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Lecture5_LawOfTheJunction_IVDerivation

# Lecture5_LawOfTheJunction_IVDerivation - Lecture Lecture 5...

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ecture 5 Lecture 5 P-N Junction Diodes Quantitative Analysis (Math, math and more math) ECE 4833 - Dr. Alan Doolittle Georgia Tech

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Quantitative p-n Diode Solution Assumptions: 1) steady state conditions ) non egenerate doping 2) non- degenerate doping 3) one- dimensional analysis 4) low- level injection Quasi-Neutral Regions 5) no light (G L = 0) Current equations: - pe - pe J=J p x  J n (x) q E +qD n/dx) epletion Region p type n type J n =q n nE +qD n (dn/dx) J p = q p pE - qD p (dp/dx) V A Depletion Region ECE 4833 - Dr. Alan Doolittle Georgia Tech
- pe - pe Quantitative p-n Diode Solution epletion Region p type n type Depletion Region 0 E 0 E 0 E -x p x n Application of the Minority Carrier Diffusion Equation ) ( ) ( ) ( ) ( ) ( 2 2 2 L p n n P n p p G p x p D t p L n p p N p n n G n x n D t n ) ( ) ( ) ( ) ( ) ( 2 2 2 Since electric fields exist in the depletion gion, the minority 0 0 2 p n n P x D n p p N x D 0 2 region, the minority carrier diffusion equation does not apply here. :  Condition Boundary : Condition Boundary : Condition Boundary : Condition Boundary ECE 4833 - Dr. Alan Doolittle Georgia Tech 0 ) ( x n p ? ) ( p p x x n ? ) ( n n x x p 0 ) ( x p n

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- pe - pe Quantitative p-n Diode Solution epletion Region p type n type Depletion Region -x x 0 E 0 E 0 E p n Application of the Minority Carrier Diffusion Equation ? ) ( : p p x x n Condition Boundary ? ) ( : n n x x p Condition Boundary    ) ( ) ( 2 kT F F i p p p p kT F E i kT E F i P N P i i N e n x x p x x n e n p and e n n ) ( ) ( ) ( ) ( 2 2 kT qV i kT qV i A p p p p p p A A e n x x n e n N x x n x x p x x n ) ( 2 o kT qV A i p p A p p A n e N n x x n N ECE 4833 - Dr. Alan Doolittle Georgia Tech 1 ) ( 1 ) ( 2 2 kT qV D i n n n kT qV A i p p A A e N n x x p x x at similarly and e N n x x n
- pe - pe Quantitative p-n Diode Solution epletion Region p type n type Depletion Region -x x 0 E 0 E 0 E p n Application of the Minority Carrier Diffusion Equation ? ) ( : p p x x n Condition Boundary ? ) ( : n n x x p Condition Boundary    kT F F i p p p p kT F E i kT E F i e n x x p x x n e n p and e n n P N P i i N ) ( ) ( 2 kT qV i kT qV i A p p p p p p e n x x n e n N x x n x x p x x n A A ) ( ) ( ) ( ) ( 2 2 aw of the Junction o kT qV A i p p A p p n e N n x x n N A ) ( 2 ) ( 2 kT qV D i n n A e N n x x p Law of the Junction ECE 4833 - Dr. Alan Doolittle Georgia Tech n kT qV A i p p x x at similarly and e N n x x n A 1 ) ( 2 1 ) ( 2 kT qV D i n n A e N n x x p

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- pe - pe Quantitative p-n Diode Solution epletion Region p type
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Lecture5_LawOfTheJunction_IVDerivation - Lecture Lecture 5...

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