How Transistor works - verifying

wbeaty

OK, thanks! And yes, comparing narrow base to extremely wide base is an excellent teaching strategy of which I previously hadn't heard.

Regarding canon, earlier you stated that the Ebers-Moll model is a CC model, and their original paper employed current-controlled current sources. Correct?

Are you certain that you're not misinterpreting something? N.b. that your assertion regarding Ebers-Moll being a CC model goes entirely contrary to numerous undergrad Uni books which give the following CV (large signal transconductance) equation as the central feature of Ebers-Moll model:

Ic=Is*(exp(Vbe/Vt)-1) (for large hfe of course, alpha ~=1)

Is this not canon? If the above CV equation isn't "Ebers-Moll model," then you've discovered a vast flaw in an enormous number of textbooks.

Studiot

Cabraham's approach in stressing the width of the interdepletion region is excellent and fundamental - or at least it was when I learned about transistors back in the 1960s. (post#68)

Pierce devotes several pages to calculations of the effect of base width on carrier density, potential diagrams etc and has an excellent diagram on page 101, which I have appended.

For expansion of these formulae (posts #68 & 69) I also recommend the monograph by E H Cooke-Yarborough of the Atomic energy Research Establishment at Harwell

An introduction to transistor circuits (1957)

go well

Attached Thumbnails

 

cabraham

Send me a message, & I'll email you the Ebers-Moll 1954 paper. It shows the bjt collector current being controlled by emitter current, i.e. a CCCS. Alpha is the parameter which determines the Ic value from Ie. They show a schematic w/ a CCCS controlling Ic.

The exp( ) relates the Vbe to Ic, but alpha is all important. The exp( ) covers the relation between Vbe & Ie. To get Ic we need alpha. The diode equation for the b-e jcn is Ie = Ies*exp((Vbe/Vt) - 1)> But Ic = alpha*Ie. So Ic = alpha*Ies*exp( ). The collector current is controlled by alpha*Ie. But Ie has a direct relation w/ Vbe as well as Ib.

All 3 eqns are relevant. A bjt offers both current gain as well as voltage gain. To compute current gain we use eqn 1) for the common emitter & emitter follower topologies. For the common base current gain, we use eqn 3). To compute voltage gain we use eqn 2). Again, all 3 eqns come into play when thoroughly analyzing bjt behavior.

We cannot make more than one quantity the controlling quantity. We generally control Ie, & Ic = alpha*Ie. Sometimes we control Ib, w/ Ic = beta*Ib. Usually this is not good due to beta dependency. We want networks that rely on well defined parameters like alpha & resistor values. Resistors have tight tolerances.

Send me a message, & I'll email you the E_M paper, the horses' mouth on the E-M eqns. BR.

Claude

wbeaty

I'll take a look.

Beware, this could be a case similar to Maxwell's Equations. Go to Maxwell's original work and you won't find his four equations. Maxwell never actually wrote those four, and probably wasn't aware they existed. Maxwell attacked the problem in an obscure way, employing magnetic vector potential, quaternions, and writing twenty equations. Later scientists came in and revised everything, producing the four equations known today. If you rely on Maxwell as the "horse's mouth," then you'd be in big trouble. (Officially the four equations are today called the Hertz/Heaviside equations. But Maxwell discovered the original mathematical form which describes EM fields.) See 2008 Microwave Journal, 23 years: Acceptance of Maxwell Theory http://bit.ly/qRQNCH

Studiot

Kirchoff's original statements are also quite different from what is often now presented under his name.
Maxwell's translation of K is quite interesting to read since if Professor Lewin followed the original he would not be able to present his famous 'conflict between K and Faraday lecture'.

This type of situation is actually not uncommon in the physical sciences.

cabraham

So Bill, is this what you're saying? Your site claims that the CC model of bjt operation is wrong, & you are right. Then you use Ebers-Moll as the source for your claim that the bjt be classified as VC, not VC, because Ebers & Moll seem to suggest that. I just showed that the E-M paper published in 1954, depicts the bjt as CC, not VC. Now you're suggesting that Drs. E & M should not be viewed as the horses' mouth.

But they were your source for your thesis. My CC model is affirmed by every semicon OEM I know of, i.e. Tex Instr, Natl Semi, Fairchild, Intl Rectif, etc. Ebers-Moll is pretty accurate, but Gummell-Poon is an improvement. The G-P model includes an additional factor to account for Early influence. The Early voltage is denoted as "Va". So Gummell-Poon is as follows:

Ic = alpha*Ies*(exp((Vbe) -1)))*(1 + (Vce/Va)).

At large values of Vce, the collector current for a given Ib, or Vbe as well, is larger than that obtained at low values of Vce. I'm sure you are well aware of the Early effect, no need to elaborate. That is the main difference between E-M & G-P.

Again, let me re-iterate that we seem to agree that the current control bjt model is a good external model when internal physics need not be considered. But when the internal charge profile & device geometry is relevant, the EE canon uses charge control as the correct bjt model. You insisted on voltage control, relying on E-M as the source, which does not support such a claim.

So when we look inside the device, & we need a better model than current control, what do we use? I say charge control, as does every semicon OEM, & uni. I say "QC", & that is my final answer. Any questions? Anyone?

Claude

wbeaty

No, not exactly.

I still haven't stated my position. Such enormous messages, and all without knowing what my arguments are. I'm very confused.

I could be wrong, but it looks to me like this is the problem here:

http://www.nizkor.org/features/fallacies/straw-man.html
Description of Straw Man
The Straw Man fallacy is committed when a person simply ignores a person's actual position and substitutes a distorted, exaggerated or misrepresented version of that position. This sort of "reasoning" has the following pattern: ...

I've been remaining silent on this issue because I'm waiting for you to notice that something important is missing. Also I'm waiting for you to stop repeatedly putting words in my mouth while constructing extensive counterarguments, over and over.

Looking back on this thread, it obviously hasn't worked.

So, what would work? You got me... I have no idea.

Suggestions from everyone would be welcome.

cabraham

Bill, please state exactly what you differ with in the EE canon. Your site makes some pointed criticisms regarding the way bjt operation is presented in engr colleges & semicon OEM app notes.

Where is the error in the common view of bjt operation? Where did I (Claude) err in presenting my understanding of bjt basics. Let's not be cryptic. Anything that I said that is not clear, or appears mistaken, or requires elaboration, is no problem at all AFAIC.

Again, I won't presume to know what your position is. So I'm asking you to state very plainly in detail the specific issues you have, if any, with OEM bjt models. We can take it from there. Best regards.

Claude

wbeaty

I can't answer that without first giving background. My article is aimed at the general public, meaning ~13yr old kids. My goal was to explain simply the inner workings of bjts, and do it without relying on a single equation. Kids have no use for advanced models which cover high frequency operation, high power, etc.

Look, I couldn't explain resistors to the public if I was forced to include the complete high-freq LC model; all we really need is Ohm's law (although even Ohm's law is quite a bit too advanced.) Isn't that obvious? And I certainly wouldn't explain diodes to them using a charge control high-freq model. And Gummel-Poon CC model of the bjt is completely inappropriate for my audience.

That's why I keep asking, did you notice who my audience was? Yes Gummel-Poon obviously is required for VHF design, for accurate spice simulations, etc. But for explaining transistors to people with zero math skills, it's just ridiculous.

Is this clear? CC is wrong. It utterly fails. It's a complete mismatch for the task at hand. It's the wrong tool for the job. (If you're looking for a tool which always works in every situation, well, good luck with that.)

So, how would we answer the following question?

What's a good way to explain the inner workings of the BJT to the math-phobic general public?

Above is the whole point of my article.

cabraham

I agree with that except for the part I highlighted in bold. So we agree that the discussion is limited to external mAcroscopic modeling, not internal physics. But then you state that CC "utterly fails", to which I say "say what!" The CC model is very accurate as long as we're dealing w/ speeds well below ft, & not saturating the device.

Of course there is no tool which works in every situation. I stated that repeatedly. Even QC (charge control) does not always provide a precise result. CC has its limitations, but since we're discussing external models, no internal physics, how is it that CC untterly fails?

Examine the following 2 current eqns:

1) Ic = beta*Ib.
3) Ic = alpha*Ie.

Again if "ft" is the device transition freq, & beta is the current gain, then fb (f_beta) = ft/beta. This "fb" value is where the beta value is 0.707 times the low frequency beta value. At freqencies below this value, eqns 1) & 3) are valid. You can rely on them provided the device is not used as a saturated switch.

The following eqn relates Vbe to Ic:

2) Ic = alpha*Ies*exp((Vbe/Vt) - 1).

Again, this is a perfectly valid relation at speeds below fb, & with the restriction that the bjt not enter saturation. These are the same restrictions for eqns 1) & 3).

For higher speeds and/or use of the device as a saturated switch, we must use QC. Stored minority carriers, distribution in space, reverse recovery charge, reverse recovery time etc. come into play. None of these useful parameters appear in eqns 1), 2), & 3).

Eqns 1), 2), & 3), are simply what I call the "terminal eqns". They are not a failure, just limited in scope. They are conditionally valid.

My final point, forgive me for repeating myself. Neither I nor the OEMs ever claimed that the CC model was valid for internal physics. We have presented the CC model as a superficial external estimate. It works under the conditions given above. No need to belabor the limitations of CC, as it is universally acknowledged.

For high speed operation, saturation, and internal physics analysis, the CC model is too oversimplified and cannot provide much help. But your whole point is to avoid complex math, & theory. On one hand you claim that CC fails, then you state that you wish to avoid heavy math & physics.

The eqn 2), Ic in terms of Vbe, is just as limited as are eqns 1) & 3). When the CC model is shown to be inadequate, you say we should use the VC model, I & the OEMs say QC model. That is where we differ. It's not about the limitations of CC model. We agree that CC is limited.

Our difference is in which model is more precise for the conditions where CC fails. Your view tha VC takes over has no support from any solid state physics theory. Only QC can handle the speed & saturation conditions. Neither Ic eqn, using Ib, Vbe, or Ie, can handle these conditions.

I'm at a loss to make it any clearer. Is my point clear?

Claude

wbeaty

We've utterly failed to communicate.

I said this:

I never said this:
Please don't take my sentences out of context. That's close to being straw-man.

OK, one more time.

Do you understand who is the intended audience of my article? My article is for children and the general public. My transistor article is for children. As I said in my previous message, Gummel-Poon and CC is wrong for children. When explaining the inner workings of transistors to children, CC fails. Using it is just stupid. It's completely the wrong tool for children.. It's like using a screwdriver to hammer nails.

If I tried to use CC and some equations to explain the inner workings of the BJT, and my audience is children, then I'd be a failure.

No we do not. The goal of my article is to explain the inner workings of transistors to children.

The goal of my article is to explain the inner workings of transistors to children.

Perhaps I didn't explain this before?

:)

We are not discussing external models.

We are explaining the internal physics of transistors ...to children.



Again, how would we answer the following question?

What's a good way to explain the inner workings of the BJT to children?

This question reveals the entire point of my transistor article.

cabraham

Bill, you ask "What's a good way to explain the inner workings of the BJT to children?"

My answer is, of course, the 2 diode back to back model. After diodes are explained to children, then the 2 diodes can be explained. A thick base region behaves like 2 back to back diodes & nothing more. As the base region is made thinner, transistor action is then observed.

The CC model, namely Ic = alpha*Ie, works very well. For 2 back to back diodes, the Ic value should only be a small value, that associated w/ the c-b jcn reverse leakage current. Namely Ic = -Ics*exp((Vbc/Vt) - 1). After all, the c-b jcn is reverse biased, so little current can flow.

The emitter current Ie is given by Ie = Ies*exp((Vbe/Vt) - 1), of course. So we have

Ic = -Ics*exp((Vbc/Vt) - 1).

Ie = Ies*exp((Vbe/Vt) - 1).

For 2 diodes, that is the truth, whole truth, & nothing but the truth.

But when the base is so thin that the 2 junctions are in extreme proximity, another term is added to the eqns.

Ic = alpha*Ies*exp((Vbe/Vt) - 1) - Ics*exp((Vbc/Vt) - 1).

The added term is in bold font. Personally, this explains bjt action w/o quantum mechanics. The "alpha term" accounts for the emitted carriers from the emitter, transporting right through the base before most can recombine, then continue onward into the collector. The better the transfer, the closer alpha is to unity.

Honestly Bill, if the target is children, & QM is off limits, is there a better explanation than the 2 back-back diodes w/ ultra-thin base width? If there is, please enlighten us. BR.

Claude

wbeaty

A bit too sophisticated for this audience.

Way overboard, we need total, total simplicity. E.g. we'd assume this Ic ~=0.

No equations allowed. Again: the audience is children. Even Ohm's law is too much. To construct equation-free explanations, one first must learn to think in equation-free terms: pure concepts, and visual/verbal/intuitive language.

wbeaty

So, how can we explain BJTs to children? To design an explanation, first describe the basic BJT operation verbally:

1. Base current controls the BE junction voltage
2. BE junction voltage determines height of BE potential-barrier
3. That potential-barrier sets the rate of charges crossing the BE junction
4. Most carriers from the emitter make it all the way to the collector
5. Ic approximately equals Ie

No heresies so far? :)

Studiot

I said before and I'll say again I like the picture of man operating a tap.

Children can easily understand how this can compass either polarity or FETs etc.

Otherwise you have all sorts of words they only half understand such as voltage, charge, current carrier etc.

(Are physicists really any better? )

cabraham

I believe the problem lies in #3. How does the potential barrier "set the rate of charges crossing the b-e junction"? I'm afraid that we are right back at the endless chicken-egg riddle. Does voltage "set the current" or does "current set the voltage"? Until we grapple with that vexing riddle, we will argue ad infinitum, which I am not going to do with anybody.

The power/signal source driving the amp stage is what sets the current. Then when carriers cross the junction recombination takes place for a small minority of carriers. Ionization occurs, & the local E field increases slightly due to the slightly increased charge distribution at the barrier zone. Vbe increases slightly.

This results in a slightly greater Vbe drop at the increased current level. The important point is that the rate of charges crossing the junction is determined by the power incident on the signal source driving the whole network. Using my singing Susan example w/ a microphone works well. Sue imparts acoustic energy to the mic diaphragm. Mechanical/acoustic power is converted to electrical power. The voltage drops due to cable resistance, the rbb' base region resistance in the bjt, the Vbe drop, & re, all subtract from the mic generated voltage.

The Vbe drop does not solely determine Ie. Rather, Ie is the net voltage after drops, divided by the total loop impedance. Vbe does not control Ic, but they are intrinsically & indirectly related. Here's how the events take place.

1) Sue sings into the mic.
2) Current & voltage are generated at the mic diaphragm. The ratio of V to I is the mic cable characteristic impedance, Zo.
3) The I & V move along the cable & encounter the bjt amp stage. Along the way cable resistance results in collisions & a charge distribution forming a potential barrier. Signal gets attenuated.
4) At the amp stage input carriers incur base side collisions due to rbb', & emitter side collisions due to re. Attenuation occurs.
5) Then the carriers cross the b-e junction. Most nake it to the collector but a few recombine in the base & ionize local atoms.
6) This changes ther barrier charge density & potential. The current is again attenuated.
7) If Sue cranks up her volume, the additional charges outputted by the mic add to the b-e barrier increasing Vbe.

Bottom line, Sue is the prime mover, she makes everything happen. Her volume determines all currents & voltages. She can sing loud, soft, or in between. Nothing happens until Sue makes it happen.

Rbb', re, cable R, cable C, b-e diffusion capacitance, b-c Miller cap, & barrier potential play a role. But none of them exclusively determine the current crossing the junction. Sue determines that current mostly, but there are drops due to rbb, re, & Vbe that diminish Sue's output. If Sue's mic outputs Vmic, each quantity cable R, rbb, re, & Vbe drop a portion of Vmic, leaving maybe 0.78*Vmic, or 0.63*Vmic, whatever.

If all drops were zero. Sue dictates the current. But nonideal parameters mentioned above rob a portion of Sue's signal. Thus, Vbe, rbb, re, & others do indeed play a partial role in "setting the current", but all are minor roles.

Sue is tha main entity that "sets" & determines the current crossing the junction. Is my explanation clear. BR.

Claude

wbeaty

Once again again again: THIS IS FOR CHILDREN. Complexity is verboten, and complex-ifying a simple situation is not any sign of competence. "Complexifers" are extremely valuable as graduate textbook authors, as RF chip designers, and for writing the best SPICE models. But for talking to children, "simplifiers" are who we need to hire.

We simplify everything by removing every smaller effect we can think of: remove the AC-source (microphone) and inject a Base current, unless you prefer a DC voltage source. Assume that rbb and re is zero, remove high-power phenomena, use the magical zero-resistance cable found in all intro courses, treat the DC case alone while ignoring dynamic AC issues such as Miller and other parasitic capacitance/inductance. We want a clear view of the most important phenomenon, so we wipe away all smaller details from our window. We don't even mention these details. (If something forces us to do so, we can add some details back in afterwards.)