In modern integrated circuits (ICs), billions of transistors are connected to each other via thin metal layers (e.g. copper, cobalt, etc) known as interconnects. At elevated process temperatures, inter-diffusion of atomic species can occur among these metal layers, causing sub-optimal performance of interconnects, which may lead to the failure of an IC. Thus, typically a thin barrier metal layer is used to prevent the inter-diffusion of atomic species within interconnects. For ICs with sub-10 nm transistors (10 nm technology node), the design rule (thickness scaling) demands the thinnest possible barrier layer. Therefore, here we investigate the critical thickness of a titanium–nitride (TiN) barrier that can prevent the cobalt diffusion using multi-scale modeling and simulations. First, we compute the Co diffusion barrier in crystalline and amorphous TiN with the nudged elastic band method within first-principles density functional theory simulations. Later, using the calculated activation energy barriers, we quantify the Co diffusion length in the TiN metal layer with the help of kinetic Monte Carlo simulations. Such a multi-scale modelling approach yields an exact critical thickness of the metal layer sufficient to prevent the Co diffusion in IC interconnects. We obtain a diffusion length of a maximum of 2 nm for a typical process of thermal annealing at 400 °C for 30 min. Our study thus provides useful physical insights for the Co diffusion in the TiN layer and further quantifies the critical thickness (~2 nm) to which the metal barrier layer can be thinned down for sub-10 nm ICs.

No abstract

No abstract

No abstract

In this paper, a physics based impact ionization model for silicon MOSFETs is proposed. The proposed impact ionization model specially addresses the physics for the low Vds or subband gap impact ionization (thermally assisted) along with the conventional (channel field assisted) high Vds impact ionization. The proposed model is implemented in industry standard BSIMSOI model and verified by comparison with experimental data of partially depleted silicon-on-insulator MOSFET. Model shows excellent agreement with the experimental data for low as well as high Vds impact ionization. The proposed unified impact ionization model shows improved convergence problem in standard test circuit simulation.