Moore’s Law vs Functional Density Law
As we all know, as the feature size of IC processes moves toward 5nm and 3nm, Moore’s Law is coming to an end. So, what law can replace Moore’s Law?
This is what we are going to propose today: “Function Density Law-Function Density Law”, referred to as “FD Law”.
First, let’s review Moore’s Law.
Moore’s Law
Moore’s Law was proposed by Gordon Moore, one of the founders of Intel, in 1965. It has been 55 years since.
Moore’s Law states: When prices remain unchanged, the number of components that can be accommodated on an integrated circuit will double approximately every 18-24 months, and the performance will also double.
Generally speaking, Moore’s Law has the following three statements:
- The number of circuits integrated on an integrated circuit chip doubles every 18-24 months;
- The performance of microprocessors doubles every 18-24 months, while the price doubles;
- The computer performance that one dollar can buy quadruples every 18-24 months.
Among the above statements, the first statement is the most common. The second and third statements involve price factors, and their essence is the same. Although the three statements have their own merits, they have one thing in common, that is, the “doubling” cycle is 18-24 months. As for “doubling” (or quadrupling) “the number of circuits integrated on the integrated circuit chip”, whether it is the “performance of the entire computer”, or “the performance that one dollar can buy” is a matter of opinion.
This law reveals the speed at which information technology advances. Although this trend has continued for more than half a century, Moore’s Law should still be considered an observation or speculation rather than a physical or natural law.
Is Moore’s Law accurate? Let us first look at the picture below. As can be seen from the picture, the sampling points are basically located near the curve. It can be seen that Moore’s Law is basically accurate.
Moore’s Law is not a mathematical or physical law, but a prediction of development trends. Therefore, both written expressions and quantitative calculations should allow a certain margin. In this sense, Moore’s prediction is quite accurate, so it is recognized by people in the industry and generates huge repercussions.
The End of “Moore’s Law”
It has been 55 years since the advent of Moore’s Law. We know that the geometric size of components on a chip cannot be reduced indefinitely, which means that one day, the number of components that can be integrated per unit area of a chip will reach a limit.
Once the feature size on the chip reaches 1 nanometer, which is equivalent to the size of only 5 silicon atoms, the physical and chemical properties of the material will undergo qualitative changes, causing the semiconductor devices using the current technology to not work properly. Moore’s Law is coming to an end.
Functional density law
Now that Moore’s Law is coming to an end, a new law is needed to replace Moore’s Law. What law can replace Moore’s Law?
That’s what we’re going to propose today: the “Function Density Law.”
The law of functional density: For all electronic systems, along the time axis, the functional density in the system space is always increasing continuously and will continue to do so.
Function Density Law: For all electronic systems, along the time axis, the function density in system space is constantly increasing and will continue.
The figure below is a curve description of the functional density law:
It can be seen from the above curve that the functional density of electronic systems will continue to grow over time. The speed of its growth will vary in different historical periods. If there are new technological breakthroughs, its growth will be faster. If there are no new technological breakthroughs, its growth will be slower, but the general trend is continuous growth.
To understand the law of functional density, we first need to understand what is functional density?
Function density: The number of Function UNITs contained in a unit volume is called function density.
The key word in functional density is functional unit, so what are functional units (Function UNITs)? We need to understand the 6-level functional classification of electronic systems.
6-levels classification of electric system:
Function cell (FC) is the smallest functional unit of an electronic system. It cannot be disassembled. If it is disassembled, its functions will be lost and cannot be restored. For example, transistors, resistors, capacitors, inductors, etc. are all functional cells.
Function block (FB) is composed of functional cells and has certain logical functions. For example, 6 Transistors can form a SRAM storage function block, 1 Transistor and 1 capacitor can form a DRAM storage function block, and 4 MOS tubes can form a NAND gate or NOR gate. Function blocks are functional units with specific functions.
Function unit (FU) is composed of functional blocks and can complete complex functions, such as arithmetic logic unit (ALU), input and output control unit (IO Control Unit), central processing unit (CPU), etc. Computer processors, DSPs, FPGAs, memories, etc. can all be classified as functional units at this level.
Micro System (MS), at this level, we begin to define the concept of a system. Micro systems can independently complete system functions and are small in size. Usually they do not deal directly with end users, such as SiP, SoC, SoP, etc. Microsystems can usually be composed of functional units, functional blocks or functional cells.
Common System (CS) can also be called a conventional system. As the name suggests, it is a system that ordinary people can access. It generally refers to a system that directly deals with end users. The end users here refer to people. For example, mobile phones, computers, household appliances, etc. can all be called regular systems. Regular systems are usually composed of microsystems and functional units;
Giant System (GS) generally refers to complex and large systems, such as wireless communication network systems, Internet systems, aerospace systems, space station systems, etc. Large systems are usually composed of general systems, micro systems, etc.
In the above definition, functional cells (FC), functional blocks (FB), and functional units (FU) can all be called functional units (FUs), and they belong to different levels of functional units.
Let’s review the definition of functional density:
The number of functional units contained within a unit volume is called functional density. The functional units (Function UNITs) can be: Function Block, Function Cell or Function Unit.
Readers should note that when comparing functional densities of systems of the same type, the same level of functional density definitions needs to be used. For example, when comparing the functional densities of systems A, B, and C, A uses Function Block as the functional unit to define functional density, then B and C also need to use Function Block as the functional unit to define functional density.
The meaning of functional density law
If the functional unit in the definition of functional density is specified as a functional cell (transistor), its space is made two-dimensional, and its time is specified, then the functional density law will be reduced to Moore’s law.
If the integration of transistors on integrated circuits is expanded from a two-dimensional plane to a three-dimensional space, transistors are expanded into functional units, and time is changed from specific to trending, then Moore’s Law will be expanded into the law of functional density.
We can also understand that for the integration of electronic systems, Moore’s Law is a special case of the functional density law in integrated circuits, and the functional density law is the extension of Moore’s Law to the entire electronic system.
Some people may ask, why is the definition of functional density not using definite functional units, but three levels of functional units (functional block FB, functional cell FC, functional unit FU)? This is due to the complexity and uncertainty of the functionality itself.
For example, with the development of new technologies, the structure of functional blocks has evolved, and only smaller functional blocks (Function Blocks) are needed to achieve the same function. In this way, even if the number of the lowest-level functional cell (Function Cell) Transistor does not change, its functional density also increases. In this way, even if the number of the lowest-level functional cell (Function Cell) Transistor does not change, its functional density also increases.
For example, the SRAM we usually use requires 6 transistors (Transistors) to implement a memory unit, called 6T. The emergence of a new technology is said to be able to implement a memory unit with 1 transistor, called 1T. In this way, even if the number of transistors per unit volume remains unchanged, its functional density increases by 6 times.
And so on…
Summary and outlook
The law of functional density predicts the trend of electronic system integration and will become an important indicator for judging the advancement of electronic systems!
Moore’s Law is a law about human creativity. It is actually a law about human belief. When people believe that something can be done, they will work hard to achieve it. When Moore originally presented his observation report, he actually gave people a belief that the trend he predicted would continue.
The law of functional density is also a law about human creativity, and it is also a law about human belief. When people believe that the functional density in the electronic system space will continue to increase, they will also work hard to achieve it.
Function Density Law (FD Law) was first formally proposed by author Suny Li (Li Yang) in this article on January 20, 2020.
Prior to this, the author has experienced 20 years of electronic system design, accumulated rich project experience, and arrived at it through long-term analysis and thinking.
Will the Functional Density Law (FD Law) become the most important law for electronic system integration like Moore’s Law?
Now, we are not in a hurry to give a conclusion, let’s wait and see ten years later in 2030!
No longer obsess over the scaling of transistors on a two-dimensional plane scale, but put your thinking into a broader space, judge and develop from multi-dimensional integration, structured innovation, and a more flexible scale!
Understand and apply the law of functional density, and you will no longer be obsessed with the end of Moore’s law, because a new space has been opened for us, and it is broader!
