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hw10 - Homework 10 Prob 10.1 We will look at the density of...

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Homework 10 Prob. 10.1 We will look at the density of states in a MOSFET inversion channel. This can be viewed as electrons being confined to a 3D box, but the gate direction (assigned as z here) has much more confinement than the channel length and width direction. Effectively, we can look at the system as a quantum box of dimension ( a, b, c ), where c << a, b . (a) Write down the eigenfunctions and eigenenergy for this system. Is there any difference from Eq. (10.6) and (10.7)? (5 pts) (b) Construct the 3D plot of ( k x , k y , k z ) and the allowable points. What is the influence from the relation of c << a, b ? (5 pts) (c) The density of state will seem to have discontinuities at energies 2 2 2 = c n m E z nz π , establish expressions for the DOS in the energy ranges 0 ≤ E ≤ E 1 , E 1 ≤ E ≤ E 2 and E nz E ≤ E nz+1 . (5 pts) (d) On the same figure of g(E) vs. E , plot DOS from (c) and the standard DOS for regular 3D box of Eq. (10.33), i.e., without the constraint of c << a, b . (10 pts) Prob. 10.2 For a 3D particle in the potential of ( 29 2 2 0 2
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