In this paper, we consider massless Dirac fields propagating in the outerregion of de Sitter-Reissner-Nordstr\"om black holes. We show that the metricof such black holes is uniquely determined by the partial knowledge of thecorresponding scattering matrix $S(\lambda)$ at a fixed energy $\lambda \ne 0$.More precisely, we consider the partial wave scattering matrices $S(\lambda,n)$(here $\lambda \ne 0$ is the fixed energy and $n \in \N^*$ denotes the angularmomentum) defined as the restrictions of the full scattering matrix on a wellchosen basis of spin-weighted spherical harmonics. We prove that the mass $M$,the square of the charge $Q^2$ and the cosmological constant $\Lambda$ of adS-RN black hole (and thus its metric) can be uniquely determined from theknowledge of either the transmission coefficients $T(\lambda, n)$, or thereflexion coefficients $R(\lambda, n)$ (resp. $L(\lambda, n)$), for all $n \in{\mathcal{L}}$ where $\mathcal{L}$ is a subset of $\N^*$ that satisfies theM\"untz condition $\sum_{n \in {\mathcal{L}}} \frac{1}{n} = +\infty$. Our maintool consists in complexifying the angular momentum $n$ and in studying theanalytic properties of the "unphysical" scattering matrix $S(\lambda,z)$ in thecomplex variable $z$. We show in particular that the quantities$\frac{1}{T(\lambda,z)}$, $\frac{R(\lambda,z)}{T(\lambda,z)}$ and$\frac{L(\lambda,z)}{T(\lambda,z)}$ belong to the Nevanlinna class in theregion $\{z \in \C, \ Re(z) >0 \}$ for which we have analytic uniquenesstheorems at our disposal. Eventually, as a by-product of our method, we obtainreconstrution formulae for the surface gravities of the event and cosmologicalhorizons of the black hole which have an important physical meaning in theHawking effect.
