The physics of particle detectors - Fermi energy · [email protected] Detector physics, Fermi level, June 8, 2016 3 Band theory of solids Bands of energy levels are determined by

The physics ofparticle detectors- Fermi energy -

SS2016, Heidelberg June 8, 2016

Silvia Masciocchi, GSI and University of Heidelberg

Detector physics, Fermi level, June 8, [email protected] 2

Fermi-Dirac distribution

Semiconductor materials: crystalline latticeElectrons are fermions → Pauli exclusion principle

Probability distribution:

Detector physics, Fermi level, June 8, [email protected] 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, [email protected] 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, [email protected] 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, [email protected] 6

Semiconductors and Fermi level

Detector physics, Fermi level, June 8, [email protected] 7

Semiconductors and Fermi level

Festkörperphysik (p. 389)Siegfried Hunklinger

Detector physics, Fermi level, June 8, [email protected] 8

Intrinsic semiconductors

Crystalline lattice, of tetravalent elements (Si, Ge)4 valence electrons → covalent bonds

Detector physics, Fermi level, June 8, [email protected] 9

Doping of semiconductors

n-type p-type pentavalent impurities trivalent impurities

Detector physics, Fermi level, June 8, [email protected] 10

n-type

Detector physics, Fermi level, June 8, [email protected] 11

p-type

Detector physics, Fermi level, June 8, [email protected] 12

Additional levels from doping elements

Festkörperphysik (p. 392)Siegfried Hunklinger

Detector physics, Fermi level, June 8, [email protected] 13

Additional levels from doping elements

Festkörperphysik (p. 394)Siegfried Hunklinger

Detector physics, Fermi level, June 8, [email protected] 14

Fermi level in doped semiconductors