The flaws in Haitz’s law
A successor to Haitz’s law is needed, now that the focus has shifted
from the brightness of the LED and its retail price to its efficacy and its colour quality
BY MICHAEL WEINOLD FROM ETH ZÜRICH / UNIVERSITY OF CAMBRIDGE
THERE’S A LOT to like about the LED bulb. It draws very little power, it comes on in an instant, it lasts for tens of thousands of hours and thanks to falling prices, it is now very inexpensive. Thanks to all these merits, sales of this source of illumination continue to climb. In the European Union and the United States, the LED’s share of the general illumination market has recently topped 50 percent, and in 2020 estimated annual electrical energy savings from the adoption of LED-based lamps in these geographies amounted to 131 TWh/year and 442 TWh/year, respectively.
The biggest drivers behind the solid-state lighting revolution have been the dramatic reductions in the cost of this emitter and the hike in its efficiency. Within just 25 years of the introduction of the first commercial white LED, the electrical efficiency of this device has rocketed by three orders of magnitude, while manufacturing costs for LED chips have fallen by two orders of magnitude. Today, bulbs based on LEDs are delivering efficacies of 200 lm/W or more, and thanks to substantial retail price reductions, purchase prices can be as low as $1 per 1000 lumen.
In scientific and technical literature, progress in LED technology tends to be illustrated with a pair of plots: those of the total luminous flux per packaged LED, and the associated up-front purchase cost-per-lumen. Both are based on logarithmic axes over time. The first prominently featured version of such a plot appeared in a report, published in 2000, that was commissioned by the United States Department of Energy and written by Roland Haitz, working at Hewlett-Packard, and co-authored by colleagues at both HP and Sandia National Labs. The striking visual and contextual similarity of both these plots to that of Moore’s law ensured its popularity in subsequent publications, while giving rise to the designation of the historical progress in these metrics as ‘Haitz’s law’ (Figure 1).
Figure 1. The original figure prepared by Roland Haitz et al. in The case for a national research program on semiconductor lighting, published in 2000. The figure presented ‘Historical and projected evolution of the performance (lm/package) and cost ($(2000)/lm) for commercially available red LEDs’. Cost was defined as ‘the price charged by the LED supplier to OEM manufacturers’.
Outdated metrics
Since the turn of the millennium, Haitz’s law has been widely used as a measure of progress in LED technology and industry. However, despite its continuing popularity, the metrics used in Haitz’s Law are no longer providing meaningful representation of technological progress in this field. That’s because there are two significant flaws in Haitz’s law. One is that in recent years, the total brightness per package has become a less relevant metric for assessing industrial progress. The other significant flaw is that recent updates to Haitz’s law are failing to normalize the brightness-per-total-chip area.
Figure 2. Summary of recent representations of Haitz’s law in scientific literature. Historical increases in luminous flux and decreases in purchase price are plotted for LED packages. Note the units on the right on the vertical axis are kilolumens (klm) as opposed to lumens (lm) in the original 2000 figure by Haitz et al. Data points for red LEDs include devices based on various materials, with original data points from Haitz et al. (2000) marked by squares. Data points for white LEDs are for GaN based, phosphor-converted cool-white LEDs. Compiled from publications: Haitz et al. 2000; Haitz et al. 2010 (10.1002/pssa.201026349 ), De Almeida et al. 2014 (10.1016/j.rser.2014.02.029), Cho et al. 2007 (10.1002/lpor.201600147)
Regarding the latter issue, recent updates to Haitz’s law figures (see Figure 2 for a summary) do not take into account the different levels of device integration found in LED products on the market today. When Haitz and co-workers published their initial figure, retail products were primarily single-chip packages. That’s not the case today, with most commercial products now containing multiple chips in a single package. Plotting the total flux of multi-chip packages together with historical single-chip packages distorts the real trend of increasing flux in high performing LED chips (see Figure 3). Correcting this skew is not easy, because even when single-chip packages are explicitly labelled, the task of normalization-per-surface area is hampered by datasheets that only detail package dimensions – and they can be considerably larger than the area of the chip they enclose.
Figure 3. Historical increase in luminous flux and decrease in purchase price for GaN-based, phosphor-converted cool-white LED chips and packages since 2000. Shown are datapoints for the best commercial performers from press releases, datasheets and industry periodicals. Different package types, containing one or more chips, are marked for reference. Note the units on the right on the vertical axis are kilolumens (klm) as opposed to lumens (lm) in the original 2000 figure by Haitz et al. Note that the overall increase in flux per single chip over time is significantly smaller than in the flux for multi-chip packages.
As for the former issue, the use of diode brightness as a metric of progress implies that brightness has remained the primary focus of research, development and manufacturing efforts in the past decades. But while that’s true of the past, it holds no longer. While low brightness has historically been a major limitation on potential applications of LEDs, this was no longer the case at the time the first commercial LED light bulbs came to the mass market around 2010.
New yardsticks
For the last decade and more, in the eyes of both industry and policy makers, the primary metric for LED-based lighting has been efficacy. Unfortunately, there is a trade-off between higher brightness and higher efficacy (see Figure 4). This occurs because brightness is a function of diode current, and electrical losses in the device increase with diode current.
Figure 4. The trade-off between brightness and efficacy in commercial white LEDs. The plot includes LED lighting products available in 2017 and 2020, ranging from low-power to high-power devices. The dashed line shows a log-linear fit of the empirical data for 2017. Data adapted and updated from the 2019 Lighting R&D Opportunities report published by the US Department of Energy.
In the last few years, western lighting manufacturers have given far more consideration to human-centric lighting to increase sales. This shift in emphasis had led to improvements in LED technology that are not focussed primarily on total brightness, but rather on other properties of this light source that matter more to consumers, such as colour-rendering performance, colour temperature ranges and minimal flicker.
Lighting design considerations limit the brightness of devices. Designers of luminaires do not want to work with small light sources of high brightness, because they have a level of glare that leads to unpleasant viewing experiences.
In addition to the two problems detailed above, associated with brightness and the number of chips per package, there are potential pitfalls associated with interpreting the cost metric of Haitz’s law. Plots tend to use up-front retail prices of LED-based luminaires, rather than actual LED manufacturing costs. While the former is certainly a metric that matters to consumers, it is not a good proxy for diode manufacturing costs. Taking a more rigorous approach is not easy, however, as it requires information on company margins, so that manufacturing costs can be deduced from price data, which is proprietary by nature.
Another weakness of the cost metric of Haitz’s law is that it obscures the real progress in LED chip manufacturing costs, as by necessity it also includes the cost of LED packaging and the luminaire. For instance, chip manufacturing costs are reduced significantly by going to larger wafer sizes, while the cost of packaging steps, particularly at the luminaire level, remains relatively stable and thus becomes the single biggest contributor to the total cost.
Understanding the shortcomings of Haitz’s law provides a foundation to proposing more meaningful metrics for tracking recent technological progress in solid-state lighting.
First, one valuable contribution would be to introduce a new yardstick for measuring improvements in performance. Today, the flux per package and the flux per chip are poor primary metrics for describing recent improvements in LED technology. Efforts in research and development have mostly focused on increasing luminous efficacy, and on improving metrics related to human-centric lighting. Considering this, it would be better to monitor performance improvements in LEDs using diode efficacy for a given colour rendering index and colour temperature.
The adoption of this methodology would not be difficult, because historical data for LED efficacy is available from product datasheets, and also from the solid-state lighting reports of the US Department of Energy (see Further Reading). There are also scientific publications and technical reports that provide data on the underlying device sub-efficiencies, describing different physical loss channels within devices. An excellent example of this is a paper from Sandia National Labs, by Jeffrey Tsao and co-workers and published in 2010. Using this metric, our team from ETH Zurich and the University of Cambridge has quantified the impact, over the last 25 years, of technological breakthroughs and performance improvements on LED manufacturing. We first presented our findings at this year’s Photonics West conference.
Second, as already pointed out, the retail price of LED luminaires per flux is of limited use as a proxy metric for LED manufacturing cost, because it includes unknown manufacturer margins, as well as the costs of LED packaging and producing the luminaires. We recommend focusing directly on LED manufacturing costs for evaluating LED technology cost reductions over time.
This might appear a challenging approach, given that LED manufacturing cost is often proprietary. However, major western manufacturers voluntarily report selected data to the US Department of Energy (DoE) as part of the SSL Industry Roundtables. This data, provided in regular reports on progress in lighting (see Further Reading), provides a deeper level of insight into decreasing manufacturing cost than the retail price of lamps (see Figure 5).
Figure 5. A proposed alternative to Haitz’s law: the historical trend of luminous efficacy in GaN-based phosphor-converted cool-white LED packages and lamps with a colour rendering index (CRI) below 90. The dashed line gives a linear fit of data for best performers, indicating an annual efficacy increase of 13 percent. Lamps have lower efficacy due to additional loss channels from the electrical ballast and additional optical elements. Data for lamps taken from the Energy Star LED Bulb database (https://www.energystar.gov/products/light_bulbs), data for best performers from scientific publications, datasheets and industry periodicals.
Note that even when specific data is not available this approach can still be adopted, as one can turn to a bottom-up manufacturing cost model. This methodology can draw on a comprehensive template provided by the LEDCOM cost model, first developed for the DoE in 2012 (see Further Reading). Making reasonable assumptions about the progress of technology allows this type of model to predict how manufacturing costs will evolve.
Two decades after the introduction of Haitz’s law, now is the time to accommodate changes in LED technology and industry. There are fundamental flaws in displaying data on contemporary multi-chip LED designs alongside historical single-chip designs – this distorts the real picture of technological progress in this field. Another pitfall is to use retail prices. While they provide valuable information to consumers, they fail to offer sufficient insight into industrial developments.
We are encouraging research, policy and industry communities to move on from Haitz’s law, which is a historically valuable but no longer relevant indicator of progress in the LED industry and technology. We propose instead to replace it with metrics that are better at representing LED technology improvements in areas that matter the most right now, rather than those that did 20 years ago.
The author would like to thank Prof Laura Diaz Anadon and Dr Sergey Kolesnikov for valuable discussions and input. This research is funded by the Alfred P. Sloan Foundation, grant number 253128. Michael Weinold further gratefully acknowledges support from the Swiss Study Foundation of Zurich, Switzerland.
FURTHER READING
† Research Project of the authors:
https://www.ceenrg.landecon.cam.ac.uk/research/climate-change-and-energy-policy/what-factors-drive-innovation-in-energy-technologies-the-role-of-technology-spillovers- and-government-investment
† Weinold et al. “Quantifying the impact of performance
improvements and cost reductions from 20 years of
light-emitting diode manufacturing”, SPIE OPTO, 2021
https://doi.org/10.1117/12.2577591
† Haitz et al. “The case for a national research program on
semiconductor lighting”, Sandia Report, 2000
https://old-www.sandia.gov/~jytsao/hpsnl_sand_
report_2000.pdf
† Tsao et al. “Solid-State Lighting: An Integrated Human
Factors, Technology, and Economic Perspective”,
Proceedings of the IEEE (Volume: 98, Issue: 7, July 2010)
https://doi.org/10.1109/JPROC.2009.2031669
† United States Department of Energy Solid-State Lighting
Research Publications:
https://www.energy.gov/eere/ssl/information-resources
