Quantitative coherent diffractive imaging of an integrated circuit at a spatial resolution of 20 nm

Abstract

The complex transmission function of an integrated circuit is reconstructed at 20 nm spatial resolution using coherent diffractive imaging. A quantitative map is made of the exit surface wave emerging from void defects within the circuit interconnect. Assuming a known index of refraction for the substrate allows the volume of these voids to be estimated from the phase retardation in this region. Sample scanning and tomography of extended objects using coherent diffractive imaging is demonstrated.

A study on new approaches in coherent x-ray microscopy of biological specimens

“…For this reason there is a component in the sum (2.1) with a distinct, lowest non-zero fundamental frequency k 1 = 2π/L -or if we define the rotational frequency as ν n = k n /2π -with the fundamental ν 1 = 1/L, corresponding to the period length of the function f L . No lower-frequency components can be contained in f L as they would have a period larger than L. In addition, no frequency components other than those with integer multiple frequencies of ν 1 can be contained as they would not be periodic with period length L. In other words, the periodicity of f L with a finite period length L leads to its spectral decomposition into components with discrete frequencies k n and spacing ∆k = k 1 = 2π/L in the space of all possible frequencies k ∈ R. On the other hand, f L is defined on a continuous real space with values x ∈ R.…”

Phase-Diverse Coherent Diffractive Imaging: High Sensitivity with Low Dose

“…Typically either the illuminating probe, or the object must be finite in extent. Phase curvature has been shown to provide reliable convergence characteristics [15], and has allowed the imaging of extended objects in 2D [6] and 3D [16]. Additional information for the solution can be provided by acquiring diffraction data from different forms of illumination.…”

“…The adaptation of CDI to image extended samples was made possible by recognizing that an illumination which is finite in extent also satisfies the conditions for a unique solution [6,7]. The method of ptychography, an approach initially proposed for electron imaging [8], uses a multitude of diffraction patterns from overlapping regions to recover the distribution of an extended object.…”

Use of Justified Constraints in Coherent Diffractive Imaging

“…However, the question of uniqueness of the reconstructed images has not been completely answered for arbitrary specimens when a finite "object support constraint" cannot be applied, as for an isolated object, or when knowledge of the illumination function is incomplete. Here, extending the work of Clark et al [8], we discuss the use of physically justified object constraints to image an extended object using Fresnel CDI [5][6][7], and compare the reconstruction rapidity and uniqueness using these constraints.…”

“…Various approaches to CDI have been developed and demonstrated with a spatial resolution rapidly approaching the few-nanometer scale [1][2][3][4][5][6][7]. However, the question of uniqueness of the reconstructed images has not been completely answered for arbitrary specimens when a finite "object support constraint" cannot be applied, as for an isolated object, or when knowledge of the illumination function is incomplete.…”