Lecture5-EquilibriumCarrierConcentrations

# Lecture5-EquilibriumCarrierConcentrations - Lecture 5...

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ECE 3040 - Dr. Alan Doolittle Georgia Tech Lecture 5 Carrier Concentrations in Equilibrium Reading: (Cont’d) Pierret 2.5-2.6

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ECE 3040 - Dr. Alan Doolittle Georgia Tech Motivation: Since current (electron and hole flow) is dependent on the concentration of electrons and holes in the material, we need to develop equations that describe these concentrations. Furthermore, we will find it useful to relate the these concentrations to the average energy (fermi energy) in the material. Developing the mathematical model for electrons and holes
ECE 3040 - Dr. Alan Doolittle Georgia Tech Developing the mathematical model for electrons and holes The density of electrons is: = band conduction of Top band conduction of Bottom E E c dE E f E g n ) ( ) ( = band valence of Top band valence of Bottom E E v dE E f E g p )] ( 1 )[ ( The density of holes is: Probability the state is filled Probability the state is empty Number of states per cm -3 in energy range dE Number of states per cm -3 in energy range dE Note: units of n and p are #/cm 3

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ECE 3040 - Dr. Alan Doolittle Georgia Tech Developing the mathematical model for electrons and holes + = band conduction of Top c f E E kT E E c n n dE e E E m m n / ) ( 3 2 * * 1 2 h π + = 0 ) ( 2 / 1 3 2 2 / 3 * * 1 ) ( 2 η η π η η d e kT m m n c n n h = = = = band conduction of Top c c f c c E Let E E when kT E E and kT E E Letting 0 , η η η This is known as the Fermi-dirac integral of order 1/2 or, F 1/2 ( η c )
ECE 3040 - Dr. Alan Doolittle Georgia Tech Developing the mathematical model for electrons and holes band valence the in states of density effective the kT m N and band conduction the in states of density effective the kT m N p v n c 2 / 3 2 * 2 /

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