IIRC I read about a thread about low power sleeping with timekeeping. I want to share something:
It's not precise timekeeping, but it's pretty low power and periodic wake up from power-down sleep mode.
I made an RC oscillator from an HEF40106 hex inverter with schmitt trigger by charging and discharging a timing capacitor through a 1N4148 diode. Charging with reverse leakage current, discharging with forward current. I found with a potentiometer voltage divider for Vdd that the oscillator uses very low current/power at low Vdd, probably sub threshold. In the finished circuit the oscillator is powered by the PORTB4 pull up resistor via a 10 M resistor and the uC turns the oscillator on/off as needed. Only one oscillation is used until wakeup.
At 3.3 V the whole circuit uses about 0.2 uA during power-down sleep. It drained an 0.33 F EDLC from 3.32 V to 3.18 V in 11:20 h with flipping PB0 at each wake up as its only action. Sleep time is 5-6 s, possibly getting longer as Vdd drops. A comparison with a smaller electrolytic suggests 34 days run (sleep) time with the 0.33 F EDLC! I'm not sure I'll wait that long.
There are probably better parts than the HEF40106 and IRL2703 MOSFET, but these are what I had at hand and they worked. A lower threshold voltage for both parts are probably better.
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Have fun :)