BZs_Bands - Energy Band Structure Band Structure/ E xtended...

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Unformatted text preview: Energy Band Structure Band Structure/ E xtended Zone Scheme First Brillouin Zone 20 18 16 14 12 10 8 6 4 2 0 -4 -3 -2 -1 0 1 2 3 4 Energy Energy ka/ i P Energy Band Structure e = e (k ) Periodic Zone Scheme 10 9 8 7 6 Energy Energy 5 4 3 2 1 0 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 ka/Pi 1 Reduced Zone Scheme 10 8 Energy Energy 6 4 2 0 -1 -0.5 0 ka/Pi 0.5 1 Bands folded into First Brillouin Zone Electronic Spectrum Energy bound free "solid" 2 Free Electron Bands n=-2 Energy E k = E k (k + G) n=1 n=-1 1D : E = 2 h2 n2p ^ k + ~ ; n = 0, 1, 2 ... 2m a n=0 k Brillouin zones - 2D BZ construction reciprocal lattice bisect vectors to the nearest neighbors area defined by bisecting lines represents 1BZ 3 Brillouin zones -2D higher order zones can be mapped directly onto the 1st BZ by simple translation all BZs have exactly the same area/volume 1BZ corresponds to the primitive lattice cell in reciprocal space 2D band diagram 16000 16000 14000 14000 12000 12000 10000 10000 8000 8000 6000 6000 4000 4000 2000 2000 0 0 5 10 15 20 25 30 35 40 45 0 0 5 10 15 20 25 30 35 40 45 4 2D band diagram K G X Brillouin zones - 3D fcc 1st BZ 2nd BZ 3rd BZ bcc 5 Free electron bands for fcc structure G center of the BZ X [100] intercept; K [110] intercept; L [111] intercept; G - X path D G - K path S G - L path L Band structure of Al (fcc) 6 Band structure of Cu (fcc) Band structure of Si (diamond) Bandgap 7 Band structure of GaAs (zb) Bandgap Band Structure of AlN (wurtzite) L-M K Bandgap First Brillouin Zone Nomenclature G 8 Curves of equal energy 2D square lattice 1st BZ deviation from circles a we approach critical points (X, K) Energy states in QN space for a 3D box 9 DOS of Si Electrical conduction 10 AlN Band Structure L-M K G First Brillouin Zone Nomenclature K. W. Kim et al (1999). Electron velocity 11 ...
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This note was uploaded on 05/05/2008 for the course RAUNVIS 09.21.22 taught by Professor Hafliði during the Spring '08 term at Uni. Iceland.

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