  Present models of the superconducting-to-normal transition in transition-edge
sensors (TESs) do not describe the current distribution within a biased TES.
This distribution is complicated by normal-metal features that are integral to
TES design. We present a model with one free parameter that describes the
evolution of the current distribution with bias. To probe the current
distribution experimentally, we fabricated TES devices with different current
return geometries. Devices where the current return geometry mirrors current
flow within the device have sharper transitions, thus allowing for a direct
test of the current-flow model. Measurements from these devices show that
current meanders through a TES low in the resistive transition but flows across
the normal-metal features by 40% of the normal-state resistance. Comparison of
transition sharpness between device designs reveals that self-induced magnetic
fields play an important role in determining the width of the superconducting
transition. [http://dx.doi.org/10.1063/1.4771984]
