ways to deal with process variation
You can trim in other ways than laser, the very high
accuracy bandgaps go as far as dense (EE)PROM cal
maps and I have done zener zap and fuse style trim
networks. You will need a minimum of two, one to get
tempco flat and one to correct for this step's change to
the output voltage value.
Your diffused resistors ar not mentioned as having
been characterized; these can have a very large
"contribution" of their own, are often not well
controlled in CMOS processes and the tempco will
vary with the sheets, potentially not well modeled
second order "effect" (if all you see is fixed TC1 and
TC2 values in the design kit, then no thought was
given to this).
The only time I tried to do a second order temp
compensation, it was a mess. The cubic term is not
something you want to count on foundry design kits
for at all. You may find it necessary to fit your own
models for all of the single-ended components (the
reference diodes, the resistors, possibly even the
startup circuit devices; think veriloga and many fun-
filled hours of curve-fitting) to do a really good job.
In my world I have to accept some degree of model
slop and design for a sub-bandgap reference that
comes off a divider, which I can make late-levels
selectable to center up the final design based on a
body of real data.