A logarithmic diode is defined as one showing a forward characteristic I α exp (eV/mkT) where the factor m is independent of voltage (though not necessarily of temperature) over at least four decades of current. Many commercial diodes show such a characteristic with m in the region of 1.5. It is shown that this behaviour cannot be explained by the theory of Sah, Noyce and Shockley and a modified theory is proposed, based on the assumption that the diode current is predominantly due to Shockley-Read-Hall traps non-uniformly distributed in the depletion layer. The theory is shown to be consistent with observed currentvoltage-temperature characteristics of a number of specimens.