# What is theoretical (physical) limit a MicroSD card's capacity?

There was time (a decade ago) when I got 8 MB (yes, 8 MB, not 8 GB) SD card for my Nokia cellphone ( At that moment, the maximum storage on the market was 32 MB, marketed as the "breakthrough in high-capacity" cards).

However, as everything, those achievements left in history and then achieved 1GB...100GB... now 1000GB for the same sized MicroSD. I am interested:

1. On what does this increase depends? transistor development or? why they didnt produce 100 GB cards 10 years ago?
2. Is there any maximum capacity limit of what technology can achieve within a single MicroSD card?
• Theoretical or physical ie purchasable in store? – Solar Mike Oct 25 '20 at 12:26
• The latest (2018) SDUC standard supports cards up to to 128 TiB. But that doesn't answer the question about "potentially undetermined" capacity increase. – alephzero Oct 25 '20 at 18:28
• @alephzero please also, transfer your comment into answer, i see it as reasonable answer. I am interested into Today's existing limits. – T.Todua Oct 27 '20 at 11:30
• I have a 128GB card (from a reputable store and manufacturer - haven't tested it though). So there's that. – user253751 Nov 3 '20 at 18:23

The Bekenstein Bound sets the theoretical maximum storage density for storage media, which is equal to the entropy of a black hole of the same volume, or roughly:

$$I<=\frac{2πkRE}{ħc\ln2}$$

where I is the information expressed in number of bits contained in the quantum states in the sphere.

This works out to

$$2.5769082 × 10^{43} × M × R$$

where M is mass in kg and R is radius in metres.

A micro SD card is $$0.015 m × 0.011 m × 0.001 m$$, or $$1.65 × 10^{-7}m^3$$ in volume, and according to the info on a local office supplies shop, weighs $$0.05kg$$, so the theoretical maximum data it can store, using some as yet unknown quantum storage technology, possibly involving tiny black holes is $$2.125949265 × 10^{35}bits$$. That's $$≈ 26,574,365,812,500,000,000,000,000,000,000,000,000 Tb$$ (decimal terabytes, but SD manufacturers always use them because they make their products look bigger). Or, to express it another way, 265.75 Sextillion Terabytes.

That's a lot of information, what would you store on it? Well the thing about the Bekenstein Bound is that this is the amount of information it takes to completely describe the physical state, to the quantum level, of a volume the size and mass of say, a Micro SD Card.

That, however involves unknown technology that may never indeed exist, and if it did would probably require colossal amounts of energy. In terms of the tech that currently exists, albeit not available yet on aliexpress, a single-molecule transistor has been demonstrated, 167 picometres in diameter, "42 times smaller than the very smallest circuits currently possible". Assuming that they're somehow packed (in a cubic lattice, there are more efficient ways, but at the same time this doesn't allow space for connecting circuits etc.) into the chip with no volume used by the container, that gives you a maximum density of $$\frac{1.65 × 10^{-7}}{(1.67 × 10^{-10})^3} = 35,427,012,517,329,713,623,060$$ transistors. Supposing each transistor stores one bit, that's 4.375 ZB.

• Fantastic answer, thanks! people will enjoy such sophisticated and detailed answer. – T.Todua Dec 26 '20 at 14:09
• Thanks, now what I'd really like is for someone with some actual electrical engineering knowledge to edit it. – stib Dec 27 '20 at 1:34

Physical limits are related to the advance in technology. 20 years ago for humans, transistors of 1 nm were unimaginable. The limit that you mention can be established by the actual technology, but we can not set the physical limit: maybe in the future, we will store data in atoms or something like that.

Maybe the question will be better like this "What's the maximum capacity on MicroSD by the actual state-of-art?"