### 3.4.2 Bipolar Transistors

Basic Concept and Operation

We are not particularly interested in bipolar transistors and therefore will treat them only cursory.
Essentially, we have two junctions diodes switched in series (sharing one doped piece of Si), i.e. a npn or a pnp configuration, with the added condition that the middle piece (the base) is very thin. "Very thin" means that the base width dbase is much smaller than the diffusion length L.
The other two doped regions are called the emitter and the collector.
For transistor operation, we switch the emitter - base (EB) diode in forward direction, and the base - collector (BC) diode in reverse direction as shown below.
This will give us a large forward current and a small reverse current - which we will simply neglect at present - in the EB diode, exactly as described for diodes. What happens in the BC diode is more complicated and constitutes the principle of the transistor.
In other words, in a pnp transistor, we are injecting a lot of holes into the base from the emitter side and a lot of electrons into the emitter from the base side; and vice versa in a npn- transistor. Lets look at the two EB current components more closely transistor:
For the hole forward current, we have in the simplest approximation (ideal diode, no reverse current; no SCR contribution):
jhole(U)  =  e · L · ni2
t · NAcc
·  exp –  e · U
kT
and the relevant quantities refer to the hole properties in the n - doped base and the doping level NAcc in the p - doped emitter. For the electron forward current we have accordingly:
jelectron(U)  =  e · L · ni2
t · NDon
·  exp –  e · U
kT
and the relevant quantities refer to the electron properties in the p - doped emitter and the doping level NDon in the n - doped base.
The relation between these currents, i.e. jhole/jelectron, which we call the injection ratio k, then is given by
k  =
Lh
th · NAc

Le
te·NDon

=  NAc
NDon
Always assuming that electrons and holes have identical lifetimes and diffusion lengths.
The injection ratio k is a prime quantity. We will encounter it again when we discuss for optoelectronic devices!
For only one diode, that would be all. But we have a second diode right after the first one. The holes injected into the base from the emitter, will diffuse around in the base and long before the die a natural death by recombination, they will have reached the other side of the base
There they encounter the electrical field of the base-collector SCR which will sweep them rapidly towards the collector region where they become majority carriers. In other words, we have a large hole component in the reverse current of the BC diode (and the normal small electron component which we neglect).
A band diagram and the flow of carriers is shown schematically below in a band diagram and a current and carrier flow diagram.
Lets discuss the various currents going from left to right.
At the emitter contact, we have two hole currents, jEBh and jBEh that are converted to electron currents that carry a negative charge away form the emitter. The technical current (mauve arrows) flows in the opposite direction by convention.
For the base current two major components are important:
1. An electron current jBe, directly taken from the base contact, most of which is injected into the emitter. The electrons are minority carriers there and recombine within a distance L with holes, causing the small hole current component shown at the emitter contact.
2. An internal recombination current jrec caused by the few holes injected into the base from the emitter that recombine in the base region with electrons, and which reduces jBe somewhat. This gives us
jBEh  =   jBe  –   jrec
Since all holes would recombine within L, we may approximate the fraction recombining in the base by
jrec   =  jEBh  ·  dbase
L
Last, the current at the collector contact is the hole current jEBhjrec which will be converted into an electron current at the contact.
The external terminal currents IE,IB, and IC thus are related by the simple equation
IE  =  IB  +  IC
A bipolar transistor, as we know, is a current amplifier. In black box terms this means that a small current at the the input causes a large current at the output.
The input current is IB, the output current IC. This gives us a current amplification factor g of
g  =  IC
IB
=  IE
IB
–  1
Lets neglect the small recombination current in the base for a minute. The emitter current (density) then is simply the total current through a pn-junction, i.e. in the terminology from the picture jE = jBEh + jBe, while the base current is just the electron component jBe.
This gives us for IE/IB and finally for g:
IE
IB
=  jBEh  +  jBe
jBe
= k + 1
g  =  IE
IB
–  1 =  k  +  1  –  1  =  k  =  NAc
NDon
Now this is really easy! We will obtain a large current amplification (easily 100 or more), if we use a lightly doped base and a heavily doped emitter. And since we can use large base - collector voltages, we can get heavy power amplification, too.
Making better approximations is not difficult either. Allowing somewhat different properties of electrons and holes and a finite recombination current in the base, we get
g =
Lh
th · NAc

Le
te · NDon

·  æ
ç
è
1  –  dbase
L
ö
÷
ø
»   NDon
NDAc
·   æ
ç
è

1  –  dbase
L
ö
÷
ø
The approximation again is for identical life times and diffusion lengths.
Obviously, you want to make the base width dbase small, and keep L large.
 Real Bipolar Transistors Real bipolar transistors, especially the very small ones in integrated circuits, are complicated affairs; for a quick glance on how they are made and what the pnp or or npn part looks like, use the link. Otherwise, everything mentioned in the context of real diodes applies to bipolar transistors just as well. And there are, of course, some special topics, too. But we will not discuss this any further, except to point out that the "small device" topic introduced for a simple p-n-junction now becomes a new quality: Besides the length of the emitter and collector part which are influencing currents in the way discussed, we now have the width of the base region dbase which introduces a new quality with respect to device dimensions and device performance. The numerical value of dbase (or better, the relation dbase/L), does not just change the device properties somewhat, but is the crucial parameter that brings the device into existence. A transistor with a base width of several 100 µm simply is not a transistor, neither are two individual diodes soldered together. The immediate and unavoidable consequence is that at this point of making semiconductor devices, we have to make things real small. Microtechnology - typical lengths around or below 1 µm (at least in one dimension) - is mandatory. There are no big transistors in more than two dimensions. Understanding microscopic properties of materials (demanding quantum theory, statistical thermodynamics, and so on) becomes mandatory. Materials Science and Engineering was born.

© H. Föll (Semiconductor - Script)