Manufacturing cost is one of the most important factors when not only designing the next graphics card, CPU or even a complete system, but also when choosing suppliers in order to reach certain specifications and production volume.
The cost of wafers
The first point is the cost of the wafers, on which the circuitry of several equal chips is printed, so that the lasers then cut the different chips. But how much does a wafer cost? It is difficult to say, as it not only depends on the materials of the wafer, but it brings with it a number of added indirect costs. These include the following:
- The cost of deploying a new manufacturing node that literally involves setting up an entire factory.
- The tax rate of the country where the factory or smelter is located,
- The energy cost of keeping the factory running
- The salary of the workers, which is usually high, since a high qualification is required.
- Research and development of new nodes.
With each new node, the cost increases, which was could be ignored thanks to Moore’s Law, but in the last nodes this law is being fulfilled more slowly and the cost per mmtwo of each of the wafers has increased. So if we compare the new nodes with the previous ones in equal area, we will see an increase in the price. Of course, it must be clarified that a new manufacturing node always implies an increase in transistors per area.
The cost of the chip
In simple terms, the cost of the chip will always depend on the number of complete chips that can be printed on a wafer, which is always circular in shape. Think of the wafer as a kind of pastry or bakery dough from which we take out pieces to bake through a mold.
For this, the first thing we need to know is the area of the wafer, they always give us the diameter, which is usually 300 mm, which translates into a radius of 150 mm, and since the formula for the area of a circumference is π * R ^ 2, where π as you know it is 3.1459. Doing the quick calculation we have that the area in mm ^ 2 of the wafer is 70,685.83 mm ^ 2. How many chips can fit per wafer? We just have to divide the area of the wafer by the area of each chip to find out how many chips we can get per wafer.
But really this is ignoring the defect rate, which translates to a defect rate per mm ^ 2, which
What are the yields when manufacturing a processor?
Many times we have heard the term yields in the news, which is often used in the face of efficiency when making a chip. Well, yields are related to what we call the defect rate per mm ^ 2. Which means that the bigger the chip, the more percentage of it that is defective and has to be discarded because it is not valid for commercialization.
The defect rate per mm ^ 2 is what leads to the larger a chip the less yields are taken out of the wafer, as there is more opportunity for a defect in the wafer to touch a crucial part of the chip. To calculate the yields we use the Bose-Einstein formula:
Yields = 1 / (1+ (defect rate per area * chjp / 2 area) ^ N)
In which N is a manufacturing complexity factor, which measures the maturity level of the manufacturing node, since each of them can have several generations that are achieved by polishing the manufacturing processes to obtain a higher performance, which is translates into more chips.
Cost of the chips taking into account the yields
Once we know the yields, and therefore the efficiency of the foundry when manufacturing the chip, we can already know its cost through the following formula:
Cost per Chip = Cost per Wafer / Number of chips per wafer * yields.
But we are not done with that, since the chip needs to be encapsulated so that it can be mounted in the socket of a motherboard or on a graphics card.
Hardware package cost
The next point is to encapsulate the chip, this means mounting it on a solo interposer if we are talking about a monolithic chip or with several chips if we are talking about an MCM.
There are different types of encapsulations with different materials for different markets and therefore with different prices that will affect their final cost. All of them are designed to protect the chip from different inclement weather and in some specific cases special packages are usually used, as is the case with computers on board space probes that have to be prepared to withstand space radiation.
At present, the cost of encapsulation is something that, like the defect rate and the efficiency of the manufacturing process, are not often disclosed by different processor factories to the public.
Parametric Yields and Their Influence on Hardware Cost
The last point is the so-called parametric yields, these do not depend on the rate of defects of the manufacturing process, but depend on elements such as clock speed, voltage. For example, it may be that we need to manufacture a GPU for a graphics card whose specifications in heat and power consumption are already closed and in production, this would mean that any functional chip that does not meet those parameters could not be placed on the board of said graphics card and therefore they have to be discarded or find another way out.
Parametric Yields are not usually included in the final cost of a chip and most hardware manufacturers recycle previously discarded chips into new products.
Final cost of the chips in the hardware
The final cost is defined by the following formula:
Integrated circuit cost = (Final cost of the Chip + Cost of the Package + Cost of the quality tests).
Any chip that does not pass the quality tests and is discarded will affect the cost of those that do end up being marketed, unless it can be given an outlet in another product. Therefore, depending on the application to which the chip is directed, the discard of chips during the quality process can increase the cost of the final hardware to a greater or lesser extent.