This letter presents a numerical investigation of the statistical distribution of the random telegraph noise (RTN) amplitude in nanoscale MOS devices, focusing on the change of its main features when moving from the subthreshold to the on-state conduction regime. Results show that while the distribution can be well approximated by an exponential behavior in subthreshold, large deviations from this behavior appear when moving toward the on-state regime, despite a low probability exponential tail at high RTN amplitudes being preserved. The average value of the distribution is shown to keep an inverse proportionality to channel area, while the slope of the high-amplitude exponential tail changes its dependence on device width, length, and doping when moving from subthreshold to on-state

Amoroso, S.M.

Asenov, A.

Compagnoni, C.M.

Gerrer, L.

Ghetti, A.

Lacaita, A.L.

Spinelli, A.S.

English

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       Amoroso, S.M., Compagnoni, C.M., Ghetti, A., Gerrer, L., Spinelli, A.S., Lacaita, A.L., and Asenov, A. (2013) Investigation of the RTN Distribution of nanoscale MOS devices from subthreshold to on-state. IEEE Electron Device Letters, 34 (5). pp. 683-685. ISSN 0741-3106   Copyright © 2013 IEEE  A copy can be downloaded for personal non-commercial research or study, without prior permission or charge   The content must not be changed in any way or reproduced in any format or medium without the formal permission of the copyright holder(s)   When referring to this work, full bibliographic details must be given      http://eprints.gla.ac.uk/85851/       Deposited on:  16 September 2013          Enlighten – Research publications by members of the University of Glasgow http://eprints.gla.ac.uk IEEE ELECTRON DEVICE LETTERS, VOL. 34, NO. 5, MAY 2013 683Investigation of the RTN Distribution of NanoscaleMOS Devices From Subthreshold to On-StateSalvatore M. Amoroso, Member, IEEE, Christian Monzio Compagnoni, Member, IEEE,Andrea Ghetti, Member, IEEE, Louis Gerrer, Alessandro S. Spinelli, Senior Member, IEEE,Andrea L. Lacaita, Fellow, IEEE, and Asen Asenov, Fellow, IEEEAbstract— This letter presents a numerical investigation ofthe statistical distribution of the random telegraph noise (RTN)amplitude in nanoscale MOS devices, focusing on the change of itsmain features when moving from the subthreshold to the on-stateconduction regime. Results show that while the distribution canbe well approximated by an exponential behavior in subthreshold,large deviations from this behavior appear when moving towardthe on-state regime, despite a low probability exponential tailat high RTN amplitudes being preserved. The average value ofthe distribution is shown to keep an inverse proportionality tochannel area, while the slope of the high-amplitude exponentialtail changes its dependence on device width, length, and dopingwhen moving from subthreshold to on-state.Index Terms— Flash memories, MOSFETs, random telegraphnoise, semiconductor-device modeling.I. INTRODUCTIONRANDOM telegraph noise (RTN) represents one ofthe most important reliability issues for modern deca-nanometer MOS technologies, attracting many research effortsdevoted to the understanding of its statistical features [1]–[5].In particular, the statistical distribution of the RTN amplitudehas been widely investigated [4], [6], [7], due to its importancein determining the RTN impact on the operation of digitaldevices, such as Flash memories and SRAM cells [8], [9].So far, results have shown an exponential behavior for thisstatistical distribution [2], [4], coming from a dominant con-tribution of percolative channel conduction on the threshold-voltage shift (VT ) obtained after electron capture/emissionin the RTN trap [4], [10]. However, these results have beenobtained extracting VT at low currents (subthreshold ornear threshold regime), and only few attempts have beenmade to investigate the VT distribution in the on-state [11].Moreover, the validity of the exponential behavior in deeply-Manuscript received January 7, 2013; accepted February 26, 2013. Dateof publication April 1, 2013; date of current version April 22, 2013. Thiswork was supported by the European Commission via the MORDREDProject 261868. The review of this letter was arranged by EditorM. Östling.S. M. Amoroso and L. Gerrer are with the University of Glasgow, GlasgowG12 8QQ, U.K. (e-mail: salvatore.amoroso@glasgow.ac.uk).C. Monzio Compagnoni, A. S. Spinelli, and A. L. Lacaita are with theDipartimento di Elettronica, Informazione e Bioingegneria, Politecnico diMilano, Milano 20133, Italy.A. Ghetti is with the R&D Technology Development, Micron TechnologyInc., Agrate Brianza 20041, Italy.A. Asenov is with the University of Glasgow, Glasgow G12 8QQ, U.K.,and also with Gold Standard Simulation Ltd., Glasgow G12 8LT, U.K.Color versions of one or more of the figures in this letter are availableonline at http://ieeexplore.ieee.org.Digital Object Identifier 10.1109/LED.2013.2250477scaled devices with channel dimensions of just a few tens ofnanometer has never been verified.In this letter, we show that the statistical distribution ofthe RTN amplitude deviates from a pure exponential whenmoving from the subthreshold to the on-state regime and whenseverely scaling device dimensions, preserving, however, anexponential tail at high VT . Results reveal that while theaverage value of the distribution (〈VT 〉) keeps an inverseproportionality to channel area both in subthreshold and in on-state conditions, the slope of the high-VT tail moves from aninverse proportionality to the square root of device width (W )and length (L) in subthreshold to an inverse proportionality toW and L in the on-state regime, also reducing its dependenceon substrate doping. This is interpreted in terms of a moreuniform conduction when moving from subthreshold to on-state, with a lower impact of atomistic doping on VT .II. SIMULATION METHODOLOGYWe performed 3-D numerical simulations of a Flash cellwith a tox = 8 nm tunnel oxide, a 70-nm polysilicon floatinggate, and a 4/3/5 nm oxide-nitride-oxide interpoly dielec-tric. Source and drain doping have a peak concentration of1020 cm−3 at the silicon surface and a Gaussian vertical profilewith a junction depth of 25 nm. Substrate is uniformly dopedwith a boron concentration equal to NA = 5 × 1017, 2 × 1018or 4 × 1018 cm−3. Three possible values of cell W and Lwere assumed, namely, 32, 64, and 128 nm, leading to ninecell geometries. Further details on the device can be foundin [12], where the cell is referred to as “rounded edges.”The statistical distribution of the RTN amplitude wascalculated by means of a Monte Carlo procedure [12],where a large number of cells having a different atomisticconfiguration of substrate doping and a different position of asingle RTN trap over the channel area were simulated. Fromeach simulation, VT was obtained as the change of thefloating-gate potential allowing the same current to flow in thecell for the empty (neutral) and the filled (negatively charged)RTN trap. A read current of 100 nA × W/L, 2 μA × W/L,and 8 μA × W/L was assumed for VT evaluation in thesubthreshold, near threshold and on-state regime, respectively,as shown in Fig. 1, where the drain current versus gatevoltage (ID − VFG) curves are shown for many atomisticallydifferent devices in the case of W = L = 32 nm andNA = 2 × 1018 cm−3. Simulations were carried out by meansof the drift-diffusion module of the gold standard simulations(GSS) atomistic simulator GARAND [13], activating density-0741-3106/$31.00 © 2013 IEEE684 IEEE ELECTRON DEVICE LETTERS, VOL. 34, NO. 5, MAY 20130 1 2 3 4 5VFG [V]10-1010-910-810-710-610-5Drain current [A]AtomisticContinuous1 2 3 4 5VFG [V]0123456789Drain current [μA]W=L=32nm100nA2μA8μA8μA2μAFig. 1. Simulated ID -VFG curve for many atomistically different deviceswith W = L = 32 nm and NA = 2 × 1018 cm−3. Dashed lines highlight theID values used for VT definition in the subthreshold, near threshold, andon-state regime. The curve corresponding to a continuous substrate doping isalso shown.gradient quantum corrections to correctly reproduce theelectrostatic effect of dopants and quantum confinement in thechannel. Note that, when referring to the on-state regime, thesesimulations underestimate the effect of localized point chargeson device current, due to the lack of a correct implementationof the impact of these charges on carrier transport [14], [15].As a consequence, these simulations underestimate variabilityin the drain current coming from atomistic doping [15] andthe reduction of this current following the filling of RTNtraps [16] in the on-state. This means that the on-state VThere reported are representative only of the electrostaticeffect of RTN traps, with the additional contribution given bymobility modulation around the traps neglected.III. SIMULATION RESULTSFig. 2(a) shows the simulated VT distributions atID = 100 nA in the case of W = L = 64 nm andW = L = 32 nm, with NA = 2 × 1018 cm−3. Both of the dis-tributions can be reasonably approximated with an exponentialtrend, in agreement with what reported in [2] and [4], witha slope λ (units: [mV/dec]) increasing with device scaling.Fig. 2(b) and (c) reveal, instead, that the distributions signifi-cantly deviate from a pure exponential behavior when increas-ing the read current to 2 μA (b) and 8 μA (c). In particular,moving to the on-state regime makes the distributions broaderat high probabilities with respect to subthreshold case, butnarrower at low probabilities, which are of more interest fortechnology reliability. This narrowing is the result of steeperdistribution tails in the graph, which, however, can still beapproximated with an exponential behavior with slope λ.In order to understand these results in more detail, Fig. 3shows that the simulated 〈VT 〉 increases as cell dimensionsare scaled keeping an inverse proportionality to the channelarea W × L, with small reductions when moving from theon-state to the subthreshold regime [17], [18]. Fig. 4 shows,instead, that the slope of the high-VT tail of the distributionsof Fig. 2 displays a different dependence on W and L in the(a) subthreshold, (b) near-threshold, and (c) on-state regimes;while λ is inversely proportional to√W × L in the firstcase [2], an inverse proportionality to W × √L appears in0 40 80 120ΔVT [mV]0 40 80 120ΔVT [mV]0 40 80 120ΔVT [mV]10-310-210-11001 - cumulative distribution64nm32nm8μA100nA 2μAλ(a) (b) (c)Fig. 2. Simulated VT distribution in the case of W = L = 64 nm andW = L = 32 nm (NA = 2 × 1018 cm−3) at (a) ID = 100 nA, (b) 2 μA,and (c) 8 μA.103 104WxL [nm2]100101102<ΔV T> [mV]100nA xW/L2μA xW/L8μA xW/LFig. 3. Simulated 〈VT 〉 as a function of channel area W × L atID = 100 nA, 2 μA, and 8 μA in the case of NA = 2 × 1018 cm−3.101 102√WxL [nm]100101102λ [mV/dec]102 103Wx√L [nm1.5]103 104WxL [nm2]Symbols: simul.Lines: fit.100nA xW/L 2μA xW/L 8μA xW/L(a) (b) (c)Fig. 4. Simulated λ at (a) ID = 100 nA, (b) 2 μA, and (c) 8 μA as afunction of different functions of W and L , for NA = 2 × 1018 cm−3.the second case [4] and to W × L in the third [7]. Thischange comes with a reduction of the absolute values of λand reflects a reduction of the impact of atomistic doping andpercolative channel conduction on VT when moving from thesubthreshold to the on-state regime [19]. From the differentdependences of 〈VT 〉 and λ on W and L appearing fromFigs. 3 and 4(a), we expect deviations from the exponentialbehavior even in subthreshold as cell scaling proceeds.Fig. 5 shows that the 〈VT 〉 and λ scaling trends arealso affected by a different dependence on NA ; while theAMOROSO et al.: INVESTIGATION OF THE RTN DISTRIBUTION OF NANOSCALE MOS DEVICES 68510-1 100 101NA [x1018cm-3]101102<ΔV T> [mV]100nA2μA8μA10-1 100 101NA [x1018cm-3]101102λ [mV/dec]100nA2μA8μAW=L=32nm W=L=32nm(a) (b)Fig. 5. Simulated (a) 〈VT 〉 and (b) λ at ID = 100 nA, 2 μA, and 8 μAas a function of NA , for W = L = 32 nm.former parameter has only a weak increase when increasingNA , the latter displays a much stronger growth, being nearlyproportional to N0.65A at 100 nA [2], to N0.5A at 2 μA [4], andto N0.2A at 8 μA. This lower dependence of λ on NA whenincreasing the read current represents a further proof of thelower impact of atomistic doping and percolative conductionon VT when moving from subthreshold to on-state.IV. CONCLUSIONA detailed numerical investigation of the statistical distrib-ution of the RTN amplitude of nanoscale MOS devices fromthe subthreshold to the on-state regime was presented. Resultsshowed that the VT distribution has significant deviationsfrom the purely exponential trend moving to the on-state,with device scaling giving the possibility of nonexponentialbehaviors even in subthreshold. The drain current dependenceof the VT distribution was interpreted in terms of a lowerimpact of channel percolation and atomistic doping on VTwhen moving toward the on-state, as highlighted also by aweaker dependence of λ on NA . The stronger λ dependence onW and L in on-state than in subthreshold should be consideredin all those devices exploiting the strong inversion condition,such as SRAM and NOR Flash memories.ACKNOWLEDGMENTThe authors would like to thank S. Markov,F. Adamu-Lema, and G. Roy from the University ofGlasgow, Glasgow, U.K., for helpful discussions, andA. Benvenuti, A. Mauri, and A. Marmiroli from MicronTechnology Inc., Agrate Brianza, Italy, for their support.REFERENCES[1] H. Kurata, K. Otsuga, A. Kotabe, S. Kajiyama, T. Osabe, Y. Sasago,S. Narumi, K. Tokami, S. Kamohara, and O. Tsuchiya, “The impact ofrandom telegraph signals on the scaling of multilevel Flash memories,”in Symp. VLSI Circuits Dig. Tech. Papers, 2006, pp. 140–141.[2] K. Fukuda, Y. Shimizu, K. Amemiya, M. Kamoshida, and C. Hu,“Random telegraph noise in Flash memories-model and technologyscaling,” in Proc. IEEE Int. Electron Devices Meeting, Dec. 2007,pp. 169–172.[3] C. Monzio Compagnoni, R. Gusmeroli, A. S. Spinelli, A. L. Lacaita,M. Bonanomi, and A. Visconti, “Statistical model for random telegraphnoise in Flash memories,” IEEE Trans. Electron Devices, vol. 55, no. 1,pp. 388–395, Jan. 2008.[4] A. Ghetti, C. Monzio Compagnoni, A. S. Spinelli, and A. Visconti,“Comprehensive analysis of random telegraph noise instability andits scaling in deca-nanometer Flash memories,” IEEE Trans. ElectronDevices, vol. 56, no. 8, pp. 1746–1752, Aug. 2009.[5] T. Nagumo, K. Takeuchi, T. Hase, and Y. Hayashi, “Statistical charac-terization of trap position, energy, amplitude and time constants by RTNmeasurement of multiple individual traps,” in Proc. IEEE Int. ElectronDevices Meeting, Dec. 2010, pp. 628–631.[6] A. Asenov, R. Balasubramaniam, A. R. Brown, and J. H. Davies,“RTS amplitudes in decananometer MOSFETs: 3-D simulation study,”IEEE Trans. Electron Devices, vol. 50, no. 3, pp. 839–845,Mar. 2003.[7] K. Takeuchi, T. Nagumo, S. Yokogawa, K. Imai, and Y. Hayashi,“Single-charge-based modeling of transistor characteristics fluctuationsbased on statistical measurement of RTN amplitude,” in Proc. Symp.VLSI Technol., Jun. 2009, pp. 54–55.[8] C. Monzio Compagnoni, M. Ghidotti, A. L. Lacaita, A. S. Spinelli,and A. Visconti, “Random telegraph noise effect on the programmedthreshold-voltage distribution of Flash memories,” IEEE Electron DeviceLett., vol. 30, no. 9, pp. 984–986, Sep. 2009.[9] K. Takeuchi, T. Nagumo, and T. Hase, “Comprehensive SRAM designmethodology for RTN reliability,” in Proc. Symp. VLSI Technol.,Jun. 2011, pp. 130–131.[10] L. K. J. Vandamme, D. Sodini, and Z. Gingl, “On the anomalousbehavior of the relative amplitude of RTS noise,” Solid-State Electron.,vol. 42, no. 6, pp. 901–905, Jun. 1998.[11] B. Kaczer, J. Franco, M. Toledano-Luque, P. J. Roussel, M. F. Bukhori,A. Asenov, B. Schwarz, M. Bina, T. Grasser, and G. Groeseneken,“The relevance of deeply-scaled FET threshold voltage shifts foroperation lifetimes,” in Proc. IEEE Int. Rel. Phys. Symp., Apr. 2012,pp. 5A.2.1–5A.2.6.[12] S. M. Amoroso, A. Ghetti, A. R. Brown, A. Mauri, C. MonzioCompagnoni, and A. Asenov, “Impact of cell shape on randomtelegraph noise in decananometer Flash memories,” IEEETrans. Electron Devices, vol. 59, no. 10, pp. 2774–2779,Oct. 2012.[13] [Online]. Available: http://www.goldstandardsimulations.com.[14] C. Alexander, A. R. Brown, J. R. Watling, and A. Asenov, “Impactof scattering in ‘atomistic’ device simulations,” Solid-State Electron.,vol. 49, no. 5, pp. 733–739, May 2005.[15] U. Kovac, C. Alexander, G. Roy, C. Riddet, B. Cheng, and A. Asenov,“Hierarchical simulation of statistical variability: From 3-D MC with‘ab initio’ ionized impurity scattering to statistical compact mod-els,” IEEE Trans. Electron Devices, vol. 57, no. 10, pp. 2418–2426,Oct. 2010.[16] C. L. Alexander, A. R. Brown, J. R. Watling, and A. Asenov, “Impactof single charge trapping nano-MOSFETs-electrostatics versus trans-port effects,” IEEE Trans. Nanotechnol., vol. 4, no. 3, pp. 339–344,May 2005.[17] G. Fiori, G. Iannaccone, G. Molas, and B. De Salvo, “Depen-dence of the programming window of silicon-on-insulator nanocrys-tal memories on channel width,” Appl. Phys. Lett., vol. 86, no. 11,pp. 113502-1–113502-3, Mar. 2005.[18] R. Gusmeroli, A. S. Spinelli, C. Monzio Compagnoni, and D. Ielmini,“Threshold-voltage statistics and conduction regimes in nanocrystalmemories,” IEEE Electron Device Lett., vol. 27, no. 5, pp. 409–411,May 2006.[19] H. Miki, N. Tega, M. Yamaoka, D. J. Frank, A. Bansal, M. Kobayashi,K. Cheng, C. P. D’Emic, Z. Ren, S. Wu, J.-B. Yau, Y. Zhu, M. A. Guil-lorn, D.-G. Park, W. Haensch, E. Leobandung, and K. Torii, “Statisticalmeasurement of random telegraph noise and its impact in scaled-downhigh-k/metal-gate MOSFETs,” in Proc. Int. Electron Devices Meeting,2012, pp. 450–453.

Investigation of the RTN Distribution of nanoscale MOS devices from subthreshold to on-state

Salvatore M. Amoroso

Christian Monzio Compagnoni

Andrea Ghetti

Louis Gerrer

Alessandro S. Spinelli

Andrea L. Lacaita

Asen Asenov

Crossref

IEEE Electron Device Letters

Investigation of the RTN Distribution of Nanoscale MOS Devices From Subthreshold to On-State

Enlighten: Publications

This letter presents a numerical investigation of the statistical distribution of the random telegraph noise (RTN) amplitude in nanoscale MOS devices, focusing on the change of its main features when moving from the subthreshold to the on-state conduction regime. Results show that while the distribution can be well approximated by an exponential behavior in subthreshold, large deviations from this behavior appear when moving toward the on-state regime, despite a low probability exponential tail at high RTN amplitudes being preserved. The average value of the distribution is shown to keep an inverse proportionality to channel area, while the slope of the high-amplitude exponential tail changes its dependence on device width, length, and doping when moving from subthreshold to on-stat

AMOROSO, SALVATORE MARIA

MONZIO COMPAGNONI, CHRISTIAN

SOTTOCORNOLA SPINELLI, ALESSANDRO

LACAITA, ANDREA LEONARDO

Archivio istituzionale della ricerca - Politecnico di Milano

Investigation of the RTN distribution of nanoscale MOS devices from subthreshold to on-state

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Investigation of the RTN Distribution of nanoscale MOS devices from subthreshold to on-state

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