Evanescent waves in high numerical aperture aplanatic solid immersion microscopy: Effects of forbidden light on subsurface imaging

Abdulkadir Yurt,Bennett B Goldberg,M Selim Ünlü,Aydan Uyar,T Berkin Cilingiroglu

doi:10.1364/oe.22.007422

Abstract

The collection of light at very high numerical aperture allows detection of evanescent waves above the critical angle of total internal reflection in solid immersion lens microscopy. We investigate the effect of such evanescent modes, so-called forbidden light, on the far-field imaging properties of an aplanatic solid immersion microscope by developing a dyadic Green's function formalism in the context of subsurface semiconductor integrated circuit imaging. We demonstrate that the collection of forbidden light allows for sub-diffraction spatial resolution and substantial enhancement of photon collection efficiency albeit inducing wave-front discontinuities and aberrations.

Highlights

The growing demand for high spatial resolution in optical inspection for failure analysis of semiconductor integrated circuits (ICs) has aroused interest in employing aplanatic solid immersions lenses [1,2,3,4,5,6,7]
The electromagnetic boundary conditions at the dielectric interface between the silicon substrate and insulating media impose that the evanescent waves originated from the objects in the insulating medium are transformed into propagating waves in silicon immersion medium at angles higher than the critical angle of total internal reflection (TIR) [8]
NaSIL nobj where kobj and kins are the wave-numbers of the light in the objective and insulating media, respectively; fobj is the focal length of the objective, kzins and kzaSIL are the longitudinal components of the wave-vectors in the insulating and immersion media, respectively; d is the distance of dielectric interface from the aplanatic point; θaSIL and θobj represent the polar angles with respect to the aplanatic solid immersions lenses (aSILs) and the objective coordinate centers, respectively

Summary

Introduction

The growing demand for high spatial resolution in optical inspection for failure analysis of semiconductor integrated circuits (ICs) has aroused interest in employing aplanatic solid immersions lenses (aSILs) [1,2,3,4,5,6,7] In such applications, aSILs are placed in intimate mechanical contact with the polished back-side of an IC chip, transforming the silicon substrate into a high refractive index immersion medium (nSi = ~3.5) for high numerical aperture (NA) sub-surface imaging. The electromagnetic boundary conditions at the dielectric interface between the silicon substrate and insulating media impose that the evanescent waves originated from the objects in the insulating medium are transformed into propagating waves in silicon immersion medium at angles higher than the critical angle of total internal reflection (TIR) [8] Such propagating waves, so-called forbidden light, can be collected by the aSIL and contribute to the farfield imaging [9, 10]. Investigation of imaging performance in the vicinity of the dielectric interface through an electromagnetic model is critical to assess the limitations of the aSIL microscopy for semiconductor failure analysis and is applicable to imaging in quantum optics [18], biophotonics [19] and metrology [20] as well, as pure ray-tracing models cannot account for the behavior of the evanescent waves discussed here [21, 22]

Theory

Results and discussion

Field amplitude and phase on the pupil plane

Image of dipoles on the detector

Image of two dimensional objects on the detector

Conclusion