Effects of Dielectric Thermal Expansion and Elastic Modulus on the Stress and Deformation Fields in Copper Interconnects
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Effects of Dielectric Thermal Expansion and Elastic Modulus on the Stress and Deformation Fields in Copper Interconnects Y.-L. Shen Department of Mechanical Engineering, University of New Mexico, MSC 01 1150, Albuquerque, NM, 87131 ABSTRACT This study aims at assessing the role played by the coefficient of thermal expansion (CTE) and elastic modulus of low-k dielectric, in affecting the stress and deformation fields in copper interconnects. Parametric finite element analyses are conducted, varying one parameter at a time, for gaining fundamental understanding of the effect of individual properties. The analyses are based on a three dimensional model containing two levels of metal lines connected by a via. It is found that both the high CTE and low modulus values of the polymer-based dielectric contribute to the evolution of stress/strain fields in the metal structure. The low-k CTE plays a more significant role. Within certain limits, decreasing the low-k CTE and/or increasing the low-k modulus can help alleviate the plastic deformation, and thus the propensity of damage initiation, in the metal. Reducing the low-k CTE will be a more efficient and safer approach. INTRODUCTION Polymer-based low-k dielectric materials typically have very high coefficients of thermal expansion (CTE) and very low elastic modulus, compared to other materials used in the interconnect structure. This inevitably gives rise to unique stress and deformation fields resulting from the thermal expansion mismatches between dissimilar materials. In recent years two-dimensional (2D) finite element analyses on infinitely long copper (Cu) lines and low-k dielectric structures have been conducted [1-3]. It was shown that the triaxial stress field in Cu is relatively insensitive to its aspect ratio, and a significant part of the tensile stress arises from the stiff barrier layers surrounding the Cu line [3]. Further, the plastic strain field suggests the top and bottom locations of Cu near the interfaces with the barrier layers are more likely to initiate electromigration and voiding damages. A recent three-dimensional (3D) study assuming elastic response of copper has been reported [4]. It was shown that, in the oxide-based dielectric system, high tensile stresses exist at the bottom of the via and along the top interface regions of the copper line. In the organic low-k-based system, however, the dominant feature is the high deviatoric stresses in the via. Another 3D study taking into account the Cu plasticity showed that the use of polymer-based low-k material in place of traditional oxide dielectric significantly reduces the triaxial tensile stresses in Cu but enhances plastic deformation, especially in the via region [5]. The compliant low-k material also causes the thin barrier layers to bear very high stresses. The present work is devoted to parametric finite element analyses on the influence of individual properties (CTE and modulus) of the dielectric: keeping one property the same while varying the other. Attention is confined to t
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