I do not know from where you have got that number, but it is meaningless.
The silicon atoms do not behave like spheres, only the atoms from many metallic or ionic substances have a behavior close to that of spheres. So it makes no sense to speak about a length "across" a silicon atom.
In the case of silicon, a meaningful number is that there are around 50 silicon atoms per cubic nanometer of silicon crystal.
The gate of a transistor (which is the active part of the transistor, and which has a much smaller volume than the complete transistor) in the latest 5-nm technologies is contained in a fin that might have a width around 5 nm, a length around 20 nm and a height around 50 nm, for a volume around 5000 cubic namometers (it is a complete coincidence that the width of a fin might be around 5 nm to 6 nm for a process named as "5 nm"; there is no relationship between the name of the process and the width of the fin; fins did not even exist for processes with names greater than "22 nm"). Such a gate of the smallest transistor might include around 250 thousand Si atoms. The volume of the complete transistor would be at least 10 to 20 times greater.
However the size of a transistor is not limited by the number of silicon atoms in the gate, but by the number of impurity atoms that control the conductivity of the silicon, and those are much less than the silicon atoms (I have not seen any number for the latest technologies, but they could be e.g. 10 thousand times less than the silicon atoms, so there might be less than 100 impurity atoms in the gate).
>I do not know from where you have got that number, but it is meaningless
Could you expand a bit? If atoms were randomly arranged, or in a non solid state I could kind of understand. But once you get to any kind of fixed structure you can infer 2d spacing from 3d spacing.
Or is your intent to say that the quantity of silicon in a gate is 3d, especially with fins, so a 2d view doesn't give a complete picture?
In silicon crystals and in most other semiconductors, the atoms are kept in their positions by covalent bonds that have certain directions in space, e.g. towards the 4 vertices of a regular tetrahedron in the case of a silicon crystal.
Because of that, the atoms are not packed together like some spheres, i.e. like the atoms in metallic aluminum or in table salt, where you may speak about the diameter of the atomic spheres. They are distributed on a lattice that has empty spaces between atoms and their bonds (i.e. the places where electrons belonging to the atoms are located with high probability).
The distance between the silicon atoms in a silicon crystal varies depending on the direction, so there is no single value that could be considered the diameter of a silicon atom.
The periodic cell of a silicon crystal has the same structure as that of cubic diamond and it has the form of a cube with 8 atoms inside it (an atom in a cube corner counts as 1/8 inside, an atom on a face counts as 1/2 inside).
While this visualization uses balls and sticks, to show the positions of the centers of the atoms, that has nothing to do with the form of the real atoms.
At most you could consider that a silicon atom has the form of the corresponding Voronoi polyhedron, in which case you would have to give several numbers, to describe its size, and not a single "across" value:
The number that I have provided, i.e. 50 Si atoms per cubic nanometer of Si crystal, can be computed by dividing 8 atoms to the volume of the cubic cell of the Si lattice. Given a volume of Si crystal, you can compute the number of Si atoms.
Like I have said, I do not know what means that 0.2 nm value, as the distance between 2 neighbor Si atoms can be larger than 0.5 nm, depending on the direction. In any case you cannot use it to compute anything about the number of atoms in a silicon device.
EDIT: I believe that you might have got your 0.2 nm from truncating the distance between 2 silicon atomic planes in the so-called "111" direction (the direction of the cube diagonal), which is the minimum distance between atomic planes in silicon.
That distance is 0.543 nm * sqrt(3) / 4 = 0.235 nm.
Because this distance is correct only for the "111" crystalographic direction, it cannot be used to compute the number of atoms in some piece of silicon, and it certainly cannot be called as the diameter of a silicon atom ("across an atom" without specifying the direction).
adrian_b's explanation is pretty good explanation of what I'm saying. To expand on that: you cannot pack transistors side-by-side without moving to global custom poly. The result is that there's a large amount of "technically not space for the transistor, but space required for the transistor to work" stuff around the transistor.
The result is that a 2nm process transistors is on the order of 10s of millions of atoms.
Source: I work with the latest nodes.
Here's a Fermi estimate: the M1 is ~16 billion transistors; assume it is 1 cm^2. That gives (10^7)^2 nm^2 / 10^10 transistors, which is ~10^4 nm^2/transistor. Assume the transistor is ~50nm high, which gives ~5x10^5 nm^3/transistor. There are ~100 SI atoms/nm^3, which gives a volume of ~5x10^7 SI/transistor.
