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Tight Binding
models - Bands in
2 and 3
dimensional
model systems
This is treated in
many textbooks
In our note we have
detail counting of the
terms
see
2010_Bloch_PDF/Ba
nd-3-dim-EXT.pdfin
2010_Bloch_PDF/
http://web.ift.uib.no/AMOS/PHYS208/2010_Bloch_PDF/Band-3-dim-EXT.pdfhttp://web.ift.uib.no/AMOS/PHYS208/2010_Bloch_PDF/Band-3-dim-EXT.pdfhttp://web.ift.uib.no/AMOS/PHYS208/2010_Bloch_PDF/Band-3-dim-EXT.pdfhttp://web.ift.uib.no/AMOS/PHYS208/2010_Bloch_PDF/index.htmlhttp://web.ift.uib.no/AMOS/PHYS208/2010_Bloch_PDF/index.htmlhttp://web.ift.uib.no/AMOS/PHYS208/2010_Bloch_PDF/index.htmlhttp://web.ift.uib.no/AMOS/PHYS208/2010_Bloch_PDF/Band-3-dim-EXT.pdfhttp://web.ift.uib.no/AMOS/PHYS208/2010_Bloch_PDF/Band-3-dim-EXT.pdf7/22/2019 Tight Binding models - Bands in 2 and 3 dimensional model systems.docx
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1-LCAO-Tight-Binding.pngThis is being evaluated see2010_Bloch_PDF/Band-3-dim-EXT.pdfin2010_Bloch_PDF/
http://web.ift.uib.no/AMOS/PHYS208/2010_Bloch_PDF/Band-3-dim-EXT.pdfhttp://web.ift.uib.no/AMOS/PHYS208/2010_Bloch_PDF/Band-3-dim-EXT.pdfhttp://web.ift.uib.no/AMOS/PHYS208/2010_Bloch_PDF/Band-3-dim-EXT.pdfhttp://web.ift.uib.no/AMOS/PHYS208/2010_Bloch_PDF/index.htmlhttp://web.ift.uib.no/AMOS/PHYS208/2010_Bloch_PDF/index.htmlhttp://web.ift.uib.no/AMOS/PHYS208/2010_Bloch_PDF/index.htmlhttp://web.ift.uib.no/AMOS/PHYS208/2010_Bloch_PDF/index.htmlhttp://web.ift.uib.no/AMOS/PHYS208/2010_Bloch_PDF/Band-3-dim-EXT.pdf7/22/2019 Tight Binding models - Bands in 2 and 3 dimensional model systems.docx
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5-
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CALCULATIONS.png
5-CALCULATIONS2.png
The counting of terms
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represent_integral_terms.png
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This is being evaluated
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5-
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CALCULATIONS.png
5-CALCULATIONS2.png
Now we really count take a given atom - with index 0 and the -a and +a neighboursin all three members of the product see2010_Bloch_PDF/Band-3-dim-EXT.pdfin2010_Bloch_PDF/
http://web.ift.uib.no/AMOS/PHYS208/2010_Bloch_PDF/Band-3-dim-EXT.pdfhttp://web.ift.uib.no/AMOS/PHYS208/2010_Bloch_PDF/Band-3-dim-EXT.pdfhttp://web.ift.uib.no/AMOS/PHYS208/2010_Bloch_PDF/Band-3-dim-EXT.pdfhttp://web.ift.uib.no/AMOS/PHYS208/2010_Bloch_PDF/index.htmlhttp://web.ift.uib.no/AMOS/PHYS208/2010_Bloch_PDF/index.htmlhttp://web.ift.uib.no/AMOS/PHYS208/2010_Bloch_PDF/index.htmlhttp://web.ift.uib.no/AMOS/PHYS208/2010_Bloch_PDF/index.htmlhttp://web.ift.uib.no/AMOS/PHYS208/2010_Bloch_PDF/Band-3-dim-EXT.pdf7/22/2019 Tight Binding models - Bands in 2 and 3 dimensional model systems.docx
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...
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see2010_Bloch_PDF/Band-3-dim-EXT.pdfin2010_Bloch_PDF/
COUNTING THIS IS ANIMATED in our PDF note
http://web.ift.uib.no/AMOS/PHYS208/2010_Bloch_PDF/Band-3-dim-EXT.pdfhttp://web.ift.uib.no/AMOS/PHYS208/2010_Bloch_PDF/Band-3-dim-EXT.pdfhttp://web.ift.uib.no/AMOS/PHYS208/2010_Bloch_PDF/Band-3-dim-EXT.pdfhttp://web.ift.uib.no/AMOS/PHYS208/2010_Bloch_PDF/index.htmlhttp://web.ift.uib.no/AMOS/PHYS208/2010_Bloch_PDF/index.htmlhttp://web.ift.uib.no/AMOS/PHYS208/2010_Bloch_PDF/index.htmlhttp://web.ift.uib.no/AMOS/PHYS208/2010_Bloch_PDF/index.htmlhttp://web.ift.uib.no/AMOS/PHYS208/2010_Bloch_PDF/Band-3-dim-EXT.pdf7/22/2019 Tight Binding models - Bands in 2 and 3 dimensional model systems.docx
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0+-0+--0.png
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only_four_gamma_remain.png see2010_Bloch_PDF/Band-3-dim-EXT.pdfin2010_Bloch_PDF/
see2010_Bloch_PDF/Band-3-dim-EXT.pdfin2010_Bloch_PDF/
http://web.ift.uib.no/AMOS/PHYS208/2010_Bloch_PDF/Band-3-dim-EXT.pdfhttp://web.ift.uib.no/AMOS/PHYS208/2010_Bloch_PDF/Band-3-dim-EXT.pdfhttp://web.ift.uib.no/AMOS/PHYS208/2010_Bloch_PDF/Band-3-dim-EXT.pdfhttp://web.ift.uib.no/AMOS/PHYS208/2010_Bloch_PDF/index.htmlhttp://web.ift.uib.no/AMOS/PHYS208/2010_Bloch_PDF/index.htmlhttp://web.ift.uib.no/AMOS/PHYS208/2010_Bloch_PDF/index.htmlhttp://web.ift.uib.no/AMOS/PHYS208/2010_Bloch_PDF/Band-3-dim-EXT.pdfhttp://web.ift.uib.no/AMOS/PHYS208/2010_Bloch_PDF/Band-3-dim-EXT.pdfhttp://web.ift.uib.no/AMOS/PHYS208/2010_Bloch_PDF/Band-3-dim-EXT.pdfhttp://web.ift.uib.no/AMOS/PHYS208/2010_Bloch_PDF/index.htmlhttp://web.ift.uib.no/AMOS/PHYS208/2010_Bloch_PDF/index.htmlhttp://web.ift.uib.no/AMOS/PHYS208/2010_Bloch_PDF/index.htmlhttp://web.ift.uib.no/AMOS/PHYS208/2010_Bloch_PDF/index.htmlhttp://web.ift.uib.no/AMOS/PHYS208/2010_Bloch_PDF/Band-3-dim-EXT.pdfhttp://web.ift.uib.no/AMOS/PHYS208/2010_Bloch_PDF/index.htmlhttp://web.ift.uib.no/AMOS/PHYS208/2010_Bloch_PDF/Band-3-dim-EXT.pdf7/22/2019 Tight Binding models - Bands in 2 and 3 dimensional model systems.docx
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6-result-2-dim.png
MATLAB - Symbolic (Mupad or Maple) - this is nice to have checked (after the lecture)>> syms x y; cos(x) + cos(y) - 2* cos( ( x + y )/ 2) * cos (( x - y ) / 2)
ans =
cos(x) + cos(y) - 2*cos(x/2 - y/2)*cos(x/2 + y/2)
>> simplify(cos(x) + cos(y) - 2*cos(x/2 - y/2)*cos(x/2 + y/2) )ans =
0
>> expand( 2*cos(x/2 - y/2)*cos(x/2 + y/2) )
ans =
2*cos(x/2)^2*cos(y/2)^2 - 2*sin(x/2)^2*sin(y/2)^2
>> simplify(ans)
ans =
cos(x) + cos(y)
>>
see2010_Bloch_PDF/Band-3-dim-EXT.pdfin2010_Bloch_PDF/
THIS IS THE STARTING FORMULA .......
http://web.ift.uib.no/AMOS/PHYS208/2010_Bloch_PDF/Band-3-dim-EXT.pdfhttp://web.ift.uib.no/AMOS/PHYS208/2010_Bloch_PDF/Band-3-dim-EXT.pdfhttp://web.ift.uib.no/AMOS/PHYS208/2010_Bloch_PDF/Band-3-dim-EXT.pdfhttp://web.ift.uib.no/AMOS/PHYS208/2010_Bloch_PDF/index.htmlhttp://web.ift.uib.no/AMOS/PHYS208/2010_Bloch_PDF/index.htmlhttp://web.ift.uib.no/AMOS/PHYS208/2010_Bloch_PDF/index.htmlhttp://web.ift.uib.no/AMOS/PHYS208/2010_Bloch_PDF/index.htmlhttp://web.ift.uib.no/AMOS/PHYS208/2010_Bloch_PDF/Band-3-dim-EXT.pdf7/22/2019 Tight Binding models - Bands in 2 and 3 dimensional model systems.docx
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THIS IS THE RESULTING FORMULA .......
9-energy.png
9-formula.png
see the end part of 2010_Bloch_PDF/Band-3-dim-EXT.pdfin2010_Bloch_PDF/
http://web.ift.uib.no/AMOS/PHYS208/2010_Bloch_PDF/Band-3-dim-EXT.pdfhttp://web.ift.uib.no/AMOS/PHYS208/2010_Bloch_PDF/Band-3-dim-EXT.pdfhttp://web.ift.uib.no/AMOS/PHYS208/2010_Bloch_PDF/index.htmlhttp://web.ift.uib.no/AMOS/PHYS208/2010_Bloch_PDF/index.htmlhttp://web.ift.uib.no/AMOS/PHYS208/2010_Bloch_PDF/index.htmlhttp://web.ift.uib.no/AMOS/PHYS208/2010_Bloch_PDF/index.htmlhttp://web.ift.uib.no/AMOS/PHYS208/2010_Bloch_PDF/Band-3-dim-EXT.pdf7/22/2019 Tight Binding models - Bands in 2 and 3 dimensional model systems.docx
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funny.png
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closest-distance.png
Band theory of solids
- Energy bands
what is energy band see pictures E(k) is band, the range of E -- ( Emin, Emax ) - the transparent color bands ....
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- Gaps between energy bands
- Where is the FERMI LEVEL for a given material
- Number of states in the band
- Metals Semiconductors Insulators
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level.png
A picture of calculated (realistic, high quality calculations) bands in Copper(from literature .... )
8-4-copper.png
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s-semicond.png
NEW TOPIC STARTED:
Semiconductors:
The P-N junction, the transistor, the computers .....but first the doping of purified crystals, electrons and holes and quantum mechanics
.... The exam text may 2010
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