Use of CEF in Cisco router

[knaik99]

switches use ASICS to store FIB & adjacency table in CAM & TCAM which are in ASICS.

hence multilayer switches can do routing & switching very fast.

But routers do not use ASICS so how do they create CEF table and where it is stored ?

[Richard Burts]

In routers the CEF table is in volatile memory.

[MHM Cisco World]

some Router is hybrid router 

[Joseph W. Doherty]

"But routers do not use ASICS so how do they create CEF table and where it is stored ?"

Where stored?  As answered by @Richard Burts, main RAM.

How CEF table created?  Likely by software.

Regarding routers not using ASICs, as described by @MHM Cisco World, often "higher end" routers (e.g. ASR 1K series) do use "extra" hardware for acceleration of some "core" routing features.