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The physics ofparticle detectors- Fermi energy -
SS2016, Heidelberg June 8, 2016
Silvia Masciocchi, GSI and University of Heidelberg
Detector physics, Fermi level, June 8, 2016S.Masciocchi@gsi.de 2
Fermi-Dirac distribution
Semiconductor materials: crystalline latticeElectrons are fermions → Pauli exclusion principle
Probability distribution:
Detector physics, Fermi level, June 8, 2016S.Masciocchi@gsi.de 3
Band theory of solids
Bands of energy levels are determined by the inter-atomic spacing:
Bands determine the density of available energy states
Detector physics, Fermi level, June 8, 2016S.Masciocchi@gsi.de 4
Band theory of solids
Bands of energy levels are determined by the inter-atomic spacing:
Bands determine the density of available energy states
Detector physics, Fermi level, June 8, 2016S.Masciocchi@gsi.de 5
Fermi energy
Intrinsic semiconductor, Low temperature
Probability distribution from Fermi-Dirac statistics
Density of available energy states
Resulting distribution of charge carriers
Detector physics, Fermi level, June 8, 2016S.Masciocchi@gsi.de 7
Semiconductors and Fermi level
Festkörperphysik (p. 389)Siegfried Hunklinger
Detector physics, Fermi level, June 8, 2016S.Masciocchi@gsi.de 8
Intrinsic semiconductors
Crystalline lattice, of tetravalent elements (Si, Ge)4 valence electrons → covalent bonds
Detector physics, Fermi level, June 8, 2016S.Masciocchi@gsi.de 9
Doping of semiconductors
n-type p-type pentavalent impurities trivalent impurities
Detector physics, Fermi level, June 8, 2016S.Masciocchi@gsi.de 12
Additional levels from doping elements
Festkörperphysik (p. 392)Siegfried Hunklinger
Detector physics, Fermi level, June 8, 2016S.Masciocchi@gsi.de 13
Additional levels from doping elements
Festkörperphysik (p. 394)Siegfried Hunklinger
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