Lecture14 p-n Junctions 4 - Quantitative

# Lecture14 p-n Junctions 4 - Quantitative - Lecture 14 P-N...

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ECE 3040 - Dr. Alan Doolittle Georgia Tech Lecture 14 P-N Junction Diodes: Part 3 Quantitative Analysis (Math, math and more math) Reading: Pierret 6.1

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ECE 3040 - Dr. Alan Doolittle Georgia Tech Quantitative p-n Diode Solution Assumptions: 1) steady state conditions 2) non- degenerate doping 3) one- dimensional analysis 4) low- level injection 5) no light (G L = 0) Current equations: J=J p ( x )+ J n (x) J n =q µ n nE +qD n (dn/dx) J p = q µ p pE - qD p (dp/dx) V A Quasi-Neutral Regions Depletion Region p-type n-type
ECE 3040 - Dr. Alan Doolittle Georgia Tech p-type n-type Quantitative p-n Diode Solution Depletion Region -x p x n 0 ) ( ) ( 0 ) ( ) ( ) ( 2 2 2 2 + = + = p n n P L p n n P n p x p D G p x p D t p τ n p p N L n p p N p n x n D G n x n D t n ) ( ) ( 0 ) ( ) ( ) ( 2 2 2 2 = + = Since electric fields exist in the depletion region, the minority carrier diffusion equation does not apply here. Application of the Minority Carrier Diffusion Equation 0 ) ( : = −∞ x n Condition Boundary p ? ) ( : = = p p x x n Condition Boundary ? ) ( : = = n n x x p Condition Boundary 0 ) ( : = x p Condition Boundary n 0 E 0 = E 0 = E

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ECE 3040 - Dr. Alan Doolittle Georgia Tech p-type n-type Quantitative p-n Diode Solution Depletion Region -x p x n Application of the Minority Carrier Diffusion Equation ? ) ( : = = p p x x n Condition Boundary ? ) ( : = = n n x x p Condition Boundary 0 E 0 = E 0 = E () ( ) () = = = = = = = = = = = = = = = = = = = 1
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Lecture14 p-n Junctions 4 - Quantitative - Lecture 14 P-N...

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