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Josephson junctions with cosputtered amorphous Nb-Si barriers are being developed at NIST for use in voltage standard circuits. These junctions have the potential for a wide range of applications beyond voltage standards because their electrical properties can be tuned by controlling both the composition and the thickness of the barrier. If the composition of the barrier is tuned so that the resistivity is close to the metal-insulator transition, the high resistivity allows junctions with a large characteristic voltage and reproducible critical-current densities, which should be ideal for high-speed digital superconductive device applications. Because these junctions are intrinsically shunted, there is no need for external shunt resistors, which could start to become a limitation as the development of devices leads to higher critical-current densities and greater circuit densities. Presently, the AlOx-barrier junctions used in digital superconducting electronics suffer from poor reproducibility, particularly for the high critical-current densities needed for high-speed applications. In this paper, amorphous Nb-Si barrier junctions with characteristic voltages on the order of 1 mV and characteristic frequencies on the order of hundreds of gigahertz are demonstrated. This junction technology looks promising for applications in high-speed digital electronics.