[sdiy] Temperature compensation results

[ASSI]

Hi all,

I hope I can give some answers...

On the standard Gummel-Poon model (SGPM) parameters ins Spice: EG is 
the bandgap voltage extrapolated back to absolute zero (a linear 
approximation is used here, while in other parts of Spice more 
sophisticated modeling is used depending on Level) and should fall into 
the range of 1.12...1.18V depending on general doping levels. XTI is 
called the temperature exponent and should fall within 3...4 depending 
again on technology. Among other things, the relative importance of 
various recombination mechanisms plays a role.

The shortcomings of the SGPM have been recognized years ago, however 
none of the three models that have been developed to overcome these 
(VBIC, MEXTRAM, HICUM) has met general approval. MEXTRAM and HICUM have 
been recommended for evaluation around the 2001 timeframe and AFAIK not 
much has happened since. All three models continue to coexist and most 
commercial simulators support all of them.

Statistical (mis)match for bipolar IC is, just as in CMOS, mainly a 
linear function of 1/sqrt(area). The proportionality factor is a 
technology constant, which is quite hard to improve. When the 
dimensions of the structure approach the technology capability limit, 
the mismatch leaves the proportional curve, which is why no competent 
analog designer will use minimum structures when trying to match 
something. Systematic mismatch, for instance due to gradients of any 
sort (doping levels, temperature, mechanical stress) can also be 
minimized by good layout practices like common centroid layout. A 
specific rule for bipolar transistors is that the emitter area to 
circumference ratio should be be maximized (which would lead to 
circular emitters, but depending on the mask-making technology that may 
not be feasible).

The physical origin of statistical mismatch is attributed to the 
discrete nature of dopants and imperfections in their distribution. 
Call them micro-defects if you will. Extended defects are generally not 
factored into the matching equation AFAIK. BTW, last I looked there 
also was no commonly accepted explanation for shot noise.

For matching discrete transistors, it is a good idea to make sure 
they're from the same batch and not just the same type if you care 
about more than Vbe matching at a single point. Using lots of them in 
parallel also improves matching as long as you can keep temperature 
gradients in check. Come to think of it, I have a large number of 
unmarked SOT transistors, maybe I should make a PCB for those... 
Another idea is to use emitter degeneration and to make sure that the 
resistors are matched. There are a number of precision matched resistor 
arrays that could be used for that, e.g. from Vishay. They're not 
cheap, but they come in single packages with up to eight resistors and 
you can't get quad or octet transistor as easily. Temperature tracking 
within a package is better than 5ppm, matching 50ppm and TC 10ppm for 
the NiCr variant and 10ppm/?/100ppm for TaN films at about a third the 
price.


Achim.
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