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ELCT363_Lecture11_Carrier_Concentration

# ELCT363_Lecture11_Carrier_Concentration - Carrier...

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ELCT 363: Intro. to Microelectronics Lecture 11; Slide Mandal/Fall 2011 Carrier Concentration Neamen, Chapter 4 1

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ELCT 363: Intro. to Microelectronics Lecture 11; Slide Mandal/Fall 2011 Determination of Electron Concentration using Fermi Distribution Function Concentrations of electrons/ holes at thermal equilibrium is a function of Fermi (energy) distribution and the density of available energy states. N C is called the effective density of states at conduction band. At thermal equilibrium, the concentration of electrons ( n 0 ) at the conduction band, E = E c is: ( 29 kT ) E - (E if exp F 2245 - - kT E E F ( 29 ( 29 kT E E c kT E E F C F C N n n - - - - = exp exp 0 0 Valence band Conduction band E F = E i = E g /2 2
ELCT 363: Intro. to Microelectronics Lecture 11; Slide Mandal/Fall 2011 Determination of Hole Concentration using Fermi Distribution Function N V is called the effective density of states at valence band. ( 29 kT ) E - (E if exp F 2245 - - kT E E F ( 29 ( 29 kT E E v kT E E V F V F N p p - - - - = exp exp 0 0 Valence band Conduction band E F = E i = E g /2 At thermal equilibrium, the concentration of holes ( p 0 ) at the valence band, E = E V is: Remember that the energy level E v is below the Fermi level; so, E v < E F so we write, E F E ̶ V 3

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ELCT 363: Intro. to Microelectronics Lecture 11; Slide Mandal/Fall 2011 Intrinsic Electron Concentration For intrinsic (pure) semiconductor, E F = E i = E g /2 The concentration of electrons at the conduction band is: ( 29 kT E E c F N n - - = exp 0 Valence band Conduction band E F = E i = E g /2 If E = E c , then (E c - E F ) = (E c - E i ) = E g /2 kT E i g N n 2 0 exp - = k = 1.38 × 10 -23
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