Chapter25_Carrier-Statistics

Chapter25_Carrier-Statistics - 2.5 Carrier Statistics 2.5.1...

Info iconThis preview shows pages 1–7. Sign up to view the full content.

View Full Document Right Arrow Icon
2.5 Carrier Statistics 2.5.1 Density of States 2.5.2 Fermi Function & Fermi Energy Physical Interpretation Characteristics 2.5.3 Carrier Densities Intrinsic/Extrinsic Semiconductor Intrinsic Fermi Energy Mass Action Law Temperature Dependence 2.5.4 Charge Neutrality Relationship 2.5.5 Non-Complete Ionization Pierret, Chapter 2.4-2.6, page 40-68 Slides courtesy of Prof. Oliver Brand
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
2 2.5.1 Density of States From quantum mechanics, we not only obtain the band structure, i.e., the E(k) relations, but also the density of states g(E)dE, i.e., how many allowed states are in the range E…E+dE: g C (E)dE = m n * 2m n * E E C ( ) π 2 3 dE E E C ( ) 1/2 g V = m p * p * E V E ( ) π 2 3 dE E V E ( )
Background image of page 2
3 Density of States Band Gap E C E V E g C (E) g V (E) g(E) Units of g(E)dE are [cm -3 ]
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
4 2.5.2 Fermi Function & Fermi Energy What determines whether an allowed state is occupied by an electron or not? Fermi Function f(E): f(E) is a probability function which gives the probability whether a state is occupied or not E F is the Fermi Energy f(E) = 1 1 + e (E E F )/kT
Background image of page 4
5 Characteristics of Fermi Function Because of Pauli principle: 0 f(E) 1 f(E = E F ) = 0.5 The probability that a state is occupied at the Fermi energy is 50% f(E) is symmetric around E F : f(E F + E) = 1 – f(E F – E) For T = 0 the Fermi function becomes a step function, i.e. all states below E F are occupied, all states above E F empty Energy E [eV] Fermi Function f(E) E F = 1 eV kT = 0.0259 eV
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
6
Background image of page 6
Image of page 7
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 22

Chapter25_Carrier-Statistics - 2.5 Carrier Statistics 2.5.1...

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online