Jongwon Seok

Multiscale material removal modeling of chemical mechanical polishing

Abstract This paper describes a multiscale model for material removal during conventional chemical mechanical polishing (CMP). Three spatial scales are considered in the integrated model: (i) abrasive particle scale; (ii) asperity scale; (iii) wafer scale. The model is based on the deformation of hyper-elastic asperities attached to a linear-elastic pad. ANSYS is used to perform finite element analyses of a single asperity to obtain the relations between the deformation of the asperity, and the contact stress and area. Those relations are used in an extended Greenwood–Williamson model to compute the local average contact pressures on the pad. The material removal model includes the abrasive wear caused by local contact stress between the abrasive particles and the wafer, the distribution of asperity heights, and the plastic deformation of the wafer. The material removal rate results for unpatterned wafers are used to predict the material removal rates on a feature. The results of a computer simulation of material removal and the time evolution of a feature are shown. Two FEM based codes, ANSYS and EVOLVE are used; the former for the contact stress analysis and the latter to generate a new surface.

Free vibrations of annular sector cantilever plates. Part 1: out-of-plane motion

Analysis of the free in-plane vibrations of a cantilevered annular sector plate is performed by means of a variational approximation procedure. The problem is treated by first obtaining the exact solution for waves in the plate satisfying the equations of plane stress including in-plane inertia with the inner and outer circumferential edges traction free. In this exact solution, new radial vector functions are obtained from a Frobenius type expansion. The solution results in a set of dispersion curves. A number of the resulting waves are used in what remains of the variational equation, in which all conditions occur as natural conditions. Roots of the resulting transcendental equation are calculated, which yield the eigensolutions and associated eigenfrequencies. The results are compared with results obtained using FEM, and good agreement is shown.

A Multiscale Elastohydrodynamic Contact Model for CMP

We present a three-dimensional multiscale elastohydrodynamic lubrication (EHL) contact model for chemical mechanical planarization (CMP) based on satisfying the fundamental mechanical force and moment balance equations appropriate for a rotational CMP tool. We describe surface-surface and fluid-surface interactions in conditions where pad asperities are in direct contact with the wafer and the effective film thickness is comparable in size to the roughness of the bounding surfaces. A hyperelastic material is used for our asperity scale model to account for large deformations of the soft polymer asperities. We iteratively solve the soft elastohydrodynamic contact problem. i.e., the solid-solid contact problem coupled with fluid pressure, until the global force and moment balances are satisfied for given operating conditions. The multiscale model computes contact stress across the wafer surface due to asperity deformation that is, in turn, caused by the externally applied load and interfacial slurry pressures. Finally, a relative measure of material removal rate across the wafer is represented by the computed local asperity contact stress. Flat, concave, and convex rigid wafers are considered. The work of this paper focuses on understanding fundamental mechanical aspects of CMP and presents a methodology to simulate mechanical aspects of the CMP process.

Critical Adhesion Energy of Benzocyclobutene-Bonded Wafers

The dependencies of critical adhesion energy (CAE) of benzocyclobutene (BCB) bonded wafers on BCB thickness, the use of an adhesion promoter, and the materials being bonded are studied using a four-point-bending technique. The thicknesses of BCB used in the experiments ranged from 0.4 to 7.0 μm. The CAE depends linearly on BCB thickness due to the thickness-dependent contribution of plastic dissipation energy of the BCB and thickness independence of BCB yield strength. The CAE increases by approximately a factor of 2 when an AP is used for both 2.6- and 0.4-μm-thick BCB bonding layers because of chemical interactions. The CAEs measured at the interfaces between a Si wafer with plasma-enhanced chemical vapor deposited (PECVD) SiO 2 and BCB and between a Si wafer with thermally grown SiO 2 and BCB are approximately a factor of 3 higher than the CAE between a PG&O 1737 aluminosilicate glass wafer and BCB. The observed bond energies are about 18 and 22 J/m 2 at the interfaces between PECVD oxide and BCB and between thermally grown oxide and BCB, respectively. These bond energies correspond to bond densities of 12-13 and 15-16 Si-O bonds/nm 2 .

Thermal Cycling Effects on Critical Adhesion Energy and Residual Stress in Benzocyclobutene-Bonded Wafers

The effects of thermal cycling on critical adhesion energy and residual stress at the interface between benzocyclobutene (BCB) and silicon dioxide (SiO 2 ) coated silicon wafers were evaluated by four-point bending and wafer curvature techniques. Wafers were bonded using BCB in an established (baseline) process, and the SiO 2 films were deposited by plasma-enhanced chemical vapor deposition (PECVD). Thermal cycling was done between room temperature and a peak temperature. In thermal cycling performed with 350 and 400°C peak temperatures, the critical adhesion energy increased significantly during the first thermal cycle. The increase in critical adhesion energy is attributed to relaxation of residual stress in PECVD SiO 2 , which in turn is attributed to condensation reactions in those films. Thermal cycling also cures the BCB beyond the ∼88% achieved in the baseline process, and the residual stress in the BCB is reset at a glass transition temperature corresponding to the increased BCB cure conversion. As more thermal cycles are performed, stress hysteresis in the BCB decreases as the cure stabilizes at 94-95%.

Evaluation of BCB Bonded and Thinned Wafer Stacks for Three-Dimensional Integration

A critical issue associated with the implementation of wafer-level three-dimensional (3D) integration is to achieve excellent bonding and thinning performance without degrading mechanical and electrical characteristics of integrated circuit (IC) chips in the 3D wafer stack. In this work, some mechanical and electrical impacts of wafer bonding and thinning processes used to fabricate 3D ICs are evaluated using patterned wafers with two-level copper interconnect test structures that included either silicon dioxide or porous low-k interlevel dielectrics (ILDs). Benzocyclobutene (BCB) (Cyclotene 3022-35 from Dow Chemical) is the adhesive used, and thinning consists of grinding, chemical mechanical polishing, and wet etching. Three procedures used to evaluate the integrity of BCB bonded and thinned wafer stacks are discussed: (i) optical inspection of the bonding interface using glass wafers with a coefficient of thermal expansion that is close to that of silicon wafers in order to check for voids, defects, and uniformity after each bonding and thinning process; (ii) four-point bending tests to quantify bond strength and to identify the weak bond interface, and (iii) electrical tests of the patterned wafers after two bonding and thinning processes and subsequent BCB removal by plasma ashing to expose the contact pads. These procedures evaluated the impacts of processing of wafer stacks without the need for interwafer interconnect processing. Some negative mechanical and electrical impacts were observed for interconnect structures that include a porous low-k ILD, while no significant changes were observed for interconnect structures with oxide ILD.

Free vibrations of rectangular cantilever plates. Part 1: out-of-plane motion

An analysis of the free in-plane vibrations of a cantilevered rectangular plate is performed by means of a variational approximation procedure. The problem is treated by first obtaining the exact solution for waves in the plate satisfying the equations of plane stress including in-plane inertia with two opposite edges traction free. The solution results in a set of dispersion curves. A number of the resulting waves are used in what remains of the variational equation, in which all conditions occur as natural conditions. Roots of the resulting transcendental equation are calculated, which yield the eigensolutions and associated eigenfrequencies. The results are compared with results obtained using FEM, and good agreement is shown.

Inverse analysis of material removal data using a multiscale CMP model

This paper describes a mechanical model for a representative dual axis rotational chemical mechanical planarization (CMP) tool. The model is three-dimensional, multiscale and includes sub-models for bulk pad deformation, asperity deformation, lubrication based slurry flow, carrier film deformation, wafer compliance and material removal by abrasive particles in the slurry. With the model, material removal rate (MRR) can be determined as a function of stress applied to the wafer, relative sliding speed, and material and geometric parameters of the pad and slurry. Experimental material removal rate profiles obtained from Cu polishing experiments performed on a wafer without rotation are analyzed as an inverse problem. We use MRR data to predict local CMP conditions such as fluid film thickness, fluid pressure and contact pressure. The results are consistent with available experimental and analytical information. This inverse technique offers promise as an improved method of CMP model verification.

Soft Elastohydrodynamic Lubrication With Roughness

A soft elastohydrodynamic lubrication model for a conformal one-dimensional sliding contact is presented. We describe surface-surface and fluid-surface interactions in conditions where asperities are in direct contact (mixed lubrication), and the effective film thickness is comparable in size to the roughness of the bounding surfaces. In the conditions considered, surfaces have a low elastic modulus, and fluid pressures have a low magnitude, relative to those found in most tribology applications. An interesting coupling is exhibited between the surface roughness, the global elasticity, and the fluid pressure. As opposed to typical tribological applications in conformal mixed lubrication contact, fluid pressure is strong enough to cause significant elastic displacement of the mean boundary surfaces. The deformation is taken into account in an iterative process to compute the resulting spatially dependent stresses, deformations and fluid pressures.

Critical Adhesion Energy at the Interface Between Benzocyclobutene and Silicon Nitride Layers

The effects of thermal cycling on residual stresses in both silicon nitride (SiN x ) deposited on silicon wafers and benzocyclobutene (BCB) coated silicon wafers are discussed. The SiN x is deposited by plasma-enhanced chemical vapor deposition (PECVD). A model for the effect of thermal cycling on residual stresses helps explain the effects of thermal cycling on critical adhesion energy (CAE) between SiN x and BCB films in bonded wafer configuration SiISiN x /BCB/SiN x /Si. The wafers are bonded with BCB using an established baseline process. CAE is measured using four-point bending. In thermal cycling experiments conducted between 25°C and either 350 or 400°C, the CAE at the interface between BCB and SiN x decreases. This trend in CAE agrees with our models prediction that an increase in residual tensile stress within SiN x after thermal cycling leads to the observed decrease in CAE. This result is compared with that obtained for bonded wafer configuration Si/PECVD SiO 2 /BCB/PECVD SiO 2 /Si, where the decrease in residual compressive stress within SiO 2 induces an increase in CAE. These opposite trends in CAEs of the structures that include SiN x or SiO 2 layers are caused by condensation reactions in the layers, followed by desorption of water, which makes the films more tensile.