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prelim2sol-08

# prelim2sol-08 - ECE 3060 Fall 2008 Prelim Exam 2 Solution...

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2 1. Define the trial function: ( ) 2 0 4 / 1 ) ( exp 2 x x α π α ψ t = , where we expect x 0 to be negative (towards left from the center of the well), and nm α 10 / 1 . 2. Find the parametrical equation for the expected energy: ( ) > =< t t t ψ H ψ x α ε | ˆ | , 0 , where H ˆ contains the piecewise-constant potential. 3. Solve for 0 / = α ε t and 0 / 0 = x ε t to obtain α opt and x opt . 4. Use α opt and x opt to give E 0 . (c) If there is one electron in the well, and the lifetime τ can give the decay probability as exp( -t/ τ ). Find the barrier width d that can give τ = 3.15 × 10 8 sec (10 years). Use E 0 from (a). Justify the reason why only the right barrier needs to be considered. This is the retention state of the Flash memory cell. (10 pts)
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