Forward-Active Terminal Currents

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1 Forward-Active Terminal urrents ollector current: (electron diffusion current density) x (emitter area) diff = ÐJ n A = qd n n po A V V th e W (why minus sign? is by def. Òpositive-in,Ó opposite to +x direction) ase current: (reverse-injected hole diffusion current density) x(emitter area) (minus sign again reßects Òpositive-inÓ convention for vs. +x direction) diff = ÐJ p A = qd p p no A V V th ( e Ð 1) W

2 Forward-Active urrent Gains mitter current: KirchoffÕs current law --> = -( + ) diff diff = Ð( ÐJ n + ÐJ p )A = Ð qd p p no A qd n A n po e V V th W W The ratio of collector current to the magnitude of the emitter current is deþned as Òalpha-FÓ ÐI qd n n po A W = qd p p no A qd n A = α F n po + W W α F --> 1... typically, α F = 0.99.

3 urrent Gains (cont.) The ratio of collector current to base current can be found in terms of α F : 1 Ð α F = ÐI Ð = Ð I α = F α F Solving for as a function of, we find that α F = I = β 1Ð α F F. A typical value is β F = with an uncertainty of +/- 50% since it is a sensitive function of the parameters and internal dimensions of the JT.

4 The Saturation Region V (sat) = 0.1 V (approx) from the characteristics --> both the emitter-base and the base-collector junctions are forward-biased Law of the Junction --> Þnd minority carrier concentrations in the emitter, base, and the collector p n (x) n p (x) p n (x) emitter base collector edge of n + buried layer W x x 0 W W + x x electrons from - junction electrons from - junction oth junctions are injecting and both are also collecting... since the electric Þeld in the depletion region remains in the same direction under forward bias. Separate the electron diffusion current in the base into two components: one due to the emitter-base junction (with zero bias on the base-collector junction) and the other due to the base-collector junction: diff J n = n po ( e V V th Ð 1) n po ( e V V th Ð 1) ÐqD n qd W n W

5 bers-moll Model lectron diffusion current in the base: multiply by the emitter area I diff ÐI S ( e V V th Ð 1) I S ( e V V th = + Ð 1) = ÐI 1 + I 2 mitter current : three components 1. - I 1 due to injection of electrons from the emitter-base junction, 2. - I 1 / β F due to reverse injection of holes into the emitter, and 3. I 2 due to collection of electrons from the base-collector junction. 1 = Ð I 1 + ( ÐI 1 β F ) + I 2 = Ð I1 + I β 2 = F 1 Ð I1 + I α 2 F ollector current : three components (by symmetry) 1. - I 2 due to injection of electrons from the base-collector junction, 2. - I 2 / β R due to reverse injection of holes into the collector, and 3. I 1 due to collection of electrons from the emitter-base junction I 2 I 1 Ð I 2 Ð I 1 β = = Ð I2 = I R β 1 Ð I2 R α R β R = α R / ( 1 - α R ) is the reverse current gain

6 bers-moll Model (cont.) ÒStandard formó for bers-moll equations: deþne two new constants mitter current: S = I S / α F and S = I S / α R, = ÐS ( e V V th Ð 1) + α R S ( e V V th Ð 1) ollector current: = α F S ( e V V th Ð 1) Ð S ( e V V th Ð 1) The collector current and the emitter current represent two diodes with currentcontrolled current sources coupling the emitter and the collector branches

7 arrier Fluxes in Saturation oth junctions injecting and collecting; holes injected into collector recombine with electrons upon reaching the n + buried layer For bias condition shown, > 0... injection from emitter-base junction still dominates. (could have = 0 or even < 0) hole diffusion flux n + polysilicon n + emitter majority hole flux from base contact n + buried layer n-type collector minority hole diffusion flux majority electron flux from collector contact to recombine with hole diffusion flux,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, majority electrons electron diffusion p-type base majority electron flux from collector contact supplying injection into base majority electron flux to collector contact

8 bers-moll quivalent ircuit α F I F I R Diode urrents: I F = S (e V V th 1) I R = S (e V V th 1) I F α R I R This model for the JT applies to general device structures, with the four parameters S, S, α F, and α R being linked by ÒreciprocityÓ α F S = α R S = I S bers-moll must be simpliþed for hand calculation

9 Forward Active Model I R is negligible --> can neglect current through - diode I F = α F α F I F I R mitter current control I F α R I R β F ase current control liminate forward-biased diode by replacing with a 0.7 V battery: β F - + _ 0.7 V + _ 0.7 V β F

10 Saturation Include both diodes in the circuit... both as batteries + + _ 0.7 V _ 0.1 V note that the batteries make the controlled current sources irrelevent to the circuit.

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