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Physics - Conductivity in Metals - Density of States

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Lecture 4 Density of States and Fermi Energy Concepts Reading: (Cont’d) Notes and Anderson2 sections 2.8-2.13 Georgia Tech ECE 3080 - Dr. Alan Doolittle How do electrons and holes populate the bands? Density of States Concept In lower level courses, we state that “Quantum Mechanics” tells us that the number of available states in a cubic cm per unit of energy, the density of states, is given by: * * mn 2mn ( E  Ec ) gc (E)  , E  Ec 2 3   gv (E)  m * 2 m * ( Ev  E ) p p   2 3 , E  Ev  Number of States    3 cm  unit   Georgia Tech eV ECE 3080 - Dr. Alan Doolittle How do electrons and holes populate the bands? Density of States Concept Thus, the number of states per cubic …show more content…

each kz  combination of nx, ny, nz) c results in a volume of “kspace”. If we add up all possible combinations, we would have an infinite  solution. Thus, we will only 0 b consider states contained in a “fermi-sphere” (see next ky page). kx  Georgia Tech a ECE 3080 - Dr. Alan Doolittle How do electrons and holes populate the bands? Derivation of Density of States Concept Cont’d... Ef   2k 2 f 2m  defines a momentum value for the average electron energy E f 3         single state “cube”: Vsingle state              a  b  c   V  4 “fermi-sphere”: Vfermi-sphere    k 3f    3   Volume of a Volume of a A “Fermi-Sphere” is defined by the number of states in k-space necessary to hold all the electrons needed to add up to the average energy of the crystal (known as the fermi energy). “V” is the physical volume of the crystal where as all other volumes used here refer to volume in k-space. Note that: Vsingle-state is the smallest unit in kspace. Vsingle-state is required to “hold” a single electron. ECE 3080 - Dr. Alan Doolittle Georgia Tech How do electrons and holes populate the bands? Derivation of Density of States Concept Cont’d... k-space volume of a single state “cube”: k-space volume of a “fermi-sphere”: Number of filled states V fermi  sphere N in a fermi-sphere: Vsin gle state Vsingle state 3                   a  b  c   V 

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