why intrinsic carrier concentration of germanium is larger than silicon ?

Intrinsic concentration (ni) is referred as the number of covalent bonds break at a given temperature per unit volume. It is a function of temperature, so as temperature increases, ni increases.
We know, energy gap is defined as the difference between lowest energy level of conduction band and highest energy level of valence band, and is the minimum energy required to break a covalent bond so that an electron from valence band can reach conduction band. When a covalent bond breaks, an electron in conduction band (free electron) and a vacancy in valence band (hole) is created.
Germanium atom has less energy gap than Silicon atom, so at a given temperature ie. For the given thermal energy, more covalent bonds will break in germanium than in silicon, so ni is more in Ge than Si.

[sateeshprathapani]

To the point, simply superb. Thank you.