Is it plausible or even conceivable that some material would offer superior properties for usage in semiconductors or microprocessors?
Could silicon chips ever be replaced by chips made by other material?
Like people said in comments, is really hard to know what material is going to break the limits of current tecnology. But there is one material is proven that have the right properties to (hopefully) replace silicon chips and integrated circuits: Graphene
You can get some info in the following link: Graphene on Wikipedia
Some of the properties:
IBM created some prototypes of Graphene CPU's and they reached speeds up to 300Ghz (Link)
If you are interested on the future of the computing tecnologies, then check Quantum computing too.
Hope this helps.