High resolution diameter estimation of microthin wires by a novel 3D diffraction model

Abstract

Micro-thin wires are of significant importance to academia, research laboratories as well as industries engaged in micro-fabrication of products related to diverse fields like micromechanics, bio-instrumentation, optoelectronics etc. Critical dimension metrology of such wires often demands diameter estimation with tight tolerances. Amongst other measurement techniques, Optical Diffractometry under Fraunhofer approximation has emerged over years as a nondestructive, robust and precise technique for on-line diameter estimation of thin wires. However, it is observed that existing Fraunhofer models invariably result in experimental overestimation of wire diameter, leading to unacceptable error performances particularly for diameters below 50 μm. In this paper, a novel diffraction model based on Geometric theory is proposed and demonstrated to theoretically quantify this diameter overestimation. The proposed model utilizes hitherto unused paths-ways for the two lateral rays that contribute to the first diffraction minimum. Based the 3-D geometry of the suggested model, a new 'diffraction formulation' is proposed. The theoretical analysis reveals the following. For diffraction experiment, the Actual diameter of the diffracting wire is a function of four parameters: source wavelength 'λ', axial distance 'z', diffraction angle corresponding to first diffraction minimum 'θd' and a newly defined characteristic parameter 'm'. The analysis reveals further that the proposed characteristic parameter 'm' varies non-linearly with diameter and presents a dependence only on the experimentally measured diffraction angle 'θd'. Based on the proposed model, the communication reports for the first time, a novel diameter-inversion procedure which, not only corrects for the overestimated but also facilitates wire diameter-inversion with high resolution. Micro-thin metallic wires having diameters spanning the range 1-50 μm are examined. Experimental results are obtained that corroborate the theoretical approach.