  Let $\Omega$ be a bounded open subset with $C^{1+\kappa}$-boundary for some
$\kappa > 0$. Consider the Dirichlet-to-Neumann operator associated to the
elliptic operator $- \sum \partial_l ( c_{kl} \, \partial_k ) + V$, where the
$c_{kl} = c_{lk}$ are H\"older continuous and $V \in L_\infty(\Omega)$ are real
valued. We prove that the Dirichlet-to-Neumann operator generates a
$C_0$-semigroup on the space $C(\partial \Omega)$ which is in addition
holomorphic with angle $\frac{\pi}{2}$. We also show that the kernel of the
semigroup has Poisson bounds on the complex right half-plane. As a consequence
we obtain an optimal holomorphic functional calculus and maximal regularity on
$L_p(\Gamma)$ for all $p \in (1,\infty)$.
