Lecture 21: BJTs (Bipolar Junction Transistors) Context

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1 Lecture 21: BJTs (Bipolar Junction Transistors) Prof J. S. Smith ontext In riday s lecture, we discussed BJTs (Bipolar Junction Transistors) Today we will find large signal models for the bipolar junction transistor, and start exploring how to use transistors to make amplifiers and other analog devices 1

2 Reading Today s lecture will finish chapter 7, Bipolar Junction Transistors (BJT s) Then, we will start looking at amplifiers, chapter 8 in the text. Lecture Outline BJT Physics (7.2) BJT Ebers-Moll Equations (7.3) BJT Large-Signal Models BJT Small-Signal Models Next: ircuits 2

3 urrents in the BJT A BJT is ordinarily designed so that the minority carrier injection into the base is far larger than the minority carrier injection into the emitter. It is also ordinarily designed such that almost all the minority carriers injected into the base make it all the way across to the collector urrent controlled So the current is determined by the minority current across the emitter-base junction I But since the majority of the minority current goes right through the base to the collector: I I e I E And so the amount of current that must be supplied by the base is small compared to the current controlled: I S >> I qv BE B 3

4 BJT operating modes orward active Emitter-Base forward biased Base-ollector reverse biased Saturation Both junctions are forward biased Reverse active Emitter-Base reverse biased Base-ollector forward biased Transistor operation is poor in this direction, becauseβ is low: lighter doping of the layer designed to be the collector means that there is a lot of minority carrier injection out of the Base. ollector haracteristics (I B ) Saturation Region (Low Output Resistance) Breakdown Reverse Active (poor Transistor) Linear Increase orward Active Region (Very High Output Resistance) 4

5 The origin of current gain in BJT s The majority of the minority carriers injected from the emitter go across the base to the collector and are swept out by the electric field in the depletion region of the collectorbase junction. The base contact doesn t have to supply that current to maintain the voltage of the base the voltage which is causing the current in the first place. The current which does have to be supplied by the base contact comes from two main sources: Recombination in the base (can often neglect in Silicon) Injection of minority carriers into the emitter If we find the ratio of the current to the current that must be supplied by the base, that will give us the current gain β. Diffusion urrents Minority holes in emitter-they recombine at the contact Minority electrons in the base Base-collector depletion extracts the minority carriers from the base The minority carriers injected into the base have a concentration gradient, and thus a current. Since emitter doping is higher, this current is much larger than the current due to the minority carriers injected from the base to the emitter. This is the source of BJT current gain. 5

6 Diffusion Revisited Why is minority current profile a linear function? The diffusion current is proportional to the gradient diffusion constant. Since current is constant gradient is constant Note that diffusion current density is controlled by width of region (base width for BJT): Density here fixed by potential (injection of carriers) It is proportional to the number of majority carriers on The other side of the barrier, and is exponential with the (lowered) barrier height. Density at the contact is equal to the equilibrium value (strong G/R) W p Decreasing width increases current! BJT urrents ollector current is nearly identical to the (magnitude) of the emitter current define Kirchhoff: D urrent Gain: I = α I E I E = I + IB I = α I = α ( I + I ) E B α =.999 I = α I = β I 1 α B B β α.999 = = = α.001 6

7 Origin of α Base-emitter junction: some reverse injection of holes into the emitter base current isn t zero E B Some electrons lost due to recombination Typical: α.99 β 100 ollector urrent Diffusion of electrons across base results in dn diff p qdnn pb0 Jn = qdn = e dx WB qv BE I S qdnn pb0 AE = WB I = I e S qv BE 7

8 Base urrent In silicon, recombination of carriers in the base can usually be neglected, so the base current is mostly due to minority injection into the emitter. Diffusion of holes across emitter results in qv BE diff dp qd ne ppne0 Jp = qdp = e 1 dx WE I B qv qd BE ppne0 AE = e 1 WE urrent Gain β qdnn pboae I W B D n n pb0 W E = = = I qd B ppneoae D p pne0 WB WE Minimize base width 2 ni n N N = = p N pb0 AB, DE, 2 ne0 ni NA, B DE, Maximize doping in emitter 8

9 Simple NPN BJT model A simple model for a NPN BJT: B Real diode, not an ideal diode I B (t) + βi B (t) V BE (t) E + I B V BE + V E I E Ebers-Moll Equations Exp. 6: measure E-M parameters Derivation: Write emitter and collector currents in terms of internal currents at two junctions VBE / Vth / ( 1 VB Vth ) α ( 1 ) I = I e + I e E ES R S VBE / Vth / ( 1 VB Vth ) ( 1 ) I = α I e I e ES S α I = α I ES R S 9

10 Ebers-Moll Equivalent ircuit Parasitic capacitances To model devices adequately at high frequencies, we need to account for the charge that we must move in or out of the devices. In the ET, this is clearly a capacitance, but in a BJT the majority of the stored charge is in the form of minority carriers which are diffusing across the device in forward operation, but aren t there when the transistor is not conducting, so obviously they must be extracted, or allowed to diffuse away. This stored charge can be modeled as a capacitance in small signal models. 10

11 Diffusion apacitance The total minority carrier charge for a one-sided junction is (area of triangle) qv 1 1 D 2 (, )( Qn = qa bh = qa W xdep p np0e np0 ) 2 2 or a one-sided junction, the current is dominated by these minority carriers: qad I ( n e n ) qv D n D = p0 p0 Wp xdep, p I = D D n Q n W x ( ) 2 p dep, p onstant! Diffusion apacitance (cont) The proportionality constant has units of time Temperature τ Q n T = = ID τ T q ( W ) 2 p xdep, p The physical interpretation is that this is the transit time for the minority carriers to cross the p-type region. Since the capacitance is related to charge: D n ( W ) 2 p xdep, p = Mobility µ n Distance across P-type base Diffusion oefficient Q = τ I n T D Q I = = τ = g τ V V n d T d T 11

12 BJT Transconductance g m The transconductance is analogous to diode conductance Transconductance (cont) orward-active large-signal current: i = I e (1 + v V ) vbe / Vth S E A Differentiating and evaluating at Q = (V BE, V E ) i q qvbe / = Ie S (1 + V E V A) v BE Q Q here means quiescent point not charge g m i v = = BE Q qi 12

13 Quiescent Point (bias) Q = ( V, V ) BE E Notation Review i = f( v, v ) BE E Large signal I + i = f( V + v, V + v ) BE BE E E transconductance I + i = f( V + v, V + v ) c BE be E ce f f i v + v c be ce vbe v Q E Q small signal D (bias) small signal (less messy!) Output conductance Remember, the point of a small signal model is to produce a set of equations which relate the small variations in currents and voltages to each other linearly and to create a linear equivalent circuit BJT Base urrents Unlike a MOSET, there is a D current into the base terminal of a bipolar transistor: BE / ( β ) qv I = I β = I e (1 + V V ) B S E A To find the change in base current due to change in base-emitter voltage: i b i = v B BE Q v be ib ib i 1 = = v i v β BE Q Q BE Q g m gm ib = v β be 13

14 Small Signal urrent Gain β i 0 = = ib i = β i i c 0 = β i 0 b β B Since currents are linearly related, the derivative is a constant (small signal = large signal) Input Resistance r π i v g β ( ) 1 1 B m r = = = π i β v BE Q BE Q r π β = g In practice, the D current gain β and the small-signal current gain β o are both highly variable (+/- 25%) Typical bias point: D collector current = 100 µa 25mV r π = 100 = 25kΩ.1mA R i = Ω m MOSET 14

15 Output Resistance r o Why does current increase slightly with increasing v E? ollector (n) W B Base (p) Emitter (n+) Answer: Base width modulation (similar to LM for MOS) Model: Math is a mess, so introduce the Early voltage i = I S v / V e BE th (1 + v E V A ) Graphical Interpretation of r o slope~1/ro slope 15

16 BJT Small-Signal Model i b = r v π be 1 i = g v + v r c m be ce o BJT Parasitic apacitors Emitter-base is a forward biased junction depletion capacitance: 1.4 jbe, jbe, 0 ollector-base is a reverse biased junction depletion capacitance Due to minority charge injection into base, we have to account for the diffusion capacitance as well =τ g b m 16

17 BJT ross Section ore Transistor External Parasitic ore transistor is the vertical region under the emitter contact Everything else is parasitic or unwanted Lateral BJT structure is also possible ore BJT Model Reverse biased junction Base ollector Reverse biased junction & Diffusion apacitance Emitter gmv π ictional Resistance (no noise) Given an ideal BJT structure, we can model most of the action with the above circuit or low frequencies, we can forget the capacitors apacitors are non-linear! MOS gate & overlap caps are linear 17

18 omplete Small-Signal Model Real Resistance (has noise) core BJT Reverse biased junctions External Parasitics ircuits! When the inventors of the bipolar transistor first got a working device, the first thing they did was to build an audio amplifier to prove that the transistor was actually working! 18

19 A Simple ircuit: An MOS Amplifier Input signal Supply Rail RD VDD v o v s I DS vgs = VGS + vs V GS Output signal 19

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