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Each part discusses a specific to-date topic on new and valuable design ideas in the area of analog circuit design. Each part is presented by six experts in that field and state of the art information is shared and overviewed. This book is number 20 in this successful series of Analog Circuit Design, providing valuable information and excellent overviews of: Robust Design, chaired by Herman Casier, Consultant Sigma Delta Converters, chaired by Prof.

Arthur van Roermund, Eindhoven University of Technology Analog Circuit Design is an essential reference source for analog circuit designers and researchers wishing to keep abreast with the latest development in the field. It already critically affects SRAM scaling [4], and introduces leakage and timing issues in digital logic circuits [5].

In Sect. The compact model strategies suitable for capturing the statistical variability in industrial strength compact models such as BSIM and PSP are outlined in Sect. Finally the conclusions are drawn in Sect. The granularity introduces significant variability when the characteristic size of the grains and irregularities become comparable to the transistor dimensions. Random dopants are introduced predominantly by ion implantation and redistributed during high temperature annealing. Apart from special correlation in the dopant distribution imposed by the silicon crystal lattice, there may be also correlations introduced by the Coulomb interactions during the diffusion process.

This is associated surface potential pinning at the grain boundaries complimented by doping non-uniformity due to rapid diffusion along the grain boundaries [3]. This is due to the elimination of the polysilicon depletion region and better screening of the RDD induced potential fluctuations in the channel from the very high concentration of mobile carriers in the gate. The metal gate also eliminates the PGG induced variability.

In the same time it introduces high-k granularity illustrated in Fig. Sandia Labs Fig. In extremely scaled transistors atomic scale channel interface roughness illustrated in Fig. Cheng Fig. Sematech [11]. Since the basis of the silicon lattice is 0.

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IBM 21 Poly-Si 2. However, without considering quantum mechanical confinement in the potential well, in classical simulation, such fine mesh leads to carrier trapping at the sharply resolved Coulomb potential wells generated by the ionised discrete random dopants. In order to remove this artifact, the DG approach is employed as a quantum correction technology for both electrons and holes [11]. The LER illustrated in Fig. The procedure used for simulating PGG involves the random generation of poly-grains for the whole gate region [3]: a large atomic force microscope image of polycrystalline silicon grains illustrated at the top of Fig.

Then the simulator imports a random section of the grain template image that corresponds to the gate dimension of the simulated device, and along grain boundaries, the applied gate potential in the polysilicon is modified in a way that the Fermi level remains pinned at a certain position in the silicon bandgap. In the worst case scenario the Fermi level is pinned in the middle of the silicon gap.

The impact of polysilicon grain boundary variation on device characteristics is simulated through the pinning of the potential in the polysilicon gate along the grain boundaries. The simulator was adjusted to match accurately the carefully calibrated TCAD device simulation results of devices without variability by adjusting the effective mass parameters involved in DG formalism, and the mobility model parameters. The electron concentration at the interface of the two transistors is mapped on top of Fig. For example acceptors in the channel of the n-channel transistor create sharp localized potential barrier for the electrons near the interface but act as potential wells for the holes in the substrate.

Good agreement has been obtained assuming that the Fermi level at the n-type polySi gate grain boundaries is pinned in the upper half of the bandgap at approximately 0. The reason for this is the presence of acceptor type interface states in the upper half of the bandgap which pin the Fermi level in the case of n-type poly-Si, and the absence of corresponding donor type interface states in the lower part of the bandgap which leaves the Fermi level unpinned in the case of p-type poly-Si [13].

## Analog circuit design : robust design, sigma delta converters, RFID

The scaling closely follows the prescriptions of the ITRS in terms of equivalent oxide thickness, junction depth, doping and supply voltage. More details about the scaling approach and the characteristics of the scaled devices may be found in [11]. Two scenarios for the magnitude of LER were considered in the simulations. In the first scenario the LER values decrease with the reduction of the channel length following the prescriptions of the ITRS of 1. In this case the dominant source of variability at all channel lengths are the random discrete dopants.

The combined effect of the three sources of variability is also shown in the same figure. Cheng 0. Previous research on statistical compact model identification was focused mainly on variability associated with traditional process variations resulting from poor control of critical dimensions, layer thicknesses and doping clearly related to specific compact model parameters [16].

## ISBN 13: 9789400790360

Unfortunately, the current industrial strength compact models do not have natural parameters designed to incorporate seamlessly the truly statistical variability associated with RDD, LER, PGG and other relevant variability sources. Despite some attempts to identify and extract statistical compact model parameters suitable for capturing statistical variability introduced by discreteness of charge and matter this remains an area of active research [16, 17].

We use the standard BSIM4 compact model to capture the information for statistical variability obtained from full 3D physical variability simulation. The statistical extraction of compact model parameters is done in two stages [17]. The RMS error for this extraction is 2. At the second stage, we re-extracted a small carefully chosen subset of the BSIM4 model parameters from the physically simulated characteristics of each microscopically different device in the statistical ensemble keeping the bulk of the BSIM parameters unchanged.

The transfer ID—VG characteristics at low and high drain bias are used as extraction target at this stage. The good match between the BSIM results and the physically device characteristics validates the choice of seven parameters which guaranty high accuracy of the compact model over the whole statistical range of physically simulated device characteristics. Relatively few simulation data points are needed to extract high accuracy statistical compact model parameters.

In order to reproduce the right statistical behavior of such devices in statistical circuit simulation, wider device are constructed by connecting in parallel minimum size devices randomly selected from the statistic compact model library. The statistical circuit simulation methodology described in the previous section, which can transfer all the fluctuation information obtained from 3D statistical device simulations into circuit simulation, is employed to investigate the impact of RDF on 6T and 8T SRAM stability for the next three generations of bulk CMOS technology.

The functionality of SRAM is determined by both static noise margin SNM defined as the minimum dc voltage necessary to flip the state of the cell and the write noise margin WNM defined as the DC noise voltage needed to fail to flip a cell during a write period. The cell ratio is defined as the ratio of the driver transistor to access resistor channel widths. At the same time, the increase in the cell ratio tends to degrade the WNM. Therefore, the approach of increasing the cell ratio becomes less attractive for extremely scaled devices even from the prospect of the yield.

More and more the strategic technology decisions that the industry will be making in the future will be motivated by the desire to reduce statistical variability. SRAM which uses 32 A. Cheng minimum channel width transistors is the most sensitive part of the integrated systems in respect of statistical variability and needs special care and creative design solution in order to take full advantage from scaling in present and future technology generations. Washington DC, Dec , p.

Bernstein, D. Frank, A. Gattiker, W. Haensch, B.

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Ji, S. Nassif, E. Nowak, D. Pearson, N. Rohrer, IBM J. Brown, G. Roy, A. Cheng, S.

## Analog Circuit Design

Agarwal, K. Chopra, V. Zolotov, D. Blaauw, Circuit optimization using statistical static timing analysis, in Proc. Asenov, Random dopant induced threshold voltage lowering and fluctuations in sub 0. Asenov, S. Kaya, A.

Watling, A. Ferrari, J. Babiker, G.