The speed of an active electronic semiconductor device is limited by RC timescale, i.e., the time required for its charging and discharging. To circumvent this ubiquitous limitation of conventional electronics, we investigate diodes under intense mid-infrared light-field pulses. We choose epitaxial graphene on silicon carbide as a metal/semiconductor pair, acting as an ultrarobust and almost-transparent Schottky diode. The usually dominant forward direction is suppressed, but a characteristic signal occurs in reverse bias. For its theoretical description, we consider tunneling through the light-field-modulated Schottky barrier, complemented by a dynamical accumulation correction. On the basis only of the DC parametrization of the diode, the model provides a consistent and accurate description of the experimentally observed infrared phenomena. This allows the conclusion that cycle-by-cycle dynamics determines rectification. As the chosen materials have proven capabilities for transistors, circuits, and even a full logic, we see a way to establish light-field-driven electronics with rapidly increasing functionality.