Random doping-induced fluctuations of subthreshold characteristics in MOSFET devices

Andrei, Petru; Mayergoyz, I.D.

doi:10.1016/s0038-1101(03)00236-3

Cited by 21 publications

(22 citation statements)

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“…The doping sensitivity function of the differential capacitance C gives a measure of how much the differential capacitance is changing if we add one dopant atom at some location r inside the semiconductor material. The doping sensitivity functions were originally introduced [1, 2] to define the sensitivity of the threshold voltage with dopant variations, and were later generalized to small-signal parameters [3,4], subthreshold voltage swing [5], and differential capacitance [6]. Alternative definitions in terms of the Fréchet derivative or Gâtaux differential have been introduced in [7] and [8], respectively.…”

Section: A Doping Sensitivity Functions Of the Differential Capacitancementioning

confidence: 99%

"Atomistic" Dopant Profiling Using Scanning Capacitance Microscopy

Aghaei

Andrei

Hagmann

2015

2015 IEEE Workshop on Microelectronics and Electron Devices (WMED)

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In this article we investigate the possibility to use scanning capacitance microscopy (SCM) for 3-D dopant profiling. It is shown that SCM with probes that have a radius under 10 nm, could be potentially used to determine the x-y-z coordinates of the doping atoms (or ionized impurities) in a layer of a thickness equal to the width of the depletion region. An inversion algorithm that computes the locations of the dopants from the experimental capacitance-voltage (C-V) measurements is presented for the first time. The algorithm is based on the evaluation of the doping sensitivity functions of the differential capacitance and uses a gradient-based iterative method to compute the locations of the dopants.

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Section: A Doping Sensitivity Functions Of the Differential Capacitancementioning

confidence: 99%

"Atomistic" Dopant Profiling Using Scanning Capacitance Microscopy

Aghaei

Andrei

Hagmann

2015

2015 IEEE Workshop on Microelectronics and Electron Devices (WMED)

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“…Equation (5) shows the well known result that the PDF of is Gaussian with the standard deviation . From (4), it can be seen that the integrand peaks at the point (6) and falls off sharply as , where…”

Section: A Linear-gaussian Theorymentioning

confidence: 99%

“…These variations are called local or within-die, because there is a different threshold voltage for each transistor on a die. At low voltage 0.5 V , local variations result primarily from random dopant fluctuations (RDFs), which are fluctuations in the number of dopant atoms in the transistor channels [4], [5].…”

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confidence: 99%

The Effect of Random Dopant Fluctuations on Logic Timing at Low Voltage

Rithe

Chou

et al. 2012

IEEE Trans. VLSI Syst.

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In order to achieve ultra-low power (ULP), ICs are being designed for 0.5 V. At these low voltages, random dopant fluctuations (RDFs) result in a stochastic component of logic delay that can be comparable to the global corner delay. Moreover, the probability density function (PDF) of this stochastic delay can be highly non-Gaussian. In order to predict the statistical impact of RDF-induced local variations on logic timing, it is necessary to incorporate these effects into a timing closure methodology. This paper presents a computationally efficient methodology for stochastic characterization of standard cell libraries at low voltage, where the cell delay is a nonlinear function of the transistor random variables (RVs), and the resulting cell delay has a non-Gaussian PDF. It also presents a computationally efficient methodology for computing any point on the PDF of a timing path (TP) delay, in the case where cell delays are non-Gaussian. The method is called nonlinear operating point analysis of local variation (NLOPALV). The general NLOPALV theory is developed. It is applied to cell library characterization, and the accuracy of the NLOPALV approach is validated by comparison to Monte Carlo simulation. NLOPALV is also applied to timing path analysis on a 28 nm DSP IC. The approach has been implemented using commercial CAD tools, and integrated into a commercial IC design flow. The NLOPALV approach gives timing results that are within 5% accuracy compared to Monte Carlo analysis at 0.5 V. This compares to errors on the order of 50% when the Gaussian approximation is used.

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“…[1][2][3] Variations of the MOSFET electronic characteristics become pronounced when the degree of spatial dopant fluctuation becomes comparable with the device dimensions. [4][5][6] A number of theoretical and experimental studies so far discussed the impacts of random dopant fluctuations on the significant variations in the threshold voltage and drive current of MOSFETs. [7][8][9] On the other hand, the technological progress offers the possibility of utilizing individual dopant atoms to realize novel functional devices at nanometer scale.…”

Section: Introductionmentioning

confidence: 99%

The impacts of electronic state hybridization on the binding energy of single phosphorus donor electrons in extremely downscaled silicon nanostructures

Moraru¹,

Muruganathan²,

Tabe³

et al. 2014

Journal of Applied Physics

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Articles you may be interested inThe electric field effects on the binding energies and the nonlinear optical properties of a donor impurity in a spherical quantum dot J. Appl. Phys. 109, 094309 (2011); 10.1063/1.3582137 Effect of polarization and self-energy on the ground donor state in the presence of conduction band nonparabolicity in GaAs-(Al,Ga)As spherical quantum dotThe effect of a spatially dependent effective mass on hydrogenic impurity binding energy in a finite parabolic quantum well with a magnetic field Towards an accurate gold carbonyl binding energy in AuCO + : Basis set convergence and a comparison between density functional and conventional methodsWe present the density functional theory calculations of the binding energy of the Phosphorus (P) donor electrons in extremely downscaled single P-doped Silicon (Si) nanorods. In past studies, the binding energy of donor electrons was evaluated for the Si nanostructures as the difference between the ionization energy for the single P-doped Si nanostructures and the electron affinity for the undoped Si nanostructures. This definition does not take into account the strong interaction of donor electron states and Si electron states explicitly at the conductive states and results in a monotonous increase in the binding energy by reducing the nanostructure's dimensions. In this paper, we introduce a new approach to evaluate the binding energy of donor electrons by combining the projected density of states (PDOS) analysis and three-dimensional analysis of associated electron wavefunctions. This enables us to clarify a gradual change of the spatial distribution of the 3D electron wavefunctions (3DWFs) from the donor electron ground state, which is fully localized around the P donor site to the first conductive state, which spreads over the outer Si nanorods contributing to current conduction. We found that the energy of the first conductive state is capped near the top of the atomistic effective potential at the donor site with respect to the surrounding Si atoms in nanorods smaller than about 27 a 0 . This results in the binding energy of approximately 1.5 eV, which is virtually independent on the nanorod's dimensions. This fact signifies a good tolerance of the binding energy, which governs the operating temperature of the single dopant-based transistors in practice. We also conducted the computationally heavy transmission calculations of the single P-doped Si nanorods connected to the source and drain electrodes. The calculated transmission spectra are discussed in comparison with the atomistic effective potential distributions and the PDOS-3DWFs method. V C 2014 AIP Publishing LLC. [http://dx.

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Random doping-induced fluctuations of subthreshold characteristics in MOSFET devices

Cited by 21 publications

References 22 publications

"Atomistic" Dopant Profiling Using Scanning Capacitance Microscopy

"Atomistic" Dopant Profiling Using Scanning Capacitance Microscopy

The Effect of Random Dopant Fluctuations on Logic Timing at Low Voltage

The impacts of electronic state hybridization on the binding energy of single phosphorus donor electrons in extremely downscaled silicon nanostructures

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