Tunneling Outline - Review: Barrier Reflection - Barrier Penetration (Tunneling) - Flash Memory

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  • Tunneling Outline

    Review: Barrier Reflection Barrier Penetration (Tunneling) Flash Memory

  • A Simple Potential StepRegion 1Region 2CASE I : Eo > VIn Region 1:

    In Region 2:

  • A Simple Potential StepCASE I : Eo > V is continuous:

    is continuous:Region 1Region 2

  • A Simple Potential StepCASE I : Eo > VRegion 1Region 2

  • Example from: http://phet.colorado.edu/en/get-phet/one-at-a-time

  • Quantum Electron CurrentsGiven an electron of mass

    that is located in space with charge density and moving with momentum corresponding to then the current density for a single electron is given by

  • A Simple Potential StepCASE I : Eo > VRegion 1Region 2

  • A Simple Potential StepCASE I : Eo > V11Region 1Region 2

  • IBM Almaden STM of CopperImage originally created by the IBM Corporation. IBM Corporation. All rights reserved. This content is excluded from our Creative Commons license. For more information, see http://ocw.mit.edu/fairuse.

  • IBM AlmadenImage originally created by the IBM Corporation. IBM Corporation. All rights reserved. This content is excluded from our Creative Commons license. For more information, see http://ocw.mit.edu/fairuse.

  • IBM AlmadenImage originally created by the IBM Corporation. IBM Corporation. All rights reserved. This content is excluded from our Creative Commons license. For more information, see http://ocw.mit.edu/fairuse.

  • A Simple Potential StepCASE II : Eo < VIn Region 1:

    In Region 2:Region 1Region 2

  • A Simple Potential Step is continuous:

    is continuous:CASE II : Eo < VRegion 1Region 2

  • A Simple Potential StepCASE II : Eo < VTotal reflection Transmission must be zeroRegion 1Region 2

  • 2a = LQuantum Tunneling Through a Thin Potential Barrier Total Reflection at BoundaryFrustrated Total Reflection (Tunneling)

  • CASE II : Eo < VRegion 1Region 2Region 3In Regions 1 and 3:

    In Region 2:A Rectangular Potential Stepfor Eo < V :

  • A Rectangular Potential Stepx=0x=L2a = LTunneling Applet: http://www.colorado.edu/physics/phet/dev/quantum-tunneling/1.07.00/Real part of for Eo < V, shows hyperbolic (exponential) decay in the barrier domain and decrease in amplitude of the transmitted wave.Transmission Coefficient versus Eo/Vfor barrier with for Eo < V :

  • Electrons tunnel preferentially when a voltage is appliedFlash MemoryErased1Programmed0ChannelFloating GateDRAINImage is in the public domain

  • MOSFET: Transistor in a NutshellTunneling causes thin insulating layers to become leaky !Conducting ChannelImage is in the public domainConduction electron flowImage courtesy of J. Hoyt Group, EECS, MIT. Photo by L. GomezImage courtesy of J. Hoyt Group, EECS, MIT. Photo by L. Gomez

  • UNPROGRAMMEDPROGRAMMEDTo obtain the same channel charge, the programmed gate needs a higher control-gate voltage than the unprogrammed gateReading Flash MemoryHow do we WRITE Flash Memory ?CONTROL GATEFLOATING GATESILICONCONTROL GATEFLOATING GATE

  • Question: What will T be if we double the width of the gap? Example: Barrier TunnelingLets consider a tunneling problem:

    An electron with a total energy of Eo= 6 eV approaches a potential barrier with a height of V0 = 12 eV. If the width of the barrier is L = 0.18 nm, what is the probability that the electron will tunnel through the barrier?

  • Consider a particle tunneling through a barrier: 1. Which of the following will increase the likelihood of tunneling?

    a. decrease the height of the barrierb. decrease the width of the barrierc. decrease the mass of the particle

    2. What is the energy of the particles that have successfully escaped?a. < initial energy b. = initial energy c. > initial energy

    Multiple Choice QuestionsAlthough the amplitude of the wave is smaller after the barrier, no energy is lost in the tunneling process

  • Application of Tunneling: Scanning Tunneling Microscopy (STM)Due to the quantum effect of barrier penetration, the electron density of a material extends beyond its surface:

    materialSTM tip~ 1 nmOne can exploit this to measure the electron density on a materials surface:Sodium atomson metal:STM imagesSingle walled carbon nanotube:VE0STM tipmaterialImage originally created by IBM CorporationImage is in the public domain IBM Corporation. All rights reserved. This content is excluded from our Creative Commons license. For more information, see http://ocw.mit.edu/fairuse.

  • Reflection of EM Waves and QM Waves= probability of a particular photon being reflected= probability of a particular electron being reflectedThen for optical material when =0:

  • MIT OpenCourseWarehttp://ocw.mit.edu6.007 Electromagnetic Energy: From Motors to LasersSpring 2011For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.

    *Answer: With twice the thickness, the exponential factor comes in twice. Therefore, T = 4(0.011)^2 =0.05%*http://www.quantum-physics.polytechnique.fr/en/ -- wave mechanics scanning tunneling microscope