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    Previous lecture 2010.10.25 Next lecture 2010.11.01 to index

    http://web.ift.uib.no/AMOS/PHYS208/2010.10.25/index.htmlhttp://web.ift.uib.no/AMOS/PHYS208/2010.10.25/index.htmlhttp://web.ift.uib.no/AMOS/PHYS208/2010.11.01/index.htmlhttp://web.ift.uib.no/AMOS/PHYS208/2010.11.01/index.htmlhttp://web.ift.uib.no/AMOS/PHYS208/index.htmlhttp://web.ift.uib.no/AMOS/PHYS208/index.htmlhttp://web.ift.uib.no/AMOS/PHYS208/index.htmlhttp://web.ift.uib.no/AMOS/PHYS208/2010.11.01/index.htmlhttp://web.ift.uib.no/AMOS/PHYS208/2010.10.25/index.html

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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.pdf

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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.pdf

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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.pdf

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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.pdf

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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.pdf

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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.pdf

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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.pdf

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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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    Previous lecture 2010.10.205 Next lecture 2010.11.01

    http://web.ift.uib.no/AMOS/PHYS208/2010.10.25/index.htmlhttp://web.ift.uib.no/AMOS/PHYS208/2010.10.25/index.htmlhttp://web.ift.uib.no/AMOS/PHYS208/2010.11.01/index.htmlhttp://web.ift.uib.no/AMOS/PHYS208/2010.11.01/index.htmlhttp://web.ift.uib.no/AMOS/PHYS208/2010.11.01/index.htmlhttp://web.ift.uib.no/AMOS/PHYS208/2010.10.25/index.html

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