The observation of negative differential conductance (NDC) in simple nanostructure geometries fabricated on high-mobility Si/SiGe strained-layer heterostructures is reported. The NDC is observed in the drain characteristic of etch-defined "point contacts" with lithographic width and length of 0.22, and 0.12 μm, respectively. Current peak-to-valley ratios as large as 2.0 are observed at T=1.3 K. The NDC is also observed in "wire" geometries as long as 19 μm, and can persist to temperatures as high as 83 K, with a minimum in the differential conductance observable at 103 K. The NDC in long wires is accompanied by the formation of a high-field domain at the drain end of the wire. The effect is only observed in laterally constricted geometries, but is not a result of quantum confinement or impurity-related trapping. We suggest that the NDC and the attendant domain formation are caused by phonon emission by hot electrons within the constricted geometry.