ECE 663 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 BJT Coordinate system and parameters

ECE 663 P+ N P n E (x’) n E0 p B0 p B (x) n C0 n C (x’’) Forward Active minority carrier distribution

ECE 663 Emitter Region Minority carrier diffusion equation: Boundary conditions: Wide emitter region Law of the junction P+ N P n E (x’) n E0 p B0 p B (x) n C0 n C (x’’)

Minority carrier diffusion equation: Boundary conditions: ECE 663 Base Region Law of the junction(s) P+ N P n E (x’) n E0 p B0 p B (x) n C0 n C (x’’)

ECE 663 Collector Region Minority carrier diffusion equation: Boundary conditions: Wide collector region Law of the junction P+ N P n E (x’) n E0 p B0 p B (x) n C0 n C (x’’)

ECE 663 Currents

ECE 663 Performance Factors and Terminal Currents

ECE 663 Solutions in QN Emitter and Collector Regions

ECE 663 Solutions in the Base Region Need to keep both positive and negative exponential terms in the general solution. Apply Boundary conditions: Solve for A 1 and A 2 and plug-in to general solution

ECE 663 Base solutions

ECE 663 Currents: Emitter hole current

ECE 663 Collector hole current E C I Ep I Cp I En I Cn IBIB IEIE ICIC

ECE 663 Simplify Active mode biasing: V EB >0 (forward bias) and V CB <0 (reverse bias) Can keep only terms with emitter-base exponential

ECE 663 Performance factors: Emitter efficiency, 

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

ECE 663 Base Transport and Common Base Gain

ECE 663 Common Emitter Gain

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

ECE 663 Narrow Base Emitter Efficiency  has If you want high emitter injection efficiency, then N B /N E << 1  High emitter doping

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

ECE 663 Performance factors: Common Base Gain  dc Want both high emitter doping and narrow base for high gain

ECE 663 Performance factors: Common Emitter Gain  dc Want both high emitter doping and narrow base for high gain

ECE 663 Circuit models If V CB =0 then the equation for the emitter current looks like the ideal diode equation:

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

ECE 663 Ebers-Moll Model The exp(V CB ) term in the emitter equation and the exp(V EB ) 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 Ebers-Moll Equivalent Circuit – pnp BJT

ECE 663 Characteristics: Common Base InputOutput Ebers-Moll equation After some manipulation

ECE 663

Common Emitter Characteristics IEIE IBIB ICIC Input Output Start with Ebers-Moll equations and some algebra to get them into the right form:

ECE 663 Common Base Characteristics Input Output

ECE 663 Common Emitter Characteristics Output (Reverse biased PN junction.. I s controlled by I B ) Input (Forward Biased PN junction) NEW

ECE 663 Resistor-Transistor Logic (RTL) NEW