E migration independent from temperature. Why, when it's a quantum effect?

JonJ678 · 17 Jul 2009 at 13:21

I know theres a materials scientist on these boards somewhere, but I can't remember the fellows name. Hopefully he'll spot this.

As far as I know, electron migration is electrons tunnelling from one place to another. So directly proportional to current, and a function of voltage. Everyone in overclocking seems convinced that it's independent of temperature, and I can't for the life of my imagine why it would be. Either the community has missed the point, the effect is considered negligible, or I've thoroughly misunderstood tunnelling.

Information would very much be appreciated

death_looms · 17 Jul 2009 at 13:45

If it's electromigration you're thinking about, that refers to the movement of IONS, caused by momentum transfer FROM electrons when undergoing a collision in an electrical track. Unfortunately, current densities in CPU's are high enough for this to occur. Fortunately, the operational life of the chip is much greater than the timescale for this effect to become serious. Heating DOES make a difference, but it should not make a difference in the operational lifetime of the product. (Black's equation I think)

So, don;t worry, be happy! Hope this helps.

btw, electron TUNNELLING does become a problem at high electron energies (can be caused by heat). This has become more of an issue as the scale of the microarchitecture decreases. The potential barriers between tracks are exponentially reduced by reduced distance (not exactly correct, but it should help illustrate). This 'reduced' barrier is considerably more friendly to tunnelling. so, keep it cool for that reason!

JonJ678 · 17 Jul 2009 at 14:02

I hadn't drawn a distinction between forced ion diffusion and electron tunnelling. Thank you.

Black's equation is lifespan before death by electromigration. It puts mean time before failure as proportional to exp(1/T). For one thing that's not independent, for another its a fairly strong relationship, with higher temperatures leading to faster death by electromigration. So we assume this dependence is negligible.

Electon tunnelling is what I have misnamed in the title, I ran into it when looking into why the q6600 had a far higher allowable voltage than the q9550. So you also think this is dependent on temperature?

If anything I don't think it helps, what I thought was one effect is in fact two, both of which kill processors faster at higher temperature. I may start pointing people at Black's equation. Thanks for your post

death_looms · 17 Jul 2009 at 14:36

The difference is because of the architecture:

Q6600: 65nm
Q9550: 45nm

The voltage difference in this case is to do with electron tunnelling; the larger tracks and seperation allow a higher potential to be used before the potential barrier will collapse (i.e. electron will 'tunnel' through the space between tracks - not 'real' tunnelling as it will not leave a hole in the medium!) . Temperature will effect this, but the voltage is the bigger influence here.

Don't worry too much about blacks equation, it was just for completeness.

So, electron tunnelling is 'short term': it occurs due to too much voltage, and will stop when the voltage is reduced.

Electromigration is 'long term': due to consistent high current densities, and cannot be reversed. Chip death. My advice; if you upgrade every 5-10 or so years, unless insanely overclocked, you should be fine

JonJ678 · 17 Jul 2009 at 14:47

I have a reasonable grasp of tunnelling, enough to know that at any applied voltage it'll happen but the odds of it happening become rather higher as voltage is increased. I also suspect the ions moving qualify as tunnelling as well, as they're moving through an energy barrier which classically would be considered too great.
Do you know the form of the relationship between temperature, voltage and electron tunnelling, and if not where I should go to find out? Something analogous to Black's. Proportional to temperature seems a fair guess, but I base this on absolutely nothing. I'd trying to work out how I translate a safe voltage at 320 degrees to one with the same electron damage at 220.

I am starting to gather the resources needed to start overclocking further. So the better the theoretical understanding of overclocking I have, the further I'll go. There's a nasty gap in my knowledge that needs to be filled before I start making things

death_looms · 18 Jul 2009 at 11:06

The ions moving is not QM, but classical, as the energy for them moving is imparted to them by momentum transfer from electrons (akin to joule heating). If you hit a brick wall with a car, the wall is going to move! If it were QM, the car would not have to hit the wall for it to move. Ions CAN tunnel, but they are so much more massive it just doesn't happen here.

The relationship between tunnelling probability and potential barrier is exponential *hunts for old uni notes*. I hope you can read crappy one line equations!:

T(probability) = {[1+(e^(kd)-E(-kd))^2]/16[(E/V0)(1-E/V0)]}^-1

where k~{2m(V0-E)/hbar}

This is further approximated by Marti and Chen to give some more computationally friendly equations.
In the above:
e: the natural exponential
d: the barrier width (i.e. distance between tracks)
E: The energy of the electron relative to a base potential
V0: The potential barrier 'height' relative to the same ground level
m: THe mass of an electron
hbar: The reduced Plancks constant

You will notice that there is no temperature dependence here! This is because the energies usually involved in silicon are of the order of electron volts (eV). At room temperature, the amount of energy an electron will possess as a result of temperature is ~1/40eV, much smaller than the energies we are talking here.

As the voltage you supply to the chip is increased, you increase the potential energy of the electrons, thus reducing the effective barrier height, and so the probability of tunnelling is expentionally increased. Also as the potential applied is increased, the electron speed (energy) is increased, resulting in more ionic/atomic collisions, juole heating, higher temps, electromigration.

I will say again; don't worry too much about this theory! This kind of theory is more applicable to design, not overclocking. I hope it helped you a little, it is difficult to try and simplify the ideas used without face to face talking and a blackboard!

joeyjojo · 18 Jul 2009 at 12:15

^ Good work

death_looms · 18 Jul 2009 at 12:33

Don't have a 1st class physics degree for nothin ya know

(only graduated last week, been d**k swingin ever since!)

JonJ678 · 18 Jul 2009 at 14:37

death_looms said:
1st class physics degree

How goes job hunting /phd funding with that? I wish you luck, some of my friends are struggling.

Very good post, thank you. I've had to write the equation out on paper as I couldn't read the one line version, but it's all good. I wont try running any numbers based on it for the obvious reasons, but the relationships are useful. Temperature independent makes sense at last, your patience is appreciated.

You're quite right, this is only useful for design. However before sending the chip below zero it would be wise to grasp at least the basics of how one kills processors. I'll head over to xtreme once I'm done trying to follow the theory and talk to the people who build fridges, but I'd rather make informed decisions about voltages than rely solely on trial and error and replacing dead components

So, electromigration is classical; ions exchanging places when energy is sufficient. Statistical still? This is strongly temperature dependent, so keeping the system appreciably below ambient will allow higher electron energies without death from this effect. I'm currently viewing this as solid state diffusion accelerated by hammering electrons into the ions, is this fair? If so I might be able to actually run some numbers on this, I think below a certain temperature even the most energetic electron just isn't going to make any difference.

Electron tunnelling is a separate effect. Keeping the system cold wont help with this, increasing voltage will steadily increase this. Memories of the maxwell-boltzmann distribution suggests that this is always going to occur, and can be safely ignored up to an approximate voltage beyond which all hell breaks lose as a significant fraction of the electrons have sufficient energy to move to where they aren't expected. I can see this ruining stability, but rogue electrical fields don't seem to be dangerous as such.

Is it a fair statement that I won't damage anything with this, but stability suddenly starting to drop off with increased voltage is a sign that it's becoming an issue? This suggests an ultimate limit, beyond which no further voltage nor cooling will help.

Cheers again man

Bubo · 18 Jul 2009 at 15:24

So you will still be using the computers "ON" button to switch it on in years to come right?

death_looms · 18 Jul 2009 at 23:00

I may have been explaining this rather loosely previously, I'll try and clear everything up as best I can, the ideas behind QM are not easily grasped unless you have a rather abstract mind, or think A LOT, like me!

JonJ678 said:
How goes job hunting /phd funding with that? I wish you luck, some of my friends are struggling.

I'm all sorted to do a PhD in Acoustics and Audio Signal Processing (my main love in life is music, it fits), although I've also applied to work on the TARANIS laser in QUB. Funding included, of course!

JonJ678 said:
... ions exchanging places when energy is sufficient ...

Not quite, if they exchanged places, there would be no overall movement. Rather the ions are pushed out of the way by the electrons, and sort of 'squish up' to make room. Gaps then appear in the track, breaking the circuit.

JonJ678 said:
This is strongly temperature dependent, so keeping the system appreciably below ambient will allow higher electron energies without death from this effect...

It's the other way around really, the high temps are CAUSED by the collisions! When an electron transfers energy to an ion, it can be given as vibrational energy, causing a temperature increase. Keeping the temps VERY low will decrease the temperature rise, as the cross section of the ions blocking the electrons will be reduced, as they will be moving a lot less. It will still happen though, just more slowly

JonJ678 said:
...I think below a certain temperature even the most energetic electron just isn't going to make any difference...

Nope, It has to do with the electron current DENSITY, which is already high in microelectronics. By increasing volts, you increase the current (as the resistance doesn't change....much). It has a lot more to do with the sheer number of electrons rather than their energy. I think. Need to read up a bit on that to be sure.

JonJ678 said:
Electron tunnelling is a separate effect. Keeping the system cold wont help with this, increasing voltage will steadily increase this.

ABSOLUTELY CORRECT! Well, it wont be a steady increase, rather an exponential one, but you get the drift

JonJ678 said:
Memories of the maxwell-boltzmann distribution suggests that this is always going to occur, and can be safely ignored up to an approximate voltage beyond which all hell breaks lose as a significant fraction of the electrons have sufficient energy to move to where they aren't expected...

The MB dist. has relatively little to do with this, in any conductor there's only a small number of electrons that have the mobility required to conduct (i.e. in the conduction band of a metal, or at the top of an unfilled valance band in an insulator, like doped silicon). It doesn't always happen, but you're right that it can be ignored up to a certain point. What you will see as you approach the voltage limit (if this is causing the instability) is only occasional errors initially, but as you increase the volts, the frequency of these errors will increase greatly

When looking at this classically, all hell will break loose at a certain point as the electron energy can overcome a potential barrier only when it has sufficient energy. Quantum mechannically however, electrons can 'borrow' energy from the surrounding vacuum (the amount is dependant on the time it is borrowed for, and is derrived from Heisenberg's uncertainty principle). With this 'borrowed' energy, it can tunnel through a barrier WHEN ITS ENERGY IS LOWER THAN THE BARRIER. Classically this could not happen.

JonJ678 said:
Is it a fair statement that I won't damage anything with this, but stability suddenly starting to drop off with increased voltage is a sign that it's becoming an issue?

It's a sign that there is an issue. It may be this, it may be something else entirely!

JonJ678 said:
This suggests an ultimate limit, beyond which no further voltage nor cooling will help.

Bingo.

JonJ678 said:
Cheers again man

You're very welcome! Sorry that was a bit long, I feel I would be doing an injustice if I didn't do my best to explain as correctly as I can! If you have any uncertianties (haha! physics joke right there!), I'll to my best to make them as observable (oh I'm cracking myself up as I write this!) as I can!

David

death_looms · 18 Jul 2009 at 23:01

Bubo said:
So you will still be using the computers "ON" button to switch it on in years to come right?

Nah, our houses will know we're in when the door opens, will boot the PC for you so your desktop's ready for you when you sit down after getting your beer! (which has been poured already for you!)

Geekazoid · 18 Jul 2009 at 23:57

omg

bragging rights thread ones i love...

ahem *clears throat*

PHD Forensic Toxicology (just started)

so if you ever get poisoned give me a call

death_looms · 19 Jul 2009 at 02:30

Where are ya doing it? Too many complicated chemicals for me, us physicists like hydrogen, helium, argon and xenon. Nice simple things. Although the team working close to mine this year was investigating protein degradation and manipulation. I just shot ions at stuff

JonJ678 · 19 Jul 2009 at 11:02

Good fun. I'm glad you've found funding

death_looms said:
Not quite, if they exchanged places, there would be no overall movement. Rather the ions are pushed out of the way by the electrons, and sort of 'squish up' to make room. Gaps then appear in the track, breaking the circuit

This is the first point you've made that I think you're wrong on.

The lattice is fixed, and the bonding energy between the ions is rather high. Momentum transfer will deform the lattice, but not much. Similarly this would be temporary were it the active mechanism, and would make electromigration badly named. Collisions transferring energy to ions with consequent increase in probability of exchange sounds more plausible. Note that this does make a difference, as the region in question is a mix of silicon, phosphorous and boron (or whichever two doping ions are popular these days). So exchanging doping ions with lattice would explain the name of the effect, why its permanent, and why it's dangerous.

It's the other way around really, the high temps are CAUSED by the collisions! When an electron transfers energy to an ion, it can be given as vibrational energy, causing a temperature increase. Keeping the temps VERY low will decrease the temperature rise, as the cross section of the ions blocking the electrons will be reduced, as they will be moving a lot less. It will still happen though, just more slowly

Not the point I was aiming at re cooling. Higher energy electrons transfer more energy to the ions, leading to more frequent electomigration events. Cooling the lattice removes energy from it, leading to less frequent migrations. Therefore sufficient cooling will offset the increase in voltage in terms of electromigration?

It has a lot more to do with the sheer number of electrons rather than their energy. I think. Need to read up a bit on that to be sure.

This sounds about right, though Id expect current density and electron energy to both matter. Going to have a look through some of my old textbooks I think.

What you will see as you approach the voltage limit (if this is causing the instability) is only occasional errors initially, but as you increase the volts, the frequency of these errors will increase greatly

Happy days

Quantum mechanically however, electrons can 'borrow' energy from the surrounding vacuum

Not very convinced by this. Looks suspiciously like lies aimed at making sense from a classical perspective. I'll have to get back to you on this one.

death_looms · 19 Jul 2009 at 13:02

Good fun. I'm glad you've found funding

Me too man, me too. There's just no way I could do one without, although the amount of new PC bits and guitar amps I'm going to buy will offset this, and the world will be normal!

The lattice is fixed, and the bonding energy between the atoms is rather high. ...Momentum transfer will deform the lattice, but not much. Similarly this would be temporary were it the active mechanism...

The lattice is fixed, yes, but it can be deformed. If an atom is displaced, the overall free energy of the system may well rise. The system would love to move it back to reduce this, but if the move resulted in a potential barrier that the atom cannot pass (say, another atom, or proximity a doped ion that the atoms electrons like very much), it will remain in its new home.

Collisions transferring energy to ions with consequent increase in probability of exchange sounds more plausible. Note that this does make a difference, as the region in question is a mix of silicon, phosphorous and boron ... So exchanging doping ions with lattice would explain the name of the effect, why its permanent, and why it's dangerous....

The VAST majority of members of the bulk are normal silicon atoms. Doping is used to either increase the number of electrons in the conduction band (n-type), or increase the number of holes in the valance band (p-type). The positions of the ions in the bulk are largely irrelevant, it is for the electronic contribution i.e. more or less electrons than plain silicon, to the bulk electric properties that they are included. IF there were exchanges involvine the dopant ions (which there may be, but it would be an extremely rare, and would have to be quantum mechanical in nature), it would make no difference.

Not the point I was aiming at re cooling. Higher energy electrons transfer more energy to the ions, leading to more frequent electomigration events. Cooling the lattice removes energy from it, leading to less frequent migrations. Therefore sufficient cooling will offset the increase in voltage in terms of electromigration?

Yes, should minimise the effect by a noticeable amount (relatively speaking). Migration is actually a very good word to use for this!

JonJ678 said:
This sounds about right, though Id expect current density and electron energy to both matter. Going to have a look through some of my old textbooks I think.

Yes it will, but more frequent collisions will have the greater impact until the energy gets stupidly high, as the atom will have time to loose the excess vibrational energy between less frequent collisions. When the current density is high however, effects from changing electron energy will have a much greater impact that at low current densities!.

Not very convinced by this. Looks suspiciously like lies aimed at making sense from a classical perspective. I'll have to get back to you on this one.

I assure you, no lies! Promise!

The uncertainty equation can be treated in several different ways depending on the circumstance, all of which are correct. The best way to explain is to consider some fundamental forces - the strong nuclear force (although not really a fundamental force, rather a 'macroscopic' overview of the colour force of quarks, but it will do nicely!), and mavity. Considering a particle treatment of these forces (bosons - field quanta). The strong force is. well, strong. By consideration of the uncertainty principle, to 'borrow' such energy to exchange a force stipulated that it can only exist for a very short time - i.e. short range. This is observed (range ~^-15m). mavity on the other hand is extremely weak in comparison, thus can borrow the energy for much longer, thus has a much longer range. Also observed.
It can be difficult to think of 'borrowing' energy, as there is NO anology in the classical world, it is purely quantum mechanical. Believe me, it happens! The same equation allows for the existence of 'virtual' excited electronic states of an atom. This has been proved, indeed I spent a good part of the year studying it while building a laser powerful enough to observe it!.

Help any? I do apologise if I don't make things clear enough, it's difficult for me to remember what I was thinking when I learnt all this stuff! Again, fire away with the questions, I'll do my best!

btw it's nice to be talking about proper physics on the boards, gives me a fuzzy feeling, ya know?