I was wondering if you would be willing to play around with some electromigration numbers. The Mean Time to Failure (MTTF) due to electromigration has been estimated empirically using:
Where A is the cross-sectional area, J is the current density, n is a scaling factor that is usually set to 2, k is the Boltzmann constant, Ea is the activation energy of the material, and T is the temperature. (
link)
Lets take a VERY conservative MTTF based on your estimation of two years. You are welcome to provide your own adjustments, but based on my experience the temperature has not changed much raising the voltage and overclock. This may just be due to favorable cooling circumstances but I will assume the temperature sensor readings are accurate.
So Ea, T, k, and A are all constant or nearly so. This leaves us with the current density being the most important change. For non-ohmic materials like semi-conductors J can be expressed as:
Where sigma is the capacitance, E is the electric field, D is the diffusion constant, q is elementary charge, and n is the electron density. Therefore in calculating the current density D, q, and n are constant for the same component. Then we can look at the electric field inside our component. For the sake of simplicity we assume that we are dealing with a small wire where E = V / d. Again d remains the same and the electric field grows linearly with voltage.
The purpose of the analysis above is to show that current density grows more or less linearly with increasing voltage in our case. This means for for n=2, MTTF will reduce by the inverse square of the change in voltage. Doubling the voltage reduces the MTTF of the junction by 4, quadrupling by 16, etc.
Therefore by increasing the voltage by .1V we reduce the MTTF by roughly 15%. For the given two years the MTTF for any given junction will reduce by 3.5 months.
(change in MTTF) ~ (modded V / stock V)^-2
Given 2 years is a fairly conservative estimate of the life of your card you may be reducing the total lifetime by a much higher amount, but the percent reduction in mean time to failure will be the same. For the sake of completeness I will estimate the difference in hashes over the life of a card in the two circumstances. I will give a very bullish reduction in life based on the calculations above of 2 weeks (even though in fact it was about 100 hours).
Overclock at stock voltages of a 5870, 425 Mhash/s for 2 years (104 weeks) ~= 27 x 10^18 hashes
Overclock at 1.25 V, 470 Mhash/s for 90 weeks ~= 26 x 10^18 hashes
Untested! 1.35 V, 490 Mhash/s for 77 weeks ~= 23 x 10^18 hashes
Therefore, you are correct you will reduce the overall hashes your card will be able to perform based on the MTTF. Also, there are numerous other points of failure and I believe electromigration in the junctions is just one to consider.
I would like to further complicate this picture by suggesting that having an extra 20 MHash/s now will be worth much more than the entire hashing power of the card at the end of two years given difficulty increases. I have not calculated this and difficulty changes are not predictable that far ahead. But you can see that increasing difficulty is an exponential and decreasing MTTF is quadratic.
I look forward to other considerations in ramping up the voltage before I do so.
Wow.. this post its without doubt the best argument reasoning that I have read about the topic. Kudos to you
