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Lec11 - Subject_10:Outline pnJunctionElectrostatics...

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Subject_10: Outline pn-Junction Electrostatics  * pn-junction electrostatics   Electric field and built-in voltage  Depletion-region width(s) * Biasing of pn junctions  Forward and reverse biasing  Quasi-Fermi levels
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• To determine the electrostatics we solve the  POISSON EQUATION  which allows us to relate the  CHARGE  DENSITY  in the junction to the electric field or built-in voltage variation * The charge density is easily determined by assuming an  ABRUPT  doping distribution * With such a doping profile and by assuming that the depletion region extends from -    x p  in the p-type material to x n  in the n-type region we obtain the charge density     variation shown below pn-Junction Electrostatics ) 1 . 10 ( , , 0 0 , 0 , - - - = n p n D p A x x x x x x qN x x qN ρ
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pn-Junction Electrostatics • We now use the Poisson equation to relate the charge density to the electric field and in  ONE-DIMENSION  this  equation takes the following form  * Note here that  ε r  is the relative  DIELECTRIC CONSTANT  of the particular material    under consideration and  ε o  is the permitivity of free space * For the charge density distribution we have assumed the Poisson equation may be    expressed as   ) 2 . 10 ( ) ( ) ( ) ( o r x x dx x dE ε ρ = = ) 3 . 10 ( , , 0 0 , / 0 , / ) ( - - - = n p n o r D p o r A x x x x x x qN x x qN dx x dE
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pn-Junction Electrostatics • Integrating Equation 10.3 and requiring there be  NO  electric field  OUTSIDE  the depletion region we obtain  expressions for the electric field variation near the depletion region ) 4 . 10 ( , , 0 0 , / ) ( 0 , / ) ( ) ( - - - + - = n p n o r n D p o r p A x x x x x x x x qN x x x x qN x E ε E(x) x -x p x n • ELECTRIC FIELD VARIATION ACROSS THE DEPLETION REGION 
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This note was uploaded on 02/28/2011 for the course EE 2 taught by Professor Vis during the Winter '07 term at UCLA.

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Lec11 - Subject_10:Outline pnJunctionElectrostatics...

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