threshold voltages. Fabricating GBs on respective 150-mm wafers and combining complementary p- and n-type GBs, we demonstrate inverter and half-adder logic circuits.