Supercaps for RTC backup

I want to back an RTC (150nA, 2-5V) for several weeks but I don’t quite have room for a CR1220 battery. I thought I would use a supercap like CBS5R5334HF-ZJ with a low-leakage diode, but was surprised to find a leakage current on the order of 10uA which drains the capacitor within 48 hours.

Now, DigiKey does not provide a filter for leakage current, though Google claims that low-leakage supercaps do exist for this purpose. So I’m coming here for help. Do supercaps exist with a leakage current less than 100nA?

Hello Marshal,
Thank you for using our TechForum.
I was not able to find any leakage that low.
These are the lowest I found.
They are from the ADCP series.
Their leakage is 2.8 to 5.2mA

Wow, those are 1200 F and up, and the discharge rate is 1000x what I was seeing for the 1F capacitors. It looks like microamps per farad is normal for supercaps.
This blog suggests that leakage current can decrease after “extended charging”, which appears to be in the hundreds of hours. Furthermore, voltage droop in the first 30 minutes is dominated by ion redistribution within the electrolyte.

What this means is I would need to charge for a week in order to get three days of battery backup. I think I need to look at other technologies.