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Homework Help: Calculate thickness of barrier for tunneling effect

  1. Mar 1, 2012 #1
    1. The problem statement, all variables and given/known data

    2. The tunnel effect predicts that electrons can "tunnel" through an energy barrier that classical mechanics predicts to be impenetrable. In a suitably fabricated “quantum dot” device, a thin energy barrier may be penetrated in this way. If the barrier is 0.2eV in height (E - V = -0.2 eV), what thickness barrier will give a probability that 1 electron in 108 will penetrate the barrier? (Hint: remember that probability is proportional to ψ^2).

    2. Relevant equations

    for tunneling effect: ψ=A*exp(ikx) or A*exp(αx) where α=ik
    normalized eigenfunction: ∫ψ^2dV=1

    3. The attempt at a solution

    I know that ψ^2 is the probability (1*10^-8) and I found the value for k (and thus α) now I am having trouble finding the constant A so that I can solve for the thickness of the barrier x
  2. jcsd
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