Reading: Pierret 11.1-11.2; Hu 8.2-8.6 Lecture 25 OUTLINE The BJT (cont’d) Ideal transistor analysis Narrow base and narrow emitter Ebers-Moll model Base-width modulation Reading: Pierret 11.1-11.2; Hu 8.2-8.6

Notation (PNP BJT) NE  NAE DE  DN tE  tn LE  LN nE0  np0 = ni2/NE NB  NDB DB  DP tB  tp LB  LP pB0  pn0  ni2/NB NC  NAC DC  DN tC  tn LC  LN nC0  np0  ni2/NC EE130/230M Spring 2013 Lecture 25, Slide 2

“Game Plan” for I-V Derivation Solve the minority-carrier diffusion equation in each quasi-neutral region to obtain excess minority-carrier profiles different set of boundary conditions for each region Find minority-carrier diffusion currents at depletion region edges Add hole & electron components together  terminal currents EE130/230M Spring 2013 Lecture 25, Slide 3

Emitter Region Analysis Diffusion equation: General solution: Boundary conditions: Solution: EE130/230M Spring 2013 Lecture 25, Slide 4

Collector Region Analysis Diffusion equation: General solution: Boundary conditions: Solution: EE130/230M Spring 2013 Lecture 25, Slide 5

Base Region Analysis Diffusion equation: General solution: Boundary conditions: Solution: EE130/230M Spring 2013 Lecture 25, Slide 6

Since we can write as EE130/230M Spring 2013 Lecture 25, Slide 7

EE130/230M Spring 2013 Lecture 25, Slide 8

BJT Terminal Currents We know: Therefore: EE130/230M Spring 2013 Lecture 25, Slide 9

BJT with Narrow Base In practice, we make W << LB to achieve high current gain. Then, since we have: EE130/230M Spring 2013 Lecture 25, Slide 10

BJT Performance Parameters Assumptions: emitter junction forward biased, collector junction reverse biased W << LB EE130/230M Spring 2013 Lecture 25, Slide 11

BJT with Narrow Emitter Replace with WE’ if emitter is narrow EE130/230M Spring 2013 Lecture 25, Slide 12

Ebers-Moll Model increasing (npn) or VEC (pnp) The Ebers-Moll model is a large-signal equivalent circuit which describes both the active and saturation regions of BJT operation. Use this model to calculate IB and IC given VBE and VBC EE130/230M Spring 2013 Lecture 25, Slide 13

If only VEB is applied (VCB = 0): aR : reverse common base gain aF : forward common base gain If only VCB is applied (VEB = 0): : Reciprocity relationship: EE130/230M Spring 2013 Lecture 25, Slide 14

In the general case, both VEB and VCB are non-zero: IC: C-B diode current + fraction of E-B diode current that makes it to the C-B junction IE: E-B diode current + fraction of C-B diode current that makes it to the E-B junction Large-signal equivalent circuit for a pnp BJT EE130/230M Spring 2013 Lecture 25, Slide 15

Base-Width Modulation Common Emitter Configuration, Active Mode Operation W IE IC P+ N P +  VEB DpB(x) IC (VCB=0) x VEC W(VBC) EE130/230M Spring 2013 Lecture 25, Slide 16

Ways to Reduce Base-Width Modulation Increase the base width, W Increase the base dopant concentration NB Decrease the collector dopant concentration NC Which of the above is the most acceptable action? EE130/230M Spring 2013 Lecture 25, Slide 17

Early Voltage, VA Output resistance: A large VA (i.e. a large ro ) is desirable IC IB3 IB2 IB1 VEC VA EE130/230M Spring 2013 Lecture 25, Slide 18

Derivation of Formula for VA Output conductance: for fixed VEB where xnC is the width of the collector-junction depletion region on the base side xnC P+ N P EE130/230M Spring 2013 Lecture 25, Slide 19

EE130/230M Spring 2013 Lecture 25, Slide 20

Summary: BJT Performance Requirements High gain (bdc >> 1) One-sided emitter junction, so emitter efficiency g  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) EE130/230M Spring 2013 Lecture 25, Slide 21