Spare Cells

We have discussed in our post titled 'Engineering Change Order' about the important to have a uniform distribution of spare cells in the design. Nowadays, there is a trend among the VLSI corporations to implement metal-only functional and timing ECOs due to their low-cost. Let us discuss about the spare cells in a bit more detail here.

Figure showing spare cells in the design

Spare cells are put onto the chip during implementation keeping into view the possibility of modifications that are planned to be carried out into the design without disturbing the layers of base. This is because carrying out design changes with minimal layer changes saves a lot of cost from fabrication point of view as each layer mask has a significant cost of its own. Let us start by defining what a spare cell is. A spare cell can be thought of as a redundant cell that is not used currently in the design. It may be in use later on, but currently, it is sitting without doing any job. A spare cell does not contribute to the functionality of the device. We can compare a spare cell with a spare wheel being carried in a motor car to be used in case one of the wheels gets punctured. In that case, the spare wheel will be replacing the main wheel. Similarly, a spare cell can be used to replace an existing cell if the situation demands (eg. to meet the timing). However, unlike spare wheels, spare cells may be added to the design even if they do not replace any existing cell according as the need arises.

Kinds of spare cells: There are many variants of spare cells in the design. Designs are full of spare inverters, buffers, nand, nor and specially designed configurable spare cells. However, based on the origin of spare cells, these can be divided into two broad categories:

• Those used deliberately as spare cells in the design: As discussed earlier, most of the designs today have spare cells sprinkled uniformly. These cells have inputs and outputs tied to either ‘0’ or ‘1’ so that they contribute minimum to static and dynamic power.
• Those converted into spare cells due to design changes: There may be a case that a cell that is being identified as a spare now was a main cell in the past. Due to some design changes, the cell might have been replaced by another cell. Also, some cells have floating outputs. These can be used as spare cells. We can also use the used buffers as spare cells if removing the buffer does not introduce any setup/hold violation in the design.

Advantages of using spare cells in the design: Introduction of spare cells into the design offers several advantages such as:

• Reusability: A design change can be carried out using metal layers only. So, the base layers can be re-used for fabrication of new chips.
• Cost reduction: Significant amount of money is saved both in terms of engineering and manufacture costs.
• Design flexibility: As there are spare cells, small changes can be taken into the design without much difficulty. Hence, the presence of spare cells provides flexibility to the design.
• Cycle time reduction: Nowadays, there is a trend to tape out base layers to the foundry for fabrication as masks are not prepared in parallel. In the meantime, the timing violations/design changes are being carried out in metal layers. Hence, there is cycle time reduction of one to two weeks.

Disadvantages of using spare cells: In addition to many advantages, usage of spare cells offers some disadvantages too. These are:

• Contribution to static power: Each spare cell has its static power dissipation. Hence, greater amount of spare cells contribute more to power. But, in general, this amount of power is insignificant in comparison to total power. Spare cells should be added keeping into consideration their contribution to power.
• Area: Spare cells occupy area on the chip. So, more spare cells mean more density of cells.

Thus, we have discussed about the spare cells here. Spare cells are used almost in every design in each device manufactured today. It is important to make an intelligent selection of spare cells to be sprinkled in the design. Many technical papers have been published stating its importance and on the structure of the spare cells that can be generalized to be used as any of the logic gate. In general, a collection of nand/nor/inverters/buffers is sprinkled more or less uniformly. The modules where more number of ECOs are expected, (like a new architecture being used for the first time) should be sprinkled with more spare cells. On the contrary, those having stable architectures are usually sprinkled with less number of spare cells as the probability of an ECO is very less in the vicinity of these modules/macros.

I hope you’ve found this post useful. Let me know what you think in the comments. I’d love to hear from you all.

­Our world – Digital or analog

There are two kinds of electronic systems that we encounter in our daily life – digital and analog. Digital systems are the ones in which the variables to be dealt with can presume only some specified values whereas in analog systems, these variables can assume any of the infinite values. The superiority of digital devices over analog devices has ever been a topic of discussion. This is the reason why digital devices have taken over analog in almost all the areas that we encounter today. Digital computers, digital watches, digital thermometers etc. have replaced analog computers, analog watches and analog thermometers, and so on. Digital devices have replaced the analog ones due to their superior performance, better ability to handle noise and reliability in spite of being more costly than analog ones. Although most of the devices used today are digital, but in general, the world around us seems to be analog. All the physical quantities around us; i.e. Light, heat, current are analog. The so called digital devices have to interface with this analog real world only. For instance, a digital camera interfaces with analog signal (light) and converts it into information in the form of pixels that collectively form a digital image. Similarly, a music system converts the digital information stored in a music CD into pleasant music which is nothing but analog sound waves. All the digital devices that we know have this characteristic in common. Simply speaking, there are devices known as Analog to Digital converters (ADC) and Digital to Analog converters (DAC) that acts as an interface between the real analog world and the digital devices and converts the data sensed by analog sensor into the digital information understood by the digital system and vice-versa. They all interface with the so called analog world. But is the analog world really analog? Is it true that analog variables can take any number of values? Or is there some limit of granularity for them too. Is this world inherently digital or analog in nature? Is digital more fundamental than analog?

 As we all know, there are many fundamental quantities in this universe viz. Mass, length, time, charge, light etc. We have been encountering these ever since the world has begun. Now the question arises – whether all these quantities are inherently analog or digital? Finding the answer to this question will automatically bring us to the answer of our main question; i.e. whether the basics of this world lie in analog or digital. It is often said that “Heart of digital devices is analog.” (See figure below). This is because, as visible on a macroscopic scale, the current and voltage waveforms produced by a digital circuit/system are not digital in fact. This can be observed from the fact that the transition from one logic state to another cannot be abrupt.  Also, there are small spikes in the voltage levels even if the system is stable in one state. But, seen at microscopic level in terms of transfer of current by transfer of electrons, since, there can only be

transfer of an integral number of electrons, current can only take one of numerous values, and not just any value. Let us take an illustration. The charge on an electron is 1.6E19 (or 0.00000000000000000016) represented as ‘e’. It is the smallest charge ever discovered. It is well known that charge can exist only in the multiples of ‘e’. Thus, electric charge is a digital quantity with the smallest unit ‘e’. When we say that the value of charge at a point is +1C, we actually mean that the charge is caused by transfer of 6250000000000000000 electrons. Since, the smallest unit of charge is 0.00000000000000000016 C, hence, there cannot exist any charge of value 1.00000000000000000015 C, since that will make the number of electrons to be a fraction. Since, the magnitude of 1C is very large as compared to charge on 1e, it appears to us as continuous and not discrete. For us, there is no difference between 1. 00000000000000000015 and 1 as the devices we use don’t measure with that much precision. Hence, we infer these quantities as analog. Similar is the case with other physical quantities.

Many laws have been formed by our great scientists postulating about the quantization of some basic physical quantities. Viz. Planck’s quantum theory states that angular momentum of an electron in the orbit of an atom is quantized. Simply stated, it states that the angular momentum can take only specified values given as multiples of h/2Π. Thus, the smallest angular momentum an electron can have is h/2Π and the angular momentum can increment only in steps of h/2Π. If we take h/2Π as one unit, then we can say that angular momentum of an electron is a digital quantity. Similarly speaking, Light is also known to consist of photons. According to Planck’s quantum theory, the light intensity is also an integral multiple of the intensity of a single photon. Thus, light is also inherently a digital quantity. Also, as stated above, the charge is also quantized.

But there are some physical quantities of which quantization is yet to be established. Mass is one of those quantities. But, it is believed that the quantization of mass will be established soon.

Thus, we have seen that most of the physical quantities known are known to be digital at microscopic level. Since, we encounter these at macroscopic level having billions and billions of basic units, the increments in these seem to be continuous to us as the smallest incremental unit is negligible in comparison to actual measure of the quantity and we perceive them as analog in nature.

Thus, we can come to the conclusion that most of the quantities in this world are digital by their blood. Once the quantization of mass will be established, we can conclude with surety that digital lies in the soul of this world. This digital is similar to our definition of digital systems; just the difference is that it occurs at a very minute scale which we cannot perceive at our own.

Read also:

• Enhancement and depletion mode MOSFETs
• Analog to digital converter