  If the potential vector field of an $\eta$-Ricci soliton is of gradient type,
using Bochner formula, we derive from the soliton equation a Laplacian equation
satisfied by the potential function $f$. In a particular case of irrotational
potential vector field we prove that the soliton is completely determined by
$f$. We give a way to construct a gradient $\eta$-Ricci soliton on a warped
product manifold and show that if the base manifold is oriented, compact and of
constant scalar curvature, the soliton on the product manifold gives a lower
bound for its scalar curvature.
