1. Plans • What does MCDE give us for the gain? • How can we use the equation to improve the gain? • Can we develop a compact circuit model for a BJT? ECE 663

2. BJT Coordinate system and parameters ECE 663

3. Forward Active minority carrier distribution P N P+ pB(x) nE(x’) nE0 pB0 nC0 nC(x’’) ECE 663

4. Emitter Region • Minority carrier diffusion equation: • Boundary conditions: P N P+ pB(x) nC0 pB0 nE(x’) nC(x’’) nE0 Wide emitter region Law of the junction ECE 663

5. Base Region • Minority carrier diffusion equation: • Boundary conditions: P N P+ pB(x) nC0 pB0 nE(x’) nC(x’’) nE0 Law of the junction(s) ECE 663

6. Collector Region • Minority carrier diffusion equation: • Boundary conditions: P N P+ pB(x) nC0 pB0 nE(x’) nC(x’’) nE0 Wide collector region Law of the junction ECE 663

7. Currents ECE 663

8. Performance Factors and Terminal Currents ECE 663

9. Solutions in QN Emitter and Collector Regions ECE 663

10. Solutions in the Base Region • Need to keep both positive and negative exponential terms in the general solution. • Apply Boundary conditions: • Solve for A1 and A2 and plug-in to general solution ECE 663

11. Base solutions ECE 663

12. Currents: Emitter hole current ECE 663

13. Collector hole current IE IC IEp ICp C E IEn ICn IB ECE 663

14. Simplify • Active mode biasing: VEB>0 (forward bias) and VCB<0 (reverse bias) • Can keep only terms with emitter-base exponential ECE 663

15. Performance factors: Emitter efficiency,  ECE 663

16. Emitter Efficiency • Want to express in terms of doping: ECE 663

17. Base Transport and Common Base Gain ECE 663

18. Common Emitter Gain ECE 663

19. Can also calculate total emitter and collector currents by adding up electron and hole currents in the collector and emitter Fortunately, for usable transistors (high gain) usually, the base is small Compared to the minority carrier diffusion length and the equations simplify ECE 663

20. Narrow Base Approximation: W<<LB • Can simplify hyperbolic functions involving W/LB • If <<1, then sinh()  and cosh ()1 + 2/2 Linear concentration dependence across the base ECE 663

21. Narrow Base Emitter Efficiency •  has If you want high emitter injection efficiency, then NB/NE << 1  High emitter doping ECE 663

22. Performance factors: Base Transport factor aT If you want high base transport (T 1) then you want as small of a Base as possible W << LB or alternatively large LB = large p ECE 663

23. Performance factors: Common Base Gain adc Want both high emitter doping and narrow base for high gain ECE 663

24. Performance factors: Common Emitter Gain bdc Want both high emitter doping and narrow base for high gain ECE 663

25. Circuit models • If VCB=0 then the equation for the emitter current looks like the ideal diode equation: ECE 663

26. Circuit models If VEB=0, then the collector current equation also reduces to one that looks like an ideal diode equation: ECE 663

27. Ebers-Moll Model The exp(VCB) term in the emitter equation and the exp(VEB) term in the collector current equation have the same prefactor: The emitter and collector current equations can be written in terms of four parameters (three are independent): Can show thatF= dc ECE 663

28. Ebers-Moll Equivalent Circuit – pnp BJT ECE 663

29. Characteristics: Common Base Input Output Ebers-Moll equation After some manipulation ECE 663

30. ECE 663

31. IC IB IE Common Emitter Characteristics Output Input Start with Ebers-Moll equations and some algebra to get them into the right form: ECE 663

32. Common Base Characteristics Output Input ECE 663

33. NEW Common Emitter Characteristics Input (Forward Biased PN junction) Output (Reverse biased PN junction .. Is controlled by IB) ECE 663

34. NEW Resistor-Transistor Logic (RTL) ECE 663