Hmm, if emission coefficients go as high as four then it is somehow
different from the non-ideality factor which is between 1 and 2.
They go as high as needed for diodes. For BJTs, they are
almost always very close to 1, at least with small signal
types I'm more familiar with, testing out against hand
calculuations. I think they are the same thing, as I've seen
both terms used interchangeably and I don't know of another
meaning for the term you are using.
I think you are just talking about this:
Ic = Is*(e^(Vbe/[n*k*T/q]) - 1)
With 'n' being your ideality thing. Elsewhere, that's just
called the emission coefficient. You can see it called
'ideality' here, under the "Shockley diode equation"
But if you read that paragraph, you will also see it called
what I call it, as well. So I really do think we are talking
about the exact same thing. If not, you need to show me the
equation you are talking about and the factor in it.
The emission coefficient isn't just about recombination, by
the way. It hides several things under a single umbrella,
including carrier generation.
And as if that wasn't enough, things are dramatically
different at different currents, as well. At low currents,
you have recombination of carriers AT THE SURFACE, which must
be accounted for. You have recombination of carriers in the
emitter base space charge layer. And you have the formation
of emitter base surface channels. Each of these (only
ideally, though again) do vary with Vbe and with different
tau's and added to the other shockley equation. At higher
currents the injection of minority carriers into the base
region starts to become significant, relative to the majority
carrier concentration. Since space charge neutrality is
maintained, the total majority carrier concentration
increases by the same amount. The non-ideality factor for
this is usually taken to be 2 and is incorporated into the
EM3 model (by Webster, I believe.) This becomes another one
of those exponentials sitting as a divisor on Is.
As mentioned, Rube Goldberg would be jealous. The underlying
physics is NOT modeled, but instead just higher level
exponential math models applied until the behavior starts to
look "mostly okay." Behavior in the corners is modeled very
badly, for example, because the various exponentials don't
reflect the actual shape there very well. It's good enough
for horseshoes, though, and engineers. Not for physicists.
Grin, sure I'm all about models being close to the real physics.
Well, the spice stuff isn't very physical. If you look at the
differential equations you find that there are multiple
exponentials. The -1 term in the Shockley equation just
mentioned is there so that you calculate out a nice Ic=0 when
Vbe=0. The exponentials are only approximations of a reality
that includes MANY taus, not just one. And as you know well,
there is no single exponential that can model the sum of
multiple ones. And there are some non-exponentials that
result from the integral equations that basically no one in
the non-FAB land bothers to use. I got myself deep into this
some time ago when attempting to model the behavior of a
Hamamatsu diode against actual observation over differing die
temperatures (from -70C to about 80C) and over light flux
varying from femptoamps to microamps. The ONLY way I got
results that were close was to go back to applying dopant
concentrations, gradients, and a vague approximation (luckily
not too hard with photodiode I can examine) of the physical
dimensions. I had thought that a 1D model would be good
enough. It wasn't.
I can see why spice doesn't go there.
For the single point calibration, I measured three diodes, Vf (at
10uA) vs T. The three diodes were picked to have high, average, and
low forward voltages at room temp. I then found that the voltage
difference as a function of temp was mostly linear with T from 77 to
400K. So with a standard curve*, I just measure Vf and T and do a
linear correction on all the points.
The temp points are all based on a ~$400 lakeshore calibrated diode.
*the standard curve is the data from the middle diode.
Okay. So you had a calibrated diode to work with. I guess my
question came from the fact that while the 1X/10X method
provides some basic removal of the Is parameter for a given
device, it does not (so far as my poor awareness permits me)
provide an absolute position which probably has to come from
somewhere external. Apparently, you had that. But if you had
a method to develop an exact calibration down to absolute
zero without any calibration, then I'd love to have learned
of it. (So would a lot of people with expensive freeze
points, I suppose.)