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4.2 - 4.2 BJT Static Analysis BJT Ideal Static Analysis...

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ECE3080, Chapter 4.2 1 June 21, 2005 ECE 3080: Chapter 4.2 – BJT O. Brand, 1 of 25 4.2 BJT Static Analysis BJT – Ideal Static Analysis 4.2.1 Calculate Carrier Densities 4.2.2 Calculate Current Densities 4.2.3 Circuit Parameters 4.2.4 Narrow Base Approximations BJT – Static Model 4.2.5 Ebers-Moll Model Pierret, Chapter 11, page 389-404 June 21, 2005 ECE 3080: Chapter 4.2 – BJT O. Brand, 2 of 25 BJT – Ideal Static Analysis I Goal: Calculate BJT currents and transistor parameters α 0 , I CB0 , β 0 Assumptions (similar to pn-junction analysis): 1-D model Homogeneous doping, i.e. N A (x), N D (x) = const.; as a result, the junctions are treated as step junctions Low-level injection No R-G currents in the depletion regions No series resistances Non-degenerate doping, i.e. Boltzmann approximation is valid Depletion layer width << base width, i.e. base width modulation is neglected No electric field outside the depletion regions No influence of contacts
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ECE3080, Chapter 4.2 2 June 21, 2005 ECE 3080: Chapter 4.2 – BJT O. Brand, 3 of 25 BJT – Ideal Static Analysis II Goal: Calculate BJT currents and transistor parameters α 0 , I CB0 , β 0 Solution Approach (similar to pn-junction analysis): 1. Calculate carrier densities in quasineutral regions 2. Calculate current densities at the edges of the depletion regions June 21, 2005 ECE 3080: Chapter 4.2 – BJT O. Brand, 4 of 25 BJT – Ideal Static Analysis III – The Model – N E = N A,E D E = D n L E = L n n E0 = n p0 τ E = τ n N B = N D,B D B = D p L B = L p p B0 = p n0 τ B = τ p N C = N A,C D C = D n L C = L n n C0 = n p0 τ C = τ n x’’ x’ x 0 0 W 0 p + p n Emitter Base Collector
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ECE3080, Chapter 4.2 3 June 21, 2005 ECE 3080: Chapter 4.2 – BJT O. Brand, 5 of 25 4.2.1 Calculate Carrier Densities Approach: Solve steady-state continuity equations in the quasi-neutral regions (no electric field, no carrier generation) of emitter, base, and collector ! n p (x,t) ! t = + n p μ n ! " ! x n " ! n p ! x + D n ! 2 n p ! x 2 + G n # n p # n p0 $ n ! p n (x,t) ! t = 0 steady state !" # $ # = # p n μ p ! " ! x # μ p " ! p n ! x = 0 no electric field ! " ### $ ### + D p ! 2 p n ! x 2 Diffusion ! " # $ # + G p = 0 no G % # p n # p n0 $ p Recomb.
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