Contains description of one research project and a list of publications.Joint Services Electronics Program Contract DAAL03-92-C-0001National Science Foundation Grant ECS 88-13250National Science Foundation Grant ECS 92-0342

Belk, Paul A.

Foxman, Ethan B.

Kastner, Marc A.

Wind, Shalom

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Chapter 2. Single Electron TransistorsChapter 2. Single Electron TransistorsAcademic and Research StaffProfessor Marc A. KastnerVisting Scientists and Research AffiliatesShalom Wind'Graduate StudentsPaul A. Belk, Ethan B. Foxman2.1 Project DescriptionSponsorsJoint Services Electronics ProgramContract DAAL03-92-C-0001National Science FoundationGrant ECS 88-13250Grant ECS 92-03427Several years ago we discovered2 that while con-ventional field-effect transistors turn from the off-state to the on-state only once as electrons areadded to them, a very small transistor turns on andthen off every time one electron is added. Thenear-term goal of our research is to understand whythe single electron transistor works the way it does.Our long-term goal is to make the device character-istics useful for applications.A sketch of our first single electron transistor3 isshown in figure la. We begin with a crystal ofGaAs which has such a high density of impuritiesthat it is metallic. This plays the role of the gate.On top of this we grow a layer of AIGaAs, which isan insulator, and a layer of pure GaAs, where theelectrons reside. If a positive voltage is appliedbetween the gate and the source or drain, electronsaccumulate at the AIGaAs/GaAs interface.Because of the strong electric field at this interface,each electron's energy for motion perpendicular tothe interface is quantized, and at low temperaturesthe electrons move only in the two dimensions par-allel to the interface. The special trick that makesthis a single electron transistor is the creation byelectron beam lithography of a pair of electrodes onthe top surface of the GaAs. When negativevoltage is applied between these and the source ordrain, the electrons are repelled and cannot accu-mulate underneath the electrodes. Consequently,the electrons are confined in a narrow channelbetween the two electrodes. Constrictions stickingout into the channel repel the electrons and createpotential barriers at either end of the channel. Aplot of the potential is shown in figure lb. For anelectron to travel from the source to the drain, itmust tunnel through these barriers. A "pool" ofelectrons accumulates between the two con-strictions, separated from the leads by the tunnelbarriers.Figure 2 shows the current through the device4 as afunction of the voltage Vg between the gate and thesource. A very small amount of voltage is appliedbetween the two leads, which is just large enoughto measure the tunneling conductance betweensource and drain. The results are astounding. Theconductance displays sharp resonances that arealmost periodic in Vg. By calculating the capaci-tance between the pool of electrons and the gate,1 IBM Thomas J. Watson Research Laboratories, Yorktown Heights, New York.2 J.H.F. Scott-Thomas, S.B. Field, M.A. Kastner, H.I. Smith, and D.A. Antoniadis, "Conductance Oscillations Periodic in the Density ofa One-Dimensional Electron Gas," Phys. Rev. Lett. 62: 583 (1989); M.A. Kastner, "The Single-Electron Transistor," Rev. Mod. Phys.64: 849 (1992).3 U. Meirav and S.J. Wind, "Single Electron Charging and Periodic Conductance Resonances in GaAs Nanostructures," Phys. Rev.Lett. 65: 771 (1990).4 E.B. Foxman, P.L. McEuen, U. Meirav, N.S. Wingreen, Y. Meir, P.A. Belk, N.R. Belk, M.A. Kastner, and S.J. Wind, "The Effects ofQuantum Levels on Transport Through a Coulomb Island," unpublished; M.A. Kastner, "Artificial Atoms," Phys. Today, 46(1): 24-31(1993).Chapter 2. Single Electron TransistorsFigure la.transistor.(a) Schematic drawing of the single electronwe can show5 that the period is the voltage neces-sary to add one electron to the pool.There is a simple way to explain the periodic con-ductance resonances; 6 the theory is called theCoulomb blockade model. When an electrontunnels from one lead onto the pool of electronsand then onto the other lead, adding a charge Q tothe pool requires energy Q2/2C, where C is the totalcapacitance between the pool and the rest of thesystem; since you can add no less than one elec-tron, the flow of current requires a Coulomb energye2/2C. A fancier way to explain this is that becauseof charge quantization there is an energy gap in thespectrum of states for tunneling: For an electron totunnel onto the pool its energy must exceed theFermi energy of the contact by e2/2C, and for ahole to tunnel its energy must be below the Fermienergy by the same amount. Consequently, theenergy gap has width e2/C. If the temperature islow enough that kT < e2/2C, neither electrons norholes can flow from one lead to the other.With the gate voltage Vg we can alter the energyrequired to add charge to the pool. Vg is appliedbetween the gate and source, but if the drain-source voltage is very small, the source, drain andpool are all at almost the same potential. With VgFigure lb. (b) Potential similar to the one in the singleelectron transistor plotted as a function of position at theGaAs/AIGaAs interface.applied the electrostatic energy of charge Q on thepool isE = QVg + Q2/2C.The first term is the attractive interaction betweenthe positively charged gate electrode and the nega-tive charge Q, and the second term is the repulsiveinteraction among the bits of charge in the pool.Equation 1 shows that the energy as a function ofQ is a parabola with minimum at Qo= - CV,.By varying Vg, we can choose any value of Q,, thecharge that would minimize the energy in equation1 if the charge were not quantized. However,because the real charge is quantized, only discretevalues of the energy E are possible. For all valuesof Qo except Qo= - (N + 1/2)e , there is a non-zeroenergy for adding or subtracting an electron. Underthese circumstances, no current can flow at lowtemperature. However, if Qo= - (N + 1/2)e, thestate with Q = - Ne and that with Q = - (N +1)e aredegenerate; the charge fluctuates between the twovalues even at zero temperature. Consequently,the energy gap in the tunneling spectrum disap-pears, and current can flow. The peaks in conduc-tance are, therefore, periodic, occurring whenever5 U. Meirav and S.J. Wind, "Single Electron Charging and Periodic Conductance Resonances in GaAs Nanostructures," Phys. Rev.Lett. 65: 771 (1990); A. Kumar, "Self-consistent Calculations on Confined Electrons in Three-dimensional Geometries," Surf. Sci. 263:335-340 (1992).6 G. Grabert and M.H. Devoret, eds. Single Charge Tunneling--Coulomb Blockade Phenomena in Nanostructures, (New York:Plenum Press, 1992).42 RLE Progress Report Number 135SourcDrainHeavily Doped GaAsGate-Chapter 2. Single Electron TransistorsFigure 2. Conductance in units of the quantum of con-ductance e2/h versus voltage on the n+GaAs substrate.On the logarithmic plot, it is clear that the transistor hasan on-to-off conductance ratio that exceeds 103 for thelowest gate voltages.the average charge on the artificial atom isQo= - (N +1/2)e, spaced in gate voltage by e/C.The Coulomb blockade model accounts for chargequantization but ignores the quantization of energyresulting from the small size of the region in whichthe electrons are confined. If one thinks of theregion between the potential barriers as a box, thelowest energy spacings are of the order h2/2ma 2where a is the size of the box. Because the energyas well as the charge is quantized, we find it usefulto think of the single electron transistor as an artifi-cial atom.The energy level spectrum of the atom can bemeasured directly by observing the tunnelingcurrent at fixed Vgas a function of the voltage (Vds)between drain and source. The Fermi level in thesource rises in proportion to Vds relative to thedrain, so it also rises relative to the energy levels ofthe artificial atom (see the inset to figure 3).Current begins to flow when the Fermi energy ofthe source is raised just above the first quantizedenergy level of the atom. As the Fermi energy is10- 17 E.B. Foxman, P.L. McEuen, U. Meirav, N.S. Wingreen, Y. Meir, P.A. Belk, N.R. Belk, M.A. Kastner, and S.J. Wind, "The Effects ofQuantum Levels on Transport Through a Coulomb Island," unpublished; M.A. Kastner, "Artificial Atoms," Phys. Today, 46(1): 24-31.10 - 210-410-5280 285 290 295 300raised further, higher energy levels in the atom fallbelow the Fermi energy, and more current flowsbecause there are additional channels for the elec-tron to use for tunneling onto the artificial atom.We measure the energies by measuring the voltageat which the current increases, or, equivalently, thevoltage at which there is a peak in the derivative ofthe current dl/dVds. We show results of such ameasurement7 in the upper part of figure 3.Increasing the gate voltage lowers all the energylevels in the atom by - eVg, so that the entire tun-neling spectrum shifts with Vg. This effect can beobserved by plotting the values of Vds at whichpeaks appear in dl/dVds, as is done in the lowerpart of figure 3. You can see the gap in the tun-neling spectrum shift lower with increasing Vg andthen disappear at the charge-degeneracy point, justas predicted by the Coulomb blockade model. Youcan also see the discrete energy levels of the artifi-cial atom. The charge-degeneracy points are thevalues of V,, for which one of the energy levels ofthe artificial atom is degenerate with the Fermienergy in the leads when Vds = 0, because onlythen can the charge of the atom fluctuate.During the past year, we have developed a thor-ough understanding of the energy spectrum ofsingle electron transistors. In addition, we nowknow what limits their operating temperature. Asshown in figure 3, the devices we have made so farhave a Coulomb-blockade gap that is about 1 meVwide and energy level spacings that are about one-fifth to one-tenth of that. As the temperature israised, the conductance resonances acquire a widthof - 4 kT. Since kT = 1 meV is equivalent to T = 12K, the peak-to-valley ratio becomes small above afew degrees K. Making the single electron tran-sistor useful will require making its operating tem-perature much higher. This requires decreasing thesize because both the Coulomb energy, whichvaries inversely with the capacitance, and theenergy level spacings will get larger for smallerstructures. This is the direction of our nextresearch effort.Chapter 2. Single Electron Transistors0.700.350-0.35.i-0.5 L-2 -1 0 1 2VdS (mV)306 307 308 309 310 311V (mV)Figure 3. Discrete energy levels of a single electrontransistor can be detected by varying the drain-sourcevoltage. When a large enough Vd, is applied, electronsovercome the energy gap and tunnel from the source tothe pool of electrons (see inset of upper panel). Upperpanel: Every time a new discrete state is accessible, thetunneling current increases, giving a peak in dl/dVds. TheCoulomb blockade gap is the region between about -0.5mV and + 0.3mV where there are no peaks. Lowerpanel: Plotting the positions of these peaks at variousgate voltages gives the level spectrum. Note how thelevels and the gap move downward as Vg increases.3052.2 PublicationsBagwell, P.F., S.L. Park, A. Yen, D.A. Antoniadis,H.I. Smith, T.P. Orlando, and M.A. Kastner."Magnetotransport in Multiple Narrow SiliconInversion Channels Opened Electrostatically intoa Two-dimensional Electron Gas." Phys. Rev. B45(16): 9214-9221 (1992).Kastner, M.A. "The Single-Electron Transistor."Rev. Mod. Phys. 64(3): 849-858 (1992).Kastner, M.A., E.B. Foxman, P.L. McEuen, U.Meirav, A. Kumar, and S.J. Wind. "TransportSpectroscopy of a Coulomb Island." In Nano-structures and Mesoscopic Systems. Eds. W.P.Kirk and M.A. Reed. San Diego, California:Academic Press, 1992.McEuen, P.L., E.B. Foxman, J. Kinaret, U. Meirav,M.A. Kastner, N.S. Wingreen, and S.J. Wind."Self-consistent Addition Spectrum of a CoulombIsland in the Quantum Hall Regime." Phys.Rev. B 45(19): 11419-11422 (1992).44 RLE Progress Report Number 135=-wExbDQ,C

Single Electron Transistors

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Single Electron Transistors

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