Homework 10Prob. 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 zhere) 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 (kx, ky, kz) 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 222=cnmEznzπ, establish expressions for the DOS in the energy ranges 0 ≤ E ≤ E1, E1≤ E ≤ E2and Enz≤ E ≤ Enz+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. 10.2For a 3D particle in the potential of (292202
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