240ln01 - PN JUNCTIONS Built-in Voltage Vbi = VT ln P N +...

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1 P N - + V R x + - qN D -qN A W 1 W 2 x E (electric field) V Potential W 1 W 2 V 1 V 2 V bi +V R P N J U N C T I O N S L N 1 Built-in Voltage 2 ln i D A T bi n N N V V = V T is the thermal voltage . At T=300K, mV q kT V T 26 = Diode is charge neutral. Therefore charge on p side = charge on n side or D A N W N W 2 1 = Electric field is linear. Voltage is determined by Poisson’s Eq according to ε ρ = 2 2 dx V d where ρ = charge density 2 2 1 1 W qN V A = and 2 2 2 2 W qN V D = ( ) 2 2 2 1 2 1 2 W N W N q V V V V D A R bi + = + = + CAPACITANCE (Reverse Bias) () Doping) (Constant 1 1 2 2 / 1 1 1 bi R jo R bi D A D A R R j V V C V V N N N N q A dV dW dW dQ dV dQ C = + = = = 3 1 bi R jo j V V C C = Æ graded doping R RA n R D A R D A MI I BV V M N N V N qN E = = + = 1 1 2 2 / 1 max Solve E max =E crit to get V R = BV= -BV I RA I V I o ) 1 ) / (exp( = V T V I I o
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2 n type p type n(x) p(x) Zero bias Forward bias V F x minority carrier Æ n(x) = n(0) exp( x/L n ) Conduction in a P N diode is by two mechanisms 1. Drift J= q μ n E E= dV/dx 2. Diffusion J= qD n dn(x)/dx Reverse Bias Æ Drift because E is large and dn(x)/dx is small Æ Io due to generation Forward Bias Æ Diffusion because E is small and dn(x)/dx is large J(V)= qD n n(0)/L n + qD p p(0)/L p –I o n(0)=N d exp(( V bi +V F )/kT) p(0)= N a exp(( V bi +V F )/kT) I(V)=[(qD n N d /L n ) + (qD p N a /L p )] exp( V bi /kT){exp(V F /kT) – 1} =I o [exp(V F /kT) – 1]
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3 n p n E BC I B I C I E V ce + - V bc + - V be + - 0 = + + cb ec be V V V EB C n E =N DE p E =n i 2 /N DE p B =N AB n C =N DC p C =2.25x10 3 cm -3 n B =2.25x10 5 cm -3 n B (0) X=0 p E (0) W n B (0)= n B exp(V BE /V T ) n B (W ) ~ 0 Electron particle flow Jn Æ Electron current flow BIPOLAR JUNCTION TRANSISTOR (BJT) Typical numbers N DE = 10 17 cm -3 N AB = 10 15 cm -3 N DC = 10 17 cm -3 p E (0)=2.25x10 3 exp(V BE /V T ) n B (0)=2.25x10 5 exp(V BE /V T ) n B (W)=2.25x10 5 exp(V BC /V T ) p C (W)=2.25x10 3 exp(V BC /V T ) For Forward Active Operation V BE Æ Forward Biased V BC Æ Reverse Biased Æ n B (W) 0 Æ For short base, the charge
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240ln01 - PN JUNCTIONS Built-in Voltage Vbi = VT ln P N +...

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