chapter 7 #1 chapter 7 #4 - delaware physicsyji/phys624/hw 6 solution.pdf · 2010-11-22 · chapter...
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![Page 1: Chapter 7 #1 Chapter 7 #4 - Delaware Physicsyji/PHYS624/HW 6 solution.pdf · 2010-11-22 · Chapter 7 #1 Chapter 7 #4 (b) The band gap at zone boundary plane normal to the end of](https://reader031.vdocuments.us/reader031/viewer/2022040109/5ea708c7e5edf921603ee4a5/html5/thumbnails/1.jpg)
Chapter 7 #1
Chapter 7 #4
![Page 2: Chapter 7 #1 Chapter 7 #4 - Delaware Physicsyji/PHYS624/HW 6 solution.pdf · 2010-11-22 · Chapter 7 #1 Chapter 7 #4 (b) The band gap at zone boundary plane normal to the end of](https://reader031.vdocuments.us/reader031/viewer/2022040109/5ea708c7e5edf921603ee4a5/html5/thumbnails/2.jpg)
(b) The band gap at zone boundary plane normal to the end of reciprocal lattice
vector is 2 times the Fourier component . From part (a), we
know this quantity equals to 0 for first order approximation. So the band gap is zero to
the first order approximation.
xa
A ˆ2π
=
r
AU r
2
![Page 3: Chapter 7 #1 Chapter 7 #4 - Delaware Physicsyji/PHYS624/HW 6 solution.pdf · 2010-11-22 · Chapter 7 #1 Chapter 7 #4 (b) The band gap at zone boundary plane normal to the end of](https://reader031.vdocuments.us/reader031/viewer/2022040109/5ea708c7e5edf921603ee4a5/html5/thumbnails/3.jpg)
Chapter 7 #6
![Page 4: Chapter 7 #1 Chapter 7 #4 - Delaware Physicsyji/PHYS624/HW 6 solution.pdf · 2010-11-22 · Chapter 7 #1 Chapter 7 #4 (b) The band gap at zone boundary plane normal to the end of](https://reader031.vdocuments.us/reader031/viewer/2022040109/5ea708c7e5edf921603ee4a5/html5/thumbnails/4.jpg)
![Page 5: Chapter 7 #1 Chapter 7 #4 - Delaware Physicsyji/PHYS624/HW 6 solution.pdf · 2010-11-22 · Chapter 7 #1 Chapter 7 #4 (b) The band gap at zone boundary plane normal to the end of](https://reader031.vdocuments.us/reader031/viewer/2022040109/5ea708c7e5edf921603ee4a5/html5/thumbnails/5.jpg)
![Page 6: Chapter 7 #1 Chapter 7 #4 - Delaware Physicsyji/PHYS624/HW 6 solution.pdf · 2010-11-22 · Chapter 7 #1 Chapter 7 #4 (b) The band gap at zone boundary plane normal to the end of](https://reader031.vdocuments.us/reader031/viewer/2022040109/5ea708c7e5edf921603ee4a5/html5/thumbnails/6.jpg)
Additional problem
![Page 7: Chapter 7 #1 Chapter 7 #4 - Delaware Physicsyji/PHYS624/HW 6 solution.pdf · 2010-11-22 · Chapter 7 #1 Chapter 7 #4 (b) The band gap at zone boundary plane normal to the end of](https://reader031.vdocuments.us/reader031/viewer/2022040109/5ea708c7e5edf921603ee4a5/html5/thumbnails/7.jpg)
)cos(4a
bm
a
Aπ=
![Page 8: Chapter 7 #1 Chapter 7 #4 - Delaware Physicsyji/PHYS624/HW 6 solution.pdf · 2010-11-22 · Chapter 7 #1 Chapter 7 #4 (b) The band gap at zone boundary plane normal to the end of](https://reader031.vdocuments.us/reader031/viewer/2022040109/5ea708c7e5edf921603ee4a5/html5/thumbnails/8.jpg)
)cos(4a
bm
a
Aπ=
![Page 9: Chapter 7 #1 Chapter 7 #4 - Delaware Physicsyji/PHYS624/HW 6 solution.pdf · 2010-11-22 · Chapter 7 #1 Chapter 7 #4 (b) The band gap at zone boundary plane normal to the end of](https://reader031.vdocuments.us/reader031/viewer/2022040109/5ea708c7e5edf921603ee4a5/html5/thumbnails/9.jpg)