This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: EEE 539—Spring 2008 Homework 5 3.5 Plot the function f( α a)=9sin( α a)/ α a+cos( α a) ≤α a ≤ 6 π . Also, given the function f( α a)=cos(ka), indicate the allowed values of α a which will satisfy this equation. 2 2 4 6 8 10 5 10 15 20 f( α a) α a Allowed regions2 2 4 6 8 10 5 10 15 20 f( α a) α a Allowed regions 3.7 Using equation (3.24), show that dE/dk=0 at k=n π /a, where n=0,1,2,…. Equation (3.24) is given as ka a a a P cos cos sin = + ′ α α α , and (3.5) relates the energy to α . m E 2 2 2 α h = Now, let us take the derivative of (3.24) with respect to α , as ka a k a a a a a P sin sin sin cos 2 − = ∂ ∂ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ − − ′ α α α α α α . When k = n π /a (n an integer), the righthand side is zero. Since, in general, the term in the brackets is nonzero, we must have = ∂ ∂ k α in order to satisfy the equation. Then, . = ∂ ∂ ∂ ∂ = k E dk dE α α 3.14 Two possible valence bands are shown in the E versus k diagram given in Fig. Two possible valence bands are shown in the E versus k diagram given in Fig....
View
Full
Document
 Spring '08
 Ferry

Click to edit the document details