I read it's common for power diodes to drop as much as 1.2 volts or more. The diode has its dynamic (self-altering) resistance, as well as a certain amount of ohmic resistance. The more Amperes you push through it, the greater the voltage drop caused by the ohmic portion. Therefore at high current the ohmic portion becomes more prevalent.
I performed similar tests with ordinary silicon diodes and led's. I plotted the data on graphs. It produced a curve which looked like a cousin of y=x^2. I tried to derive a simple equation to obtain Amperes, given a voltage. I came up with:
A = ( V x 1.25) ^21
Your graph looks like it could be (approximately):
A = (V x 1.1) ^5