Lec_21 - Professor N Cheung, U.C. Berkeley Lectre 21 EE143...

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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 (cm-3 ) p : hole concentration (cm-3 ) N D : donor concentration (cm-3 ) N A : acceptor concentration (cm-3 ) 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 D-N A ) ! Assume completely ionized to form N D + and N A-Professor 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 d-N a > 10 n i : n N d-N 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 10-5 eV/K The Fermi-Dirac 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 f-E ) / kT] Properties of the Fermi-Dirac Distribution (1) f(E) exp [- (E-E 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 (n-type) E f (p-type) 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.

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Lec_21 - Professor N Cheung, U.C. Berkeley Lectre 21 EE143...

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