Department of EECS University of California, Berkeley EECS 105 Fall 2003, Lecture 14 Lecture 14: Bipolar Junction Transistors Prof. Niknejad

EECS 105 Fall 2003, Lecture 14Prof. A. Niknejad Department of EECS University of California, Berkeley Lecture Outline Diode Small Signal Model Diode Charge Storage (6.4.4) Diode Circuits The BJT (7.1) BJT Physics (7.2) BJT Ebers-Moll Equations (7.3) BJT Small-Signal Model

EECS 105 Fall 2003, Lecture 14Prof. A. Niknejad Department of EECS University of California, Berkeley Diode Small Signal Model The I-V relation of a diode can be linearized

EECS 105 Fall 2003, Lecture 14Prof. A. Niknejad Department of EECS University of California, Berkeley Diode Capacitance We have already seen that a reverse biased diode acts like a capacitor since the depletion region grows and shrinks in response to the applied field. the capacitance in forward bias is given by But another charge storage mechanism comes into play in forward bias Minority carriers injected into p and n regions “stay” in each region for a while On average additional charge is stored in diode

EECS 105 Fall 2003, Lecture 14Prof. A. Niknejad Department of EECS University of California, Berkeley Charge Storage Increasing forward bias increases minority charge density By charge neutrality, the source voltage must supply equal and opposite charge A detailed analysis yields: Time to cross junction (or minority carrier lifetime) Extra charge Stored in diode

EECS 105 Fall 2003, Lecture 14Prof. A. Niknejad Department of EECS University of California, Berkeley Ideal BJT Structure NPN or PNP sandwich (Two back-to-back diodes) How does current flow? Base is very thin. A good BJT satisfies the following Base (P) Collector (N) Emitter (N) Base (N) Emitter (P) Collector (P)

EECS 105 Fall 2003, Lecture 14Prof. A. Niknejad Department of EECS University of California, Berkeley Actual BJT Cross Section Vertical npn sandwich (pnp is usually a lateral structure) n+ buried layout is a low resistance contact to collector Base width determined by vertical distance between emitter diffusion and base diffusion

EECS 105 Fall 2003, Lecture 14Prof. A. Niknejad Department of EECS University of California, Berkeley BJT Layout Emitter area most important layout parameter Multi-finger device also possible for reduced base resistance

EECS 105 Fall 2003, Lecture 14Prof. A. Niknejad Department of EECS University of California, Berkeley BJT Schematic Symbol Collector current is control by base current linearly Collector is controlled by base-emitter voltage exponentially

EECS 105 Fall 2003, Lecture 14Prof. A. Niknejad Department of EECS University of California, Berkeley BJT Collector Characteristic Ground emitter Fix V CE Drive base with fixed current I B Measure the collector current

EECS 105 Fall 2003, Lecture 14Prof. A. Niknejad Department of EECS University of California, Berkeley Collector Characteristics (I B ) Forward Active Region (Very High Output Resistance) Saturation Region (Low Output Resistance) Reverse Active (Crappy Transistor) Breakdown Linear Increase

EECS 105 Fall 2003, Lecture 14Prof. A. Niknejad Department of EECS University of California, Berkeley Base-Emitter Voltage Control Exponential Increase Forward Active Region (High Output Resistance) Reverse Active (Crappy Transistor) Saturation Region (Low Output Resistance) ~0.3V Breakdown

EECS 105 Fall 2003, Lecture 14Prof. A. Niknejad Department of EECS University of California, Berkeley Transistor Action Base-emitter junction is forward biased and collector-base junction is reverse biased Electrons “emitted” into base much more than holes since the doping of emitter is much higher Magic: Most electrons cross the base junction and are swept into collector Why? Base width much smaller than diffusion length. Base-collector junction pulls electrons into collector Base (p) Emitter (n+) Collector (n) e h e h h recombination

EECS 105 Fall 2003, Lecture 14Prof. A. Niknejad Department of EECS University of California, Berkeley Diffusion Currents Minority carriers in base form a uniform diffusion current. Since emitter doping is higher, this current swamps out the current portion due to the minority carriers injected from base

EECS 105 Fall 2003, Lecture 14Prof. A. Niknejad Department of EECS University of California, Berkeley BJT Currents Collector current is nearly identical to the (magnitude) of the emitter current … define Kirchhoff: DC Current Gain:

EECS 105 Fall 2003, Lecture 14Prof. A. Niknejad Department of EECS University of California, Berkeley Origin of α F Base-emitter junction: some reverse injection of holes into the emitter  base current isn’t zero Typical: Some electrons lost due to recombination

EECS 105 Fall 2003, Lecture 14Prof. A. Niknejad Department of EECS University of California, Berkeley Collector Current Diffusion of electrons across base results in

EECS 105 Fall 2003, Lecture 14Prof. A. Niknejad Department of EECS University of California, Berkeley Base Current Diffusion of holes across emitter results in

EECS 105 Fall 2003, Lecture 14Prof. A. Niknejad Department of EECS University of California, Berkeley Current Gain Minimize base width Maximize doping in emitter

EECS 105 Fall 2003, Lecture 14Prof. A. Niknejad Department of EECS University of California, Berkeley Ebers-Moll Equations Exp. 6: measure E-M parameters Derivation: Write emitter and collector currents in terms of internal currents at two junctions

EECS 105 Fall 2003, Lecture 14Prof. A. Niknejad Department of EECS University of California, Berkeley Ebers-Moll Equivalent Circuit Building blocks: diodes and I-controlled I sources

EECS 105 Fall 2003, Lecture 14Prof. A. Niknejad Department of EECS University of California, Berkeley Forward Active Region B-C junction is not forward-biased  I R is very small Typical Values:

EECS 105 Fall 2003, Lecture 14Prof. A. Niknejad Department of EECS University of California, Berkeley Simplified Ebers-Moll Forward-Active Case: Saturation: both diodes are forward-biases  batteries B C E B C E

EECS 105 Fall 2003, Lecture 14Prof. A. Niknejad Department of EECS University of California, Berkeley Analogy from MOSFET s.s. model:

EECS 105 Fall 2003, Lecture 14Prof. A. Niknejad Department of EECS University of California, Berkeley Transconductance g m The transconductance is analogous to diode conductance

EECS 105 Fall 2003, Lecture 14Prof. A. Niknejad Department of EECS University of California, Berkeley Transconductance (cont) Forward-active large-signal current: Differentiating and evaluating at Q = (V BE, V CE )

EECS 105 Fall 2003, Lecture 14Prof. A. Niknejad Department of EECS University of California, Berkeley Comparison with MOSFET Typical bias point: drain/coll. current = 100  A; Select (W/L) = 8/1,  n C ox = 100  A/V 2 BJT: MOSFET:

EECS 105 Fall 2003, Lecture 14Prof. A. Niknejad Department of EECS University of California, Berkeley BJT Base Currents Unlike MOSFET, there is a DC current into the base terminal of a bipolar transistor: To find the change in base current due to change in base-emitter voltage:

EECS 105 Fall 2003, Lecture 14Prof. A. Niknejad Department of EECS University of California, Berkeley Small Signal Current Gain

EECS 105 Fall 2003, Lecture 14Prof. A. Niknejad Department of EECS University of California, Berkeley Input Resistance r π In practice, the DC current gain  F and the small-signal current gain  o are both highly variable (+/- 25%) Typical bias point: DC collector current = 100  A

EECS 105 Fall 2003, Lecture 14Prof. A. Niknejad Department of EECS University of California, Berkeley Output Resistance r o Why does current increase slightly with increasing v CE ? Model: math is a mess, so introduce the Early voltage Base (p) Emitter (n+) Collector (n)

EECS 105 Fall 2003, Lecture 14Prof. A. Niknejad Department of EECS University of California, Berkeley Graphical Interpretation of r o slope~1/ro slope

EECS 105 Fall 2003, Lecture 14Prof. A. Niknejad Department of EECS University of California, Berkeley BJT Small-Signal Model

EECS 105 Fall 2003, Lecture 14Prof. A. Niknejad Department of EECS University of California, Berkeley BJT Capacitances Base-charging capacitance C b : due to minority carrier charge storage (mostly electrons in the base) Base-emitter depletion capacitance: C jE = 1.4 C jEo Total B-E capacitance: C  = C jE + C b

EECS 105 Fall 2003, Lecture 14Prof. A. Niknejad Department of EECS University of California, Berkeley Complete Small-Signal Model