At what temperature will ni=10^14/cm^3 in silicon? And ni=10^16/cm^3?

2 answers

ni is the intrinsic carrier (electron and hole) concentration. You can find the ni(T)equation at this website:
http://pvcdrom.pveducation.org/SEMICON/NI.HTM

It is based on experimental data obtained up to 375 K. You may have to extrapolate to higher temperatures to get ni = 10^16
The site that I referenced has a calculation tool that says that
ni = 10^14 cm^-3 at T = 470 K , and
ni = 10^16 at T = 645 K.

Just be aware that you are extrapolating beyond the experimental data base.