Random telegraph signals and 1/f noise in a silicon quantum dotM. G. Peters, J. I. Dijkhuis, and L. W. Molenkamp Citation: Journal of Applied Physics 86, 1523 (1999); doi: 10.1063/1.370924 View online: http://dx.doi.org/10.1063/1.370924 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/86/3?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Random telegraph signal and 1/f noise in forward-biased single-walled carbon nanotube film-silicon Schottkyjunctions Appl. Phys. Lett. 100, 213102 (2012); 10.1063/1.4719094 Random telegraph signal noise in gate-all-around silicon nanowire transistors featuring Coulomb-blockadecharacteristics Appl. Phys. Lett. 94, 083503 (2009); 10.1063/1.3089240 Fabrication and integration possibilities of ultrasmall quantum dots in silicon-on-insulator material J. Appl. Phys. 90, 942 (2001); 10.1063/1.1379352 GRT model for random telegraph signals in MOSFETS AIP Conf. Proc. 466, 96 (1999); 10.1063/1.58294 Spectroscopy of a silicon quantum dot Appl. Phys. Lett. 74, 1576 (1999); 10.1063/1.123621

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Random telegraph signals and 1/ f noise in a silicon quantum dotM. G. Peters and J. I. Dijkhuisa)

Faculty of Physics and Astronomy, and Debye Institute, University of Utrecht, P.O. Box 80.000,3508 TA Utrecht, The Netherlands

L. W. Molenkamp2. Physikalisches Institut, RWTH-Aachen, D-52056 Aachen, Germany

~Received 19 April 1999; accepted for publication 27 April 1999!

We investigated random telegraph signals and 1/f noise in a submicron metal–oxide–semiconductor field-effect transistor at low temperatures in the Coulomb-blockade regime. The richnoise characteristics were studied as a function of gate voltage, drain current, and temperature, bothin and beyond the Ohmic regime. The results can be understood within a simple model assuming auniform potential fluctuation of constant magnitude at the location of the dot. Clear signatures ofelectron heating are found from the noise at higher currents. ©1999 American Institute of Physics.@S0021-8979~99!06215-5#

I. INTRODUCTION

Coulomb oscillations observed in the conductance of aquantum-dot system originate from the discreteness of elec-trical charge and the spatial confinement of particles. Al-ready in an early stage, it was recognized that such a systemcan be employed as an ultrasensitive electrometer, able todetect charge variations well below that of a single electron.1

By the same token, the quantum dot is inherently sensitive tofields induced by background charges from defects and im-purities. Since not all charges are stationary, the conductanceis expected to fluctuate in time, producing noise. In submi-cron semiconductor devices, it is often observed that the re-sistance fluctuates randomly between two discrete levels.These so-called random telegraph signals~RTSs! haveyielded detailed information on the transport properties ofdevices made of silicon2,3 and III–V materials.4,5 Further-more, since a RTS generally represents the action of onesingle fluctuator, it can serve as a basis for generally under-standing and controlling other types of noise where severalfluctuators are acting simultaneously4,5 ~e.g., 1/f noise!. De-spite the fact that single electron tunneling has received awide interest, noise phenomena have proven difficult toinvestigate1,6,7at the ultralow temperatures and voltages gen-erally required in order to find the devices in the Coulomb-blockade regime. In this article, we present and discuss therich phenomena that accompany the effects of RTS and 1/fnoise on the Coulomb oscillations in submicron metal–oxide–semiconductor field-effect transistors~MOSFETs!.We make the noise properties in this regime accessible toexperiments over a wide range of currents and temperaturesby choosing a device that possesses a quite small quantumdot ~radius;35 nm! with a typical charging energy of sev-eral milli-electron volts. In our experiment, we observed aclear oscillatory behavior of the noise intensity with a two-times shorter period than the Coulomb oscillations for lowcurrents and a strong suppression for high currents. All ob-

servations are accounted for by a simple model based on afluctuating potential at the quantum dot. Beyond the Ohmicregime, our analysis clearly shows that electron heating playsa prominent role.

II. DEVICE

All measurements reported here are performed on a nar-row silicon-on-insulator MOSFET with a lengthL50.2mmand widthW50.1mm. In contrast to conventional devices,the 100-nm-thick silicon channel is surrounded on threesides by a poly-silicon gate.8 At liquid helium temperaturesand around threshold, a series of roughly equidistant conduc-tance peaks is observed when varying the gate voltageVG .These Coulomb oscillations mark the presence of a quantumdot in the random potential landscape in the silicon channel.8

III. TELEGRAPH SIGNALS

In the experiments, a constant current was driventhrough the device and the drain voltage was measured usinga low-noise amplifier~LI-75A! and a digital voltage meteror, in the frequency domain, an Advantest spectrum ana-lyzer. At liquid helium temperatures and specific gate volt-ages, the voltage on the drain is found to fluctuate randomlybetween two discrete levels~Fig. 1, upper panel!, pointing tothe action of one single fluctuator. However, occasionallyadditional discrete levels were encountered, evidence forseveral fluctuators acting simultaneously. Although in thesecases the contributions were generally found to be indepen-dent, in a few cases a clear interaction between the fluctua-tors was observed~Fig. 1, lower panel!.

A. Gate-voltage dependence

In order to study the RTS amplitude,VG was slowlyscanned, while keeping the bias current constant. The drainvoltageVD was monitored with a high time resolution. It isclearly seen from Fig. 2~a! that VD switches randomly be-tween two or more conductance curves. All these curves ex-hibit the same Coulomb oscillations, but are shifted along thea!Electronic mail: j.i.dijkhuis@phys.uu.nl

JOURNAL OF APPLIED PHYSICS VOLUME 86, NUMBER 3 1 AUGUST 1999

15230021-8979/99/86(3)/1523/4/$15.00 © 1999 American Institute of Physics

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horizontal axis. The amplitude of the telegraph signals, i.e.,the difference between the curves in Fig. 2~a!, is depicted inFig. 2~b!. Sharp minima are observed coinciding with thecrossings of the Coulomb curves. At these positions, the de-vice is apparently insensitive to the fluctuating environment.Maxima in the RTS amplitude are reached in between twocrossings. Hence, the amplitude of the RTS varies with aperiod half that of the Coulomb-blockade oscillations.

From Fig. 2~a! we observe that the most prominent ef-fect of the fluctuator is to produce a shift of the conductancecurves along the horizontal axis. Since the potential of ourquantum dotf is directly proportional to the voltage on thegate, we conclude that the fluctuating entity affects the po-tential of the dot and as a result the conductanceG. If weassume that the potential at the position of the dot fluctuatesuniformly, the geometry of the quantum dot can be takenconstant and the potential shiftDf acts as an effectivechangeDVG

eff in VG . In that picture,VD switches randomlybetween two identical, but shifted Coulomb-blockade curves.

For most RTSs the horizontal shift appears to be smallcompared with the oscillation period. Therefore, we can ap-proximate the conductance fluctuation to first order, usingthe direct proportionality betweenf and VG : DG

'(]G/]f)Df5(]G/]VG)DVGeff . This approach is similar to an

earlier analysis of our group for RTS in quantum pointcontacts.4,5 These equations by their nature produce a van-ishing RTS amplitude exactly at the conductance peaks andvalleys, where]G/]VG vanishes. Indeed, the experimentallyobserved minima in the amplitude coincide with theCoulomb-curve crossings that are located close to the peaksand valleys. We will see later that our simple picture pro-vides a way to further analyze and understand the RTS as itdepends on current and temperature, where the characteris-tics of the RTS do not appear so evident as in Fig. 2.

B. Current dependence

The upper panel of Fig. 3 shows the time-resolvedcurrent–voltage (I –V) characteristics of the quantum dot.For a constant gate voltage, the current is slowly increasedwhile the fluctuating drain voltage is monitored with a hightime resolution. The voltage on the drain is apparently fluc-tuating randomly between two discrete values. In fact, twodifferent I –V curves can be distinguished. To show this tobetter advantage, the switching amplitude is plotted in themiddle panel of Fig. 3. At low currents, alinear increase inamplitude is observed, implying that the fluctuations of thedrain voltage are the result of a fluctuating resistance: Thecurrent only serves to probe the resistance fluctuations, butdoes not affect them. For higher currents, however, theswitching amplitude is observed to saturate, reach a maxi-mum, and finally drops to zero. Around 50 nA, before theRTS amplitude reaches the zero value, the RTS becomesquite faint. Studies of the dynamics of the RTS indicate thatat these currents the switching rates increase rapidly and be-come too fast to be tracked by our setup. This behavior co-

FIG. 1. Two RTS traces atT54.0 K, with the bars indicating 0.5 s in bothpanels. The upper panel shows a simple RTS, where the resistance switchesbetween two discrete levels. In the lower panel, we are dealing with twointeracting telegraph signals. It is clearly seen that the rapid switching isturned on and off.

FIG. 2. Drain voltage and switching amplitude vs gate voltage atT54.2 K andI D56 nA. Minima in the switching amplitude coincide with thecrossings of the Coulomb curves.

FIG. 3. Drain voltage, switching amplitude, and]VD /]VG vs current atT51.9 K andVG51.274 V. ~a! The drain voltage switches randomly betweentwo I –V curves.~b! The RTS amplitude which is the distance between theI –V curves, increases linearly at low biasing. At higher currents, the am-plitude saturates and falls back to zero, evidence of current heating.~c!Equivalent behavior is observed for the factor]VD /]VG .

1524 J. Appl. Phys., Vol. 86, No. 3, 1 August 1999 Peters, Dijkhuis, and Molenkamp

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incides with the nonlinearities apparent in theI –V curves inthe upper panel and reflects the rich physics of transportthrough our quantum dot at high biasing, that we now wishto elucidate.

At this point, we carry the analysis to the regime of highcurrent biasing, where the relation between drain voltage andthe differential conductance is not immediately obviousand we rewrite the RTS in terms ofVD , DVD

'(]VD /]VG)DVGeff . When the properties of our quantum

dot are all known to sufficient precision, the factor]VD /]VG

can, of course, in principle be computed from standard trans-port theories, but only in the linear response. Since we willnot limit ourselves to low-bias conditions and do not knowall the details of the dot, we choose an empirical approach.We determine the response of the quantum dot to a fluctuat-ing signal by adding a small voltage modulation~41 Hz! tothe gate contact and measuring the resulting drain voltagemodulation at the same frequency. The applied voltagemodulation takes over the role of the potential fluctuationcaused by the microscopic entity and we directly measure thederivative]VD /]VG .

In the lower panel of Fig. 3, the resultingu]VD /]VGu isplotted versus current forVG51.274 andT51.9 K. It exhib-its exactly the same characteristics as the amplitude of thetelegraph signal, but can be measured at currents where theRTS becomes too fast to observe. At around 70 nA thisquantity becomes zero and rises again, which corresponds toa sign reversal of]VD /]VG . This behavior of the RTS am-plitude versusVD can be traced back to current heating in thequantum-dot system. In conventional conductance measure-ments we have found namely, that the Coulomb peaksbroaden for currents higher than approximately 20 nA. Theconductance at the peaks decreases while the conductance atthe valleys increases with current. This is exactly the samebehavior that we have found for the temperature dependenceat low currents. Since the Coulomb-blockade oscillationsversusVG flatten and vanish, the RTS amplitude decreasesstrongly for currents higher than 40 nA. We note that thesign reversal observed foru]VD /]VGu in Fig. 3~c! can befound in the RTS amplitude, for some fluctuators that can bemonitored over a larger current span. A vanishing RTS am-plitude and a striking insensitivity of the quantum dot forpotential fluctuations, are thus not only observed at the cross-ings in the gate–voltage dependence but also in the currentdependence. At these specific bias conditions, the drain volt-age is constant in time despite the fact that the quantum dotis exposed to a fluctuating potential.

C. Temperature dependence

Next, we examine the temperature dependence of theRTS amplitude. For a range of temperatures, the RTS ampli-tude and]VD /]VG versusT were measured at a fixed gatevoltage and low constant current. The results of Fig. 4, againshow that the RTS amplitude is linearly proportional to]VD /]VG between 1.8 and 10 K and that both quantitiesdecrease monotonously for increasing temperature. As in

case of current heating described earlier, this decrease is theresult of a broadening of the conductance peaks, but now dueto purely thermal equilibrium effects.

Apparently, all phenomena concerning the amplitude ofthe RTS in our quantum dot versus gate voltage, current, andtemperature can be traced back to a microscopic fluctuatorproducing a single, fixed potential fluctuationDf at the lo-cation of the quantum dot. Generally,Df depends on thenature of the fluctuator, the distance to the dot, and the ef-fectiveness of electronic screening. Using the conversion fac-tor a determined previously from the electrical properties ofour dot,8 Df can be computed fromDVG

eff . For the shift ofFig. 2, we findDf50.7 mV which corresponds with an in-duced polarization chargeDq on the dot of 0.17 e. OtherRTSs in the same device produce values forDf rangingfrom 0.19 to 0.8 mV. These numbers are comparable to thosereported in III–V devices.9,10We stress that the magnitude ofthe potential shift as determined from our type of noise ex-periments can provide fundamental insight on the nature ofelectronic screening in mesoscopic disordered systems.

IV. 1/f NOISE

So far, we have focused on RTSs which can be easilyidentified in the time domain because the resistance is fluc-tuating between discrete values. At this point we broaden ourscope and focus on less evident types of noise that must bestudied in the frequency domain. The RTSs discussed untilnow, are found exclusively in specific gate–voltage rangesand obviously result in a noise spectral densitySVD

with aclear Lorentzian line shape. At other gate voltages however,SVD

is substantially weaker and generally intermediate be-tween a Lorentzian and pure 1/f noise.

A. Current Dependence

To elucidate the origin of the weaker noise sources, westudied the current dependence~not shown!. In the Ohmicregime, no change in the shape of the spectrum is observed,indicating that the dynamical properties are independent ofcurrent. Further,SVD

increases quadratically withI D and inthis regime therefore quadratically withVD . This is clearevidence that we are dealing with resistance noise. For

FIG. 4. Temperature dependence of the switching amplitude and the factor]VD /]VG , at VG51.245 V andI D50.9 nA.

1525J. Appl. Phys., Vol. 86, No. 3, 1 August 1999 Peters, Dijkhuis, and Molenkamp

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higher currents, however, beyond the Ohmic regime,SVDis

found to collapse while at same time the characteristic fre-quencies shift to higher values. This typical behavior exhibitsstrong analogies with Fig. 3~b!, where a strong decline inRTS amplitude is accompanied with an enhanced switchingrate.

B. Gate–voltage dependence

Our analysis can be elaborated further by examining thegate–voltage dependence. Figure 5 displaysVD versusVG

~upper panel! and the noise versusVG ~lower panel! for asmall constant current. We have plottedSVD

f /VD2 because

SVDis generally close to 1/f and increases quadratically with

VD . The period of the variation of the noise in Fig. 5~b! isagain half that of the Coulomb oscillations in Fig. 5~a!, ex-actly what we observed for the RTS amplitude in case of asingle fluctuator@Fig. 2~b!#. Furthermore, our observationsclearly show that the shape of the spectrum, and hence, thedynamical properties depend on gate voltage: atVG

'1.24 V, for example, the data forf 510 Hz and f5100 Hz coincide and a purely 1/f spectrum is observed~not shown!, while aroundVG51.26 V, the two data setsdiffer considerably and a Lorentzian contribution to the spec-trum is found~not shown!. The prime feature of Fig. 5~b!,however, is the explicit oscillation in the noise intensity ver-sus VG over almost two orders of magnitude and a strongsuppression of the noise at the conductance peaks and val-leys. We now demonstrate that the low-frequency noise inthe quantum-dot system is consistent with a uniformly fluc-tuating potential created by a fixed distribution of fluctuators:SVD

can be written in terms of a fluctuating effective gatevoltage: SVD

5(]VD /]VG)2SVG, where SVG

denotes thespectral density of fluctuations in the effective gate voltage.In Fig. 5~b! the relative noise intensitySVD

f /VD2 is found to

virtually coincide with the factor (1/VD)2(]VD /]VG)2 as de-termined from the time-averaged characteristics@Fig. 5~a!#.Any deviations originate from the fact that we did not incor-porate the gate–voltage dependence of the shape of the noisespectrum. Our findings demonstrate that a simple modelbased on thetime-averagedtransport properties can repro-duce the overall behavior of the relative noise intensity atlow currents if one treats the low-frequency noise as theresult of a complex superposition of an ensemble of fluctua-tors.

V. CONCLUSIONS

In conclusion, we have studied low-frequency noise in adisordered quantum-dot system. We observe RTS and 1/fnoise depending on the gate voltage used. A clear oscillatorybehavior is found for both types of noise versusVG . TheRTS amplitude is strongly suppressed for high currentspointing to heating of the electrons. All results can be ac-counted for by a simple model, based on a temporal fluctua-tion of the local potential. For the RTS this potential fluctua-tion is produced by one single fluctuator and ranges from0.19 to 0.8 mV. The potential fluctuations are roughly con-stant over the range of parameters, while the dependences ofthe low-frequency noise on gate voltage, current, and tem-perature are exclusively determined by the time-averagedproperties of the dot. Our work shows that a detailed analysisof the RTS amplitude and dynamics is feasible in siliconquantum dot systems. This will prove to be important to shednew light on screening and electronic heating effects in nar-row silicon channels.

ACKNOWLEDGMENTS

The authors would like to thank F. Wollenberg and P.Jurrius for technical assistance. The SIMOX MOSFET de-vices were fabricated by O. J. A. Buyk at Philips ResearchLaboratories~Eindhoven!. This work is partly supported bythe Dutch foundation ‘‘Stichting voor Fundamenteel Onder-zoek der Materie’’~FOM! and the foundation for Dutch Sci-entific Research~NWO!.

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FIG. 5. Gate–voltage dependence of~a! the drain voltage and~b! the rela-tive noise intensityf SVD

/VD2 at T51.9 K andI D56 nA. The solid line in

the lower panel displays the factor (1/VD)2(]VD /]VG)2 ~times a prefactor!.

1526 J. Appl. Phys., Vol. 86, No. 3, 1 August 1999 Peters, Dijkhuis, and Molenkamp

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