Screening Beneficial Dopants to Cu Interconnect by Modeling
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Screening Beneficial Dopants to Cu Interconnect by Modeling Chun-Li Liu Motorola Advanced Process Development and External Research Laboratory, Mesa, AZ 85202 I. INTRODUCTION Cu is currently being used as the new generation of advanced interconnects. Beneficial additives or dopants to Cu have been sought to improve the electromigration performance of the Cu interconnects primarily through experimental approaches [1]. As a vital alternative, we have established a virtual simulation procedure to screen the potential dopants to Cu by modeling. There are many factors such as film density, stress, stressvoiding, grain boundary defect / diffusion, interface adhesion / defect / diffusion, grain structures (texture, grain size and size distribution) and so on that can affect the electromigration. Here we assume that Cu diffusion along the grain boundaries (GBs) is the dominant mechanism that is responsible for the electromigration performance of the Cu interconnects. As schematically shown in Fig.1, if a dopant is added to Cu, most of the dopant will reside in bulk initially. In order for the dopant to play a beneficial role, it has to be able to segregate to the grain boundary. Then, the dopant is supposed to slow down Cu diffusion along the grain boundary and this can be achieved if the dopant can increase the overall activation energy of Cu grain boundary diffusion.
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Figure 1. Schematic of the physical processes needed for a dopant to play a beneficial role to slow down Cu grain boundary diffusion. In order to simulate the above physical processes as closely as possible, the virtual simulation procedure was designed to consist of the following modeling steps: 1. Dopant segregation to GB 2. Dopant bulk diffusion 3. Cu and dopant self-diffusion along the grain boundary 4. Effect of the dopant on Cu grain boundary diffusion • Dopant blocking mechanism • Dopant dragging mechanism 5. Sanity checks whenever possible AA7.13.1
II. COMPUTATIONAL METHODS A supercell containing a special Cu grain boundary - symmetric tilt Σ5(310)[001] was constructed with 34 Cu atoms. The relaxed grain boundary structure is identical to the one previously used [2], as shown in Fig. 2 (a). The actual supercell has a dimension of 23.844 Å x 5.839Å x 3.661Å. A software package, VASP (Vienna Ab-initio Simulation Package)[3], was used for the calculations, which features Vanderbilt’s ultra-soft pseudopotentials [4] with a GGA option and a plane wave basis set. A plane wave cut-off energy of 234.00 eV for Cu was used. For this particular supercell, a k-point mesh of 1x4x6 was used and the actual number of the k-points was automatically generated with a built-in routine in VASP in the Monkhorst scheme. All the quantities in this work were calculated with full relaxation. Grain Boundary Plane
4 3 4 2 3 4 I
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Figure 2. (a) Relaxed structure of symmetric tilt Σ5(310)[001] grain boundary in Cu. Two structure unit cells were outlined. Numbers in the upper structure unit cell were given
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