about Resistor matching

integrated resistor matching

If we want the σ(R)/R ≤ 0.001,what area per square of the resistor should be used?
Does any guideline exist?
Just like that of MOS matching, we use Avt and Aβ?
does anyone know about it?
Thank you very much!!

Resistor matching is not characterized as well as or near as transistor matching. Resistor types have different matching properties also these matching properties changes with different processes (feature size, lithography and wafer processing machine tolerances) so it is hard to come by a reliably guidance with todays fast pacing feture shrinking processes.

A good guideline is to make or obtain some matching measurement results in a particular process (or extract the info indirectly from performance of some designed IC's like A/D or D/A those uses resitors) than considering layout, lithography and fab machine tolerances (extract them from whatever appropriate or available like delta-L, Delta-W, gradient effects, back bias effects etc.) make an educated estimate.

What contributes to matchin of resistors are well analysed (mathematicaly) in text books so one can try to get the values of effects and plug in numbers.

This is one of the area where designing gets thick (also no one teaches the ropes since its ugly). Mostly you are your own.

u can learn about silicide also in resistor

generally, to minimize the mismatch, wider resistors are used.
Also, they need to be properly interdigitized.

But, again, the effect of all these precautions/ design techniques can be quantized only through data from silicon.

Resistor mismatch is depends on a AR (%.um) parameter

σ(ΔR/R) = AR / SQR(W*L)

So, just as MOS transistors, you just have to increase area to improve matching. However, matching parameter AR is given for closely placed devices.

Thus 0.001% is not feasible on integrated resistors (maybe except those trimmed by laser). 0.001% is barely attainable with integrated MIM capacitors.