Fourier series based diffraction tomography reconstruction of multidimensional gratings

Diffraction tomography, which falls under the general area of inverse scattering, is applied to reconstruct multidimensional periodic complex refractive index distributions commonly found in the microelectronics industry and referred to as latent image gratings. Latent image gratings are formed in photoresist layers during the lithographic step in microelectronic manufacturing. With the continuing advancement in semiconductor circuitry, it has become of crucial importance to successfully and nondestructively monitor latent image formation.;Owing to its integral formulation of the diffracted field, the inverse scattering problem in diffraction tomography, i.e., reconstructing periodic objects from scattered fields, is linearized via first order, or weakly scattering, approximations, namely, the first Born and first Rytov approximations. and thus solved. Within the weakly scattering regime, a newly formulated closed-form solution to the Fourier diffraction theorem (FDT) for periodic structures is obtained. The ill-posed dimensional discrepancy in the FDT is remedied by mathematically expanding the periodic refractive index distributions of latent images into their Fourier series representations, hence the name Fourier series reconstruction (FSR) technique. Consequently, a well-posed reconstruction relation between Fourier series coefficients and scattered fields is obtained. The FSR technique requires as input the diffracted field from latent images generated by nonexposing incident electromagnetic sources. No a priori knowledge pertaining to the structures is needed. The reconstruction procedure in turn produces reconstructed versions of the latent images.;Finally, this technique has only been tested on simulated data. In particular, exact scattered fields were calculated by rigorous electromagnetic modeling techniques and used as input data. It is shown that perfect reconstructions of latent images from reflected waves are achieved as long as the first order approximations are met and the desired reflection diffraction orders are observable.