Analog
Design
Kevin
Aylward B.Sc.
The
Voltage Controlled
Bipolar
Junction Transistor
Abstract
This paper attempts to rectify a very common
misconception or misunderstanding regarding the basic operation of the Bipolar
Junction Transistor. This misconception is the erroneous, but very commonly
held, notion that the bipolar transistor is a current controlled current source
(CCCS). That is, that the collector and emitter current of the bipolar transistor
is in some way casually determined by the base current. This notion is
false.
It may be stated, without reservation, that the
Bipolar Junction Transistor is a voltage controlled device, and to a good
approximation a voltage controlled current source (VCCS).
Many elementary, layman or Bantam paperback type
references, and unfortunately, even some rare semi academic books often give
generic reference to the base current controlling the collector or
emitter current. The argument for this usually involve no use of semiconductor
physics, and rests on various ad hoc arguments on the the notion of the
collector current being equal to hfe/beta times the base current. The root
cause of this misconception is often the inability to distinguish a functional
relation from a causal relation. That is, whilst it is certainly
true that in a practical transistor base current must exist, transistor action
is not causally dependant on such current. Base current is an effect
that results from an application of a voltage at the base emitter junction.
The Voltage Controlled Bipolar Transistor
The bipolar transistor is, fundamentally, a voltage
controlled device and this principle is usually not open to much debate in
academic environments. Any reasonably advanced academic physics text book
directly shows that the currents of the transistor are causally related
to the device terminal voltages. To this authors knowledge, there are no
technical physics arguments that derive transistor collector and emitter
currents from direct knowledge of the base current.
Verification of this view can be obtained by
referring to, arguably, one of the foremost papers on modeling the bipolar
junction transistor, the paper "An Integral Charge Control Model Of Bipolar Transistors" by
H.K. Gummel and H.C. Poon":
"We present in this paper a compact model of
bipolar transistors, suitable for network computer programs. Through the use of
a new charge control relation linking junction voltages, collector current and
base charge, the model includes high injection effects..."
Indeed, the more advanced VBIC model dispenses with the concept
of the current gain Beta/hfe entirely:
“…From the physical analyses above, it is clear
that the collector current primarily depends on the base doping, and the base
current depends primarily on recombination and generation in the emitter
region. Consequently, very different physical mechanisms control the collector
and base currents. Relating them via a phenomenological parameter such as Bf,
which is done in the SGP model, is therefore undesirable, and causes problems
for statistical BJT modeling (McAndrew, 1997). This is why VBIC explicitly
separates the base and collector current modeling….”
Fundamentally, having a small current directly control
a large current violates conservation of energy. It is equivalent to throwing a
small pebble at a large rock and attempting to make that rock travel at the
same speed as the pebble.
Gummel-Pool Model
Unfortunately, the nature of the "Gummel-Poon"
"charge control model" model is very often misunderstood. The
"charge control" aspect of the model is the principle that the
collector current of the transistor is a causal effect of the charge in the
base region. However, this base region charge, by construction of the
model, is caused by the terminal voltages of the transistor. The
model does not assume or rely in any way on any notion that the charge in the
base region is actually caused by charge injected via the base terminal.
Indeed, the model explicitly calculates the base region charge by calculating
the charge injected from the emitter. It is this principle that leads to
the very name "Emitter" for the bipolar transistor. It is the Emitter
that emits (injects) the majority of the charge into the base region, however,
and somewhat unfortunately, a small amount of this charge leaks away via the
base terminal as base current. However, any base current is simply a side
effect of applying a voltage to the base emitter junction and just reflects the
fact that the collector is unable to suck up all of the charge that is injected
from the emitter region. This is illustrated in the Gummel-Poon model by the
following:
The second page of the Gummel-Poon paper, noted as
page 828, states:
“…The new charge control relation arises from the treatment of the transport
equation for the carriers that pass between emitter and collector. Use is made
of the fact that recombination has only a very small effect on the
junction-voltage dependence of the current passing from emitter to collector
(later called the dominant current component). Hence for this dependence, but
of course not for the base current, recombination is neglected. A direct
closed-form solution of the transport equation from inside the emitter to
inside the collector is possible…”
In other words, the base current (recombination in
the base) is neglected (initially) in the Gummel–Poon method, and base charge
is calculated for the "junction-voltage dependence of the current passing
from emitter to collector". That is, the 1st order calculation of
the base charge is not effected or reliant on base terminal current, but by the
terminal voltages. Thus, the bipolar transistor is inherently described as a voltage
controlled device.
It is further noted that once the 1st order charge
and currents have been determined, the Gummel–Poon model goes on to calculate
and include the effects of base current as a 2nd order term, for example,
by calculating the effective base emitter voltage by allowing for the voltage
drop across the internal base resistance due to this base current.
Basic Transistor Operation
The emitter current of a bipolar transistor is
generated in the same way as that of the current in a simple diode. That is,
applying a voltage to the (base emitter) diode junction results in the same
current that would flow in a normal diode. That is:
However, unlike in the simple diode case, the
(base) current that is required from the generator of this diode junction
voltage, (Vbe), is much reduced because most of the injected emitter current
gets sucked up into the Collector region due to the electric field at the
Collector. A key factor for this to occur is that the base region is very
thin.
There is thus an effective functional relationship
between collector current and this reduced base current described by ß (beta or
hfe), the common-emitter current gain, which is the ratio of collector current
to base current. It is typically greater than 100 for small-signal transistors
but may be smaller in transistors designed for high-power applications. Beta is
not linear in general, and depends on the emitter current and collector-emitter
voltage. For the typical case of larger current gains, the base current loss is
negligible and has minimal effect on collector current, such that the collector
current is simplified to IC= Io.exp(q.VBE/kt). 2nd order base current effects
may be included by calculating the voltage drop to the internal base-emitter
node due to this current and an internal base spreading resistance, by
ib.rbb'.
The summary of this is:
1) The base emitter
junction is a diode junction.
2) It can be shown that the
current in a diode is causally related to the voltage across it. The relation
is:
- (1)
where Vt
is KT/q, and Io is a constant dependant on temperature.
This equation dictates that however Vd is achieved, Id through the junction
will be related by the above equation.
3) A voltage instigated via
the base and emitter of the transistor is, essentially, equal to Vd of (1),
therefore the current that exists through such junction must be related by (1).
That is, the emitter emits charge into the base
region of the transistor, due to the application of Vbe.
4) The emitted charge, once in
the base experiences the influence of the voltage at the collector, and as the
base is very thin, collects the charge at the collector terminal and thereby
prevents most of the charge flow that would over wise attempt to exit out of
the base terminal. Some charge does in fact "leak" out of the base,
but this is incidental to the notion that the emitter current is, essentially,
a causal function of applied Vbe, via the diode equation. As most of this
current is collected by the collector, the collector current may also be said
to be a direct casual function of the applied base emitter voltage.
5) It can also be stated that is electric field
that, ultimately, is what causes charges to move, by virtue of the Lorentz
force F=qE. It is thus, the electric field due to the base-emitter voltage that
causes charges to be emitted into the base region, and the electric field due
to the collector voltage that attracts those charges to the collector region.
Summary
The bipolar transistor is described as a voltage
controlled device that is spoilt by a non-linear resister across its base
emitter junction. For some simple applications one might consider in a very
loose way that the collector current is "caused" by a base current as
there is indeed a functional relation, but this is only a descriptive approach
of limited value that is difficult or impossible to apply in general
situations.
Indeed, if one looks at ones watch and the motions
of the planets, we can usually say that the sun will reappear when we see the
watch hands rotate twice, but this functional relation is certainly not causal.
Stopping the hands moving wont stop the sun moving!
References
McAndrew, C. C., Bates, J., Ida, R. T., and
Drennan, P. (1997) “Efficient statistical BJT modeling, why b is more than
Ic/Ib.” Proc. IEEE BCTM.
© Kevin Aylward 2015
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