When Gordon Moore proposed Moore’s Law in 1965, it stated that the number of transistors integrated into a semiconductor chip would double every year. In 1975, he amended Moore’s Law to change “doubling every year” to “doubling every 18 to 24 months” according to the actual situation at that time.

Moore’s Law has been developed for more than 50 years, and during these 50 years, some people have put forward the view that “Moore’s Law is dead”.

Today, we look at the reasons for the end of Moore’s Law from two perspectives, one from a micro-view and one from a macro-view, which we can call: the two problems facing Moore’s Law.

## Micro-Problem

Although chip makers have used various means to keep pace with Moore’s Law, there is no way to avoid the fact that the doubling effect of Moore’s Law has begun to slow down, and there is always a physical limit to the constant reduction of chip size: the characteristic size of the latest process is now only 7nm, and the radius of silicon atoms is 0.117nm, which means that the characteristic size of transistors in a 7nm process chip This means that the feature size of a transistor in a 7nm chip is composed of less than 30 silicon atoms (actually less because of atomic space utilization, see later analysis), and its number will be further reduced as the feature size is further reduced.

As more and more transistor circuits are integrated into the same area size, it is difficult to solve problems such as increased leakage current, large heat dissipation problems, and slower clock frequency growth.

1) Is the feature size the minimum size in a transistor structure?

Let’s look at the microstructure of a transistor first. The structure of the most mainstream FinFET (FinField-EffectTransisto) transistor. The feature size refers to the width of the gate, and the current mainstream chip is 7nm minimum.

The feature size is not the smallest size in the transistor, and the width of the Fin is at least smaller than the feature size.

In the next generation of transistor structures with stacked nanosheets, the trend is even more pronounced, and the minimum size required to be fabricated (e.g., the thickness of the nanosheet) in a transistor with a feature size (gate width) of 3 nm is much less than 3 nm, or even less than 1 nm.

What are the problems encountered with smaller than 1 nm? We need to understand the atomic structure of silicon.

2) The physical structure of silicon atoms

The cell is the smallest unit reflecting the symmetry of the crystal. In a face-centered cube (8 vertices + one silicon atom on each of the 6 faces) composed of silicon atoms, there are four other silicon atoms located at 1/4 of the diagonal of each of the four spaces, and the average number of atoms in each silicon cell is 8 (8*1/8+6*1/2+4=8).

The cell length of silicon is a (lattice constant), and at 300 K, a=5.4305Ã… (0.543 nm), 1 nm corresponds to less than 2a, which means that no two cells can fit in a width of 1 nm.

Silicon atomic space utilization: silicon atomic volume/unit atom in the cell occupies the volume, silicon crystal space utilization is about 34%, that is, 1/3 of the cell space is atoms, 2/3 is empty space.

In other words, we see that silicon is no longer smooth and continuous, but consists of discrete clusters of atoms.

At this point, many of the laws and regulations that apply in continuous systems fail, and the transistor does not work properly. Therefore, from a microscopic point of view, Moore’s law is not sustainable.

## Macro-Problem

Moore’s Law, whether it was proposed in 1965: “The number of transistors integrated on a semiconductor chip will double every year” or amended in 1975: “Double every 18 to 24 months”, in a mathematical sense, the curve is exponential growth.

Assuming that the number of transistors integrated on a chip is X at a certain point in time, then 2X after 18 months, 4X after 2 18 months, and 2^n*X after n 18 months, then from now on we can estimate the number of transistors produced by humans: Y=X(1+2+4+8… +2^n), and multiplying both sides of the equation by (2-1) gives Y=X(2^(n+1)-1).

From the formula 1+2+4+8… +2^n=2^(n+1)-1 we can see that no matter how much was produced before, by the next cycle, the amount produced (consumed) in one cycle will be more than the sum of the amounts produced in all previous cycles1.

From another point of view, as long as the growth in the number of transistors continues to follow an exponential curve, then each future generation will look back on the past era as one in which there was little or no progress. This is in fact a paradox.

There are only 10^80 atoms in the universe, and if the number of transistors grows exponentially, it would take only a century and a half (150+ years) before all the atoms in the universe would be consumed, which is obviously impossible! (It should be noted by the reader that this paper makes some prerequisite assumptions when estimating, and the actual values will be related to changes in the prerequisites, but will not change by orders of magnitude)

At this point of writing, we can conclude that exponential curves are basically unsustainable in a physical sense. Therefore, Moore’s Law is also unsustainable from a macroscopic point of view.

“Moore’s law is a law about human creativity, not a law of physics”. We cannot deny that Moore’s Law has driven the white-hot semiconductor industry, which on the one hand can force the evolution of technology, but on the other hand, it also extremely reflects the idea of profit maximization that capitalists have prepared for a long time, so Moore’s Law is not called a law in the real sense, but just a means to seek benefits.

Based on the above ideas, is Moore’s Law dead? In fact, there is no real meaning, perhaps in the next 10 years will be replaced by other so-called “law of the times”, but the spirit of innovation is still worth passing on.