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'.
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.