Lecture #25 OUTLINE • BJT: Deviations from the Ideal – Base-width modulation, Early voltage – Punch-through – Non-ideal effects at low |VEB|, high |VEB| • Gummel plot Reading: Chapter 11.2 Measured BJT Common-Emitter Output Characteristics: Spring 2007 EE130 Lecture 25, Slide 1 Base-Width Modulation Common-Emitter Configuration, Active Mode Operation W IE P+ N P IC IC dc IB 1 niE 2 DE N B W n 2 DB N E LE iB 2 + VEB niB DB N E LE 2 niE DE N BW DpB(x) IC pB 0 e qVEB / kT 1 (VCB=0) x 0 Spring 2007 VEC W(VBC) EE130 Lecture 25, Slide 2 12 W 2 LB The base-width modulation effect is reduced if we (a) increase the base width, W, or (b) increase the base dopant concentration, NB, or (c) decrease the collector dopant concentration, NC . Which of the above is the most acceptable action? Spring 2007 EE130 Lecture 25, Slide 3 Early Voltage, VA 1 Output resistance: I C VA r0 IC VEC A large VA (i.e. a large ro ) is desirable IC IB3 IB2 IB1 VA Spring 2007 0 EE130 Lecture 25, Slide 4 VEC Derivation of Formula for VA Output conductance: g 0 VEC VEB VBC dI C I C dVEC VA dI C dI C so g o dVEC dVBC dI C dW dI C dxnC go dW dVBC dW dVBC Spring 2007 N VA IC g0 for fixed VEB where xnC is the width of the collector-junction depletion region on the base side xnC P+ P EE130 Lecture 25, Slide 5 IC qA DB LB pB 0 sinh(W1 / LB ) (eqVEB / kT 1) DC LC nC 0 DB LB cosh(W / L qAni2 DB qVEB / kT IC e 1 WN B dI C qAni2 DB qVEB / kT IC 2 e 1 dW W NB W C JC dQdepC dVBC d (qN B xnC ) dxnC qN B dVBC dVBC dxnC C JC dVBC qN B VA Spring 2007 IC g 0 dI C dW IC dxnC I C dVBC W IC qN BW C JC C JC qN B EE130 Lecture 25, Slide 6 pB 0 sinh(W / LBB )) eqVCB / kT 1 BJT Breakdown Mechanisms • In the common-emitter configuration, for high output voltage VCE, the output current IC will increase rapidly due to one of two mechanisms: – punch-through – avalanche Spring 2007 EE130 Lecture 25, Slide 7 Punch-Through E-B and E-B depletion regions in the base touch, so that W = 0 As |VCB| increases, the potential barrier to hole injection decreases and therefore IC increases Spring 2007 EE130 Lecture 25, Slide 8 Avalanche Multiplication • Holes are injected into the base [0], then collected by the B-C junction – • PNP BJT: Some holes in the B-C depletion region have enough energy to generate EHP [1] The generated electrons are swept into the base [3], then injected into the emitter [4] – Each injected electron results in the injection of IEp/IEn holes from the emitter into the base [0] For each EHP created in the C-B depletion region by impact ionization, (IEp/IEn)+1 > dc additional holes flow into the collector i.e. carrier multiplication in C-B depletion region is internally amplified VCE 0 where VCB0 = reverse breakdown voltage of the C-B junction VCB 0 ( dc 1)1 / m 2 m 6 Spring 2007 EE130 Lecture 25, Slide 9 Non-Ideal Effects at Low VEB • In the ideal transistor analysis, thermal R-G currents in the emitter and collector junctions were neglected. I Ep I Ep I En I R G • Under active-mode operation with small VEB, the thermal recombination current is likely to be a dominant component of the base current low emitter efficiency, hence lower gain This limits the application of the BJT for amplification at low voltages. Spring 2007 EE130 Lecture 25, Slide 10 Non-Ideal Effects at High VEB • Decrease in F at high IC is caused by: – high-level injection qAni2 DB qVEB / kT IC e 1 WN B – series resistance – current crowding Spring 2007 EE130 Lecture 25, Slide 11 Gummel Plot and dc vs. IC high level injection in base 10-2 IC 10-4 10-6 dc IB 10-8 excess base current due to R-G in depletion region 10-10 10-12 From top to bottom: VBC = 2V, 1V, 0V 0.2 0.4 0.6 0.8 1.0 1.2 VBE Spring 2007 EE130 Lecture 25, Slide 12 Gummel Numbers For a uniformly doped base with negligible band-gap narrowing, the base Gummel number is N BW GB DB (= total integrated “dose” (#/cm2) of majority carriers in the base, divided by DB) 1 qAni2 DB qVEB / kT qAni2 qVEB / kT IC e 1 e 1 WN B GB Emitter efficiency 1 ni E 2 D N W E B ni B 2 DB N E WE 1 GB 1 GE GE is the emitter Gummel number Spring 2007 EE130 Lecture 25, Slide 13 Notice that dc 1 ni E 2 D N W E B ni B 2 DB N E LE 1 W 2 2 LB GE GB In real BJTs, NB and NE are not uniform, i.e. they are functions of x The more general formulas for the Gummel numbers are W GB 0 W GE 0 Spring 2007 2 ni N B ( x) dx 2 ni B DB ( x) 2 ni N E ( x) dx 2 ni E DE ( x) EE130 Lecture 25, Slide 14 Summary: BJT Performance Requirements • High gain (dc >> 1) One-sided emitter junction, so emitter efficiency 1 • Emitter doped much more heavily than base (NE >> NB) Narrow base, so base transport factor aT 1 • Quasi-neutral base width << minority-carrier diffusion length (W << LB) • IC determined only by IB (IC function of VCE,VCB) One-sided collector junction, so quasi-neutral base width W does not change drastically with changes in VCE (VCB) • Based doped more heavily than collector (NB > NC) (W = WB – xnEB – xnCB for PNP BJT) Spring 2007 EE130 Lecture 25, Slide 15 Review: Modes of Operation Common-emitter output characteristics (IC vs. VCE) IC βdc is lower for inverted active mode operation. Why? IB Spring 2007 EE130 Lecture 25, Slide 16