Molecular simulation on the material/interfacial strength of the low-dielectric materials
Introduction
As feature sizes for the advanced IC continue to shrink, the semiconductor industry is focusing the development on minimizing the intrinsic time delay for signal propagation, quantified by the resistance–capacitance (RC) delay [1], [2]. The increasing demands for the electronic performance of the IC wiring have recently driven the replacement of aluminum with copper traces, and of SiO2 film with alternative materials with lower dielectric constant (k-value) [1], [2], [3], [4], [5]. The silicon oxide based low-k materials (SiOC:H, also called black diamond, illustrated in Fig. 1) are preferred by the industry because the fabricating processes of this materials exhibits high IC compatibility and high yielding rate. The k-value can be reduced in two ways: either chemically by replacing oxygen by the methyl groups, H or OH or physically by generating porosity within the material [4]. The porosity, and basic building groups of Q, T, D and M, are shown in Fig. 1.
However, the delamination and reliability issues around the advanced IC back-end structure remain, due to the low mechanical stiffness of the low-k material [6]. Among the materials of advanced IC back-end structures, the low-k material has a relatively low mechanical stiffness: approximately 5–15 GPa [2], [3], [4]. Experiments [6], [4] show that enhancing the Young’s modulus of the low-k material increases the toughness of the critical interfaces. Although a total understanding of the low-k material and interface of IC back-end can essentially resolve these mechanical issues, the difficulties arise from the measurement technique of the mechanical/chemical status at interface.
Fracture/delamination is a phenomenon which spans many different geometrical scales. The macroscopic dimensions of the crack and the specimen determine the intensity of the stress at the crack tip and are equally important as the microstructure of the material, which provides preferred fracture paths. Ultimately, mechanism of fracture can be reduced to the breaking of atomic bonds, which in the case of brittle fracture occurs at an atomically sharp crack tip [7], [8]. In a perfectly brittle material, the crack moves by no other process than the breaking of individual bonds between atoms.
Nevertheless, traditional theory of brittle fracture processes does not focus on individual atomic bonds but resorts to the treatment of Griffith [9], which is based on continuum thermodynamics. Following Griffith’s theory, one may regard the static crack as a reversible thermodynamic system for which one seeks equilibrium. The equilibrium condition leads to the so-called Griffith criterion, which balances the crack driving force and the material resistance against fracture. With the implication of thermodynamic equilibrium, Griffith’s picture provides a reference value for the analysis of the crack driving forces. It however cannot explain why and how fracture proceeds [10]. Hence using the molecular modeling method, like molecular dynamics (MD) method, can essentially represent the fracture mechanism in atomistic scale.
In order to implement the molecular simulation, the atomic structure and interaction between atoms should be well defined beforehand. For the low-k material, due to the uncertainty of an amorphous material, it is quite difficult to precisely describe the exact chemical structure. There are several methods to predict the chemical structure. One can simulate the whole fabrication process of the amorphous material, but is time-consuming if the fabrication process was not interested. Another trick is to generate the reasonable structure based on the known chemical characterization information. Without explicitly considering the real fabrication process of glass silica, Bell and Dean [11] developed a hand-build random network model. Gaskell and Tarrent [12] applied a strain energy minimization onto the previous model. Guttman and Rahman [13] has obtained the random network by starting with placing Si atom randomly and then inserting the O between Si atoms. However, difficulties occurs when applying the aforementioned methods on the amorphous/porous SiOC:H network, which consisted of several different basic building blocks (e.g., Q, T, D, etc).
Two tasks are focused in this paper: mechanical modeling of the amorphous/porous low-k (SiOC:H) material and the interfacial strength between low-k and silica. A fast molecular generating algorithm is established to formulate the atomic structure of low-k material based on the inputs from its chemical composition (by experiment). The accuracy of this generating algorithm will be validated by the mechanical stiffness of low-k which is obtained by nano-indenter experiment. Moreover, an engineering approach is developed to model the chemical configuration at interface between the amorphous silica and low-k. Two remarkable simulation results are discussed: one shows the importance of the covalent bond and the other demonstrates the crack propagation path at the interface. A recommendation of improving the interfacial strength is proposed based on the simulation result.
Section snippets
Molecular dynamics method
The molecular dynamics (MD) method, which is widely used in material science of IC technology, provides a theoretical and numerical framework for many particle problems. Based on the Newton’s second law of motion, the movements of the particle are described by the coordinate variables:for each particle i in a system constituted by N particles. In Eq. (1), mi is the mass of particle i, ai is its acceleration, and Fi is the force acting on the particle. Therefore, MD is a deterministic
Molecular model of amorphous/porous SiOC:H
The building blocks (Fig. 1), Q, T, D and M, represent Si atoms having 4, 3, 2, and 1 capabilities to connect other basic blocks, respectively. Instead of building the amorphous structure manually [12] and constructing the model based on amorphous silicon [13], in this paper the concept of filling the basic blocks into a pre-defined framework [15] is proposed. Additionally, the size of the void is assumed to be the same as the basic blocks. Basic groups are not allowed to connect to pores. In
Material strength simulation of SiOC:H
In order to understand the accuracy of the amorphous structure which generated by the proposed method, two molecules, the SiOC:H before and after UV treatment, are used as the qualitative validation. In reference [4], the concentrations of the basic building blocks and oxygen bond angle of two molecules have been measured by nuclear magnetic resonance (NMR) and Fourier transform infrared spectroscopy (FTIR), respectively. The basic block concentrations are listed in the case BU and AU of Table 1
Conclusion
In this paper, a prediction method for mechanical/interfacial strengths of amorphous low-k material (SiOC:H) is presented. The molecular dynamics (MD) method is used because the atomic structure can be described as well as the interaction force between atoms. Before the simulation of the interfacial strength, an engineering approach is applied to model the chemical configuration at the interface. The same simulation procedure, which used in the fracture strength simulation, is applied to obtain
Acknowledgements
The authors are grateful to Dr. F. Iacopi (IMEC, Belgium) for sharing her experimental results and experience of the low-k material. Also, the authors thank Dr. N. Iwamoto (Honeywell, USA) for valuable discussions on the molecular dynamics simulation technique. C. Yuan thanks Dr. C. Menke, Dr. J. Wescott (Accelrys, UK) for discussions on numerical simulation technique, and experimental methods, and Prof. B. J. Thijsse (TUDelft, Netherlands) for the atomic structure at interface.
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