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Metal contacts play an important role in nanowire devices and are expected to exhibit qualitatively different properties from those of planar contacts due to small contact cross sections. We numerically investigate certain unique properties of nanowire-metal contacts and demonstrate that contact resistivity increases as nanowire radius shrinks. This increase is more significant for nanowire-three-dimensional metal contacts than for nanowire-one-dimensional metal contacts. The underlying cause for this size effect is identified as the strong fringing field effects, which become more significant as temperature decreases. Our simulation provides a more complete understanding of the size effects on nanowire-metal contacts.