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# 14 - ECE331 Notice Second Midterm Date and Time Date(Mon...

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Lu ECE331 Date: 5/5/2008 (Mon) Time: 1:30 – 2:18 PM Coverage: stuff after the first midterm Second Midterm Date and Time Notice

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Lu ECE331 More on Carrier Concentrations Previously we derived expressions for the electron and hole concentrations in NON-DEGENERATE semiconductors In an INTRINSIC semiconductor these concentrations are IDENTICAL and denoted as n i * Using E i to denote the position of the FERMI LEVEL in the intrinsic semiconductor we may reorganize the above equations to write [] ) 5 . 5 ( 2 2 , / ) ( exp 2 / 3 2 * = = h T k m N T k E E N n B n c B c F c π [] ) 6 . 5 ( 2 2 , / ) ( exp 2 / 3 2 * = = h T k m N T k E E N p B p v B F v v ) 2 . 6 ( ] / ) exp[( ) 1 . 6 ( ] / ) exp[( T k E E n N T k E E n N B v i i v B i c i c = =
Lu ECE331 More on Carrier Concentrations We now substitute Equations 6.1 & 6.2 into Equations 5.5 & 5.6 and obtain two VERY IMPORTANT relations * Note that while Equations 6.1 & 6.2 are only valid for INTRINSIC semiconductors Equations 6.3 & 6.4 are valid for ALL non-degenerate semiconductors These relations may be used to determine how the carrier density varies when the material is DOPED to form an EXTRINSIC semiconductor They may also be used to determine the POSITION of the Fermi level if the electron or hole concentrations are known ) 4 . 6 ( ] / ) exp[( ) 3 . 6 ( ] / ) exp[( T k E E n p T k E E n n B F i i B i F i = =

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Lu ECE331 More on Carrier Concentrations Yet another very important result follows by MULTIPLYING Equations * Note how the right hand side of this equation is INDEPENDENT of the doping density and is determined instead by MATERIALS parameters and by TEMPERATURE * This equation therefore indicates that in any given material at fixed temperature the PRODUCT of the electron and hole and concentrations is INDEPENDENT of the doping n -type doping must therefore simultaneously INCREASE the electron density and DECREASE the hole density (and vice-versa for the case of p -type doping)! In
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14 - ECE331 Notice Second Midterm Date and Time Date(Mon...

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