Lecture5-Drift+-+Diffusion+Chap+3+Pierret_marked

Lecture5-Drift+-+Diffusion+Chap+3+Pierret_marked - ECE...

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ECE 3040 - Dr. Ying Zhang Georgia Tech ECE 3040: Microelectronic Circuits Lecture 5 Reading: Pierret 3.1-3.2
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ECE 3040 - Dr. Ying Zhang Georgia Tech Equilibrium carrier concentration (nondegenerate case) Recapture kT E E v kT E E c f v c f e N p and e N n / ) ( / ) ( = = kT E E i kT E E i f i i f e n p and e n n / ) ( / ) ( = = 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 / 3 2 * 2 ) ( 2 2 ) ( 2 = = h h π
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ECE 3040 - Dr. Ying Zhang Georgia Tech np product (nondegenerate case) Recapture Known as the Law of mass Action Independent of Fermi Level and doping
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ECE 3040 - Dr. Ying Zhang Georgia Tech Charge Neutrality: all charge within the semiconductor must cancel. (total ionization case) From the Law of Mass Action and Charge Neutrality => Carrier concentration calculation Recapture () ( ) 0 = + n N N p D A 2 2 2 2 2 2 2 2 i D A D A i A D A D n N N N N p or n N N N N n + + = + + = If N D >>N A and N D >>n i D i D N n p and N n 2 If N A >>N D and N A >>n i A i A N n n and N p 2
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ECE 3040 - Dr. Ying Zhang Georgia Tech Example: An intrinsic Silicon wafer at 470K has 1e14 cm -3 holes. When 1e14 cm -3 acceptors are added, what is the new electron and hole concentrations? Carrier Concentration Calculations
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ECE 3040 - Dr. Ying Zhang Georgia Tech Example: An intrinsic Silicon wafer at 600K has 4e15 cm -3 holes. When 1e14 cm -3 acceptors are added, what is the new electron and hole concentrations? Carrier Concentration Calculations
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ECE 3040 - Dr. Ying Zhang Georgia Tech Determination of Fermi Level Since we started with descriptions of intrinsic materials then it makes sense to reference energies from the intrinsic Fermi level, E i . Intrinsic Material: p e N e N n kT E E v kT E E c f v c f = = = / ) ( / ) ( kT E E v kT E E c i v c i e N e N / ) ( / ) ( = + + = c v v c i N N kT E E E ln 2 2
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ECE 3040 - Dr. Ying Zhang Georgia Tech Determination of Fermi Level Intrinsic Material: + + = * * ln 4 3 2 n p v c i m m kT E E E 2 / 3 * * = n p c v m m N N But, Letting E v =0, this is E g / 2 or “Midgap” -0.007 eV for Si @ 300K ( 0.6% of E G )
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ECE 3040 - Dr. Ying Zhang Georgia Tech Determination of Fermi Level Extrinsic Material: kT E E i f i e n p / ) ( = kT E E i i f e n n / ) ( = = >> >> = >> >> = = i
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This note was uploaded on 09/05/2009 for the course ECE 3040 taught by Professor Hamblen during the Spring '07 term at Georgia Tech.

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Lecture5-Drift+-+Diffusion+Chap+3+Pierret_marked - ECE...

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