Beyond Moore’s law (by Dr Ed Jordan)

After almost 60 years, Moore’s law, related to the doubling of computing power every year-and-a-half-ish, still holds. At the current exponential speed, there is a brick wall looming in the foreground: the physical limitations of silicon chips. The most straightforward example of how that might impact a company is to look at Intel Corp. But first more on Moore’s law and the more general idea of learning curves.

At some point, the semiconductor material currently in use will no longer support the improvements necessary to meet the requirements of an expanding Information Technology infrastructure. In times past, the way Moore’s law characterized how the growth in the density of computer chips was at the heart of the IT revolution, we have experienced. Interesting, Moore himself viewed this so-called law as an observation, not some grand organizing principle that helps us understand a set of observations that have stood the test of time with many replications. The reason we speak of Newton’s Third Law of Motion, for instance, as a Law is because of the profound success in explaining what we now call Classical Mechanics (Newton’s Laws of Motion, 2020). On the other hand, Moore simply graphed the growth of the number of components on computer chips vs. time using semi-log paper. While the resulting straight line is striking, it does not explain some underlying physical phenomenon (Jordan, 2010). For this reason, the purists among us will always refer to this observation using the lowercase form of law. Below is a picture of the original presentation that Gordon Moore made in 1965 of the characterization (Rhines, 2019).

Figure 1: Moore’s law, as presented in 1964. From Predicting semiconductor business trends after Moore’s law. Used with permission

The impact that Moore’s observation on the semiconductor industry proved to be more of an organizational imperative than an organizing principle that explains a body of observations. As Rhines (2019) points out, over time, Moore has added serval caveats to the original observation.

Figure 2: Moore’s caveats vs time. From: Predicting semiconductor business trends after Moore’s law. Used with permission

Recently, I had the great privilege of attending a webinar hosted by SemiWiki (Rhines, 2020). In this Webinar, Walden Rhines presented where he thought the semiconductor industry was going, what could be called the Learning Curve Roadmap to device improvement, and when some new material may be required to replace the current technologies. Dr. Rhines suggested that if one considers the mathematics of the learning curve, plotting revenue per transistor vs. cumulative transistors shipped using a log-log graph, you have a better picture (Figure 3) of where the industry has gone than the original Moore’s law.

Figure 3: Log-Log View: From: Predicting semiconductor business trends after Moore’s law. Used with permission

The idea of learning curves takes several forms (Learning Curve, 2020). From the shape of the plot presented by Rhimes (2019), it appears what was meant was a power-law relationship between learning and experience. With the correct selection of coefficients, one can imagine a cure, such as we see in Figure 4 (Learning Curve, 2020).

Figure 4: Learning vs Experience – Power Law: From https://en.wikipedia.org/wiki/Learning_curve

As part of the discussion during the webinar, Rhimes goes on to show (Figure 5) that if you plot (log-log) cost per function vs. time (Rhines, 2019, p. 20), you see the same kind of straight-line suggestive of a power-law relationship between learning and experience (Learning Curve, 2020).

Figure 5: Normalized Chip Cost. From: Predicting semiconductor business trends after Moore’s law. Used with permission

Rhimes further suggest that it is instructive to think of semiconductor trends in terms of the so-called Gompertz Curve (Figure 6). This curve has a characteristic “S” shape and is often used to predict saturation, among other things (Rhines, 2019, p. 22).

Figure 6:Gompertz Curve. From: Predicting semiconductor business trends after Moore’s law. Used with permission

The Gompertz Curve is a specialized application of the sigmoid function, again from the mathematics of learning (Learning Curve, 2020). As described by Rhimes, the so-called point of inflection of the Gompertz Curve is particularly interesting (Figure 7).

Figure 7: Lifecycle S Curve. From: Predicting semiconductor business trends after Moore’s law. Used with permission

In the context of this discussion, this particular application suggests the point that growth of the cumulative unit volume of transistors will begin to slow. This point is around 2038. As the title of Figure 8 suggests, that is the point at which a new technology will be necessary.

Figure 8: Projected Transition Point. From: Predicting semiconductor business trends after Moore’s law. Used with permission

In 2010, Jordan found that a new technology should emerge in the timeframe of 10 to 30 years (which should be before 2040). What constituted emergence was also defined in the study. Emergence was defined to mean that point when a prototype would be available for full-scale testing (Jordan, 2010). This definition seems to fit comfortably in the construct, as presented during the webinar (Rhines, 2019). The work by Rhimes (2019) and Jordan (2010), separated by almost a decade, suggest approximately the same answer. By about 2040, a new technology should emerge that will ultimately replace the semiconductor materials that are in current use today. What is important is that these two lines of reasoning, using profoundly different approaches and divergent frames of reference, arrive at essentially the same conclusion. This convergence suggests the confirmability of both.

So what does this have to do with scenario planning in general, and what does that mean for chip companies like Intel? And, what will the likely disruptive technology be that replaces the silicone chip? Jordan (2010) identified likely disruptive technologies.

We at ScenarioPlans.com previously talked about Intel in these two blog posts: how the future of computing is taking on a life of its own, as well as, outa time — the tic toc of Intel and modern computing. It will be interesting to see if Intel remains standing in 2040 or 2050.

References

Jordan, E. A. (2010). The semiconductor industry and emerging technologies: A study using a modified Delphi method (3442759) [Doctoral dissertation, University of Phoenix]. UMI.

Learning curve. (2020, April 7). WIKIPEDIA: The Free Encyclopedia. Retrieved April 21, 2020, from https://en.wikipedia.org/wiki/Learning_curve

Newton’s laws of motion. (2020, March 8). WIKIPEDIA: The Free Encyclopedia. Retrieved April 19, 2020, from https://en.wikipedia.org/wiki/Newton’s_laws_of_motion

Rhines, W. (2019). Predicting semiconductor business trends after Moore’s law. A SemiWiki.com Project. https://semiwiki.com/

Rhines, W. (2020, April 1). Predicting semiconductor business trends after Moore’s law [Webinar]. SemiWiki. https://app.gotowebinar.com/unified/index.html#/webinar/4339831074971239694/attend/3541623017104899086

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## 1 Comment

1. #### DelphiMan

There have been several posts here related to Moore’s law. http://delphiplan.com/?s=moore
The Tic-Toc of Intel has been broken for about 5 years. That is new hardware one year, new software for that hardware the next. After decades that Tic-Toc clock has been broken. http://delphiplan.com/2016/08/04/outa-time-the-tic-toc-of-intel-and-modern-computing/
But more recently the discussion has been on other ways to squeeze out improvements in computing when the brick-wall of hardware improvements has been hit. Discussion here and an underlying article pertaining to it. https://twitter.com/SBPlan/status/1269667328788254721