Monday, November 19, 2012

Currently, highest density DRAM is 4Gb/chip.
Currently, highest density DRAM is 4Gb/chip. Highest density flash is 128Gb/chip. Highest density hard drive is 1Tb/in^2. Let's say that we have about 10^11 bits/cm^2 and about 10^12 bits/gram right now.

If we look on the chip surface only, silicon atoms and about 1nm long, there are 10^14 of them on 1cm^2 chip, i.e. 1000 atoms/bit. Storage density is doubling every year, so we will be storing 1 bit per surface atom on a chip in 10 years or 10 terabytes.

18" (=450mm) wafers are 1mm thick to support their own weight. Thus 1cm^2 die weights 0.25 grams. Let's stack 4 of them for the round number of 1 gram.

1g of silicon/aluminum has 10^22 atoms, i.e. currently we store 1 bit per 1G of atoms, mostly because of the thickness of the chips/platters. The "column" is 1M or atoms thick or 1mm. Storage density is doubling every year, so we will be storing 1 bit per atom on a chip in only 30 years (in 2045) or 1 billion terabytes.

In order to maximize information content of a chip, i.e thermodynamic entropy, we'd have to heat it up.  Maximum amount of energy weighting 1g is mc^2=10^14 joules [1]. When an ideal gas with such total energy is confined to a volume of 1cm^3, it'll have temperature of 1 billion Kelvins [2]. Entropy is  Energy/Temperature/(Boltzmann constant) = 10^28 bits. After we reach 10^22 bits/gram, it'll be 20 more years till 10^28 bits/gram.

And if we compress 1-gram chip into a back hole of radius 7.4*10^-31 m [3], the entropy will be equal to the 1/4 horizon area in Plank units or 2.65*10^10 bits. That's about what we have right now! This may seem like a stupid thing to do, but it's not. We'll address the usefulness of it in a later post.

[1] = 30M kWh or \$3M worth of electricity.
[2] = 100 eV. For comparison, nuclear bomb is 10^6-10^7K, LHC is 10^13K.
[3] ~=10^–30 meter. For comparison, proton has radius of 10^–15 meter, and Plank length is 10^-35 meter.