Does anyone has any idea on how to make minor modification to the CMOS inverter(can be multiple stage cascaded if necessary) so that  it's input threshold voltage is approximately independent to the power supply? Say, when the power supply is changed from 3V to 6V, the switching point of the inverter is always around 2V(or a very tight range 1.8~2.2). This is will very helpful in my BGR startup circuits design.

Really appreciate your time.

Thanks Aaron. The problem has been solved. The idea used is almost  the same as yours. Other than using a threshold reference which has a litle bit wider distribution, with a DIODE reference, the Monte Carlo simualtion shows the inout threshold voltage of the inverter(cascaded) is now between 1.8 and 2.4. This will make my BGR well starts up across all corners and full 3~6V power supply range.

-Mikay