Hmm, this needs some math:
A yottabyte is 1024^8*8=9671406556917033397649408 bits. = 9.671*10^24 bits.
On a modern HDD, the density of the bits are 5 atoms apart. The diameter of one atom (this is ridiculous, because every atom varies in size) is about 0.2nm.
sqrt(9.671*10^24 bits * 5 * 0.2nm) = 98'343.309m^2.
Diameter of the HDD = sqrt(98'343.309m^2 / pi)*2 =
11.1 km
Just for comparison,
11.1 km is approximately the diameter of earth.
Sooooo, no, this won't be happening...
Anyway, what on earth would you need that space for?
TheComet