EECS 105 Spring 2004, Lecture 21
Lecture 21: BJTs (Bipolar Junction Transistors)
Prof J. S. Smith
Department of EECS University of California, Berkeley
EECS 105 Spring 2004, Lecture 21 Prof. J. S. Smith Context
In Monday’s lecture, we discussed minority injection in forward biased PN junctions. Today we will discuss three terminal devices which use this effect for amplification, called:
z BJTs (Bipolar Junction Transistors)
Department of EECS University of California, Berkeley
1 EECS 105 Spring 2004, Lecture 21 Prof. J. S. Smith Reading
Today’s lecture will covering chapter 7, Bipolar Junction Transistors (BJT’s) Next , we will start looking at amplifiers, chapter 8 in the text.
Department of EECS University of California, Berkeley
EECS 105 Spring 2004, Lecture 21 Prof. J. S. Smith Lecture Outline
z Review of minority current injection in PN Diode
z The BJT (7.1)
z BJT Physics (7.2)
z BJT Ebers-Moll Equations (7.3)
z BJT Small-Signal Model
Department of EECS University of California, Berkeley
2 EECS 105 Spring 2004, Lecture 21 Prof. J. S. Smith PN diode Minority Carrier Close to Junction Thermal - + Generation p-type − - + n-type - + Jn, diff - + − - + J p, diff - + - + − J - + + p, drift - + - + Jndrift, - + ND - + N A - +
E0 qφ + bi Carrier with energy Recombination below barrier height − z As you increase the forward bias on a PN junction, the barrier keeping the holes from diffusing into the N side, and keeping the electrons from diffusing to the P side, is reduced
z As the barrier height decreases, the diffusion of carriers across the barrier increases exponentially. Department of EECS University of California, Berkeley
EECS 105 Spring 2004, Lecture 21 Prof. J. S. Smith Band edge diagram (forward bias)
The number of Electrons the density of electrons, here is determined by at this energy, over here
The number of holes determines the over here, at this energy number of holes over here
Forward bias → reduced barrier height, so more minority carriers on both sides
Department of EECS University of California, Berkeley
3 EECS 105 Spring 2004, Lecture 21 Prof. J. S. Smith Forward bias → Increased population of minority carriers
The minority carrier concentrations at the edges of the depletion region will be given by:
−q(φB −VD ) / kT pn (x = xn ) = N Ae
−q(φB −VD ) / kT np (x = −x p ) = NDe
Note: NA and ND are the majority carrier concentrations on the other side of the junction, with the assumption
that pn << ND and np << NA Also note: This neglects net recombination inside the depletion region
Department of EECS University of California, Berkeley
EECS 105 Spring 2004, Lecture 21 Prof. J. S. Smith Quasi-Neutrality
z Since the regions outside the depletion regions are going to be very close to electrically neutral (called quasi-neutrality) the number of majority carriers will increase slightly as well (slightly because there are usually many more majority carriers than minority carriers anyway)
Carrier Nd concentrations
Minority carriers
distance Department of EECS University of California, Berkeley
4 EECS 105 Spring 2004, Lecture 21 Prof. J. S. Smith Diffuse and Recombine
z Once the minority carriers have been injected across the depletion region, they will diffuse, and they will recombine. 2 z They will recombine, because now pn > n i and since recombination is proportional to pn, it will now cause carriers to recombine at a rate faster than they are generated.
z They will also diffuse into the other side, because there are more of them (the minority carriers) at the edge of the depletion region than there are further in.
Department of EECS University of California, Berkeley
EECS 105 Spring 2004, Lecture 21 Prof. J. S. Smith Excess injected minority carriers
qVA kT pn0e
p side n side
qV A x kT ⎛⎞qVA − nep0 kT Lp pnnn()xp=+00 pe⎜⎟ − 1 e ⎝⎠
Minority Carrier
pn0 Diffusion Length np0
-Wp -xp xn Wn Once the minority carriers are injected into the other side of the junction, the minority carrier concentration in the bulk region for forward bias is a decaying exponential.
Department of EECS University of California, Berkeley
5 EECS 105 Spring 2004, Lecture 21 Prof. J. S. Smith Ambipolar diffusion
z The diffusion constant for minority carriers is complicated by the fact that the minority carriers are dragged on (or pulled!) by the majority carriers, in a mechanism called ambipolar diffusion
z There is a small E field which keeps the excess holes and electrons together.
z The ambipolar diffusion constant for minority carriers comes out to be the diffusion constant for the other, majority carriers, in the cases where the majority carriers greatly outnumber the minority carriers. In other words, minority holes diffuse with Dn and electrons with Dp! z The minority diffusion length is a function of the ambipolar diffusion constant for the minority carriers, as well as the variability in the lifetime, etc. We will just take it to be a number!
Department of EECS University of California, Berkeley
EECS 105 Spring 2004, Lecture 21 Prof. J. S. Smith Steady-State Concentrations
Lnp,,>> W np In silicon, it is easy for the diffusion lengths to be much longer than the distance to the contacts, if none of the diffusing holes and electrons recombine until they get to the contactsÆ get a linear concentration gradient.
qVA kT pn0e
p side n side
The population is assumed qVA nekT to be the equilibrium p0 population at the contacts because of the many traps (defects) there
pn0 np0
-Wp -xp xn Wn
Department of EECS University of California, Berkeley
6 EECS 105 Spring 2004, Lecture 21 Prof. J. S. Smith Diode Current Densities
qVA kT pn0e qVA kT p side n side dnp npp00 e− n qVA kT ()x ≈ nep0 dx−−− xp () Wp
pn0 2 ni np0 np0 = Na -Wp -xp xn Wn
Under this linear approximation, we can calculate the current due to the holes diffusing into the N side, and the electrons diffusing into the P side. Notice that we are using the electron diffusion constant for the minority holes, and visa versa. dn ⎛⎞qVA Notice that the currents diff p Dn kT JqDnn=≈ qne p0 ⎜⎟ −1 due to the injected dx Wp Minority carriers on xx=− p ⎝⎠ Each side are not equal, D ⎛⎞qVA But are proportional diff dpn p kT JqDqpepp=− ≈− n0 ⎜⎟1 − dx W To the carrier xx= n n ⎝⎠concentrations Department of EECS University of California, Berkeley
EECS 105 Spring 2004, Lecture 21 Prof. J. S. Smith Bipolar Junction Transistor (BJT)
z A BJT is physically just two back to back PN diodes, with three contacts, but the current between the emitter and the collector is a minority carrier current in the base.
z Essentially, a forward biased diode is used to create a minority current, most of which then goes all the way across to the depletion region of another, reverse biased diode.
z The geometry can be such that almost all the current goes across to the second diode, so that the controlling electrode doesn’t have to supply much of the current, maybe 1:100 to 1:400
Department of EECS University of California, Berkeley
7 EECS 105 Spring 2004, Lecture 21 Prof. J. S. Smith Ideal BJT Structure + IC IE VEB Collector (N) IB + Emitter (P) + − + V V Base (P) CE Base (N) EC VBE − IB − −I −I Emitter (N) − E Collector (P) C
z A BJT transistor consists of a pair of diodes which have their junctions very close together, so that the minority currents from one junction go through the thin middle layer to the other junction.
z They are called PNP or NPN transistors by the layers they are made up of.
Department of EECS University of California, Berkeley
EECS 105 Spring 2004, Lecture 21 Prof. J. S. Smith Currents in a BJT
z Usually, a BJT is operated in a mode where one of the junctions is forward biased, and the other is reverse biased.
z The reverse biased diode injects minority carriers into the middle layer
z The minority carriers are then swept through the reversed biased junction.
Department of EECS University of California, Berkeley
8 EECS 105 Spring 2004, Lecture 21 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 21 Prof. J. S. Smith Band edge diagram
z The band edge diagram for an NPN transistor in operation
N P N (heavily doped) (Lightly doped)
Department of EECS University of California, Berkeley
9 EECS 105 Spring 2004, Lecture 21 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
EECS 105 Spring 2004, Lecture 21 Prof. J. S. Smith Actual BJT Cross Section
z Vertical npn sandwich (pnp is usually a lateral structure)
z n+ buried layout is a low resistance contact to collector
z Base width determined by vertical distance between emitter diffusion and base diffusion
Department of EECS University of California, Berkeley
10 EECS 105 Spring 2004, Lecture 21 Prof. J. S. Smith BJT Layout
z Emitter area most important layout parameter z Multi-finger device also possible for reduced base resistance
Department of EECS University of California, Berkeley
EECS 105 Spring 2004, Lecture 21 Prof. J. S. Smith BJT Schematic Symbol
ICB= β I
qVBE kT IIeCS≈ IB +
+ VCE
VBE − −I The arrow on the symbol − E shows the controlling diode.
z Collector current is control by base current linearly, a typical value would be β = 100 , because only one in 100 electrons would stop in the base instead of making it across to the collector
z Collector is controlled by base-emitter voltage exponentially
Department of EECS University of California, Berkeley
11 EECS 105 Spring 2004, Lecture 21 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 21 Prof. J. S. Smith BJT Collector Characteristic
z Ground emitter
z Fix VCE
z Drive base with
fixed current IB
z Measure the collector current
Department of EECS University of California, Berkeley
12 EECS 105 Spring 2004, Lecture 21 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 21 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
13 EECS 105 Spring 2004, Lecture 21 Prof. J. S. Smith Base-Emitter Voltage Control
Saturation Region ~0.3V (Low Output Resistance) Breakdown
Exponential Increase
Reverse Active (Crappy Transistor)
Forward Active Region (High Output Resistance)
Department of EECS University of California, Berkeley
EECS 105 Spring 2004, Lecture 21 Prof. J. S. Smith Diffusion Currents
z 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
Department of EECS University of California, Berkeley
14 EECS 105 Spring 2004, Lecture 21 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
EECS 105 Spring 2004, Lecture 21 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
15 EECS 105 Spring 2004, Lecture 21 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
EECS 105 Spring 2004, Lecture 21 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
16 EECS 105 Spring 2004, Lecture 21 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
EECS 105 Spring 2004, Lecture 21 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
17 EECS 105 Spring 2004, Lecture 21 Prof. J. S. Smith Ebers-Moll Equivalent Circuit
Building blocks: diodes and I-controlled I sources
Department of EECS University of California, Berkeley
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