Lecture_28

Lecture_28 - PHYS 342 Fall 2011 Lecture 28: The Reciprocal...

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PHYS 342 Fall 2011 Lecture 28: The Reciprocal Lattice on Reifenberger Ron Reifenberger Birck Nanotechnology Center Purdue University cos sin i i ei   2 2 1 1 1; i Ni e e eN a n y integer Lecture 28 1
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Atomic Physics – confined electrons have quantized energies r U(r) 2 1 () 4 o Ze Ur r   +Ze 2
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Transition to Crystalline Solids aa a +Ze +Ze +Ze +Ze 3
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Schematic U(x) for a periodic 1D solid surface Weakly bound states “ eorganize” Electrons are Fermions : at most two electrons per energy level aa a vacuum metal reorganize Work function φ lence valence electrons Ze Ze Ze Ze Tightly bound states “shift energy” core states 4 +Ze +Ze +Ze +Ze in energy 2 clicks
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How to approximate U(x) for a periodic solid? Free electron model early free ? ? ? ? Nearly free electron model ? ? ? ? ronig Penny Kronig Penny model ? ? ? ? aa a x=0 5
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The simplest model: 1D Free Electron Model Free electron model 2 * () ! ! ikx xA e x x A independent of x   : I dimensions U(x)=0 ree lectron E(k): 2 2 3: (,) () (,) 2 : e n rt Ur rt i E rt mt dimension    free-electron E(k): 2 2 2 e Ek k m 2 2 2 1: 2 e x In xEx m x  E(k) 2 2 2 2 let ikx ikx x Ae Ake k x k 6 22 2 2 ee e kk p EE p k mm m     ANY E and k are allowed
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How realistic is the free electron odel? model?
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Lecture_28 - PHYS 342 Fall 2011 Lecture 28: The Reciprocal...

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