Couple of basic transistor questions for the experts

[Digital Larry]

I rummage frequently, both online and in the dusty chasms of my memory.

#1 I cannot remember exactly why a diode or transistor B-E junction has the exponential relationship between voltage and current.  I do remember that a P-N junction develops a depletion zone due to the mobile charge carriers moving away from each other without an applied voltage, but I can't recall why the relationship is exponential.  I presume that it has something to do with the geometry of the junction itself (which is usually represented as just a flat surface).  Do point-contact transistors have a different characteristic (like anyone still alive would know)?

#2 I read recently about Ge transistor's voltage-temperature coefficient.  As I recall, Si's temp coefficient is about 25 mV/degree C.  I think Ge's is different, but not ten times or one tenth or anything like that.  If what I read was correct, it wasn't that much different at all.  So why is Ge regarded as super temp sensitive while Si is not?

Thanks!

DL

[R.G.]

#1 I cannot remember exactly why a diode or transistor B-E junction has the exponential relationship between voltage and current.  I do remember that a P-N junction develops a depletion zone due to the mobile charge carriers moving away from each other without an applied voltage, but I can't recall why the relationship is exponential.  I presume that it has something to do with the geometry of the junction itself (which is usually represented as just a flat surface).  Do point-contact transistors have a different characteristic (like anyone still alive would know)?

The exponential relationship is founded on the physics of charge carriers at the junction. The geometry of the junction can diddle this around a bit but can't fundamentally change the curves, which are part of Mother Nature's Rules regarding How The Universe Works.  I think point contacts have the same math, but the forward voltage is microscopic because one of the sides of the junction is a metal point, something like modern Schottky junctions, which amount to half-a-junction.

#2 I read recently about Ge transistor's voltage-temperature coefficient.  As I recall, Si's temp coefficient is about 25 mV/degree C.  I think Ge's is different, but not ten times or one tenth or anything like that.  If what I read was correct, it wasn't that much different at all.  So why is Ge regarded as super temp sensitive while Si is not?

As I remember, the difference in tempcos is not huge, but Ge has leakage in a junction of about 1000 times the leakage of a silicon junction, again based on the material physics. The amount of leakage is about 1000 times as much for same temp swing, but the coefficient is similar as I remember. It's been a long time since I sat through Dr. Allison's lecture on that one.

Germanium happens to be much, much easier to make a junction with. The first transistors were literally baked in a laboratory oven by putting indium snippets on both sides of a slab of germanium and cooked until the indium diffused into the germanium "base".  Germanium was humanity's learner semiconductor.

In the future, we'll probably migrate to something like silicon carbide for power devices; that's already happening for some devices. SiC Schottkys are very interesting power devices, and so are the few reports of SiC MOSFETs.

[Digital Larry]

Here's what I got from my textbook by the kindly, and most certainly late, Ralph J. Smith (Electronics Circuits and Devices, 2nd Edition):

"Calculation of the current flow in a PN junction is usually based on a detailed analysis of the minority carrier density gradients at the edges of the transition region.... the injection process is related to the statistical probability of electrons and holes having sufficient energy".  Then it immediately jumps to the term A1 * e ^ (eV/kT).  e/kT is about 25 at 20 degrees C.

Well then, it must not be a matter suitable for undergraduate discourse and so I will be satisfied to leave it at that.

Regarding temperature sensitivity of Ge, I now see that it is not the typical forward current which is dominating here, it is the leakage current.  Thanks for the clarification.

[induction]

Here's a derivation of the ideal diode equation, which you may find interesting.

This is also pretty good reading.

[Seljer]

I can't be bothered to go look at my old books but if I recall right in my third year undergraduate class on semiconductors we derived that ideal diode equation in the same way as it is there.

[PRR]

> why a diode or transistor B-E junction has the exponential relationship between voltage and current

Diffusion.

The more charge-carriers in the junction, the faster diffusion happens. Or: more current makes the conduction better. So not a resistance, not a dead-short, but some line in between. Exponential (or Log if you see it the other way).

Here's another way to look. Small-signal transconductance of a BJT is inverse to current, *exact*, for any practical current (above leakage and below parasitic resistances). The only way this could be true is the exp/log.

> Ge transistor's voltage-temperature coefficient

Cowles says Si leaks 1/100 to 1/10,000 the current of Ge, for comparable devices.

http://i.imgur.com/bqZyeb2.gif

Ge often winds up "marginal". 1,000 times better means that Si's leakage is usually "nothing" until you get to temperatures too hot to play.

[brett]

Hi
just a final 2c worth...
I'm no expert, but here's how I see these things...

In exponential decline there is a "half-life" or "half-matter" aspect to the behaviour. Exponential increase has a "double-life" or "double-matter" characteristic.

These "first order" behaviours ("kinetics" to the nerds) are some of the simplest things in nature. Radioactivity is a well-known exponential decay. The half life is very stable and totally determines the rate of decline. Unconstrained population growth is a well-known example of exponential growth. Snowballs do the same thing. So do millions of other things, including transistor current.

Basically, if 2 can make 4, and 4 can make 8, then 8 makes.... and so on. Also, if 2 makes 2.2, and 2.2 makes 2.42, then 2.42 makes...and so on. Same behaviour, just a different coefficient, and only 1 coefficient (the rate coefficient - that's why it is "first order").

cheers

[Digital Larry]

Many thanks for the responses.

Here's my summary of why the characteristic is exponential - which implies generally that the rate at which something changes depends on how much of it there is.

The resistance is related directly to the volume density of the mobile charge carriers.

In a regular conductor, such as a resistor, the volume density of mobile charge carriers depends on the material used but is not affected by the presence of an electrical field.

In a junction diode, the depletion zone results from oppositely charged mobile charge carriers moving away from each other (like 6 graders at their first dance), but statistically some of them will recombine anyway.  However the density of mobile charge carriers in the depletion zone is quite small without any voltage/field to push them closer together (the parents).  Thus the resistance to current flow is high.  

When the voltage increases, more MCCs move across and start recombining.  The volume density of MCCs increased, so the resistance to MORE current flowing under incremental voltage changes went down.  And, err... y'know, Q.E.D. and all that.  This seems like a satisfying perspective.

My second favorite explanation was the link to the derivation of the diode equation, where it appears to be the solution to a differential equation based on continuity equations for mobile charge carriers flowing through a volume of semiconductor material.  However the terms were not really explained all that well before constructing the equation.

I think I'll take my kids to the park now.