On Apr 12, 4:24 pm, Jon Kirwan <
j...@infinitefactors.org> wrote:
> On Fri, 12 Apr 2013 09:26:40 -0700 (PDT), George Herold
>
>
>
>
>
> <
gher...@teachspin.com> wrote:
> >On Apr 12, 12:09 pm, John Devereux <
j...@devereux.me.uk> wrote:
> >> <snip of pulsed current through diode-connected BJT idea>
> >> Is this accurate to +/- 0.2'C (without calibration)?
> >Not in my experience. (but my experience is fiarly limited... a few
> >transitors tested.)
>
> >I always got a number that was a bit off ~0.3%, so about 1 degree at
> >room temp. I always assumed the error was due to the transistor
> >beta... Since the current is Ic and Ib. (I think I got a temperature
> >that was always a bit high, but I'd have to check my notebook.) You
> >could add some beta 'fudge factor'.... but then beta changes with
> >temperature too.
>
> >It also depended a bit on the collector current. (1 uA to 10uA were
> >'nice' currents)
>
> Hi, George. I posted up a link to Linear's AN45 elsewhere
> under this topic. See page 7 there. But I take your
> experiences here seriously and wanted to think about this,
> not at the 'charged gas' theory level but at the higher (and
> more usual for an EE) device modeling level.
>
> The two-current pulse method, using say 1X and 10X currents,
> depends upon the following:
>
> dV = (k/q) * ln( 1+Ic/Is ) dT
>
> Although k and q are known, the entire factor that includes
> the ln( 1+Ic/Is ) part isn't knowable in advance. But if one
> assumes that the +1 term is negligible then the two pulsed
> currents results in:
>
> dV1/dT = (k/q) * ln( Ic1 ) - (k/q) * ln( Is )
> dV2/dT = (k/q) * ln( Ic2 ) - (k/q) * ln( Is )
>
> Subtracting dV1/dT from dV2/dT yields:
>
> dV1 - dV1 = (k/q) * ln( Ic2/Ic1 ) ) dT
>
> And if the ratio of Ic2/Ic1 is known a priori then the entire
> factor, (k/q) * ln( Ic2/Ic1 ) ), is also known. And as a
> consequence could be used to measure temperature without
> having to calibrate the system. Or so it seems at first
> blush.
>
> But it's also the case that the value of the saturation
> current, Is, is itself a rather complex function of T:
>
> Is(T) = Is(Tn) * (T/Tn)^3 * e^( -(q*Eg/k) * (1/T-1/Tn) )
>
> Where Tn is some chosen T(nominal).
>
> In fact, this particular component is what overwhelms the
> first equation (which is positive vs temperature) and yields
> the usually quoted -2mV/K figure (very approximately.) So, in
> fact, Is(T) is the dominant factor in Vbe change over T and
> in no possible way is it a simple function of T!
>
> (Even the above Is(T) equation itself is a simplification.
> The power ((T/Tn)^3) for example is an approximation and not
> strictly true in practice. Same with Eg, which itself is also
> taken as a single approximation value.)
>
> Just as a guess, the idea of ln( Is ) being cancelled
> entirely out of the equation by ratiometry, even assuming
> that the die is at thermal equilibrium, would make me worry a
> little. (I accept that pulsing the 1X/10X current change fast
> enough or that using low enough currents, like the 1uA and
> 10uA you mention, would yield a near-equilibrium state.) I'm
> just not sure that at this level of modeling, that _Is_
> remains dead stable as a modeling parameter when facing a 10X
> current change. There is a lot of linearity over orders of
> magnitude change, as a broad statement. But exactly how
> linear is it when provided a two point ratio a decade apart,
> vs device variation?
>
> I wonder that some temperature error is swept under this
> Is(T) rug and hidden from the analysis, so to speak. Even
> assuming thermal equilibrium. Because it may really be that
> Is(V,T), not Is(T), as both the power (^3) and Eg are taken
> as simple constants for simplification when they aren't, in
> fact, invariant at this level of modeling.
>
> You mention base currents as a possible error. I've ignored
> that so far. The equation:
>
> dV = (k/q) * ln( 1+Ic/Is ) dT
>
> in the diode connected case refers to Ic. The currents
> through it, on whole, are (beta+1)/beta times as much. If you
> cobble up precision current sources at exactly 1X and 10X,
> the ratio of Ic2/Ic2 would still be 10, even though you are
> driving Ie, I think. However, beta itself changes vs Ic. So
> there is that to account for, if you were only using a beta
> level model. But the:
>
> dV1 - dV1 = (k/q) * ln( Ic2/Ic1 ) ) dT
>
> method doesn't use or rely upon beta. So I'm not imagining a
> problem there because (1) the ratio is still 10X and (2) beta
> isn't used in the analysis method.
>
> Interesting problem getting past a certain level of accuracy,
> though. There must be several papers that go beyond the AN45
> app note I'd posted up earlier. I haven't seen one, yet.
>
> Jon- Hide quoted text -
>
> - Show quoted text -
Hey Jon, I was thinking about this, and it seems like the error is
due to the non-ideality factor (NIF) in the equation. Now I've only
read about the NIF in the context of pn junctions, but wouldn't there
be something similar in a diode connected transistor?
Now according to Streetman the NIF arises because of carrier
recombination in the transition region. I know when I looked at the
temperature dependence of some pn diodes (maybe 1n4148's?) that the
NIF was much closer to 2.
So then what transitors would have NIF's close to 1?
I wonder if they list NIF's in the spice models?
George H.