The Cryogenic P-N Junction

[BravoV]

So if I'm going to get good measurements on the second try, I'm going to need to be mindful of these picoamp sources.

Shaving included ? 

Nice thread and thanks for sharing this. 

[uwezi]

Whether you trust my derivation or not - it's been quite silent here - I do not only want to give negative feedback.

If you want to do interesting stuff at low temperatures consider the following:

• take a yellow-green LED (GaP-type, not the "modern" InGaN ones), cool it down while running it at a modest forward current (5-10 mA). Look at the color of the light emission and describe it here!
• if you are in AVR µcontrollers: try to characterize the internal reference voltage and oscillator frequency over temperature. It would be interesting information, which sadly is missing in otherwise brilliant datasheets.

These are experiments which I really would like to do myself, if I had the time...

[T3sl4co1l]

So, back in Inorganic Chemistry, we had a lab about solid state physics... band gap etc.  So, we dug out a box of LEDs and lit them up at room temperature and under LN2.

The stated premise was that BG is inverse with temperature, so the color changes "up" on cooling (red (GaAsP) towards yellow; blue (GaN) towards violet; etc.).

So, naturally, I grabbed a green LED (GaP).  And it went red, not blue.  Asked the instructor... he said "oh, well this one's different, go pick a different color"...

Chemistry is a lot like English: they like to have their rules and all (compare Lewis Octet Rule to "I before E except after C"), but... they have an awful lot of them.  And a far more massive list of exceptions to those rules.  So, they aren't really *rules*, are they?

I suppose this is true of all fields.  Certainly, textbook (HS to undergrad level) electronics has the same problem, where only the simplest, least useful approximations are taught as fact.  Thevenin's theorem, maximum power transfer theorem: yes all well and good, but I don't suggest applying both at the same time to *my* audio amp.  But go ahead, do try it with *your* amp.

Tim

[uwezi]

So, back in Inorganic Chemistry, we had a lab about solid state physics... band gap etc.  So, we dug out a box of LEDs and lit them up at room temperature and under LN2.

The stated premise was that BG is inverse with temperature, so the color changes "up" on cooling (red (GaAsP) towards yellow; blue (GaN) towards violet; etc.).

So, naturally, I grabbed a green LED (GaP).  And it went red, not blue.  Asked the instructor... he said "oh, well this one's different, go pick a different color"...

Chemistry is a lot like English: they like to have their rules and all (compare Lewis Octet Rule to "I before E except after C"), but... they have an awful lot of them.  And a far more massive list of exceptions to those rules.  So, they aren't really *rules*, are they?

That's actually what I was after! The explanation can be found in the textbook by E. Fred Schubert, http://www.ecse.rpi.edu/~schubert/Light-Emitting-Diodes-dot-org/ - but it really is not straight forward!

[CaptnYellowShirt]

Sorry its been a few days. Work and all getting in the way of the fun stuff...

So in interest of investigating the big difference in leakage currents from my two HP 3457a DMM's as mentioned previously in this post, I cracked both of them open tonight and took a look-see. The things I found were interesting (at least to me).

To review, the problem was the two meters were generating wildly different leakage currents (2e-12 A vs 9e-12 A) when operating in their DCV mode. My initial thought was about the rear terminals of the devices -- the one with the large leakage current had them, the other didn't. Perhaps the wall the meters were shoved up against were causing a source effect?

The first attached picture shows the leads of the front and rear terminals joining up to the DMM's mainboard. The top leads are from the rear terminals, the bottom are from the front terminals. Clearly they are isolated and switched. However, the spacing there is only a few mm. So I decided to unplug the wires from the rear terminal face... That is the wires are still attached to the mainboard, but the molex-like connector that joins up with the rear face place was unplugged and left resting on top of one of the aluminum shields in the box (local ground - not mains earth).

I hooked the meters back up, and what I saw surprised me.  Rather than quickly (5sec) floating up to around the +2.5v that was common in both meters before. The modified one *slowly* (50sec) floated up to around 0.6v. The non-modified one continued to quickly float at around 2.5v.

So I thought, what's going on here? There's no rear terminals.... oh but there is a switching card! So I opened 2nd meter up and found a similar situation. Here, I did the same thing -- unhooked the molex-like connector from the switching card, wrapped it back up and found that the 2nd meter acted like the 1st one.... taking about 50sec to float up to around 0.6v.

Now, with a 1MOhm resistor across the terminals, the first meter measures 1.121 uV and the second measures (1.319 uV)... compared to the 1.82 and 8.5 uV before.


Case and point though.... even after the modifications, the hp 3457a would be loading diode with something like 1pA

[ejeffrey]

I'd like to get everybody's input for what I should try next. The main goal of the first experiment was to see if I could measure the "Built-In Voltage" to test my understanding of the quasi-steady, zero current bias state of the diodes.

As I explained before, the zero current bias state of a diode is zero voltage (if the diode is at the same temperature as the meter).  Any non-zero value you measure is a measurement error, of which there are several possible sources.

[CaptnYellowShirt]

How do you explain the drawing I posted showing the "Built In Voltage" for a p-n junction in thermal equilibrium? Is that non-sense? I'm really asking.

The point of these experiments is to drill down on this built in voltage idea... its critical to the way many texts explain the inner workings of a p-n junction (not just how to mathematically model them in a "small-signal" sense). So if built in voltage and carrier diffusion stuff is non-sense I'd like to conduct an experiment to demonstrate that to myself.

So I'm addressing your #1 concern about the meter biasing the junction. And I've found its a real possibility... so I'm looking into another meter. My thought here is to use a differential null meter.
As far as #2 goes -- that I'm picking up some EMI and rectifying it -- also a possibility. I didn't do it during the test, but an easy check here would be to switch modes on the DMM to AC and see if there's an AC signal?
For #3, thermal emfs... this is a common misunderstanding.  Thermal emf's are not created *at* junctions. They are a result of thermal differences throughout an entire circuit. But either way, I agree with you in noting the measured voltages seem to be a few orders of magnitude off to be explained by thermal emf.
Lastly, #4 - glass diodes and the photo-electric effect. Two of the three diodes were glass, the 3rd was a metal can. I think the glass ones were effected by light (and the shadow of my hand moving over the dewar to reach the multimeter), but in broad strokes, all three diodes showed the same voltage effects.

Are there any more? I'm never been that great at double-checking myself on things I don't yet know.

[muvideo]

Now, with a 1MOhm resistor across the terminals, the first meter measures 1.121 uV and the second measures (1.319 uV)... compared to the 1.82 and 8.5 uV before.


Case and point though.... even after the modifications, the hp 3457a would be loading diode with something like 7 or 8 uA.

Sorry, I'm not following you here, in voltmeter mode?
If so 7-8uA is huge, perhaps you meant 7-8pA, if so AFAIK it's pretty good.

Did you measure a 1MOhm shorting the inputs or a 1MOhm in series with a V-source?
Do you have a pAmmeter or a stable enough V-source to take the above measurements?

[CaptnYellowShirt]

Now, with a 1MOhm resistor across the terminals, the first meter measures 1.121 uV and the second measures (1.319 uV)... compared to the 1.82 and 8.5 uV before.


Case and point though.... even after the modifications, the hp 3457a would be loading diode with something like 7 or 8 uA.

Sorry, I'm not following you here, in voltmeter mode?
If so 7-8uA is huge, perhaps you meant 7-8pA, if so AFAIK it's pretty good.

Did you measure a 1MOhm shorting the inputs or a 1MOhm in series with a V-source?
Do you have a pAmmeter or a stable enough V-source to take the above measurements?

My mistake! I'll correct that.

My finger slipped when using iPython to do the math. Big difference between 10*6 and 10**6!

Should just be 1 pA.

[uwezi]

I'd like to get everybody's input for what I should try next. The main goal of the first experiment was to see if I could measure the "Built-In Voltage" to test my understanding of the quasi-steady, zero current bias state of the diodes.

As I explained before, the zero current bias state of a diode is zero voltage (if the diode is at the same temperature as the meter).  Any non-zero value you measure is a measurement error, of which there are several possible sources.

Exactly.

Just look at the diode equation, which describes so nicely how current and voltage in a diode behave (neglecting series and shunt resistances) in the dark

I = I₀₀e^-Eg/kT (e^qV/kT - 1)

The only point where current I is zero is at V=0 and vice versa at I=0 you will only measure V=0 give or take some additional factors like light-induced currents, thermal EMF, offset currents,...

The built-in potential is not a voltage which can be measured at the terminals of a diode.

[CaptnYellowShirt]

Isn't this a little like saying a real-world capacitor won't exhibit a self recharge effect or an ESR because the equation V = 1/C int{0}{t} i(tau) d_tau doesn't predict it?

All electrical components exhibit odd, non-modeled-for behaviors if you look closely enough.

I'm still not saying I *can* measure a diode's built in voltage, but if I can't, it's surely not because of an exponential-law modeling equation of an in-circuit-diode says I can't. 

Data, data, data, I cannot make bricks without clay.

[uwezi]

Isn't this a little like saying a real-world capacitor won't exhibit a self recharge effect or an ESR because the equation V = 1/C int{0}{t} i(tau) d_tau doesn't predict it?

You have a good point here, but you are also talking to someone who has written a PhD thesis on diodes and spends half of his job time working with solar cells (essentially pn junctions in the light) and the other half teaching electronics.

Of course the diode equation is only a model on how a diode should behave, it is not a law of nature but a description of an observation (first) and the result of a model (later). Furthermore the form I quoted is neglecting the effects of shunt- and series-resistance which you will find in every real-world device. But from measurements under controlled conditions I can tell you that the diode equation holds. At zero current the voltage over a diode is zero. Actually we regularly measure the current-voltage characteristics of solar cells between 100 K and room temperature, both in the light and under dark conditions. From the open-circuit voltage under illumination of a well-behaved pn-junction at different temperatures you can extract the bandgap of the semiconductor, but whatever you do, the built-in potential is nothing which will show up on the terminals of a diode.

Coming back to the diode equation: what you very often will see is that the current-voltage characteristic deviates from a pure exponential behavior at very low applied voltages, much lower than the value of the built-in voltage (still better: built-in potential). But you will always find that the direction of the current changes at an applied voltage of zero volts - showing zero current at zero volts.

So then the model of a built-in voltage must be wrong?

No, it is not, it is just not the full truth. I just tried to find suitable material on the net, perhaps the following will help to make things a bit more clear:

http://www.ee.sc.edu/personal/faculty/simin/ELCT563/04%20P-n%20junction%20basics.pdf

[CaptnYellowShirt]

I performed another test today.

In this experiment, I hooked up several of the 5.6v zener diodes (Motorola 1N5232B) I used in the first experiment in different configurations. I measured their output with my electrometer. Here's what I found:

Diode Configuration	Cathode-to-Positive	Cathode-to-Negative
One	-2e-9 A	+2e-9 A
Two-parallel	-4e-9 A	+4e-9 A
Three-parallel	-6e-9 A	+6e-9 A
Two-series	-0.6e-9 A	+0.6-9 A
Three-series	-0.8e-9 A	+0.8-9 A
Two(+)/One(-)	-2e-9 A	+2e-9 A

The last entry there is measuring three diodes in parallel -- one turned against the other two.

Room temp: 22.4C

Electrometer input impedance is 100MOhms in this setup. So a current of 2e-9A translates into about 0.2V. The fact they seem to add in parallel suggests its less a 'built-in voltage' and more of a built-in charge-rate source. Next I'll need to do a set of tests to form a load-line to get a better idea of the equivalent circuit of the diode.

Attached are pictures.

The rod is teflon.

[CaptnYellowShirt]

After the tests with the zener diodes, I wanted to know if these tests would hold for a regular diode.

I stopped off at radioshack and grabbed one of their 'assorted bags'. I mainly got stuff from the 1N400x series.

I ended up using a group of a few 1N4001's. At first nothing happened. But then I realized that after handling them I had some kind of goo building up on my finger tips. From the way they look, I wouldn't be surprised if Tandy swept them up off a factory floor.

Anway, I put the diodes though a wash of alcohol and this is what I got:

Diode Configuration	Cathode-to-Positive	Cathode-to-Negative
One	4e-13 A	-3e-13 A
Two-parallel	5e-13 A	-5e-13 A
Two-Series	1.6e-12 A	-1.8e-12 A
Four-series	4e-12 A	-3.2e-12 A

These lower values there were somewhat unrepeatable. They were measured with the electrometer in its 100G Ohm mode, so  a hair or slightly moist air current (or a bit of goo on the diode body) could have thrown the experiment off.

So maybe what I'm seeing here isn't the built in voltage after all? *Something* is happening with these zeners. And to some extent its happening with a 'regular' diode, but its certainly not as strong of an effect.

[T3sl4co1l]

The obvious absurdity that should be screaming at you is...

If there IS a terminal voltage difference...

How much current is behind it?  And where does the V*I = power come from?

Doing the experiment in light vs. dark conditions (or with glass vs. plastic packages) may provide additional clues.

Incidentally, vacuum tube diodes exhibit short circuit leakage current (typically on the order of uA), and O/C voltages around 2V (the current in this region transitions from V^(3/2) law to an exponential tail, so the available power is considerably less than SCC * OCV; the tail, BTW, is exponential for the same reason semiconductor diodes are exponential over most of their range -- statistics!).  This is thermodynamically acceptable because the cathode is hotter than the plate; indeed, a vacuum tube is a [ridiculously inefficient] electric heat engine!  Likewise, applying a thermal gradient to a semiconductor diode results in nonuniform mobility and built-in potentials and such, but not an isothermal diode.

Tim

[CaptnYellowShirt]

If there IS a terminal voltage difference...

A 10M Ohm resistor in the place of the diodes in both tests yields a reading of zero.

Doing the experiment in light vs. dark conditions (or with glass vs. plastic packages) may provide additional clues.

If you look closely at the photographs, you'll see the diode chosen for the experiment is in a silvered case. However, I'll look at it under a microscope tomorrow. Maybe there's a window to the semiconductor I didn't see?

And where does the V*I = power come from?

Good question. Its something I've been wondering too. In the 'built-in voltage' model I'm exploring with the experiment, charge carriers are forced across the p-n junction by a diffusion pressure until the electric field of the separated charges arrests any further diffusion. I'm not sure if the diffused or undiffused state contains less entropy? I'd have to think about this first before making any further guesses. But you're right, its gotta come from somewhere... or does it?! Naw, just joshin' ya. Seriously though, if this ends up being a time machine or perpetual motion machine, I call dibs...

[CaptnYellowShirt]

So then the model of a built-in voltage must be wrong?

No, it is not, it is just not the full truth. I just tried to find suitable material on the net, perhaps the following will help to make things a bit more clear:

http://www.ee.sc.edu/personal/faculty/simin/ELCT563/04%20P-n%20junction%20basics.pdf

Could be. It is rather simplistic.

I've been reading this book: http://ecee.colorado.edu/~bart/book/book/title.htm

Any sections you think I should focus on?

[T3sl4co1l]

If there IS a terminal voltage difference...

A 10M Ohm resistor in the place of the diodes in both tests yields a reading of zero.

Relative to an electrometer (or an ice cold junction at an arbitrarily low voltage), 10M is a short circuit.   I'd be curious to see what a polystyrene cap (if you can find one) of about 100pF does over time (if the electrometer is on the order of 10^12 ohms, we're talking minutes of time constant).  That should be much more representative of a junction near zero bias.

Remember, an experiment doesn't prove anything if it's self-validating.  Test every counter-case you can,  especially the simple ones, and you have a much more convincing proof!

Down at some level, there should still be a residual current, due to cosmic rays. It may be very difficult to detect.

Tim

[uwezi]

I've been reading this book: http://ecee.colorado.edu/~bart/book/book/title.htm

Any sections you think I should focus on?

Well from just quickly scrolling down the long page, Ch.4 seems to be quite ok.

Back to your recent experiments: now do them in a shielded Faraday cage. As a kid I had a quartz wristwatch running on the rectified power from a nearby AM radio station (AFN in northern Germany). I don't expect that you are living near a strong AM transmitter like I was, but as pointed out by T3sl4co1l, now that you see voltage and current you either have tapped a source of completely free energy which I missed when studying the current-voltage curves of hundreds of diodes close to V=0 and I=0 OR you are getting the power from somewhere else. Any diode (Schottky and pn) has the ability to rectify stray RF and mains signals...

[CaptnYellowShirt]

Back to your recent experiments: now do them in a shielded Faraday cage. As a kid I had a quartz wristwatch running on the rectified power from a nearby AM radio station (AFN in northern Germany). I don't expect that you are living near a strong AM transmitter like I was, but as pointed out by T3sl4co1l, now that you see voltage and current you either have tapped a source of completely free energy which I missed when studying the current-voltage curves of hundreds of diodes close to V=0 and I=0 OR you are getting the power from somewhere else. Any diode (Schottky and pn) has the ability to rectify stray RF and mains signals...

Well I thought about this too. Lets see what you think. I used the Hp 3457a dmm to measure the DC and AC voltages on one zener diode that was used in this experiment. At room temperature, with the diode wired directly to the screw terminals on the dmm, and left alone for 10mins, I found a DC voltage of around 0.21 volts and two AC voltages -- 3mv / 24kHz (with my florescent lights on) and 1mv / 60hz (with the lights off).

And I actually already am in a bit of a faraday cage. My workshop is sheet metal clad on all 5 sides, and the bench where I am taking these measurements is in-set into a hill (so its like 5-6 feet below ground). Nothing works in the shop -- no cell phones, no FM radio, no AM radio.  But there's always setting the experiment up inside of another cage. The electrometer is battery powered, so I'll take a look at that.

[CaptnYellowShirt]

Relative to an electrometer (or an ice cold junction at an arbitrarily low voltage), 10M is a short circuit.   I'd be curious to see what a polystyrene cap (if you can find one) of about 100pF does over time (if the electrometer is on the order of 10^12 ohms, we're talking minutes of time constant).  That should be much more representative of a junction near zero bias.

Good idea. I'll see if I can find something in my parts bin.

[CaptnYellowShirt]

And where does the V*I = power come from?

Good question. Its something I've been wondering too. In the 'built-in voltage' model I'm exploring with the experiment, charge carriers are forced across the p-n junction by a diffusion pressure until the electric field of the separated charges arrests any further diffusion. I'm not sure if the diffused or undiffused state contains less entropy? I'd have to think about this first before making any further guesses. But you're right, its gotta come from somewhere... or does it?! Naw, just joshin' ya. Seriously though, if this ends up being a time machine or perpetual motion machine, I call dibs...

In thinking about the problem from an entropy perspective,  I may have found what is really at issue here -- terminology. And it is like you all have been saying: you can't measure the 'built-in voltage' with a voltmeter because the term 'voltage' in 'built-in voltage' and 'voltage' with respect to a voltmeter are two entirely different things.

Check me on this explanation  ...

When I say voltage as in something my voltmeter can measure I'm actually talking about galvanic potential -- or the *net* force motivating the flow of electronics in a circuit. The source of this really could be anything. Classically its generated by a chemical potential, but any system that wants to dump/accept electrons has a galvanic potential. This is the voltage that is measured by a voltmeter.

When I say 'built-in voltage', I'm talking about a simple electric field -- which, if one could probe using magic-physics-text-book probes, it would have a scalar potential of X volts. But since no such device actually exists, I do the next best thing which is to rely on the flow of electrons to divine where the field is and how strong it is. Again, the net force  causing this flow is the galvanic potential. Its measured with a voltmeter.  And for most cases it is taken to be equivalent to the potential developed by the electric field in question.

However in the case of the p-n junction the built-in voltage electric field is balanced by the diffusion force. These forces (which also include thermal and photonic) are only acting on a narrow slice of the p-n junction. Sure, there's a galvanic potential to be measured, but it only exists over this narrow window because there's no motivation for electrons to leave the p-n junction. Since its way easier for the electrons to balance the competing forces of diffusion and built-in eletric fields by simply drifting across the p-n junction (rather than around a larger circuit), "built-in voltage" is not something you can measure with a voltmeter.

Really the diagram that I posted earlier should show the voltage potential dying off as distance from the junction is increased --reflecting the non-divergence of the electric field and the effective nullification of the electric dipole in the p-n junction as distance from the diode increases to infinity.

[uwezi]

Hi CaptnYellowShirt,

I guess we are approaching a common denominator here.

However, your last paragraphs would imply that - if you only would make the slab of silicon thin enough - you still would expect to see a flow of current and an external voltage over the diode. But this is not the case. It would still defy the other basic law of physics, the conservation of energy.

Any even so slight flow of electrons driven by an even so small potential difference would mean that your diode would deliver electric power to the outside world. This power would have to come from somewhere - possible source being an external flow of heat through the diode, light hitting the diode, external electromagnetic fields,...

Just a junction in thermal equilibrium with its surrounding, either at room temperature or at cryogenic temperatures is not good enough.

[T3sl4co1l]

Like I said, you can get a difference in potential from a thermal gradient.  Under isothermal conditions?  This is silly.

[CaptnYellowShirt]

However, your last paragraphs would imply that - if you only would make the slab of silicon thin enough - you still would expect to see a flow of current and an external voltage over the diode.

The paragraph that starts with "However..." or "Really..." ?