Question

2. Based on the Kroing-Penney model, the periodic potential energy of an electron in a solid is shown aside. Ass urne that for a given allowed band αα<< 1 and ka<<1. Psin(aa) (a) Prove that the E -k relatione)+ cos(aa) - cos(ka)) may be put in the form: E -Ak' +B Write the constants A and B in terms of P, a, h, m, and h (b) If U-3 eV, a-0.3 nm, and b 0.025 nm i- Find numerical values for ( and B). ii- Calculate the minimum energy in the band (in meV iii-Calculate the ratio --at k = TI ST 30a 72 (c) Sketch the (vg-k) and (m -k) curves in the range:-k< (Hint; for x<< 1 : sin(x ) $(-_ and cos(x ) #1-_ ) sin(aa) mba Psilaat?-cos(aa)-cos(ka) where P- U , and α. Ξ2mE

Answer 1

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