Note for ECE 352 at UA
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This 2 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Arizona taught by a professor in Fall. Since its upload, it has received 40 views.
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Date Created: 02/06/15
Depletion Approximation Using 1 V Ef Ex We write nnlequot V and pnlequot V The Poisson equation 61211 q dxz 6 Or using the voltage concentration relation 3 Znl ewV equot V N N p nN N 61211 q i 2n s1nhzlNd Na Not solvable analytically Typical approximations a depletion approximation np0 in depletion region b analysis of solution aroung xp and x n Example of analysis around x where p 0 and N g 0 thus 6121 q abc2 g nNd For xgtgt xquot zznconst and nnlequot V N Around x m x field differs slightly from the constant by the function 5 and thus we write 1 11 5 Because 11quot const we can write 2 nm Us1ng n new V we wr1te 5W 2 quotKevinV gigV EH N5 nnlequot 39 Therefore we can write ZN Ne 5Vr Because 5 is small we can use the series expansion e Wr 1 5V5V2 5V3 Which yields LN g dxz e K I Changing the variable y x x we write d 9 J 5 dy2 e K This equation can be solved analytically yielding V y Ae39yLD BeyLD where LD EN is the Debye length 9 a This result indicate that the increment of potential 5 changes exponentially with the departure from xquot with the rate dictated by the Debye length In a 3 to 5 Debye lengths from x the increment becomes negligible In conclusion if Debye length is negligible with respect to the depletion width than the depletion approximation is adequate
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