Existence of Inverse Laplace Transform

Question

Let $F(s)$ the Laplace transform of a function $f(t)$ .

Under which conditions on $f(t)$ there exist a unique $g(t)$ such that $g(t) = \mathcal{L}^{-1}\{e^{- F(s)}\}(t) \quad $ ?

($\mathcal{L}^{-1}$ is the inverse Laplace transform operator.)