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

Ariel, Imadiel

Gold, Alfred

Kinaret, Jari M.

Lee, Patrick A.

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Chapter 5. The Quantum Hall Effect in Narrow MOSFETsChapter 5. The Quantum Hall Effect in NarrowMOSFETsAcademic and Research StaffProfessor Patrick A. LeeVisiting Scientists and Research AffiliatesDr. Alfred Gold'Graduate StudentsJari KinaretTechnical and Support StaffImadiel Ariel5.1 Project DescriptionSponsorJoint Services Electronics ProgramContract DAAL03-89-C-0001We are investigating the conductance ofnarrow MOSFETs that are subject to a strongmagnetic field. This investigation was moti-vated by an experiment conducted by Pro-fessor Marc A. Kastner's group two yearsago, 2 in which the group studied the trans-port properties of narrow MOSFETs(width ~ 500A) subject to a large magneticfield of 5T to 10T. In these fields, only thelowest few Landau levels - in the quantumHall regime - are occupied. At the sametime, the cyclotron orbit is comparable to thesample width, making the finite size effect ofthe sample important. The experimentalistsobserved thresholds for large increases inconductance as a function of magnetic field,as well as ill-defined steps in the conduc-tance of approximately 2e2/h. We tackled thisproblem using both computer simulation andanalytic treatment of many-body effects.3We use computer simulation to model disor-dered conductors subject to a large magneticfield. The model is defined on a tightbinding lattice of finite width and lengthwhich is extended to infinity in bothdirections by connecting it to ideal latticeswithout randomness to simulate the source-drain leads. The novel feature of the modelis that the leads are also subject to the samequantizing magnetic fields so that (1) theedge states in the leads consist of Landaulevel subject to a lateral boundary condition,and (2) the states at the Fermi level are edgestates which are bound to the edge andpropagate to the right along the upper edgeand left along the lower edge. The conduc-tance is then related to the transmissionprobability of these edge states using theLandauer formula. These transmission prob-abilities are computed numerically.When the width of the wire is large com-pared with the cyclotron radius, the edgestates are basically forward scattered in thedisorder region so that the transmissionprobability is unity, leading to quantized Hallconductance of e2/h. It is only when thewidth becomes comparable to the cyclotron1 Department of Physics, University of Munich, Germany.2 J. Scott-Thomas, S.B. Field, M.A. Kastner, H.1 Smith, and D.A. Antoniades, Phys. Rev. Lett. 62:583 (1989).3 J. Kineret and P.A. Lee, to be published.123Chapter 5. The Quantum Hall Effect in Narrow MOSFETsradius that the edge state can scatter acrossthe width of the sample and is then reflected.The reduction in the transmission probabilityleads to ordinary metallic conduction. As thefield is increased, the simulation shows athreshold for the appearance of quantizedsteps in the conductance in agreement withthe experiment. The simulation also showsthat in the step between plateaus, the systembehaves as a metal in the sense that itexhibits conductance fluctuations in theorder of e2/h. The period of the fluctuation asgiven by the condition that the flux throughthe sample area is a flux quantum just as inuniversal conductance fluctuation.The next puzzle to be resolved is under-standing why the quantum Hall step is inunits of 2e 2/h. We believe that the 2e 2/h stepis due to the presence of two degeneratevalleys in the silicon interface, which is notresolved. In ordinary two dimensionalsamples, the valley degeneracy is resolveddue to the exchange effect. It is more ener-getically favorable to occupy one valley first,rather than occupying both valleys equally,because the exchange energy is nonlinear inthe density. However, this mechanism willbe weakened in narrow wires, because theLandau level is no longer completely flat andit costs kinetic energy to preferentiallyoccupy one valley. We calculated theexchange energy for a model system con-fined by a parabolic potential demonstratingthis competition between kinetic andexchange terms in quasi-one-dimensionalMOSFETs. We conclude that the combina-tion of numerical simulation and analyticwork to account for the many-body effectgives a quite satisfactory account of thetransport properties of a narrow MOSFETwire in a quantizing magnetic field.124 RLE Progress Report Number 132

The Quantum Hall Effect in Narrow MOSFETs

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The Quantum Hall Effect in Narrow MOSFETs

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