  Let $F/{\mathbb Q}_p$ be a finite field extension, let $k$ be a finite field
extension of the residue field of $F$. Generalizing the $\psi$-lattices which
Colmez constructed in \'{e}tale $(\varphi,\Gamma)$-modules over
$k[[t]][t^{-1}]$, we define, study and exemplify $\psi$-lattices in \'{e}tale
$(\varphi,\Gamma)$-modules over $k[[t_1,\ldots,t_d]][\prod_it_i^{-1}]$ for
arbitrary $d\in{\mathbb N}$.
