diodes, ideal diode equation, and temperature coefficients

The ideal diode equation seems to predict that for a given current
there will be a fixed ratio between temperature and voltage. I took
some measurements and worked out the equation for several diodes, and
also plotted the values on graph paper. For all of the diodes I
tried, 1N4003, 1N4148, two shottkys 1N5818 and MBR3035PT, and a red
led, I got a nice straight line when I graphed 8 or so data points of
the voltage versus the log of the current (using an ordinary
mulitimeter and graphing by hand).
I derived the equation for the 1N4003 and see what the equation
predicted for the temperature coefficient as it relates to current.
tempco: Vd/T = (nk/q)ln(I/Is+1)
For I>>Is, the 1 in the parentheses is insignificant.
Plugging in the values I got and simplifiying,
Vd/T=.0001484(lnI+20.05)
By my interpretation and calculations the temperature coefficient
varies. For the 1N4003, based on my measurements the equation
predicts a temperature coefficient of 1.6 mV/C at 100uA. The equation
predicts the commonly cited 2.2mV/C at about 5.4 mA of forward
current. By the time you get to an amp, it's up to 29.7 mV/C.
Now the interesting thing is that, calculated as a proportion of the
forward voltage drop in the diode, the tempco a stays right around
3350 ppm, for all currents from 1uA to 1A.
If that's the case, then instead of seeing the temperature coefficient
of a diode always cited as 2.2 mV/C, it out to be expressed in a ratio
to to the forward voltage drop. But I've never seen tempco defined
that way.
Maybe somebody can show me what's wrong with my reasoning.

.

Relevant Pages

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    ... there will be a fixed ratio between temperature and voltage. ... For all of the diodes I ... predicted for the temperature coefficient as it relates to current. ...
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