EECS 105 Spring 2004, Lecture 22
Lecture 21: BJTs (Bipolar Junction Transistors)
Prof J. S. Smith
Department of EECS University of California, Berkeley
EECS 105 Spring 2004, Lecture 22 Prof. J. S. Smith Context
In Friday’s lecture, we discussed BJTs (Bipolar Junction Transistors) Today we will find large signal models for the bipolar junction transistor, and start exploring how to use transistors to make amplifiers and other analog devices
Department of EECS University of California, Berkeley
1 EECS 105 Spring 2004, Lecture 22 Prof. J. S. Smith Reading
Today’s lecture will finish chapter 7, Bipolar Junction Transistors (BJT’s) Then, we will start looking at amplifiers, chapter 8 in the text.
Department of EECS University of California, Berkeley
EECS 105 Spring 2004, Lecture 22 Prof. J. S. Smith Lecture Outline
z BJT Physics (7.2)
z BJT Ebers-Moll Equations (7.3)
z BJT Large-Signal Models
z BJT Small-Signal Models
Next: Circuits
Department of EECS University of California, Berkeley
2 EECS 105 Spring 2004, Lecture 22 Prof. J. S. Smith Currents in the BJT
z A BJT is ordinarily designed so that the minority carrier injection into the base is far larger than the minority carrier injection into the emitter.
z It is also ordinarily designed such that almost all the minority carriers injected into the base make it all the way across to the collector
Department of EECS University of California, Berkeley
EECS 105 Spring 2004, Lecture 22 Prof. J. S. Smith Current controlled
z So the current is determined by the minority current across the emitter-base junction
qVBE kT IIeCS≈
z But since the majority of the minority current goes right through the base to the collector:
ICE≈ −I z And so the amount of current that must be supplied by the base is small compared to the current controlled: ICB>> I
Department of EECS University of California, Berkeley
3 EECS 105 Spring 2004, Lecture 22 Prof. J. S. Smith BJT operating modes
z Forward active – Emitter-Base forward biased – Base-Collector reverse biased
z Saturation – Both junctions are forward biased
z Reverse active – Emitter-Base reverse biased – Base-Collector forward biased – Transistor operation is poor in this direction, becauseβ is low: lighter doping of the layer designed to be the collector means that there is a lot of minority carrier injection out of the Base.
Department of EECS University of California, Berkeley
EECS 105 Spring 2004, Lecture 22 Prof. J. S. Smith
Collector Characteristics (IB)
Saturation Region Breakdown (Low Output Resistance)
Linear Increase Reverse Active (poor Transistor)
Forward Active Region (Very High Output Resistance)
Department of EECS University of California, Berkeley
4 EECS 105 Spring 2004, Lecture 22 Prof. J. S. Smith The origin of current gain in BJT’s
z The majority of the minority carriers injected from the emitter go across the base to the collector and are swept out by the electric field in the depletion region of the collector- base junction.
z The base contact doesn’t have to supply that current to maintain the voltage of the base—the voltage which is causing the current in the first place.
z The current which does have to be supplied by the base contact comes from two main sources: – Recombination in the base (can often neglect in Silicon) – Injection of minority carriers into the emitter
z If we find the ratio of the current to the current that must be supplied by the base, that will give us the current gain β.
Department of EECS University of California, Berkeley
EECS 105 Spring 2004, Lecture 22 Prof. J. S. Smith Diffusion Currents
Minority holes Base-collector in emitter-they recombine at depletion extracts the contact the minority Minority electrons carriers from the in the base base
The minority carriers injected into the base have a concentration gradient, and thus a current. Since emitter doping is higher, this current is much larger than the current due to the minority carriers injected from the base to the emitter. This is the source of BJT current gain. Department of EECS University of California, Berkeley
5 EECS 105 Spring 2004, Lecture 22 Prof. J. S. Smith Diffusion Revisited
z Why is minority current profile a linear function? z The diffusion current is proportional to the gradient×diffusion constant. Since current is constant→gradient is constant z Note that diffusion current density is controlled by width of region (base width for BJT): Density here fixed by potential (injection of carriers) It is proportional to the number of majority carriers on The other side of the barrier, and is exponential with the (lowered) barrier height.
Density at the contact is equal to the equilibrium value (strong G/R)
Wp z Decreasing width increases current!
Department of EECS University of California, Berkeley
EECS 105 Spring 2004, Lecture 22 Prof. J. S. Smith BJT Currents
Collector current is nearly identical to the (magnitude) of the emitter current … define
ICFE= −α I α F = .999 Kirchhoff: −IE =+IICB DC Current Gain:
ICFEFBC= −=α IIIα () +
α F α F .999 ICBFB==IIβ βF ===999 1−α F 1.001−α F
Department of EECS University of California, Berkeley
6 EECS 105 Spring 2004, Lecture 22 Prof. J. S. Smith
Origin of αF
Base-emitter junction: some reverse injection of holes into the emitter Æ base current isn’t zero Some electrons lost due to recombination
E BC
β ≈100 Typical: α F ≈ .99 F
Department of EECS University of California, Berkeley
EECS 105 Spring 2004, Lecture 22 Prof. J. S. Smith Collector Current
Diffusion of electrons across base results in
dn⎛⎞ qD n qVBE diff pnpB0 kT JqDnn==⎜⎟ e dx⎝⎠ WB
⎛⎞qDnpBE n0 A IS = ⎜⎟ ⎝⎠WB
qVBE kT IIeCS=
Department of EECS University of California, Berkeley
7 EECS 105 Spring 2004, Lecture 22 Prof. J. S. Smith Base Current
In silicon, recombination of carriers in the base can usually be neglected, so the base current is mostly due to minority injection into the emitter. Diffusion of holes across emitter results in
⎛⎞qD p ⎛⎞qVBE diff dpnE pnE0 kT JqDpp=− =⎜⎟⎜⎟ e −1 dx⎝⎠ WE ⎝⎠
⎛⎞qD p A ⎛⎞qVBE pnEE0 kT IeB =−⎜⎟⎜⎟1 ⎝⎠WE ⎝⎠
Department of EECS University of California, Berkeley
EECS 105 Spring 2004, Lecture 22 Prof. J. S. Smith Current Gain
⎛⎞qDnpBoE n A ⎜⎟⎛⎞n IDCn⎝⎠WB ⎛⎞pB0 ⎛⎞WE βF == =⎜⎟⎜⎟⎜⎟ qD p A ⎜⎟ IDpWBpnEB⎛⎞pnEoE ⎝⎠⎝⎠0 ⎝⎠ ⎜⎟ ⎝⎠WE
Minimize base width
2 ni
⎛⎞npB0 NNAB,, DE ⎜⎟==2 ⎝⎠pNnE0,ni A B
NDE, Maximize doping in emitter
Department of EECS University of California, Berkeley
8 EECS 105 Spring 2004, Lecture 22 Prof. J. S. Smith Simple NPN BJT model
z A simple model for a NPN BJT: C
I (t) → B B + βiB (t) C
VBE (t) IB +
− + VCE
Real diode, not E VBE − −I an ideal diode − E
Department of EECS University of California, Berkeley
EECS 105 Spring 2004, Lecture 22 Prof. J. S. Smith Ebers-Moll Equations
Exp. 6: measure E-M parameters Derivation: Write emitter and collector currents in terms of internal currents at two junctions
VVBE// th VV BC th IIeEES=−( −11) +α RCS Ie( − )
VVBE// th VV BC th IIeCFES=−−−α ( 11) Ie CS( )
α FESI = α RCSI
Department of EECS University of California, Berkeley
9 EECS 105 Spring 2004, Lecture 22 Prof. J. S. Smith Ebers-Moll Equivalent Circuit
Department of EECS University of California, Berkeley
EECS 105 Spring 2004, Lecture 22 Prof. J. S. Smith Parasitic capacitances
z To model devices adequately at high frequencies, we need to account for the charge that we must move in or out of the devices.
z In the FET, this is clearly a capacitance, but in a BJT the majority of the stored charge is in the form of minority carriers which are diffusing across the device in forward operation, but aren’t there when the transistor is not conducting, so obviously they must be extracted, or allowed to diffuse away.
z This stored charge can be modeled as a capacitance in small signal models.
Department of EECS University of California, Berkeley
10 EECS 105 Spring 2004, Lecture 22 Prof. J. S. Smith Diffusion Capacitance
z The total minority carrier charge for a one-sided junction is (area of triangle) 11 qVD QqAbhqAWx=⋅ =⋅()() − nekT − n ndepppp222,00
z For a one-sided junction, the current is dominated by these minority carriers:
qVD qADn kT IDpp=−()ne00 n Wxpdepp− ,
I D D = n Constant! Q 2 n ()Wxpdepp− ,
Department of EECS University of California, Berkeley
EECS 105 Spring 2004, Lecture 22 Prof. J. S. Smith Diffusion Capacitance (cont)
z The proportionality constant has units of time Distance across 2 Wx− P-type base Qn ( pdepp, ) τT == IDDn 2 Diffusion Coefficient q (Wxpdepp− , ) τ = Mobility T kT µ Temperature n
z The physical interpretation is that this is the transit time for the minority carriers to cross the p-type region. Since the capacitance is related to charge:
QInTD=τ ∂Q ∂I Cg==n τ =τ dTdT∂∂VV Department of EECS University of California, Berkeley
11 EECS 105 Spring 2004, Lecture 22 Prof. J. S. Smith
BJT Transconductance gm
z The transconductance is analogous to diode conductance
Department of EECS University of California, Berkeley
EECS 105 Spring 2004, Lecture 22 Prof. J. S. Smith Transconductance (cont)
z Forward-active large-signal current:
vVBE/ th iIeCS=+(1 vV CEA ) Q here means quiescent point not charge
• Differentiating and evaluating at Q = (VBE, VCE ) ∂i q C =+IeqVBE / kT (1 V V ) ∂vkTSCEA BE Q ∂iqI g ==CC m ∂vkT BE Q Department of EECS University of California, Berkeley
12 EECS 105 Spring 2004, Lecture 22 Prof. J. S. Smith Notation Review
Large signal ifvvCBECE= (,)
IC+∆ifVvV C =(,) BE +∆ BE CE +∆ v CE Quiescent Point small signal (bias) DC (bias)
ICc+ ifVvVv=+(,) BEbeCEce + small signal ∂∂ff (less messy!) QVV= (,) iv≈+ v BE CE cbece∂∂vv BEQ CE Q
transconductance Output conductance Remember, the point of a small signal model is to produce a set of equations which relate the small variations in currents and voltages to each other linearly → and to create a linear equivalent circuit
Department of EECS University of California, Berkeley
EECS 105 Spring 2004, Lecture 22 Prof. J. S. Smith BJT Base Currents
Unlike a MOSFET, there is a DC current into the base terminal of a bipolar transistor:
qVBE / kT IBCF==IIeVVββ( SF) (1 + CEA )
To find the change in base current due to change in base-emitter voltage:
∂iB ∂∂∂iiiBBC1 ivbbe= ==g ∂v ∂∂∂vivβ m BE Q BEQQ CQ BE F
gm ivbbe= βF
Department of EECS University of California, Berkeley
13 EECS 105 Spring 2004, Lecture 22 Prof. J. S. Smith Small Signal Current Gain
∆iC β0 = = βF ∆iB
∆iiCB=∆β0
iicb= β0
z Since currents are linearly related, the derivative is a constant (small signal = large signal)
Department of EECS University of California, Berkeley
EECS 105 Spring 2004, Lecture 22 Prof. J. S. Smith
Input Resistance rπ
−1 ∂i 1 ∂ig ()r ==B Cm = π ∂∂vvβ β BEQQ F BE F
βF rπ = gm
z In practice, the DC current gain βF and the small-signal current gain βo are both highly variable (+/- 25%)
z Typical bias point: DC collector current = 100 µA
25mV r =100=Ω 25k π .1mA
MOSFET Ri = ∞Ω
Department of EECS University of California, Berkeley
14 EECS 105 Spring 2004, Lecture 22 Prof. J. S. Smith
Output Resistance ro
Why does current increase slightly with increasing vCE? Collector (n)
WB Base (p)
Emitter (n+)
Answer: Base width modulation (similar to CLM for MOS) Model: Math is a mess, so introduce the Early voltage
vBE /Vth iC = IS e (1+ vCE VA)
Department of EECS University of California, Berkeley
EECS 105 Spring 2004, Lecture 22 Prof. J. S. Smith
Graphical Interpretation of ro
slope~1/ro
slope
Department of EECS University of California, Berkeley
15 EECS 105 Spring 2004, Lecture 22 Prof. J. S. Smith BJT Small-Signal Model
irvbbe= π 1 igvcmbece=+ v ro
Department of EECS University of California, Berkeley
EECS 105 Spring 2004, Lecture 22 Prof. J. S. Smith BJT Parasitic Capacitors
z Emitter-base is a forward biased junction Æ depletion capacitance:
CCjBE,,0≈1.4 jBE
z Collector-base is a reverse biased junction Æ depletion capacitance
z Due to minority charge injection into base, we have to account for the diffusion capacitance as well
CgbFm=τ
Department of EECS University of California, Berkeley
16 EECS 105 Spring 2004, Lecture 22 Prof. J. S. Smith BJT Cross Section
Core Transistor
External Parasitic
z Core transistor is the vertical region under the emitter contact
z Everything else is “parasitic” or unwanted
z Lateral BJT structure is also possible
Department of EECS University of California, Berkeley
EECS 105 Spring 2004, Lecture 22 Prof. J. S. Smith Core BJT Model
Reverse biased junction
Base Collector
gmvπ
Fictional Resistance (no noise) Reverse biased junction & Diffusion Capacitance Emitter
z Given an ideal BJT structure, we can model most of the action with the above circuit
z For low frequencies, we can forget the capacitors
z Capacitors are non-linear! MOS gate & overlap caps are linear
Department of EECS University of California, Berkeley
17 EECS 105 Spring 2004, Lecture 22 Prof. J. S. Smith Complete Small-Signal Model
Real Resistance “core” BJT Reverse biased junctions (has noise)
External Parasitics
Department of EECS University of California, Berkeley
EECS 105 Spring 2004, Lecture 22 Prof. J. S. Smith Circuits!
z When the inventors of the bipolar transistor first got a working device, the first thing they did was to build an audio amplifier to prove that the transistor was actually working!
Department of EECS University of California, Berkeley
18 EECS 105 Spring 2004, Lecture 22 Prof. J. S. Smith A Simple Circuit: An MOS Amplifier
Input signal Supply “Rail” VDD RD
vo
I DS vs
vVvGS=+ GS s Output signal VGS
Department of EECS University of California, Berkeley
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