Someone who has access to market and someone who has access to capital came up with an evil plan. They want to make a VLSI circuit and then they will fabricate it and sell it to puny humans to make money [Evil laugh]. What they want to create will surely depend on what their consumers will find useful. So they hire someone who has expertise in consumer electronics and pays her to figure out what they can sell to them with some good profit. After doing her tricks, she gives them certain product requirements. Now these product requirements are sent to us - the engineers. We try very hard to concentrate on them and after some time under the influence of burnt-out neurons, we are able to draw up specifications of VLSI circuit. These specification usually describes the behaviour of the circuit (e.g. in VHDL, Verilog). Moreover, this specifications are embedded inside the model of the environment in which this circuit suppose to work. For example, a chip designed to work over Himalayas needs to be tested for temperature range -20 to -50 degree centigrade, however if the targeted consumers are normal lesser mortals working in their cozy rooms, these conditions of negative temperature can be relaxed or dropped altogether. Now, my job starts. Based on these specifications, I have to come up with a design. Depending on the level of my experiences and expertise in design, I refine my design over the time mostly by trial and error, and educated guesses. During all these trials, errors, and educated guesses, I ‘ll have my moment of genius which even I can not control.  Normally, all these testing and designing are done with T-CAD tools. Ultimately I’ll produce a layout of the circuit which is to be manufactured. The layout then converted into masks which are used to fabricate this circuit in a fabrication facility.

# Testing, Verification and Validation

I do have trouble making distinction among these words but there are few things which are different in them and are easy to see. Here, I define these terms as defined by our Professor, Madhav P. Desai during the course on Verification and Testing of VLSI Circuits.

• By testing, we normally refer to the process used to determine that the manufactured circuit is functional. Every manufactured circuit needs to be tested, and the result of the test should, with a high degree of confidence, determine that the circuit is functional.
• By verification, we normally refer to the process used to confirm that refinements in the design process are consistent with the circuit specification. For example, when a logic circuit is implemented using transistors, we need to verify that the transistor network is equivalent to the logic circuit which it is supposed to implement. This is done at each refinement step in the design process.
• By validation, we normally refer to the process used to confirm that a functional manufactured circuit will fulfill the requirements to which it was designed. This usually involves construction of a prototype and a test setup which mimics reality to the maximum extent possible.

After the fabrication, circuit must behave the way it was designed for, else we have failed as engineers. However, since no process is fault free, it could happen that the end product behave in unexpected ways. I like to think of it as this chip has developed a sense of humor. Now all these above mentioned processes can be utilized to remove this sense of humor out of the chip to make it behave in boring and rigid ways again. At the end of the day, it should work as it is told. Humor is the prerogative of Humans, machines must be humorless.

# Faults in VLSI

Faults in VLSI can occur due to various reasons. Most prominent among them is due to flaws and variation fabrication processes (when engineer is competent). These causes of faults are discussed in [Mally, 1987]. Break in metal lines, over and under deposition of material, alien particles in fabrication process are the major sources of faults. As a designer, we need to test these faults as early as possible. Later the fault is located, costlier it gets by an order of magnitude (I do not have exact numbers here). Following figure 1 shows a messed-up device fabricated by me with the help of lab-staff during my M. Tech. Though it was useless for us then, it is useful for us for our present discussion. [caption id=”attachment_85” align=”alignleft” width=”570”] Figure 1 : Faults in fabrication[/caption] [caption id=”attachment_77” align=”alignright” width=”364”] Figure 2 : Alien particles during fabrication. Short of tacks.[/caption] Figure 2 shows the alien particles causing the short. Extra deposition and less deposition of materials cause most of the shorts and open circuits problem. Figure 3 shows the less deposition of material causing a track to be less conductive. Any logic propagated through this track will be weaker than the perfect track. Figure 4 shows that in spite of material deposition was sufficient, part of the track may still come off due to less adhesion between the deposited material and the substance. [caption id=”attachment_88” align=”alignleft” width=”289”] Figure 4 : SEM image shows that gold may not stick very well to the Si substrate. Same thing can happen with other pairs of material.[/caption] [caption id=”attachment_78” align=”alignleft” width=”50”] Figure 3 : Less materical deposition causing partial break in track.[/caption] These faults, among others, are classified as spot defects. Geometrically, these are randomly distributed over the entire fabrication area. For more details on these faults we refer to [Mally, 1987]. To summarize,

• Spot defects are regions of missing or extra material, (or drastically changed with physical material characteristics) that may occur in any layer of the fabricated IC.
• These are expressed as number of defects per unit area. However, some defects such as oxide pinholes and substrate dislocation can be expressed in density only.
• Cluster per unit area describes proneness of a region for defects. Distribution of defect size is also a prominent fault-matrix component.
• Short is generally caused by extra material deposition at a spot of missing insulating material between two conductive tracks.
• Break is generally caused by missing conductive material or extra insulating material in insulating windows.
• Shorts and breaks occur both in horizontal and vertical direction. Since these days there are multi layer fabrication process are done in modern chip fabrication. Vertical shorts and breaks are as important as the horizontal one.

# Fault Modeling

## Test Sequence Detectability

Let’s make a gauge to measure how fault-free my circuit is. If I do a test, can I answer this question. What are the chances that a successfully tested IC still contains undetected faults? Such is measure which one can name **test sequence detectability, $latex D$. It is defined as,

$D = \prod_{i=1}^{n_e}(1-{p_i})$

where, $p_i$ is the probability of the occurrence of faults and  $latex n_e$ are the faults that can not be detected by a given test sequence. Well, defining it this make sense to me. If I can list out all the possible faults that can occur in my circuit and their number is $latex n$. Let assume that $latex n_f$ is the number of faults which I am testing my circuit for and let  $latex n_e$ are the faults which I can NOT detect during my test. Then, $\frac{n_f-n_e}{n_f}$ represent traditional fault coverage and, of course, $latex n > n_f$. Hence an ultimate fault model must list out all the possible faults with their probability of occurrence. Practically, these faults model are based on the experience of an Institute or company. [Birolini, 1994] gives details about fault occurrence in VLSI circuits. Some figures are given below.

 Components Short % Open % Degradation % Functional % digital, bipolar ICs 30 30 10 30 digital MOS ICs 20 10 30 40 linear ICs 30 10 10 50 bipolar transistors 70 20 10 -- field-effect transistors 80 10 10 --

# Stuck at Models

A traditional model is stuck at model. In this model, one prescribe to the lines in the logic representation on the IC either state ‘1’ or state ‘0’ as permanent state. TODO : Give a brief overview. Meanwhile readers can refer to a book by Kohavi. Naturally, one uses probabilistic models while studying them.