MIT6_012F09_lec06

MIT6_012F09_lec06 - 6.012 Microelectronic Devices and...

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Clif Fonstad, 9/29/09 Lecture 6 - Slide 1 Announcements First Hour Exam - Oct. 7, 7:30-9:30 pm; thru 10/2/09, PS #4 Review Minority carrier flow in QNRs: 1. L min << w, 2. L min >> w I-V relationship for an abrupt p-n junction Assume: 1. Low level injection 2. All applied voltage appears across junction: 3. Majority carriers in quasi-equilibrium with barrier 4. Negligible SCL generation and recombination Relate minority populations at QNR edges, -x p and x n , to v AB Use n'(-x p ), p'(x n ) to find hole and electron currents in QNRs Connect currents across SCL to get total junction current, i D Features and limitations of the model Engineering the minority carrier injection across a junction Deviations at low and high current levels Deviations at large reverse bias 6.012 - Microelectronic Devices and Circuits Lecture 6 - p-n Junctions: I-V Relationship - Outline
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Clif Fonstad, 9/29/09 Lecture 6 - Slide 2 QNR Flow : Uniform doping, non-uniform LL injection We use the 5 QNR flow conditions* to simplify our 5 equations. .. (assuming a p-type sample) q " ( x ) p ( x , t ) # n ( x , t ) + N d + ( x ) # N a # ( x ) [ ] = dE x ( x , t ) dx J h ( x , t ) = q μ h p ( x , t ) E ( x , t ) " qD h # p ( x , t ) x J e ( x , t ) = q μ e n ( x , t ) E ( x , t ) + qD e n ( x , t ) x p ( x , t ) t + 1 q J h ( x , t ) x = n ( x , t ) t # 1 q J e ( x , t ) x $ g L ( x , t ) # n ( x , t ) p ( x , t ) # n i 2 [ ] r ( t ) d 2 n '( x , t ) dx 2 " n '( x , t ) D e e = " 1 D e g L ( x , t ) ..and end up with one equation in n': the static diffusion equation! " 1 q dJ h ( x , t ) dx = # 1 q dJ e ( x , t ) dx $ g L ( x , t ) # n '( x , t ) % e Quasi-static Quasi-static LLI LLI Uniform doping Negligible minority drift Quasi-neutrality " q μ h p o ( x ) E ( x , t ) # qD h dn '( x , t ) dx " J e ( x , t ) # qD e dn '( x , t ) dx " q p '( x , t ) $ n '( x , t ) [ ] * Five assumptions that define flow problems AND should be validated at the end.
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Clif Fonstad, 9/29/09 Lecture 6 - Slide 3 QNR Flow , cont. : Solving the steady state diffusion equation The steady state diffusion equation in p-t ype material is: and for n-t ype material it is: d 2 n '( x ) dx 2 " n '( x ) L e 2 = " 1 D e g L ( x ) d 2 p '( x ) dx 2 " p '( x ) L h 2 = " 1 D h g L ( x ) d 2 p '( x ) dx 2 " p '( x ) L h 2 = 0 d 2 n '( x ) dx 2 " n '( x ) L e 2 = 0 In a basic p-n diode, we have g L = 0 which means we only need the homogenous solutions, i.e. expressions that satisfy: n-side : p-side : L e " D e # e In writing these expressions we have introduced L e and L h , the minority carrier diffusion lengths for holes and electrons, as: L h " D h h We'll see that the minority carrier diffusion length tells us how far the average minority carrier diffuses before it recombines.
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Clif Fonstad, 9/29/09 Lecture 6 - Slide 4 QNR Flow , cont. : Solving the steady state diffusion equation We seldom care about this general result. Instead, we find that most diodes fall into one of two cases:
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This note was uploaded on 11/07/2011 for the course COMPUTERSC 6.012 taught by Professor Charlesg.sodini during the Fall '09 term at MIT.

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MIT6_012F09_lec06 - 6.012 Microelectronic Devices and...

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