Statistical modeling of metal-gate Work-Function Variability in emerging device technologies and implications for circuit design

Abstract

For the first time, a new source of random threshold voltage (Vth) fluctuation in emerging metal-gate transistors is identified, analytically modeled and investigated for its device and circuit-level implications. The new source of variability, christened work-function variation (WFV), is caused by the dependency of metal work-function on the orientation of its grains. A statistical framework is developed, which enables estimation of the key parameters of work-function distribution by identifying the physical dimensions of the devices and properties of materials used in the fabrication. This paper offers three major contributions for process, device and circuit designers. First, the proposed model can be employed to identify suitable materials and fabrication processes that can reduce the impact of Vth fluctuation due to WFV. For instance, four types of metal nitride gate materials (TiN and TaN for NMOS and WN and MoN for PMOS devices) are studied and it is shown that TiN and WN result in lower Vth fluctuation. Second, device engineers can benefit from the result of this work by evaluating the WFV level of various types of classical or non-classical metal-gate CMOS transistors. As an example, it is shown that FinFET transistors are less affected by WFV compared to FD-SOI and bulk-Si devices due to their larger gate area. Third, circuit designers can utilize this model to investigate the impact of such a variation on the key performance and reliability parameters of the circuits. For instance, an SRAM cell is analyzed in the presence of Vth fluctuations due to WFV and it is shown that such variations can result in considerable performance and reliability degradation.