lec_2.2 - 2.2 Carrier Statistic 2.2.1 Density of States...

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ECE3080, Chapter 2.2 1 May 25, 2005 ECE 3080: Chapter 2.2 – Device Fundamentals O. Brand, 1 of 23 2.2 Carrier Statistic 2.2.1 Density of States Physical Interpretation Characteristics 2.2.3 Carrier Densities Intrinsic/Extrinsic Semiconductor Intrinsic Fermi Energy Mass Action Law Temperature Dependence 2.2.4 Charge Neutrality Relationship 2.2.5 Non-Complete Ionization Pierret, Chapter 2.4-2.6, page 40-68 May 25, 2005 ECE 3080: Chapter 2.2 – Device Fundamentals O. Brand, 2 of 23 2.2.1 Density of States I 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 ( ) " 2 ! 3 dE # E ! E C ( ) 1/2 g V (E)dE = m p * 2m p * E V ! E ( ) " 2 ! 3 dE # E V ! E ( ) 1/2
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ECE3080, Chapter 2.2 2 May 25, 2005 ECE 3080: Chapter 2.2 – Device Fundamentals O. Brand, 3 of 23 Density of States II Band Gap E C E V E g C (E) g V (E) g(E) Units of g(E)dE are [cm -3 ] May 25, 2005 ECE 3080: Chapter 2.2 – Device Fundamentals O. Brand, 4 of 23 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
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ECE3080, Chapter 2.2 3 May 25, 2005 ECE 3080: Chapter 2.2 – Device Fundamentals O. Brand, 5 of 23 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 May 25, 2005 ECE 3080: Chapter 2.2 – Device Fundamentals O. Brand, 6 of 23 Physical Interpretation of Fermi Energy E F
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This note was uploaded on 08/28/2010 for the course ECE 3080 taught by Professor Staff during the Spring '08 term at Georgia Tech.

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lec_2.2 - 2.2 Carrier Statistic 2.2.1 Density of States...

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