Computing complex dispersive refractive indices from thin film optical properties of materials

2019 Aug. 14

Authors S. Banerjee, I. Takayanagi, K. Mori, J. Nakamura, J. B. Cole*, T. Hoshino** and M. Itoh**
*National Academy of Sciences
**University of Tsukuba

SPIE, Novel Optical Systems, Methods, and Applications XXII, 2019

Nanophotonic devices, such as CMOS image sensor (CIS) pixels, are formed by stacking multiple layers of semiconductor materials. The complex refractive indices of these materials vary with the wavelength of light. Currently, industrial development of photonic devices includes a design step where light propagation is simulated using numerical methods, such as finite-difference time-domain (FDTD). Such simulations require that the refractive indices of the constituent materials be known accurately. Most commonly employed methods for computing the real and imaginary parts of the dispersive refractive indices are based either on the evaluation of the Kramers-Kronig (K-K) integral, or on the use of theoretical models of permittivity. These methods rely on the experimentally measured reflectivity or transmissivity spectra of thin films of a material to determine its refractive indices. In the first part of this paper, we describe the computation of the dispersive refractive indices of certain materials using an optimization routine based on a genetic algorithm and the coherent reflectivity and transmissivity spectra of thin-films. This approach finds the global optimum unlike earlier methods based on local optimization techniques. In the second part of the paper, we evaluated the K-K integral and used the Lorentz model of permittivity to compute the real part of the refractive index of Rhodamine B from its imaginary part. The imaginary part was determined from the transmission spectrum of a thin film of Rhodamine B. Recently, we used a similar strategy to compute the dispersive refractive index of an on-chip color filter commonly used for CIS pixel.