Parameters Estimation for PEDOT:PSS Based UV Light Sensors Using an Improved Numerical Platform

Abstract

This work proposes a combined mathematical-numerical approach based on modeling, simulation, and optimization procedures to numerically evaluate the photoelectrical performances of innovative nanomaterials based UV-photodetectors (PDs). The improved platform is based on the Lambert W function combined with the enhanced Nelder–Mead (NM) algorithm and the root mean squares error (RMSE) function. The novelty of the proposed platform lies primary in the improvement of the classical principles of the NM algorithm search direction: 1) optimization of the initial guess choice by integrating two different choice strategies; 2) incorporating of complementary conditions to prevent obtaining unacceptable negative values of resistances; and 3) this combination reflects the simplicity and the efficiency of the technique more specifically, for complex and multidimensional problems. It is also relevant for incomplete and undefined curves but requires in return a good choice of initial parameters. The proposed algorithm was applied for several zinc oxide nanorods (ZnO NRs) based hybrid structures such as Poly(3, 4ethylenedioxythiophene):Poly(styrenesulfonate) (PEDOT: PSS/ZnO NRs) and Poly(1,4-phenylenevinylene) (PPV- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\text{C}_{{6}}$ </tex-math></inline-formula> ) derivative (PPV- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\text{C}_{{6}}$ </tex-math></inline-formula> /ZnO NRs) based devices. More importantly, high accuracy ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\text {RMSE} \sim {10}^{-{6}}$ </tex-math></inline-formula> ) in terms of extracted electrical parameters was obtained thanks to the proposed improvements at the numerical level of the platform, which translates a better fitting quality between the theoretical and experimental <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${I}$ </tex-math></inline-formula> – <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${V}$ </tex-math></inline-formula> curves in both operating range (forward and reverse bias). Therefore, the algorithm seems to be quite promising for providing accurate simulations of PDs characteristics.