Energy Bands - 物理系spin/course/102F/Ch7-1.pdfThe crystal behaves as an insulator if the allowed...
Transcript of Energy Bands - 物理系spin/course/102F/Ch7-1.pdfThe crystal behaves as an insulator if the allowed...
![Page 1: Energy Bands - 物理系spin/course/102F/Ch7-1.pdfThe crystal behaves as an insulator if the allowed energy bands are either filled or empty, for then no electrons can move in an electric](https://reader033.fdocuments.in/reader033/viewer/2022050308/5f701fb590829d35b2598ca2/html5/thumbnails/1.jpg)
Chapter 7
Energy Bands
![Page 2: Energy Bands - 物理系spin/course/102F/Ch7-1.pdfThe crystal behaves as an insulator if the allowed energy bands are either filled or empty, for then no electrons can move in an electric](https://reader033.fdocuments.in/reader033/viewer/2022050308/5f701fb590829d35b2598ca2/html5/thumbnails/2.jpg)
Free Electron Model (Sommerfiled):
Success:
• Heat capacity
• Thermal conductivity
• Magnetic susceptibility
• Electrodynamics of metals
Failure:
• Distinction between metals,
semimetals, and insulators.
• Positive Hall coefficient
• Magneto transport
![Page 3: Energy Bands - 物理系spin/course/102F/Ch7-1.pdfThe crystal behaves as an insulator if the allowed energy bands are either filled or empty, for then no electrons can move in an electric](https://reader033.fdocuments.in/reader033/viewer/2022050308/5f701fb590829d35b2598ca2/html5/thumbnails/3.jpg)
![Page 4: Energy Bands - 物理系spin/course/102F/Ch7-1.pdfThe crystal behaves as an insulator if the allowed energy bands are either filled or empty, for then no electrons can move in an electric](https://reader033.fdocuments.in/reader033/viewer/2022050308/5f701fb590829d35b2598ca2/html5/thumbnails/4.jpg)
Free Electron Model
Brief Review:
![Page 5: Energy Bands - 物理系spin/course/102F/Ch7-1.pdfThe crystal behaves as an insulator if the allowed energy bands are either filled or empty, for then no electrons can move in an electric](https://reader033.fdocuments.in/reader033/viewer/2022050308/5f701fb590829d35b2598ca2/html5/thumbnails/5.jpg)
The electrons
![Page 6: Energy Bands - 物理系spin/course/102F/Ch7-1.pdfThe crystal behaves as an insulator if the allowed energy bands are either filled or empty, for then no electrons can move in an electric](https://reader033.fdocuments.in/reader033/viewer/2022050308/5f701fb590829d35b2598ca2/html5/thumbnails/6.jpg)
Nearly Free Electron Model
for a 1-D linear lattice
![Page 7: Energy Bands - 物理系spin/course/102F/Ch7-1.pdfThe crystal behaves as an insulator if the allowed energy bands are either filled or empty, for then no electrons can move in an electric](https://reader033.fdocuments.in/reader033/viewer/2022050308/5f701fb590829d35b2598ca2/html5/thumbnails/7.jpg)
Free Electron Model Nearly Free Electron Model
Solutions in 1-D
![Page 8: Energy Bands - 物理系spin/course/102F/Ch7-1.pdfThe crystal behaves as an insulator if the allowed energy bands are either filled or empty, for then no electrons can move in an electric](https://reader033.fdocuments.in/reader033/viewer/2022050308/5f701fb590829d35b2598ca2/html5/thumbnails/8.jpg)
Standing wave solutions
![Page 9: Energy Bands - 物理系spin/course/102F/Ch7-1.pdfThe crystal behaves as an insulator if the allowed energy bands are either filled or empty, for then no electrons can move in an electric](https://reader033.fdocuments.in/reader033/viewer/2022050308/5f701fb590829d35b2598ca2/html5/thumbnails/9.jpg)
![Page 10: Energy Bands - 物理系spin/course/102F/Ch7-1.pdfThe crystal behaves as an insulator if the allowed energy bands are either filled or empty, for then no electrons can move in an electric](https://reader033.fdocuments.in/reader033/viewer/2022050308/5f701fb590829d35b2598ca2/html5/thumbnails/10.jpg)
Standing waves
cos2x/a
sin2x/a
![Page 11: Energy Bands - 物理系spin/course/102F/Ch7-1.pdfThe crystal behaves as an insulator if the allowed energy bands are either filled or empty, for then no electrons can move in an electric](https://reader033.fdocuments.in/reader033/viewer/2022050308/5f701fb590829d35b2598ca2/html5/thumbnails/11.jpg)
U(x) = U Cos2x/a See Fig. 2
![Page 12: Energy Bands - 物理系spin/course/102F/Ch7-1.pdfThe crystal behaves as an insulator if the allowed energy bands are either filled or empty, for then no electrons can move in an electric](https://reader033.fdocuments.in/reader033/viewer/2022050308/5f701fb590829d35b2598ca2/html5/thumbnails/12.jpg)
Felix Bloch
(1905-1983,
Swiss)
Awarded the 1952 Nobel Prize for
"their development of new ways
and methods for nuclear magnetic
precision measurements
![Page 13: Energy Bands - 物理系spin/course/102F/Ch7-1.pdfThe crystal behaves as an insulator if the allowed energy bands are either filled or empty, for then no electrons can move in an electric](https://reader033.fdocuments.in/reader033/viewer/2022050308/5f701fb590829d35b2598ca2/html5/thumbnails/13.jpg)
![Page 14: Energy Bands - 物理系spin/course/102F/Ch7-1.pdfThe crystal behaves as an insulator if the allowed energy bands are either filled or empty, for then no electrons can move in an electric](https://reader033.fdocuments.in/reader033/viewer/2022050308/5f701fb590829d35b2598ca2/html5/thumbnails/14.jpg)
Demonstration of the energy gap !
![Page 15: Energy Bands - 物理系spin/course/102F/Ch7-1.pdfThe crystal behaves as an insulator if the allowed energy bands are either filled or empty, for then no electrons can move in an electric](https://reader033.fdocuments.in/reader033/viewer/2022050308/5f701fb590829d35b2598ca2/html5/thumbnails/15.jpg)
*
Note ϵ < Uo
![Page 16: Energy Bands - 物理系spin/course/102F/Ch7-1.pdfThe crystal behaves as an insulator if the allowed energy bands are either filled or empty, for then no electrons can move in an electric](https://reader033.fdocuments.in/reader033/viewer/2022050308/5f701fb590829d35b2598ca2/html5/thumbnails/16.jpg)
(0) = *(0)
d(0)/dx = d*(0)/dx
(a) = *(-b) exp{ik(a+b)}
d(a)/dx = d*(-b)/dx exp{ik(a+b)}
![Page 17: Energy Bands - 物理系spin/course/102F/Ch7-1.pdfThe crystal behaves as an insulator if the allowed energy bands are either filled or empty, for then no electrons can move in an electric](https://reader033.fdocuments.in/reader033/viewer/2022050308/5f701fb590829d35b2598ca2/html5/thumbnails/17.jpg)
![Page 18: Energy Bands - 物理系spin/course/102F/Ch7-1.pdfThe crystal behaves as an insulator if the allowed energy bands are either filled or empty, for then no electrons can move in an electric](https://reader033.fdocuments.in/reader033/viewer/2022050308/5f701fb590829d35b2598ca2/html5/thumbnails/18.jpg)
Certain allowed values of Ka, thus giving rise to allowed values of ϵ
![Page 19: Energy Bands - 物理系spin/course/102F/Ch7-1.pdfThe crystal behaves as an insulator if the allowed energy bands are either filled or empty, for then no electrons can move in an electric](https://reader033.fdocuments.in/reader033/viewer/2022050308/5f701fb590829d35b2598ca2/html5/thumbnails/19.jpg)
Energy gaps in ϵ at n !
ϵ = ħ2K2/2m
![Page 20: Energy Bands - 物理系spin/course/102F/Ch7-1.pdfThe crystal behaves as an insulator if the allowed energy bands are either filled or empty, for then no electrons can move in an electric](https://reader033.fdocuments.in/reader033/viewer/2022050308/5f701fb590829d35b2598ca2/html5/thumbnails/20.jpg)
Exact Proof of the Bloch Theorem
![Page 21: Energy Bands - 物理系spin/course/102F/Ch7-1.pdfThe crystal behaves as an insulator if the allowed energy bands are either filled or empty, for then no electrons can move in an electric](https://reader033.fdocuments.in/reader033/viewer/2022050308/5f701fb590829d35b2598ca2/html5/thumbnails/21.jpg)
![Page 22: Energy Bands - 物理系spin/course/102F/Ch7-1.pdfThe crystal behaves as an insulator if the allowed energy bands are either filled or empty, for then no electrons can move in an electric](https://reader033.fdocuments.in/reader033/viewer/2022050308/5f701fb590829d35b2598ca2/html5/thumbnails/22.jpg)
L = 20 a
![Page 23: Energy Bands - 物理系spin/course/102F/Ch7-1.pdfThe crystal behaves as an insulator if the allowed energy bands are either filled or empty, for then no electrons can move in an electric](https://reader033.fdocuments.in/reader033/viewer/2022050308/5f701fb590829d35b2598ca2/html5/thumbnails/23.jpg)
central equation to solve the C(K), and e
![Page 24: Energy Bands - 物理系spin/course/102F/Ch7-1.pdfThe crystal behaves as an insulator if the allowed energy bands are either filled or empty, for then no electrons can move in an electric](https://reader033.fdocuments.in/reader033/viewer/2022050308/5f701fb590829d35b2598ca2/html5/thumbnails/24.jpg)
![Page 25: Energy Bands - 物理系spin/course/102F/Ch7-1.pdfThe crystal behaves as an insulator if the allowed energy bands are either filled or empty, for then no electrons can move in an electric](https://reader033.fdocuments.in/reader033/viewer/2022050308/5f701fb590829d35b2598ca2/html5/thumbnails/25.jpg)
U= 0
![Page 26: Energy Bands - 物理系spin/course/102F/Ch7-1.pdfThe crystal behaves as an insulator if the allowed energy bands are either filled or empty, for then no electrons can move in an electric](https://reader033.fdocuments.in/reader033/viewer/2022050308/5f701fb590829d35b2598ca2/html5/thumbnails/26.jpg)
![Page 27: Energy Bands - 物理系spin/course/102F/Ch7-1.pdfThe crystal behaves as an insulator if the allowed energy bands are either filled or empty, for then no electrons can move in an electric](https://reader033.fdocuments.in/reader033/viewer/2022050308/5f701fb590829d35b2598ca2/html5/thumbnails/27.jpg)