### 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 d base 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 jB e 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 | = jEB h · | dbase L
--- | --- | ---
| Last, the current at the collector contact is the hole current jEBh – jrec 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 I B , 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 |
--- | --- | ---
| L e 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 (Semiconductors - Script)