Urban Kovac

Advanced simulation of statistical variability and reliability in nano CMOS transistors

Increasing CMOS device variability has become one of the most acute problems facing the semiconductor manufacturing and design industries at, and beyond, the 45 nm technology generation. Most problematic of all is the statistical variability introduced by the discreteness of charge and granularity of matter in transistors with features already of molecular dimensions [i]. Two transistors next to each other on the chip with exactly the same geometries and strain distributions may have characteristics from each end of a wide statistical distribution. In conjunction with statistical variability [ii], negative bias temperature instability (NBTI) and/or hot carrier degradation can result in acute statistical reliability problems. It already profoundly affects SRAM design, and in logic circuits causes statistical timing problems and is increasingly leading to hard digital faults. In both cases, statistical variability restricts supply voltage scaling, adding to power dissipation problems [iii]. In this invited paper we describe recent advances in predictive physical simulation of statistical variability using drift diffusion (DD), Monte Carlo (MC) and quantum transport (QT) simulation techniques.

Statistical simulation of random dopant induced threshold voltage fluctuations for 35 nm channel length MOSFET

Abstract Intrinsic parameter fluctuations have become a very important problem for the scaling and integration of future generations of nano-CMOS transistors impacting on circuit and systems yield and reliability. In this paper random discrete dopant (RDD) induced threshold voltage variations have been studied using the Glasgow 3D atomistic drift/diffusion simulator. For the first time, we have carried out statistical simulation based on groundbreaking sample of 100,000 transistors which may assess more than 4σ of the statistical distribution. In order to correctly access the accuracy and the confidence level of the statistical parameters, we have carried out comprehensive statistical analysis using state-of-art statistical tools amenable to our problem. We use the first four moments to fit distribution of RDD induced fluctuations in the threshold voltage by means of several statistical approaches.

Hierarchical Simulation of Statistical Variability: From 3-D MC With “ ab initio” Ionized Impurity Scattering to Statistical Compact Models

Quantum corrections based on density gradient formalism, recently introduced in the 3-D Monte Carlo (MC) module of the Glasgow “atomistic” simulator, are used to simultaneously capture quantum confinement effects as well as “ab initio” ionized impurity scattering. This has allowed us to consistently study the impact of transport variability due to scattering from random discrete dopants on the on-current variability in realistic nano-CMOS transistors. Such simulations result in an increased drain current variability when compared with the drift diffusion (DD) simulation. For the first time, a method that is used to accurately transfer the increased on-current variability obtained from the “ ab initio” MC simulations to the DD simulations is subsequently presented. The MC-corrected DD simulations are used to produce the target I-V characteristics from which the statistical compact models are extracted for use in preliminary design kits at the early stage of new technology development.

Modeling and simulation of transistor and circuit variability and reliability

Statistical variability associated with discreteness of charge and granularity of matter is one of limiting factors for CMOS scaling and integration. The major MOSFET statistical variability sources and corresponding physical simulations are discussed in detail. Direct statistical parameter extraction approach is presented and the scalability of 6T and 8T SRAM of bulk CMOS technology is investigated. The standard statistical parameter generation approaches are benchmarked and newly developed parameter generation approach based on nonlinear power method is outlined.

A general approach for multivariate statistical MOSFET compact modeling preserving correlations

As feature sizes shrink, random fluctuations gain importance in semiconductor manufacturing and integrated circuit design. Therefore, statistical device variability has to be considered in circuit design and analysis to properly estimate their impact and avoid expensive over-design. Statistical MOSFET compact modeling is required to accurately capture marginal distributions of varying device parameters and to preserve their statistical correlations. Due to limited simulator capabilities, variables are often assumed to be normally distributed. Although correlations may be captured using Principal Component Analysis, such an assumption may be inaccurate. As an alternative, Nonlinear Power Models have been proposed. Since we see some limitations in this approach, we analyze whether the multivariate Generalized Lambda Distribution is an alternative for statistical device modeling. Applying both approaches to extracted statistical device parameters, we conclude that both methods do not differ significantly in accuracy, but the multivariate Generalized Lambda Distribution is more general and less computationally expensive.

A novel approach to the statistical generation of non-normal distributed PSP compact model parameters using a nonlinear power method

Statistical variability (SV) is one of the fundamental limiting factors for future nano- CMOS scaling and integration of. Variability aware design is essential to achieve reasonable yield and reliability in the manufacture of circuit and systems. To develop effective variability aware design technologies it is essential to have a reliable and accurate statistical compact modeling strategy. In this study a nonlinear power method (NPM) based statistical compact modeling strategy is presented. The results indicate that statistical compact model parameters generated by a NPM approach are significantly better at capturing the tails and non-normal shape of statistical parameter distributions when compared with principal component analysis (PCA).

The effect of compact modelling strategy on SNM and Read Current variability in Modern SRAM

It has been shown that sub 100nm SRAM is particularly sensitive to stochastic device variability. In this paper we consider two correlated figures of merit for SRAM, Static Noise Margin (SNM) and Read Current. For the purposes of this paper 1,000 3D atomistic simulations of microscopically different 25nm P and N bulk MOSFETs were performed, and statistical compact models were then extracted for each device. Using these models simulations are performed to calculate the SNM and Read Current distributions of SRAM cells constructed using devices from the device ensemble. Variability in device performance has been then introduced via Gaussian or skewed Gaussian threshold voltages (Vt) and by using values of Vt extracted directly from the individual device compact models and the results of these simulations are then compared to the baseline simulations using fully extracted models. The results clearly demonstrate the errors that can be introduced in the estimation of SNM and Read Current distribution of a 6T SRAM cell when statistical device variability is not correctly modelled.

Statistical estimation of electrostatic and transport contributions to device parameter variation

An efficient method to model accurately the statistical drain current variability in nano-scale MOSFETs is presented. Two linear regression models are proposed for the estimation of the percentage drain current variation obtained by Monte Carlo (MC) from analogous Drift Diffusion (DD) simulation. The total variation observed in MC may be attributed to in part electrostatic variation and in part transport variation. The combined effects of the electrostatic and transport variations are estimated by an absolute and conditional model, assuming that DD simulation accounts for the entire electrostatic variation and that this is identically recovered within MC. The analysis is applied to atomistic substrate dopant induced current variation over a range of scaled mMOS devices.

Compact model extraction from quantum corrected statistical Monte Carlo simulation of random dopant induced drain current variability

An efficient method to accurately capture quantum confinement effects within Monte Carlo (MC) simulation while simultaneously resolving ‘ab initio’ ionized impurity scattering via the density gradient (DG) formalism is presented. The model is applied to study the impact of transport variability due to scattering from random discrete dopants on the on-current variability in realistic nano CMOS transistors. Such simulations result in an increase in drain current variability when compared with similarly quantum corrected drift diffusion (DD) simulation. Following this, an efficient three-stage hierarchical strategy is presented that propagates the increased on-current variability captured in 3D quantum corrected ‘ab initio’ MC into efficient 3D DD simulations that are in turn used to obtain target ID-VG characteristics for the extraction of statistical compact models.

A unified density gradient approach to ‘ab-initio’ ionised impurity scattering in 3D MC simulations of nano-CMOS variability

A methodology for incorporating quantum corrections into self-consistent atomistic Monte Carlo (MC) simulations via the density gradient effective potential is presented. The quantum corrections not only capture charge confinement effects, but accurately represent the electron-impurity interaction used in previous ‘ab initio’ atomistic MC simulations, showing agreement with bulk mobility simulation. The effect of quantum corrected transport variation in statistical atomistic MC simulation is then investigated using a series of realistic scaled devices. Increased current variation is observed compared with quantum corrected drift diffusion simulation and with previous classical MC results.