Conductance noise in nano-patterned PbS quantum dot arrays Tamar S. Mentzel,∗ Nirat Ray,∗ Neal E. Staley, and Marc A. Kastner† Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, U.S.A. Darcy D. W. Grinolds and Moungi G. Bawendi Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, U.S.A. (Dated: January 9, 2015) We report unexpectedly large noise in the current from nanopatterned PbS quantum dot films. The noise is proportional to the current when the latter is varied by changing the source-drain bias, gate voltage or temperature. The spectral density of the noise is given by a power law in 5 frequencyatroomtemperature,butremarkably,weobserveatransitiontotelegraphnoiseatlower 1 temperatures. The probability distribution of the off-times follows a power law, reminiscent of 0 fluorescenceblinkingincolloidalquantumdotsystems. Ourresultsareunderstoodsimplyinterms 2 of conductance fluctuations in a quasi-one dimensional percolation path, and more rigorously in n termsofamodelinwhichchargethroughthefilmistransmittedindiscretetimeintervals,withthe a distribution of intervals completely described by Levy statistics. J 8 Quantum dots made in various ways have received ] greatattentionbecausetheirpropertiescanbecontrolled l 80 295 K l by their size. They are artificial atoms, for which the SiO a 2 120 23.2 V h charge and excitation energies are quantized and deter- A)60 80 p - mined by their dimensions. Transport measurements on Ti/Au nt ( 40 es individual dots have revealed Coulomb blockade [1, 2] urre40 0 20Time (4s0) 60 m and fascinating many-body phenomena including the C 20 . Kondo effect [3]. Colloidal quantum dots can be eas- (a) 500 nm (b) t ily made to self assemble into two and three dimensional a arrays, and their unique optical properties have already 0 5 10 15 20 m Source-drain bias, V (V) found application in displays and light-emitting diodes ds - d [4]. They are attractive for application in photovoltaics n and optoelectronics because they are low-cost and solu- FIG.1. (Coloronline)(a)Falsecolorscanningelectronmicro- o tion processable [5]. Additionally, their predicted un- graph of a device similar to those used for current measure- c conventional charge and spin transport properties hold mentsonbutylamine-cappedPbSdotfilms. Thenanopattern [ is 80 nm wide and 600 nm long (the black rectangle overlap- promise for quantum computation and spintronics [6]. ping the Ti/Au is the nanopattern). (b) Current as a func- 1 However, their electronic transport properties are still tion of the voltage between the Ti/Au electrodes (drain and v poorly controlled, compared to their optical properties. source) measured at room temperature. Inset shows the cur- 6 If one were able to control the tunneling rates between rent as a function of time for V = 23.2 V. Note that the 7 ds quantum dots in an array, one would have a system de- fluctuations of the current occur in the time domain and are 8 scribed by a tunable Hubbard model, just as the single- as large as approximately 30% of the current. 1 electron transistor is described by a tunable Anderson 0 . model that underlies the Kondo effect, thus providing 1 a platform for a deeper insight into correlated electron understand 1/f noise in the granular arrays that may 0 5 physics. impact device performance [12–15]. The second direc- 1 Until now, studies of charge transport in quantum dot tion is the study of fluorescence intermittency or blink- : arrays have revealed signatures of disorder, giving lim- ing in colloidal dots, where the dots alternate between v ited insight into the electronic properties intrinsic to the on (fluorescing) and off (non-fluorescing) states. More i X quantum dots [7–9]. A careful study of noise in a ma- recently, blinking behavior has been observed from indi- r terial can provide additional insights into its properties, vidualcore/shellPbS/CdSandInAs/CdSedots[16],sug- a and can even be used to characterize exotic states such gesting that the processes governing stochastic blinking aschargedensitywaves[10]andquasi-particlesinafrac- incolloidaldotsareuniversal,andinsensitivetoinherent tional quantum hall state [11]. Noise studies in colloidal material properties. However, to our knowledge, trans- quantum dot systems have been primarily focused in port signatures of blinking have never been observed. two directions. Because of the effort to integrate col- Inthisletter,wepresentmeasurementsofcurrentnoise loidal dots into devices, the first direction has been to in nanopatterned PbS colloidal quantum dot assemblies. We use nanolithography to make patterns estimated to be as small as 12 dots wide. We find very large and un- ∗ Thesetwoauthorscontributedequallytothiswork. expected noise in the current through them. The noise † [email protected] is proportional to the current, consistent with what is 2 expected from conductance rather than charge-density 0 V fluctuations, and it increases as the width of the sam- u.)1.2 13.6 V 22.1 V 23.2 V 295 K ple decreases. In some cases, particularly at lower tem- 60 (a.0.8 18.6 V 20.3 V pA)10 peratures, the noise is telegraph-like, switching suddenly X 1 ∆I ( btiemtweeleenadtiwngo tsotaatnes.ovTerhaellodffectaiymoefstbheecocmurerelnatr,gearndwiwthe ensity 0.4 1 1 10 findthatthecurrentcanberestoredbyheatingthesam- Int Ia v (pA) 0.0 pletoanelevatedtemperature. Alloftheseobservations 0 20 40 60 80 100 120 140 Current (pA) are consistent with a model, in which charge transport through the film occurs in discrete intervals through a FIG.2. (ColorOnline)Histogramofthecurrentmeasuredas quasi one dimensional percolation path. a function of time at 295 K for different values of the source We use PbS dots with a mean diameter of approxi- drainbias,asindicatedinthefigure. Thedashedlinesinthe mately 4.5 nm. The dots are synthesized air-free using a histograms are Gaussian fits. The current noise, ∆I, is given Schlenk line by high temperature pyrolysis of Pb and S bythefullwidthathalfmaximumfromthefits. Insetshows precursors in an oleic-acid/octadecene mixture [17, 18]. log-logplotofthecurrentnoise,∆I,asfunctionoftheaverage current, I , above the noise floor of our circuit. The current We process the growth solution to remove remaining av noise,∆I,islinearlyproportionaltotheaveragecurrent,I , products and, if desired, perform a solution exchange av as seen from the slope near unity on the log-log plot. The of the native oleic acid capping ligand for a smaller black dashed line is a fit to ∆I = 0.27 I . av molecule, n-butylamine. For electric current measure- ments we create a field-effect structure, using doped Si asthegateand100-300nmofSiO asthegateinsulator. 2 effective band width of 100 Hz. We histogram the cur- Thesourceanddrainelectrodesaremadeof7nm/50nm rent measured for relatively short timescales (60-600 s) Ti/Au, and patterned using electron beam lithography. at different values of source drain bias, as shown in Fig. We create the nanopatterned PbS films using a novel 2. For these short timescales, each histogram can be ap- technique based on electron beam lithography followed proximately described by a Gaussian distribution, and by a lift-off process as detailed in [19]. Nanopatterning we estimate the average fluctuation size, ∆I, from the allowsustominimizemacroscopicstructuraldefectssuch full-width at half maximum. The inset of Fig. 2 shows ascrackingandclustering,andenablesthemeasurement a plot of ∆I as a function of the average current, I , av of properties intrinsic to the colloidal dots. For some of above the limit given by our circuit noise. From the the our measurements the Ti/Au electrodes are much wider slopenearunityonthelog-logplot,wefindthatthecur- than the dot array, as shown in Fig. 1(a), but in other rentnoiseislinearlyproportionaltotheaveragecurrent, casestheyareasnarrowasthe80-200nmwidenanopat- consistent with what is expected for conductance rather tern. Sample processing occurs in the inert glovebox en- than charge-density fluctuations. vironment, and the dots are only briefly exposed to air Wehavealsostudiedthenoiseasafunctionoftemper- while wirebonding and loading the cryostat. The sample atureandgatevoltage, andfindthattheproportionality is thereafter always kept in high purity He or vacuum. holds irrespective of how the current is changed. This We perform two-point DC measurements to study the is illustrated in Fig. 3(a) for the temperature variation, noise and current voltage characteristics of the film, us- where we show that ∆I decreases with temperature in a ing a Femto low noise current amplifier and a NI-6110 way that is approximately proportional to I. high speed voltage card. This large excess noise has not been observed previ- A plot of current versus voltage is shown in Fig. 1(b) ously on large scale patterns because ∆I/I grows with forafilmofn-butylamine-cappeddotsthatis80nmwide decreasing pattern size. This is illustrated in Fig. 3(b) and 600 nm long. Because the dot diameter is 4.5 ± 0.2 whereweplot∆I/Iasafunctionofinversesamplewidth. nmandthespacingbetweendotsbecauseofthecaplayer Thewiderpatternsaremadeidenticallyandhaveathick- is∼0.6nm,assumingacubicpackingofthedots,wees- nessvariationof±20nmfromsampletosample. Despite timate that the film consists of layers that are about 15 thelargesample-to-samplevariation,illustratedforsam- dots wide and 120 dots long. From atomic force micro- ples of width approximately 80 nm, the general trend, scope (AFM) measurements of the nanopattern height, that the noise is smaller for wider samples, is clear. we estimate that the film is approximately 4 monolayers At room temperature, we find the power spectral den- thick. The current is below the noise limit of our ampli- sityofthenoiseatlowfrequencytobeoftheform1/fγ, fierforvoltageslessthan10V,butathighervoltageswe with γ = 1.4 ± 0.1. Figure 3(c) shows this dependence observe large fluctuations in the current. andalsohowtheamplitudeofthe1/fγ noisegrowswith To determine how the noise varies with current when increasing source-drain bias, while the exponent γ re- the voltage between the source and drain, V , is varied, mains almost unchanged. Our observation of large noise ds we fix the voltage and monitor the current as a function evenwhencracksandclustersareminimizedbynanopat- of time. The inset in Fig. 1(b) shows the observed fluc- terning, suggests an intrinsic origin of the noise. tuations as a function of time. For these time traces, Thegeneralfeaturesofthenoiseremainunchangedfor we sample the current every 0.01 s, corresponding to an PbSdotswithadifferentcappingmoleculeorligand. We 3 temperatures. This is shown in Fig. 4(c) where the av- pA) 10 ∆I aIv 10-22 295 K 22214208....1136 VVVV ed±reac0ga.ey1.ccuaFrnriegnbuterecfil4eta(drtlo)ysadheopcworeswaetsrheselawlwairt,ghte−sttiαm,oebw.sheTrehvreeedoαbcsu=errrve0en.d4t nt ( 13.6 V decay with an exponent α = 1.0 ± 0.2, measured in n- urre 1 -23 0.0 V butylamine-capped dots. The magnitude of the decay C 10 exponent varied from sample to sample, but has been (a) z) observedtosatisfy0<α<1,withintheerrorbarofthe 0.1 H 4 61000/8T (K - 11 )0 12 2S (A /i10-24 meTahsuerespmeecnttrsa.l density of the noise at higher tempera- tures is again of the form 1/fγ, with γ = 1.4 ± 0.1, as (b) 60 -25 shown in Fig. 4(e). At lower temperatures where we see 10 % ) discrete switching events with a power law distribution ∆I / I ( 40 -26 ofrfeqwuaeitnctyimweist,htahesinmoiilsaersepxepcotnruenmt,iassaolspopoasepdowtoeralawwhiitne 20 10 spectrum expected for poissonian processes [21]. 295 K The very large size of ∆I/I, its increase with decreas- 0 (c) 0 5 10 15 20 25 1 10 ing sample width and the observation of telegraph noise 1/width (µm - 1 ) Frequency (Hz) stronglysuggeststhatthecurrentinthefilmiscarriedby quasi-one-dimensional channels. The quantity ∆I/I ap- proaches 70% at a width of 40 nm, suggesting that this FIG.3. (ColorOnline)(a)Measurement(withadifferentbut isapproximatelythetypicalseparationofthesechannels identically prepared sample) of ∆I and I as functions of in- versetemperatureatV =15V.Thatthecurvesareroughly for the n-butylamine-capped dots, or about 10 times the ds parallelindicatesthat∆I/IisconstantasTisvaried.(b)Rel- diameter of the dots. Following the arguments of Am- ative current noise ∆I/I for nanopatterns of different width. begaokar, Halperin and Langer (AHL) [22], for variable Atawidthof80nm,weshowthesample-to-samplevariation. range hopping in disordered semiconductors, we should (c)Thepowerspectraldensityofthenoise,fordifferentvolt- not be surprised at this. The high resistance of the bar- ages,showingthatithasanapproximate1/fγ dependenceon riers between dots results in exponentially small tunnel- frequency, f, below 10 Hz, with γ equal to 1.4 ± 0.1. ing rates between them, and small variations of tunnel barrier heights and widths will therefore result in expo- nentially large variations in tunneling resistances. The perform noise measurements on 200-nm-wide nanopat- AHL recipe for calculating the overall resistance with ternsofoleic-acid-cappedPbSdots. Thoughthepatterns such an exponentially broad distribution of microscopic arewider,ifwetakeintoaccountthelengthofthenative resistancesistobeginwiththesmallestresistorsandput ligands,thenumberofdotsarecomparabletothe80-nm- insuccessivelylargeronesuntilapercolationpathiscre- widenanopatternsmadewithn-butylamine-cappeddots. ated across the sample. Such a path is necessarily quasi- Figure 4(a) shows traces of the current as a function of one-dimensional. Ifaresistorinthecriticalpathswitches time with a fixed applied voltage of 9 V at various tem- between two values of resistance and if there are only a peratures. We see clear telegraph noise with switching small number of parallel paths in the sample, telegraph ratesthatincreasewithincreasingtemperature. Therel- noise will be seen. ativeamplitudeofthetelegraphswitchesalsoincreasesas The power-law dependence of the off times in the tele- thecurrentisincreasedbygoingtohighertemperatures. graph noise is also known as Levy statistics. This be- We have observed telegraph switches in n-butylamine- havior has been observed in the blinking of the photo- capped dots as well, particularly at lower temperatures luminescence of individual quantum dots [23, 24], and is (< 100 K). They are, however, seen much more clearly typically understood by the existence of trap states that inthecurrentfromoleic-acid-cappeddots, andathigher facilitate non-radiative recombination [25, 26]. We as- temperatures. In most cases where switching noise has sume that trapping of charge also strongly modifies the been observed in the past, such as in the conductance of resistancealongthepercolationpath. Thiscouldhappen, mesoscopicMOSFETS[20],ahistogramoftheoff(lower forexample, ifthetrappedchargealtersatunnelbarrier current) times or the on (high current) times shows an along the path, and a power law dependence of the off exponential decay. However, as illustrated in Fig. 4(b), time could result from a distribution of trap depths. ahistogramoftheofftimesat200Kisapowerlawwith Thehypothesisthattrappingisthecauseoftheoverall an exponent of 1.6 ± 0.15. decay of the current is substantiated by raising the tem- Theexistenceofapowerlawdistributionofwaittimes perature after the average current is allowed to decay. also means that the more time passes, the more likely it We find that such annealing restores much of the lost is that the current is in the low state. As the rate of current. To quantify this effect, we measure the current- the current decay is scaled by the magnitude of the av- voltage characteristics of a 200-nm-wide n-butylamine- erage current, it is observed more prominently at higher capped PbS nanopattern at room temperature and sub- 4 capped with trioctylphosphine oxide [8]. The authors 2 295 K 100 200 K 0 considered the array to be made of a finite number of -2 conducting channels, and showed that both a decay of 2 230 K nts the average current in a single channel and 1/f noise can u A) 0 Co10 result from a power-law tail for the distribution of off- p ( -2 times (τ), given by: I(t)-Iav 02 200 K (b) A 1 p(τ)= ,0<µ<1. (1) -2 10 τ1+µ 2 180 K t (s) off 0 The decay of the average current is characterized by -2 (a) the exponent α, where α = 1 - µ and 0 < α < 1. Sub- 10 0 500 1000 1500 2000 sequently, it has been suspected that the behavior is not Time (s) 295 K generalizable, because the CdSe films are found [8] to 7.0 2A /Hz) 1 hmaivgehtbltohcekrienfgorceonbteacatscotontTaic/tAeuff,etcht.edFercoamyoofutrhmeceuarsruernet- ent (pA)6.0 100 S (pi0.1 200 K mtheendtse,caifyweexpaosnsuenmteαa=po0w.4er±la0w.1,deiscacyonosfisttheentcuwrirtehntµ, urr C ∼ 0.6 from the distribution of wait times. 10 (c) (d) (e) The results reported here suggest that the limitation 5.0 0.01 of the current by quasi-one-dimensional channels and 0 400 800 100 1000 0.01 0.1 Time (s) Time (s) Frequency (Hz) its noise and decay may be general features of colloidal quantum dots. Our results also suggest that charge is FIG. 4. (Color Online) (a) Current as a function of time in transmitted in discrete time intervals, described by Levy nanopatterned arrays of oleic-acid-capped PbS dots showing statistics. This insight into the mechanism of charge telegraph noise. (b) Histogram of the off times at 200 K transmission in a film of colloidal dots is an essential fit to a power law, P(toff)∝1/t1o+ffµ, with µ = 0.6 ± 0.15. steptowardaccessingthepredictedcomplexelectronand (c) Observed decay of the current immediately after setting spinbehaviorinquantumdotfilms. Furthermore,under- the voltage to 8 V at room temperature. The decay can be standing the electrical properties of the films unimpeded approximated by a power law, I = I t−α, with α = 0.4 ± o bystructuraldefectswillmakeitpossibletooptimizethe 0.1. (d) Log-log plot of the largest observed decay of the efficiency of nanocrystal-based devices and applications. current, measured in n-butylamine-capped PbS dots. Power We acknowledge useful discussions with Prof. Leonid law fit to the data gives α = 1.0 ± 0.2. (e) Spectral density S. Levitov. We are grateful to Mark Mondol and the of noise at room temperature and at 200 K where discrete telegraph events are seen showing a 1/fγ spectrum, where γ RLE SEBL facility for experimental help with electron- is comparable to 1+µ for the wait time distributions. beam lithography. This work was supported in part by the U. S. Army Research Laboratory and the U. S. Army Research Office through the Institute for Soldier sequentlyheatthesampleundervacuumto303K,while Nanotechnologies, under contract number W911NF-13- continuously monitoring the current. From the temper- D-0001(synthesisandnano-patterningofcolloidalquan- ature dependence of the current at lower temperatures, tum dots), by the Department of Energy under award weexpectthecurrenttoincreasebyafewpercentasthe numberDE-FG02-08ER46515(transportandnoisemea- temperature is raised to 303 K; instead we observe that surement on colloidal quantum dots, including device the current almost doubles with heating. 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