The IC ICL232 needs some capacitors. Should these capacitors be ceramic or any other type?
When does the capacitor type matter?
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From the datasheet it is clear that the capacitors have been used for a charge-pump circuit. So it's always preferred to have polarized capacitors in such applications for stability purposes. Since the values are comparatively smaller, you can go for tantalum capacitors.
Yes, the type of capacitor can matter. Different types of capacitor have different properties.
Some of the properties that vary between capacitor types:
In your link, the diagram shows polarised capacitors, which suggests that they weren't intended to be ceramic (which are unpolarised).
Two types of polarised capacitors are aluminum and tantalum electrolytics. In your case, I'd use tantalum.
Capacitor type can matter quite a bit. Small, high value, type 2 Ceramic capacitors have two significant disadvantages, one of which applies to use in this application with the ICL232:
So, for large value bypass caps, or for switched-capacitor power supplies, try to use polarized tantalum (smaller and more stable, but more expensive), electrolytic (cheaper, larger packages, less stable with age), or larger-bodied ceramic (moderate cost, more stable, require more board area).