# Optimizing the Drude-Lorentz model for material permittivity: Examples for semiconductors

## TL;DR

This paper presents an optimized method for fitting the Drude-Lorentz model to experimental permittivity data of semiconductors, improving the accuracy of optical property modeling across different frequency ranges.

## Contribution

It introduces a systematic optimization approach for the Drude-Lorentz model parameters tailored for semiconductors, enhancing the modeling of their permittivity dispersion.

## Key findings

- Optimized parameters for Si, GaAs, and Ge across various frequency ranges.
- Up to five pairs of Lorentz poles can be effectively fitted.
- The method reduces the deviation between model and measured permittivity.

## Abstract

Approximating the frequency dispersion of the permittivity of materials with simple analytical functions is of fundamental importance for understanding and modeling their optical properties. Quite generally, the permittivity can be treated in the complex frequency plane as an analytic function having a countable number of simple poles which determine the dispersion of the permittivity, with the pole weights corresponding to generalized conductivities of the medium at these resonances. The resulting Drude-Lorentz model separates the poles at frequencies with zero real part (Ohm's law and Drude poles) from poles with finite real part (Lorentz poles). To find the parameters of such an analytic function, we minimize the error weighted deviation between the model and measured values of the permittivity. We show examples of such optimizations for various semiconductors (Si, GaAs and Ge), for different frequency ranges and up to five pairs of Lorentz poles accounted for in the model.