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Unformatted text preview: Professor N Cheung, U.C. Berkeley Lectre 21 EE143 F2010 1 Microfabrication controls dopant concentration distribution N D (x) and N A (x) Electron Concentration n(x) Hole Concentration p(x) Electrical resistivity Sheet Resistance Fermi level E f (x) , Electric Field PN Diode Characteristics MOS Capacitor MOS Transistor Carrier Mobility Professor N Cheung, U.C. Berkeley Lectre 21 EE143 F2010 2 Electron and Hole Concentrations for homogeneous semiconductor at thermal equilibrium n : electron concentration (cm3 ) p : hole concentration (cm3 ) N D : donor concentration (cm3 ) N A : acceptor concentration (cm3 ) 1) Charge neutrality condition: N D + p = N A + n 2) Law of Mass Action : n p = n i 2 Note : Carrier concentrations depend on NET dopant concentration ( N DN A ) ! Assume completely ionized to form N D + and N AProfessor N Cheung, U.C. Berkeley Lectre 21 EE143 F2010 3 How to find n, p when Na and Nd are known n p = N d N a (1) pn = n i 2 (2) (i) If N dN a > 10 n i : n N dN a (ii) If N a N d > 10 n i : p N a N d * Either n or p will dominate for typical doping situations Professor N Cheung, U.C. Berkeley Lectre 21 EE143 F2010 4 Probability of available states at energy E being occupied f(E) = 1/ [ 1+ exp (E E f ) / kT] where E f is the Fermi energy and k = Boltzmann constant=8.617 105 eV/K The FermiDirac Distribution (Fermi Function) T=0K 0.5 E E f f ( E ) Professor N Cheung, U.C. Berkeley Lectre 21 EE143 F2010 5 (2) Probability of available states at energy E NOT being occupied 1 f(E) = 1/ [ 1+ exp ( E fE ) / kT] Properties of the FermiDirac Distribution (1) f(E) exp [ (EE f ) / kT] for (E E f ) > 3kT Note: At 300K, kT= 0.026eV •This approximation is called Boltzmann approximation Probability of electron state at energy E will be occupied Professor N Cheung, U.C. Berkeley Lectre 21 EE143 F2010 6 Fermi Energy (E i ) of Intrinsic Semiconductor Ec Ev E i E g /2 E g /2 Professor N Cheung, U.C. Berkeley Lectre 21 EE143 F2010 7 E c E v E i E f (ntype) E f (ptype) q F  Let q F E f E i n = n i exp [(E f E i )/kT] n = n i exp [ q F /kT] How to find E f when n(or p) is known Note: E f is not very sensitive to carrier concentration When n doubles, E f changes by kT/q (ln 2) = 18mV Professor...
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This note was uploaded on 03/03/2012 for the course EECS 142 taught by Professor Ee142 during the Spring '04 term at Berkeley.
 Spring '04
 ee142

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