Three-dimensional Poole-Frenkel analytical model for carrier transport in amorphous chalcogenides

• Published in: Journal of applied physics 2013-01, Vol.113 (4)
• Main Authors: Betti Beneventi, Giovanni, Guarino, Lucrezia, Ferro, Massimo, Fantini, Paolo
• Format: Article
• Language: English
• Subjects: Amorphous materials; Carrier transport; Chalcogenides; Devices; Electric fields; Mathematical analysis; Mathematical models; Three dimensional
• ISSN: 0021-8979; 1089-7550
• DOI: 10.1063/1.4788798

In this work, we propose a three-dimensional Poole-Frenkel (3DPF) analytical model for carrier transport in amorphous chalcogenides. 3DPF is based on the original Poole-Frenkel (PF) theory of non-interacting Coulombic traps responsible for carrier conduction in the bulk of the material. However, while in the original PF equation the device current-voltage characteristics is calculated by considering the barrier-lowering on the applied electric field direction only, in 3DPF we overcome this approximation by calculating the electronic current due to the integral effect of the Coulombic barrier shaping in three dimensions upon application of an electric field. As a consequence, 3DPF is capable to describe both the relatively-low and relatively-high electric fields regimes, while the PF equation implicitly assumes the device to be operated at high electric fields only. Thus, 3DPF features a better agreement with experimental data compared to original PF, predicting both (i) Poole-like behavior at low-fields, i.e., I∝sinh(V), and (ii) PF-like dependence in the higher fields regime, i.e., I∝exp(V), within a single coherent physical picture. The model is validated through I–V characterization on phase-change memory devices integrating amorphous Ge2Sb2Te5 as active material. Moreover, to address the model consistency, temperature dependence and correlations between model parameters are validated in comparison with experimental data.