Contains research goals and objectives, reports on six research projects and a list of publications.Joint Services Electronics Program Contract DAAL03-92-C-0001Joint Services Electronics Program Grant DAAH04-95-1-0038National Science Foundation Grant ECS 92-0342

Abusch-Magder, David

Goldhaber-Gordon, David J.

Kastner, Marc A.

Klein, Olivier

Lyszczarz, Theodore M.

Mankiewich, Paul M.

Morgan, Nicole Y.

Shaver, David C.

Wind, Shalom

Contains goals, objectives, summary of recent work, fabrication and results of one research project.Joint Services Electronics Program Grant DAAH04-95-1-0038National Science Foundation Grant ECS 92-03427U.S. Army Research Office Grant DAAH04-94-G-011

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Chapter 2. Artificial AtomsChapter 2. Artificial AtomsAcademic and Research StaffProfessor Marc A. Kastner, Dr. Olivier KleinVisiting Scientists and Research AffiliatesTheodore M. Lyszczarz,1 Paul M. Mankiewich,2 David C. Shaver,' Shalom Wind 3Graduate StudentsDavid Abusch-Magder, David J. Goldhaber-Gordon, Nicole Y. Morgan2.1 Goals and ObjectivesSponsorsJoint Services Electronics ProgramGrant DAAH04-95-1-0038National Science FoundationGrant ECS 92-03427U.S. Army Research OfficeGrant DAAH04-94-G-0119When electrons are confined to a small particle ofmetal or a small region of semiconductor, both theenergy and charge of the system are quantized. Inthis way such nanometer-sized systems behave likeartificial atoms.4 The quantization of energy isfamiliar: The solutions of the Schrodinger equationin an isolated region have discrete energies. Insome ways, however, the quantization of charge ismore mysterious. We are quite comfortable withthe idea that the charge of a collection of electronsis discrete. However, the charge in any smallvolume of a large sample of conductor is not dis-crete because the electronic wavefunctions areextended over the entire sample. Only when thestates are localized is the charge quantized.Artificial atoms have been constructed using metalsand semiconductors, and they have been given avariety of names: single-electron-tunneling tran-sistor, quantum dot, single-electron transistor, andzero-dimensional electron gas. The physics of allthese devices is the same, although the limits inwhich they operate may be quite different. Thegoal of our research is to better understand thephysics of these devices in order to optimize theirperformance so that circuit design may commence.2.2 Summary of Recent WorkOur work this year has been successful in twoarenas. First, we have followed up our studies,reported one year ago,5 showing that electrons in asingle-electron transistor in GaAs undergo phasetransitions as a function of magnetic field. We haverecently reported the observation of low energyexcitations which correspond to the critical fluctu-ations of these transitions. Second, we haverecently fabricated metal oxide silicon SETs(MOSSETs) which show single electron phenomenaup to 20 K. We concentrate here on the latterresearch.A single-electron transistor (SET) is an island ofcharge which is coupled to leads by tunnel barriers.There are two energies that are encountered inchanging the electronic state of the SET: theenergy required to add an electron to the island, U,and the energy required to excite the electronsalready on the island, AE. Both these energiesincrease as the size of the island is diminished.Since the resolution of single electron phenomenais limited by the temperature of the electrons, wemay increase the operating temperature by1 MIT Lincoln Laboratory, Lexington, Massachusetts.2 AT&T Bell Laboratories, Short Hills, New Jersey.3 IBM Corporation, Thomas J. Watson Research Laboratories, Yorktown Heights, New York.4 M.A. Kastner, "Artificial Atoms," Phys. Today 46(1): 24 (1993).5 0. Klein, C. de C. Chamon, D. Tang, D.M. Abusch-Magder, S.-G. Wen, M.A. Kastner, and S.J. Wind, "Exchange Effects in anArtificial Atom at High Magnetic Fields," Phys. Rev. Lett. 74: 785 (1995).Chapter 2. Artificial AtomsFigure 1. Schematic of the device: (a) The cross section shows the p-silicon substrate with 20 nm thermal SiO 2, lowermetal gate patterned by electron beam lithography and liftoff, chemical vapor deposited SiO 2, and upper gate. In stan-dard operation, the upper gate is held at a voltage above the inversion threshold while the voltages on the lower gatesare kept below threshold. Electrons are then induced at the Si-SiO 2 interface where the lower gate does not screen thefield of the upper gate. (b) Sketch of a top view of our device with an isolated island of electrons coupled to two leadsby tunnel junctions. The lead on the left is the source and is biased at Vs; the lead on the right, called the drain, isconnected through an ammeter to ground. Our measurements are made by biasing the source and measuring thecurrent that flows to the drain.50 RLE Progress Report Number 138Chapter 2. Artificial Atomsreducing the size of the SET. The purpose of ourwork is to fabricate small SETs and, in addition toachieving higher operating temperatures, to exploitthe improved relative resolution to explore coherentinteraction between the electrons in the leads andthe electrons on the island.An island of charge can be created by electrostaticdepletion of a two-dimensional electron gas(2DEG). By changing the voltages on metallicgates which lie a short distance above a 2DEG, theelectrostatic fields can be adjusted; in this way,both the number of electrons on the island and thesize of the tunnel barriers may be varied. The sizeof the island is limited by the depletion width, whichdecreases as the gates are brought closer to the2DEG; a small depletion width allows the possibilityof a small island. Thus, to make small SETs oneneeds a material system in which the gates can bebrought close to the 2DEG. The Si-SiO 2 MOSsystem is ideal for this purpose because SiO 2 is arobust insulator; layers as thin as 10 nm have lowleakages, high breakdown voltages, and are easilyfabricated. We have therefore chosen to fabricateSETs in the silicon MOS system, rather than in themore extensively studied GaAs-AIGaAs system.Previously observed coulomb blockade (CB) effectsin electrostatically patterned MOS structures haveresulted from impurities. More recent work6 hasachieved CB in a Si-SiO 2 system using pattern-dependent oxidation. However, our studies are thefirst showing well-defined CB phenomena inlithographically defined MOSSETs where the tunnelbarriers are created by gate electrodes.2.3 FabricationStandard silicon fabrication techniques have beenused in combination with electron beam lithographyto fabricate MOSSETs, thus taking advantage ofexisting technology. Figure la shows the basiclayer structure .of our devices. We start with alightly doped p-silicon substrate (25-45 Q cm) andgrow a 20 nm thick dry thermal oxide on its surface.Using electron beam lithography, we pattern a 50nm layer of PMMA, which then serves as a lift-offmask for our lower metal gate, a 20 nm layer ofchromium. A scanning electron micrograph of atypical lower metal gate pattern is shown in figure2. After chemical vapor deposition of 85 nm of Si0 2on top of the gate structure, we anneal our sampleat 900 degrees C for 30 seconds in dry nitrogen.The upper metal gate and interconnects are thenFigure 2. A scanning electron micrograph is shown ofone of our SETs. Note that the gap between gates 1 and3 is 25 nm. The full diameter of the gap between thelower gates is 120 nm. The measurements discussed inthis paper were made on a larger SET whose diameter isabout twice as large.deposited by sputtering aluminum and are pat-terned photolithographically. Ohmic contact to theinversion layer is made by degenerately doped n+implants.In standard operation, the upper metal gate is heldat a voltage above the inversion threshold while thevoltages on the lower metal gates are kept belowthreshold. Electrons collect at the Si-SiO2 interfacein regions where the upper gate potential is notscreened by the lower metal gates (see figure Ib);in this way, it is possible to pattern the 2DEG intoan isolated island of electrons coupled to leads bytunnel junctions. Because this device uses SiO2,which is a robust insulator, we can apply large volt-ages to the gates: > 20 V can be applied to thelower gates, while 50 V can be applied between theupper and lower gates. The relative transmission ofthe tunnel barriers can be tuned by applying a6 Y. Takahashi, M. Nagase, H. Namatsu, K. Kurihara, K. Iwadate, Y. Nakajima, S. Horiguchi, K. Murase, and M. Tabe, "FabricationTechnique for Si Single-Electron Transistor Operating at Room Temperature," Electron. Lett. 31: 136 (1995).Chapter 2. Artificial Atomsvoltage difference of up to 2 V between left andright lower gates.2.4 ResultsWe have observed periodic conductance oscil-lations resulting from CB in a MOSSET, with anaddition energy U = 15 meV, which corresponds totemperature T = U/kB = 175 K. Figure 3 shows theconductance as a function of upper gate voltage forseveral temperatures in a MOSSET whoselithographic diameter is approximately 250 nm. Wesee the periodic peaks in conductance typical of CBwith a spacing of 200 mV. One of the most strikingfeatures of our data is that the conductance peakspersist to high temperatures: the traces in figure 3are taken at 0.315 K, 6 K, and 20 K with an offsetadded for clarity. The peaks are still well resolvedFigure 3. The conductance as a functionvoltage is shown here for three differentNote that the conductance peaks are stillof upper gatetemperatures.sharp at 6 K,while a periodic modulation of the conductance is stillpresent even at 20 K. This is consistent with a chargingenergy corresponding to 175 K. The measurement wasmade using standard lock-in techniques at 8.7 Hz with anexcitation voltage of 65 pV for the traces at 6 K and 20 Kand an excitation voltage of 20 pV for the trace at 0.315K. The excitation voltage in all our measurements waschosen to be less than kBT/e so that we measure thelinear response of the system. The curves at 6 K and 20K are offset by 0.1e 2/h and 0.2e2/h for clarity; the curve at6 K is shifted by 0.06 V to the left.at 6 K, and there is a clear periodic modulation ofthe conductance which persists up to 20 K, con-sistent with a CB charging energy of 175 K.There are four important energy scales that deter-mine the transport in CB: AE is the typical excitationenergy of the island with a fixed number of elec-trons; F is the lifetime broadened natural line widthresulting from tunneling between the island and theleads; U is the charging energy of the island; andkBT is the temperature of the SET. To observewell-separated CB peaks, kBT < U/5. Past studiesof SETs have been restricted to two differentregimes, both of which have kBT> F. For metalSETs, where kBT > AE, theory predicts that a con-ductance peak has full width at half maximumFWHM = 4.2 kBT/co, where ox = Cg/Cz, the ratio ofthe gate capacitance to the total capacitance. Theamplitude is predicted to be independent of temper-ature. In the other previously studied regime,kBT<AE, and the transport is dominated bytunneling though a single quantum state. Again theFWHM is linear in temperature, but is now given by3.5 kBT/ox, while the peak amplitude varies as 1/T.Thus, by examining both the amplitude and width ofthe peaks as a function of temperature we maydetermine both the transport regime and the factorc(.In our data, we find that the width of the peak at9.8 V is linear in temperature (figure 4a). However,in contrast to the prediction of the simplest model,the width extrapolates to a finite value at T=0. Thisresult suggests that our MOSSET is operating inthe regime where F> kBT. In this regime, weexpect the line shape to be a convolution of thenatural line shape of the zero-temperature conduc-tance resonance with the derivative of the Fermi-Dirac distribution function. If the line shape isLorentzian with FWHM = F, the width is predictedto be linear in temperature, with a finite intercept:FWHM = (3.5kBT + F)o, which agrees well with thebehavior seen in figure 4a. As discussed below,we find that r = 1.3 meV, corresponding to a tem-perature of 15 K, for the peak at 9.8 V. Further-more, in this regime the amplitude is expected tohave a 1/T dependence for ksT > F, and below thistemperature the amplitude is expected to saturate.Figure 4b shows such a crossover in the amplitudeof the peak at 9.8 V, providing further evidence thatthe finite intercept in figure 4a is due to a largenatural line width.From the slope of the peak width versus temper-ature (figure 4a), we estimate oc = 0.08. The phys-ical meaning of oc is simple: when the gate potentialis changed by AVg, the potential of the electronisland is changed by oxAV,. We thus use oc toconvert the gate voltage periodicity of CB peaks toan energy scale: U = echAV9 = 15 meV, or U/kB =52 RLE Progress Report Number 1380.5,0.40.3P 0.200.10 L -9.5 9.6 9.7 9.8 9.9 10.0 10.1VU (v)Chapter 2. Artificial Atoms0.100.08 (a)0.060.040.02012.5 (b)10.07.5S5.0 P *2.500 2.5 5.0 7.5 10.0 12.5 15.0T (K)Figure 4. The full width at half maximum (a) and theinverse of the peak height (b) are shown as functions oftemperature for the conductance peak at an upper gatevoltage of 9.8 V (see figure 3). Notice that the widthdoes not have a zero intercept, while the inverse of themaximum conductance saturates at low temperature.This behavior is results from the large natural line widthG of the state. The line in (a) is a fit to all the points,while the line in (b) fits the high temperature points with azero intercept.175 K. Similarly, we use o to convert the peakwidths and find Fs of 500 peV, 1.3 meV, and 3.3meV for the three peaks in figure 3, in order ofascending gate voltage.We have also measured the differential conduc-tance dl/dV, as a function of Vs the source voltage,which we call the tunneling spectrum. This spec-trum (shown in figure 5) is proportional to thedensity of single-particle states on the island whichcouple to the leads. The first feature to notice infigure 5 is the CB gap around zero bias. In addi-tion, there are several features whose spacing isreproducible; these are marked with arrows. Weassociate these features in the density of stateswith excited states of the artificial atom (SET). Thefirst peak in the spectrum on the right of the plot(arrow labeled gs N) is the current contribution fromthe ground state of the island with N electrons,while additional features (arrow labeled exc) aredue to excited states of the N-electron island. Simi-larly, the peak on the left of the plot (arrow labeledgs N-1) is due to current through the ground stateof the N-1-electron island.The typical energy spacing of bound states in theSET is - 4 meV; we have converted the voltageaxis in figure 5 into an energy scale by accountingfor the capacitive coupling between the lead andthe island. This large value reflects the very smallspatial extent of the electron droplet. Furthermore,this direct measurement of AE confirms thatksT<AE, as we have seen in the temperaturedependence data.2.5 PublicationsKastner, M.A. "MesoscopicAtoms." Comments onPhysics. Forthcoming.Physics with ArtificialCondensed MatterKastner, M.A., 0. Klein, C. de C. Chamon, D.Tang, D.M. Abusch-Magder, U. Meirav, X.-G.Wen, and S.J. Wind. "Exchange Effects in Arti-ficial Atoms." Jpn. J. Appl. Phys. 34: 16 (1995).Klein, O., C. de C. Chamon, D. Tang, D.M. Abusch-Magder, S.-G. Wen, M.A. Kastner, and S.J.Wind. "Exchange Effects in an Artificial Atom atHigh Magnetic Fields." Phys. Rev. Lett. 74: 785(1995).Chapter 2. Artificial AtomsFigure 5. Tunneling spectrum of the SET at T = 0.315 K. The peaks correspond to variations in the density of states ofthe island. Peaks marked gs are due to tunneling through the ground state, while those marked exc are due to tunnelingthrough excited states. The measurement was made using a lock-in amplifier at 8.7 Hz with an excitation voltage of 26pV.54 RLE Progress Report Number 1382.5 ' " I2.0 - z= 1.540.50-50 -25 0 25 50V. (mV)

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