­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.

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Engineering Change Order (ECO)

A semiconductor chip undergoes synthesis, placement, clock tree synthesis and routing processes before going for fabrication. All these processes require some time, hence, it requires time (9 months to 1 year for a normal sized chip) for a new chip to be sent for fabrication. As a result of cut-throat competition, all the semiconductor companies stress on Cycle-time reduction to be ahead of others in the race. New ways are being found out to achieve the same. New techniques are being developed and more advanced tools are being used. Sometimes, the new chip to be produced may be an incremental change over an existing product. In such a case, there may not be the need to go over the same cycle of complete synthesis, placement and routing. However, everything may be carried out in incremental manner so as to reduce engineering costs, time and manufacture costs.

It is a known fact that the fabrication process of a VLSI chip involves manufacture of a number of masks, each mask corresponding to one layer. There are two kinds of layers – base and metal. Base layers contain the information regarding the geometry and kind of transistors, resistors, capacitors and other devices. Metal layers contain information regarding metal interconnects used for connection of devices. For a sub-micron technology, the mask costs may be greater than a million dollars. Hence, to minimize the cost, the tendency is to reuse as many masks as possible. So, it is tried to implement the ECO with minimal number of layers change. Also, due to cycle time crunch, it is a tradition to send the base layers for the manufacture of masks while the metals are still modified to eliminate any kind of DRC’s. This saves around two weeks in cycle time. The base layer masks are developed while metal layers are still being modified.

What conditions cause an Engineering Change Order: As mentioned above, ECO are needed when the process steps are needed to be executed in an incremental manner. This may be due to-

• Some functionality enhancement of the existing device. This functionality enhancement change may be too small to undergo all the process steps again
• There may be some design bug that needs to be fixed and was caught very late in the design cycle. It is very costly to re-run all the process cycle steps for each bug in terms of time and cost. Hence, these changes need to be taken incrementally.

Normally, there is a case that design enhancements/functional bug fixes are being implemented after the design has already been sent for fabrication. For instance, the functional bug may be caught in silicon itself.  To fix the bug, it is not practical to restart the cycle.

The ECO process starts with the changes in the definition to be implemented into the RTL. The resulting netlist synthesized from the modified netlist is, then, compared with the golden netlist being implemented. The logic causing the difference is then implemented into the main netlist. The netlist, then, undergoes placement of the incremental logic, clock tree modifications and routing optimizations based upon the requirements.

Kinds of ECO: The engineering change orders can be classified into two categories:

• All layers ECO: In this, the design change is implemented using all layers. This kind of ECO provides advantage in terms of cycle time and engineering costs. It is implemented whenever the change is not possible to be carried out without all layer change e.g. there is an updation in a hard macro cell or the change may require updation of 100’s of cells. It is almost impossible to contain such a large change to a few layers only.
• Metal-only ECO: As discussed above, due to incurring costs, sometimes, it may not be practical to use all the layers (base + metal) to do the ECO. In that case, to minimize the cost, it is required to be completed with changes only in minimal number of metal layers. These days, it is expected that every design will be re-opened for the ECOs. So, an adequate number of spare cells are sprinkled during the implementation all over the design to be used later on. These cells are spread uniformly over the design. The inputs of these cells are tied. Whenever the need for an ECO arises, the cells to be implemented can be mapped into the existing spare cells. Hence, there is no need to change the base layers in such a case. Only the connections need to be updated which can be done by changing the metal layers only. Hence, the base layer cost is saved.

Steps to carry out an ECO: The ECOs are best implemented manually. There exist some automated ways to carry out the functional ECOs, but the most efficient and effective method is to implement manually. Generally, following steps are employed to carry out Engineering Change Orders:

1. The RTL with ECO implemented is synthesized and compared with the golden netlist.
2. The delta is implemented into the golden netlist. The modified netlist is then again compared with the synthesized netlist to ensure the logic has been implemented correctly.
3. The logic is the placed incrementally. However, if it is metal-only ECO, spare cells in the proximity of the changed logic are found out.
4. The connections are, then, modified in metal layers.

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