{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Homework07_solution - Homework 7 Solution Problem 1...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Homework # 7 - Solution Problem # 1 Consider the free electron energy bands of an fcc crystal lattice in the reduced zone scheme in which all k 's are transformed to lie in the first Brillouin zone. Plot roughly in the [111] direction the energies of all bands up to six times the lowest band energy at the zone boundary at k = (2 π /a)(½,½,½). Explain what happens with these bands in the presence of a weak crystal potential. The reciprocal lattice is a bcc lattice with primitive translation vectors: 1 2 ˆˆˆ () a π =− + + bx y z , 2 2 a + y , z 3 2 a = +− y z All the reciprocal lattice vectors are given by 11 2 2 33 2 ( nn n h k l a ) =++ = + + Gbbb x y z The energy within the first Brillouin zone: 2 22 2 xx yy zz Ek G k G k G m ⎡⎤ =+ + + + + ⎣⎦ = 2 z Along [111] direction: and therefore xy kk k k === 2 2 G k G k G m 2 z = + ++ = ; k varies from a to a Low energy bands are given in the table and plotted in the figure below. bands n 1 n 2 n 3 h k l E / 2 2 m = E / 2 2 m = at k =0 E / 2 2 m = at k = a 1 000 000 2 3 k 0 2 3( ) a 2,3,4 100, 010, 001 111, 111 2( ) ( ) kk aa 2 12( ) a 2
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page1 / 4

Homework07_solution - Homework 7 Solution Problem 1...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon bookmark
Ask a homework question - tutors are online