Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?