Thank you everyone for the provided information.
Let me add more details.
I'm using the
BQ25570 chip. The chip is so efficient, that I can charge the battery indoors. As I mentioned the available space is so tight, something around 20cmx12cmx5cm maximum.
For the test, I tried
This solar panel.
First, I tried a 5F supercap, but I saw the self-discharge is so high and I thought it would be better to use a secondary battery.
The battery I'm using now is a 105mA Li-Po. To test, I connected a load that draws 10mA each second with a pulse width of 8ms(on-time). In my room (considering low daylight and night with a roof lamp) I can say the daily voltage drop is about 0.005v.
If I put the solar panel in direct sunlight, it could charge the battery full in around 10 minutes(from ~3.9v to ~4.2). So, I'm hopeful it may work in shade for a long time if I choose a bigger battery by considering the winter.
But still, the main problem is not the sun, it's the temperature.