Measurements of the incremental slope resistance of a GaAs-(Al,Ga)As-GaAs single barrier structure have been made at temperatures between 70 and 230 K. In contrast with other work we deliberately concentrate on the region close to zero applied bias. The deficiencies in the often-used Wentzel-Kramers-Brillouin analysis of the electrical characteristics are exposed in this regime, and an exact, Airy function approach is found to be essential to describe our observations.