Rd = (k*T)/(I1*q)
K = boltzmann's constant
q = electron charge
I1 = forward DC current through the diode
Rd is the slope of the tangent line at !1 on the ampere versus voltage curve for the diode.
It's not really a basic property of a diode. A diode can be said to have an internal resistance AT a certain steady-state operating point. But move away from that operating point significantly and the resistance changes. It's a quiescent value, very much like the transconductance of a transistor. It changes with temerature and bias current, and is only valid for small-signal AC riding on top of it's bias current. It will give a rough estimate of how much the voltage across the diode will change with changing current.
So if internal resistance is specified, it must be done so at a certain bias current and temperature. And is only used to compare one diode to the next.
In order to talk about diode resistance you need to be very clear about what you mean.
It varies from a few ohm up to a few thousands ohm depending on the type and power rating.
