I think he wants to backup the internal RAM of the uC in case the power shutdown.

In that case, i think you have to use the external interrupt to sense the power, and in the ISR for this interrupt, you have to change the uC from the normal mode to the power-down mode.

Maybe you have to use the capacitor to maintain the voltage in a little while as long as the uC can run that ISR to change the mode.
And of course, you need the 3V battery to maintain the uC in the power-down mode.

When you want to change back to the normal mode, you can you reset or external interrupt.

You can read more about the power-down mode in the datasheet

Regards,
Cuong Vu