While science has good knowledge of semiconductor bandgaps, there is not much information regarding the steepness of the band-edges. We find that a plot of absolute conductance, I/V versus voltage, V, in an Esaki diode or a backward diode will reveal a best limit for the band tails, defined by the tunneling joint density of states of the two band-edges. This joint density of states will give information about the prospective subthreshold swing voltage that could be expected in a tunneling field effect transistor. To date, published I-V characteristics indicate that the joint band-tail density of states is not steep enough to achieve less than 60mV/decade. Heavy doping inhomogeneity, among other inhomogeneities, result in a gradual density of states extending into the band gap. The steepest measured tunnel diodes have had a tunneling joint density of states greater than 90mV/decade.