Tikalon Blog by Dev Gualtieri

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Gigayear Data Storage

November 25, 2013

If your office is similar to my office, you have stacks of digital media that are not readable on your present computer . There's the stray 3-1/2-inch floppy diskette , perhaps some 5-1/4-inch floppy disks , and a few ZIP disks , on my shelves. There are some eight-inch disks stored in a box, somewhere, for historical purposes. I have several nine-track tapes that I use as show-and-tell items (I have a box of vacuum tubes for the same purpose). My data backups are on CDs and DVDs , and my desktop computer has an optical drive to read these.

Most computers don't have an optical drive, since data storage is expected to be on USB flash drives , SD cards , or the "cloud ."[1] I object to cloud computing , since I don't want to relinquish the safety of my data to another party. No matter what media are used, we always have the expectation that careful storage will allow our data to be read at any future time, provided we have a physical reader.

Eighty column punch-card

Eighty column punch-cards were once so common that artisans would make Christmas wreaths and Easter flowers from them. (Via Wikimedia Commons.)

I don't have any punched cards on my shelves, but it's likely the data on those will be readable long after my present media can't be read. According to the US National Institute of Standards and Technology (NIST), a DVD will retain your data less than fifteen years as a worst case, although CD-R media have about double the life expectancy (see graph).[2]

Optical media lifetime.

Optical media lifetime, as determined by NIST.

CD-R is more archival than DVDs (all types).

(Graph rendered by author from data in ref. 1 using Gnumeric.)[1]

Most data centers of the later 20th century stored archives on reel-reel magnetic tape , since these have a very low per bit cost , and they were expected to be readable after 15-30 years.[3] Cautious system administrators would re-record data (transcribe) onto other reels every 5-10 years. Floppy disks and diskettes, although also magnetic , will have a shorter lifetime, since rubbing erodes the media. Today, magnetic tape storage in on tape cassettes .

Such studies on media longevity have been done by accelerated-aging experiments , which use a first-principles model of how long data will remain in a media system. A memory material will have an energy barrier between its two data states (logical "0" and logical "1"), as shown in the figure. For such a system, an Arrhenius law model can be used, and such a model has been applied to model the longevity of magnetic media .[4]

Energy barrier between two states.

Material stability modeled as an energy barrier ΔE between two states,
I and II.

(Illustration by by author using Gnumeric.)[1]

According to an Arrhenius law model, data is corrupted by thermal fluctuations that randomly push a bit from its intended state to its complement . The probability P for this to occur is an exponential function of temperature ; viz.,

P = 1 - exp (-t/τ(T)
where
τ(T) = (1/f₀) exp (ΔE/(k_BT)

In these equations , τ is the decay time, k_B is the Boltzmann constant , T is the absolute temperature , and f₀ is the attempt frequency . The attempt frequency can be estimated as the atomic vibration frequency , which can be as large as 10¹³ Hz . These equations allow a calculation of what the energy barrier must be for a desired media lifetime. Allowing for error correction , a million year memory needs an energy barrier of 63 k_BT. Boosting the barrier just a little, to 70 k_BT (1.8 eV at room temperature ), gives you a billion year memory.[5]

Scientists from the University of Twente (The Netherlands), the University of Freiburg (Germany) and KIST-Europe (Saarbrücken, Germany) have published a proposal for a billion year memory on arXiv .[5-6] It consists of a physical pattern of one material embedded in another, and they demonstrated such a memory with tungsten embedded in silicon nitride (Si ₃ N ₄) (see figure). While using the Arrhenius law model, The authors caution against "black swan " events, such as "theft , meteor impact or the sun entering the red giant phase ."[5]

Line-type archival WORM memory cells.

The tungsten -silicon nitride billion year memory.

There are two possible architectures; transparent, so it can be read by imaging with electron or photon beams, and another that uses interference effects.

(Figs. 3 and 4 of ref. 5, via arXiv.[5])

The experimental memory consisted of 100 nanometer tungsten lines embedded in silicon nitride. Tungsten was chosen because of its high melting point (3422 °C) and low thermal expansion (4.5 x 10^-6/K). Silicon nitride was chosen not only for its low thermal expansion (3.3 x 10^-6/K), but its high fracture toughness and transparency to light; and, in a thin slab, its transparency to electrons. These two materials are commonly used in microfabrication , so fabrication processes are well developed.[5-6]

According to the Arrhenius law model, a million year memory of this type, stored at room temperature, would need to survive for an hour at 445 kelvin (172 ° C). The memory survived this temperature, but there was significant information loss at 848 kelvin (575 ° C). The high temperature test was not really an appropriate aging test, since the thermal expansion difference between tungsten and silicon nitride caused cracks to appear.[5-6]

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