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Lec9 - Subject_08:Outline *Continuityequations...

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Subject_08: Outline Equations of State for Semiconductors * Continuity equations  Minority-carrier diffusion equations  Simplifications & applications  Haynes-Schockley experiment
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Continuity Equations • So far we looked  SEPARATELY  at the problems of carrier drift, diffusion, recombination and generation in  semiconductors * In reality however  ALL  of these processes will be active at  ANY  time and will  EACH    cause  CHANGES  in the carrier concentration * To determine the  NET  change in the carrier concentrations with time we therefore      SUM  over the changes produced by the individual carrier processes ) 2 . 8 ( ) 1 . 8 ( Other G R thermal diff drift Other G R thermal diff drift t p t p t p t p t p t n t n t n t n t n + + + = + + + = - - “OTHER” SOURCES OF R-G PROCESSES INCLUDE  ILLUMINATION IMPACT IONIZATION , etc.
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Continuity Equations • Next we note that the rate of change of carrier concentration due to the  DRIFT  and  DIFFUSION  currents may be  written as • Combining this with Equations 8.1 & 8.2 we obtain the electron and hole  CONTINUITY   EQUATIONS ) 4 . 8 ( 1 ) 3 . 8 ( 1 Other G R thermal P Other G R thermal N t p t p q t p t n t n q t n + + - = + + = - - J J THE CONTINUITY EQUATIONS PROVIDE THE  MOST BASIC  STARTING POINT FOR THE ANALYSIS OF  SEMICONDUCTOR DEVICES … NOTE HOW THE R-G PROCESSES DO  NOT  CONTRIBUTE TO CURRENT FLOW! P diff drift q p t p t p t p J v r - = = = + 1
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Continuity Equations • An important application of the continuity equations lies in the derivation of the  MINORITY-CARRIER DIFFUSION  EQUATIONS * To derive these equations we once again consider applying a sudden excitation to a    semiconductor to produce a  SMALL  and  UNIFORM  increase in carrier concentration * We focus in particular on the decay of minority carriers in a p-type semiconductor     and proceed by making a number of important  ASSUMPTIONS   t n t n t n n n t t n x n x n x n n n x x n x n qD x n qD nE q J o o o o n n x n N = + = + = = + = + = 2245 + = ) ( . 3 ) ( . 2 . 1 μ • SINCE THE PERTURBATION PRODUCES A  UNIFORM   AND  SMALL  CHANGE IN CARRIER CONCENTRATION  WE ASSUME THE ELECTRIC FIELD WITHIN THE SEMICONDUCTOR IS  ZERO • WE CONSIDER A  UNIFORMLY  DOPED SEMICONDUCTOR IN  WHICH THE EQUILIBRIUM ELECTRON AND HOLE  CONCENTRATIONS n o  & p o  DO  NOT  DEPEND ON EITHER  POSITION  OR  TIME
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Continuity Equations • By introducing these assumptions we obtain the  MINORITY-CARRIER DIFFUSION EQUATIONS    * Note here that we have exploited Equations 7.5 & 7.6 7 and have also used the 
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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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Lec9 - Subject_08:Outline *Continuityequations...

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