Exam1Spring2008

Exam1Spring2008 - pb The electron energy is such that E pa...

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Take home problem (15 Points): Carefully remove from exam and work ALONE at home. This is an open book – open notes question but you must reference any materials you use. Due Monday February 25 th at the start of class. Note: In order to encourage ethical behavior (i.e. no discussions among students and no group projects), I am offering a 10 point bonus for credible evidence of cheating on this assignment – can you really trust “that person” to keep quite or will they turn you in to get the points?????? In semiconductor-insulator barriers such as in a MOSFET or superconductor-insulator barriers such as in some supercomputers or even “Electric field emission devices” such as found in plasma displays, electron tunneling through a barrier is important. Consider an electron moving in a potential E pa incident on a barrier of thickness L and potential E
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Unformatted text preview: pb . The electron energy is such that E pa =E pc <E<E pb and ONLY electron motion in the +x direction is considered, (i.e. there are no reflections at either the x=0 or x=L boundary) . Part a) determine the probability of the electron tunneling from x=0 to x=L (your answer will be written in terms of algebraic variables). Hint: use the exponential form of the wave function and your boundary conditions between regions. Part b) If the electron has energy E= ½kT eV (equal to the peak in the energy distribution above the conduction band) and the barrier E pb-E pa =0.34 eV as could be found for an GaAs-AlGaAs barrier, what is the probability of tunneling (numeric answer) for the electron having an effective mass of 0.067m o at room temperature for a 2 nm barrier....
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Exam1Spring2008 - pb The electron energy is such that E pa...

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