random telegraph signal noise simulation of decanano mosfets subject to atomic scale structure...

Superlattices and Microstructures 34 (2003) 293–300

www.elsevier.com/locate/superlattices

Random telegraph signal noise simulation ofdecanano MOSFETs subject to atomic scale

structure variation

Angelica Lee, Andrew R. Brown, Asen Asenov, Scott Roy∗Device Modelling Group, Department of Electronics and Electrical Engineering, University of Glasgow,

Glasgow G12 8LT, UK

Available online 16 April 2004

Abstract

As MOSFETs shrink into the decanano regime it is predicted that random telegraph signals(RTS), resulting from trapping events in defect states near the Si/SiO2 interface, will significantlyaffect analogue and digital circuit performance. At these same scales, intrinsic parameter fluctuationsintroduced by atomic differences between devices will also be significant. In this work, amethodology based on 3D simulation is developed which can correctly model RTS noise in thetime and frequency domain in the presence of randomdiscrete dopants. The approach is illustratedwith results obtained for 30× 30 nm devices. We find that atomicity can significantly increase RTSmagnitude in devices with particular doping configurations, and ensemble average RTS effects varymarkedly from those predicted on an assumption of continuous doping.© 2004 Elsevier Ltd. All rights reserved.

Keywords: MOSFET; Atomistic; Random telegraph signals; Noise; Simulation

1. Introduction

The low frequency noise performance of silicon MOSFETs continues to be a subjectof interest to both academia and industry. As the channel length of mass produced devicescontinues to shrink into the decanano regime, it becomes a significant factor in analoguecircuit performance [1], dynamic random access memory operation [2], and will eventuallyimpact critically upon the reliability of digital logic. Random telegraph signals (RTS)of Lorentzian power spectrum, resulting from the capture and emission of charge from

∗ Corresponding author. Tel.: +44-141-330-5250; fax: +44-141-330-4907.E-mail address: [email protected] (S. Roy).

0749-6036/$ - see front matter © 2004 Elsevier Ltd. All rights reserved.doi:10.1016/j.spmi.2004.03.027

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294 A. Lee et al. / Superlattices and Microstructures 34 (2003) 293–300

Fig. 1. Dependence of relative RTS amplitudeon drain current (at low drain voltage,VD = 10 mV) for a set ofsquare MOSFETs of differing size. Trap is placed for maximum RTS amplitude in continuously doped device.

defect states near the Si/SiO2 interface and an associated modulation in carrier densityand mobility, dominate the low frequencynoise performance of small MOSFETs aroundand below threshold [3]. RTS with amplitudes larger than 60% have been reported fordevices at room temperature [4]. There have been a number of recently proposed modelsdescribing the nature of RTS events and 1/ f noise—which can usefully be described as asuperposition of Lorentzian spectra in MOSFETs [4–6].

Another category of effects which are of critical concern as device dimensions shrink,are those arising from the granularity of charge and matter. Among them, thresholdvoltage and current fluctuations between nominally identical devices due to random dopantconfigurations [7] have been much studied recently. Of particular interest to this work arethe consequences of such atomistic effects on the RTS noise in a single decanano device,or ensembles of decanano devices. We considerhow the magnitude and timing parametersof RTS drain current noise are altered when random discrete dopants are taken into accountin 3D MOSFET simulations instead of assuming continuous doping. An extension to thesimulator whichcan model RTS noise in the time domain has also been developed.

2. Simulation of RTS amplitude

Our approach, described in detail in [5], uses a 3D drift-diffusion simulator which ap-propriately accounts for the electrostatic effects associated with random discrete dopants,and is well suited to describe RTS in the sub-threshold regime.Fig. 1 illustrates RTS am-plitudes obtained from this simulator for a set of devices with dimensions from 100× 100nm down to 30× 30 nm, assuming continuous doping and a single electron trapped in thecentre of the channel at the Si/SiO2 interface where it will havethe maximal effect. As can

A. Lee et al. / Superlattices and Microstructures 34 (2003) 293–300 295

Fig. 2. Potential barrier between source and drain in a 30× 30 nm MOSFET showing the effect of a singleunscreened trapped charge at the interface.

be seen, the nominal drain current drops by 5%–40% on activation of the trap in the sub-threshold regime depending on device size, although the magnitude of the RTS signal be-comes much reduced at higher gate voltages for both ‘long’ and ‘short’ channel devices dueto screening. Note that all these results are taken at low drain voltage (VD = 10 mV) to re-main within the regime of applicability of the drift-diffusion model.Fig. 2plots the poten-tial across one of these devices, clearly showing thepotential barrier of the channel in sub-threshold, and indicating how that barrier is augmented by trap activation. The mesh size ischosen to resolve well the long range part of the Coulomb potential which determines themobile charge exclusion region in sub-threshold. FromFig. 2it is qualitatively obvious thatif the trap is found nearer to the source or drain junction its effect on sub-threshold currentwill be markedly reduced, eitherbecause in the source/drain depletion regions the trap is nolonger at the peak of the potential barrier, or because further into the source/drain regions itis heavily screened. In addition, a trap found offset from the centre of the channel width willleave the opposite region of the channel augmented by a lower Coulomb field, amelioratingthe overall channel RTS current reduction. These results are shown quantitatively inFig. 3,which maps the fractional RTS magnitude as a function of trap position in the channel.

An advantage ofour 3D approach is that RTS amplitudes can be obtained in the presenceof the fluctuating channel potentials found in realistic MOSFETs subject to discrete randomdopants.Fig. 4 shows threedifferent discrete profiles (ordered by increasing thresholdvoltage from left to right) for 30× 30 nm devices, and the positional dependence of RTSamplitude in each configuration. In the middle plot, most of the dopants within 3 nm of theSi/SiO2 interface are found to be to the ‘north’ side of the channel, raising the potentialin this area. For any given gate voltage, current will flow most easily from source to drainalong the lower potential ‘southern’ region of the channel. Trap activation in this regionwill have greatest effect on the overall current flow. In the left hand plot most dopants


Fig. 3. Positional dependence of the magnitude of RTS fluctuations in the drain current of a 30×30 nm MOSFETwith an assumed continuous spread of doping, as a function of trap position in the channel region.

Fig. 4. Positional dependence of the magnitude of RTS fluctuations in drain current caused by a single trap/de-trapevent inone of three 30× 30 nm MOSFETs subject to discrete randomdopants in the channel region. Dopantposition saturation indicates whether they fall within the 1st, 2nd or 3rd nm from the Si/SiO2 interface.

are again found to the ‘north’ of the channel, with one additional dopant in the ‘south’producing a narrow percolation path. Trap activation in this path gives RTS amplitudes ofup to 70%. In the right hand plot, in addition to ahigher dopant density near the Si/SiO2interface raisingVT , the dopants are more uniformly distributed across the width of thechannel, and the positional dependence of the RTS fluctuations more closely approachesthat of a continuously doped device.

Fig. 5 shows the mean positional dependence of RTS amplitude for an ensemble of100 atomistic devices. Although a particular atomistic device may exhibit RTS amplitudesover 70%, approaching twice that of devices with a continuous dopant spread, the ensembleaverage has approximately the same peak value as that of an ostensibly continuous device.


Fig. 5. Average positional dependence of the magnitudeof RTS fluctuations in the drain current of an ensembleof 30×30 nm MOSFETs subject to discrete random dopants, asa function of trap position in the channel region.

However the formation of percolation paths in the presence of atomicity means that trapactivation atany point along the width of the channel may produce strong fractional RTSamplitudes, a distinct feature resulting from the consideration of more realistic devices.

3. Time domain simulation

Having calculated the distribution of the RTS amplitudes, the simulator may beextended to obtain time domain results (and hence power spectral densities of noise inultra-small MOSFETsin the sub-threshold regime) once statistics of trap capture andemission times,τc, τe, areknown. Both are thermally activated processes, and soτc, forexample is given by [8],

τc = exp(�Ec/kBT )

nνσo

where�Ec is the activation energy,n the inversion layer charge density, and for lowVD, νandT are the average thermal electron velocity and the lattice temperature.�Ec is a func-tion of the Si conduction band energy at the interface, and the trap energy, and will varywith VG and the depth of the trap in the oxide layer (we assume a random depth distribu-tion). Sample data for capture and emission times in this work are obtained [8], with spe-cific τc andτe requiring recalculation for each atomistic configuration and bias conditions.

The methodology is overviewed inFig. 6. Thetop graph shows the probability of a givenRTS amplitude in an ensemble of 30×30 nm MOSFETs. The right hand cartoon indicatesthe introduction of specific trap/de-trap timing by Monte Carlo. The lower graph inFig. 6is partof a typical simulation combining both amplitude and timing. It is a small segment


Fig. 6. Methodology overview for extracting time domain results from ‘atomistic’ device simulations (where RTSamplitudes may be obtained as a function of trap position—top right graph from [5]) and trap/de-trap statistics(as a function of trap energy level, andelectron density).

takenfrom one member of the ensemble near threshold at low drain voltage,VG = 0.5 V,VD = 0.01 V, and clearly indicates the effect of twoactive traps in the device. From the fulltrace—in this case over a simulation time period of>400 s—the power spectral density ofFig. 7 is obtained. (The black trace calculates thepower spectral density down to 0.01 Hz,the central trace re-samplesthe time domain data in the frequency range of interest tobetter characterize the noise.) As expected, the noise shows typical 1/ f behaviour, with acharacteristic frequency,

fc = 1

τc+ 1

τe

around 20 Hz, agreeing with simulation capture and emission times of approximately100 ms in this case. It should be noted [3], that although the power spectral density usefullycharacterizes aspects of the data, time domain traces are always retained, both for furthersimulation in circuit models, butalso because, for instance, the power spectral density of asingle trap is proportional to,

PSD∝ β

1 + β2

fc

f 2c + f 2 whereβ = τc

τe

so it is impossible to confirm, solely from the power spectral density, theτc/τe ratio.


Fig. 7. Power spectral density obtained from time domain simulation of 30×30 nm MOSFET in the subthresholdregime (VD = 10 mV, VG = 500 mV) containing two active traps with corner frequencies of approximately20 Hz and 100 Hz.

4. Conclusions

Wehave developed a methodology and corresponding simulation tools which can modelboth the magnitude and timing of RTS noise indecanano MOSFETs subject to atomic scalevariations in dopant positions. The approach has been illustrated simulating the noise in a30 × 30 nm devices. We have shown that the source/drain percolation paths associatedwith random discrete dopants in real MOSFETshave a strong effect on the positionaldependence of the magnitude of RTS fluctuations indevice drain current.

Acknowledgements

This work was carried out under an Engineering and Physical Sciences ResearchCouncil grant GR/R47325.

References

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random telegraph signal noise simulation of decanano mosfets subject to atomic scale structure...

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