Contains description of one research project.Joint Services Electronics Program Contract DAAL03-89-C-000

Ariel, Imadiel

Kinaret, Jari M.

Lee, Patrick A.

Meir, Yigal

Wingreen, Ned S.

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Chapter 5. Coulomb Blockade in Narrow MOSFETsChapter 5. Coulomb Blockade in Narrow MOSFETsAcademic and Research StaffProfessor Patrick A. Lee, Dr. Yigal Meir, Dr. Ned S. WingreenGraduate StudentJari M. KinaretTechnical and Support StaffImadiel Ariel5.1 Project DescriptionSponsorJoint Services Electronics ProgramContract DAAL03-89-C-0001We are investigating the conductance through aquantum dot where the discrete nature of the elec-tron charge on the dot and the Coulomb energy Uassociated with the addition or removal of acharge dominate the physics. This theoreticalwork is inspired by the experimental work of Pro-fessor Kastner's group, which discovered periodicstructures in the conductance as a function of gatevoltage in a narrow MOSFET structure with twoconstrictions. These constrictions create aquantum dot through which the electron musttunnel. There are two energy scales in theproblem: (1) the energy spacing As betweenenergy levels in the quantum dot which we esti-mate to be As?0.1 meV for a 50 nm x 1 umquantum dot in GaAs and (2) The Coulomb inter-action energy between electrons U which isapproximately equal to the capacitive chargingenergy of the quantum dot e2/C where C is thecapacitance and we estimate e22/C ^ 1 meV, sothat U > As. Under these conditions, an electronmust overcome the Coulomb energy in order totunnel, a phenomenon known as the Coulombblockade.We treat a model consisting of two ideal leadscoupled to a site with n energy levels and aCoulomb interaction energy U every time an extraelectron is added to the site. This model is remi-niscent of the Anderson model of magnetic impuri-ties, in which electrons of either up or down spin(n = 2) can occupy a site, and there is an on-siterepulsion U for double occupation. The presentproblem is richer because the Fermi level in theright and left ideal leads can be separatelyadjusted.Earlier we had examined the low temperature limitof this model,' and we found important correlationbetween the electron state on the quantum dotand the electrons in the lead when the temperatureT is less than TK, the Kondo temperature.However, in most cases TK is very low, and wehave recently developed a formalism to describethe high temperature limit 2 when T>TK. We notethat As can be comparable to kT, and there areinteresting changes in the lineshape of the con-ductance peaks as kT goes from kT<As tokT > As. For kT < As, the lineshape is a Lorentzianbroadened by the derivative of the Fermi function.As kT is increased through Ae, this is no longerthe case, and we find that the peak height canincrease or decrease with temperature, dependingon the way the levels couple to the leads. Thisfeature, which was observed experimentally, hasbeen a puzzle for some time.According to our theory, the observed temperaturedependence is explained by simultaneous transportthrough multiple levels whose coupling to theleads increases rapidly with energy near the top ofthe tunnel barriers. Our theory gives a satisfactoryaccount of the temperature dependence of theperiodic structure in conductance, thus providingstrong support for the validity of the Coulombblockade model.1 T.-K. Ng and P.A. Lee, "On Site Coulomb Repulsion and Resonant Tunnelling," Phys. Rev. Lett. 61:1768 (1988).2 Y. Meir, N. Wingreen, and P. Lee, "Transport Through a Strongly Interacting Electron System: Theory of PeriodicConductance Oscillations," submitted to Phys. Rev. Lett.129Chapter 5. Coulomb Blockade in Narrow MOSFETs5.1.1 PublicationsKinaret, J., and P.A. Lee. "Exchange Interaction ina Quantum Wire in a Strong Magnetic Field."Phys. Rev. B 42(18): 768-773 (1990).Kinaret, J., and P.A. Lee. "Conductance of a Disor-dered Narrow Wire in a Strong Magnetic Field."Phys. Rev. B. Forthcoming.Meir, Y., N. Wingreen, and P.A. Lee. "TransportThrough a Strongly Interacting ElectronSystem: Theory of Periodic Conductance Oscil-lations." Submitted to Phys. Rev. Lett.Professor Patrick A. Lee's recent work is focused on the effect of Coulomb repulsion onthe tunneling probability through a quantum dot.130 RLE Progress Report Number 133

Coulomb Blockade in Narrow MOSFETs

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Coulomb Blockade in Narrow MOSFETs

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