Statistical variations including random dopant fluctuations in nominally identical MOSFETs

Abstract

Statistical variations in physically proximate iso-drawn MOSFETs limit the yield and performance of VLSI circuits and thus receive the attention of integrated circuit communities. As technology scales, variations must be made to scale as well. Some variations can be reduced by tighter control of processes. However, some variations such as random dopant fluctuations (RDF) may not be controllable, or are amenable to control only by radical and expensive changes in manufacturing methodology. Before undertaking such changes, it is prudent to see whether RDF really is a problem, and to do this we need an accurate estimate of the size of RDF effects. This work advances these goals. The first part of this dissertation provides an experimental assessment of different variation sources and a comparison of their contributions to transistor performance variation. Our study shows that macroscopic geometrical variations are significant and cannot be ignored. The second part of the dissertation presents a novel approach to assessing how potential at any position in the MOSFET channel is affected by accidental arrangements of point charges. The potential and the statistics are treated exactly for the first time. We find that as device scaling reaches the sub-10 nm regime, the earlier RDF work becomes unacceptable because the approximation made of lumping charge on numerical mesh nodes becomes too inaccurate. Our method is freed from this approximation because the potential and the statistics are determined analytically. Moreover, our method proves efficient computationally compared to the existing numerical analyses. The remaining part assesses the impact of MOSFET scaling on the potential variation introduced by RDF. It is shown for the first time that charge location variations dominate charge number variations. We examine the role of structural parameters upon the potential variation, including oxide thickness t, depletion width w, device area L², number nu of charges present, number N of sites available for the charges to reside, and average charge density/cm² N(S). Our study shows that reduction in L at a fixed N(S), t and w has no effect until the device radius becomes smaller than a screening radius. At this point, further reduction gives rise to a smaller standard deviation of potential σ and mean potential μ, but a larger σ/μ. This last trend is due to charge location variations, and contradicts previous approximate treatments that show an opposite trend in σ.