Amorphous silicon staggered‐electrode thin‐film transistors (TFT’s) can show current crowding near the origin in the output characteristics. The degree of current crowding is governed by the voltage dependence of the current flowing from then+contact to the conducting channel. This current is a space‐charge‐limited current whose magnitude depends on the bulk density of states in the undoped intrinsic layer. For a 0.5‐&mgr;m‐thickilayer, calculations predict negligible current crowding forN(E)<1016cm−3 eV−1, but severe current crowding forN(E)>3×1016cm−3 eV−1. Experimental results are consistent withN(E) in the range 1016cm−3 eV−1–2×1016cm−3 eV−1. This is lower than the value derived from the transfer characteristic of the TFT (∼1017cm−3 eV−1), which is evidence for an inhomogeneous distribution of deep gap states through the 0.5‐&mgr;m film of &agr;‐Si:H.