Here is a quick teardown of a cheap generic solar-powered desk calculator.
Apparently the solar panel is only for show. There were no leads connecting the panel and device was powered by a non-rechargable AG10 coin cell battery.
This calculator relies almost entirely on a single integrated circuit that was epoxy sealed.
I made a poor attempt to reveal the IC. Initially I tried using a scraping tool which wasn’t terribly effective. I then switched using a Dremel which worked a little too well. After the chip was exposed, it cracked and flaked off of the board. In the photos below you can see some of the traces where leads attached to the chip.