Efficacy Limits for Solid-State White Light Sources

A new study compares color rendering properties of light sources with maximum theoretical efficacy, chromaticity and correlated color temperature.


Several recently published road maps for solid-state light have called for systems with efficacies of 200 to 240 lm/W. Luminous efficiency, or efficacy, is a common performance metric for light sources. It is the ratio of the perceived brightness to the input power and, because the brightness of a light source is measured in lumens and electrical power is measured in watts, the units of efficacy are lumens per watt. Several assumptions were made to arrive at the 200 to 240 target, with only passing comments on color rendering properties.

Of the current lighting technologies, low-pressure sodium lamps have the highest efficacy and operate at up to 200 lm/W. But because their output is essentially monochromatic light at 589 nm, low-pressure sodium lamp sources have extremely poor color rendering properties. In fact, the color rendering index (CRI) for low-pressure sodium is negative (–47). The theoretical efficacy for a monochromatic light at 589 nm is 525 lm/W, so this translates to a wall plug efficiency of 38.1 percent. Although other light sources, most notably infrared laser diodes, have even higher efficiencies (electrical power to optical power), low-pressure sodium remains the benchmark technology in terms of efficacy.

There have been studies that examined the maximum color rendering performance of polychromatic LED light sources, but these have used simplified (Gaussian) emission spectra for LEDs and did not include reports on the chromaticity coordinates associated with different correlated color temperature values.

To more accurately study these color issues, I developed a Monte Carlo simulation package that allows sampling the parameter space of a wide variety of potential solid-state lighting systems. The simulation includes detailed LED emission spectrum models for InGaN and AlInGaP LEDs, which is important because other studies on color rendering have used Gaussian or modified Gaussian spectral distributions to represent LEDs.

The more detailed models take into account that many LEDs have low-intensity emission tails that can affect color rendering calculations, and they are based on measured spectral power distributions for commercial LEDs with peak wavelengths between 390 and 550 nm for InGaN-based devices and from 580 to 670 nm for AlInGaP-based LEDs. Measurements were made using a calibrated spectroradiometer with resolution of <1 nm. The models were verified to represent LED emission spectra accurately to within 0.1 percent over three orders of magnitude.

This study focused on the simplest solid-state lighting systems (laser diodes and LEDs) for two, three or four color primaries. A future study is planned that will include phosphor converted systems.

An early report by David L. MacAdam gave the maximum possible efficacy of a light source matching the chromaticity coordinates of Illuminant C (0.3101, 0.3162) as 400 lm/W. Henry F. Ivey repeated MacAdam’s results and included an estimate of maximum efficacy versus color temperature. Ivey reported a maximum efficacy of 500 lm/W at a color temperature of 2800 K.

This data represents metameric white light (two monochromatic sources); therefore, it represents the absolute maximum efficacies attainable. At the time of these studies, few if any practical light sources could produce monochromatic light at the wavelengths required, but today many laser sources can produce light at almost any wavelength. Thus, a system easily could be designed to match these spectra. For laser-based solid-state light sources, it is assumed that semiconductor laser diodes will be used, but how efficient will these light sources be?

As a result of the DARPA Super High Efficiency Diode Source program, both AlfaLight of Madison, Wis., and JDS Uniphase of Milpitas, Calif., have reported laser diode wall plug efficiencies in excess of 70 percent. But these devices operate outside the visual spectrum. The ultimate goal of this program is to produce devices with wall plug efficiencies of 80 percent.

45% efficiency

For visible laser diodes, the maximum efficiency has been reported at 45 percent (610 nm). It should be noted that the efficiencies at the required wavelengths in the blue and amber portions of the spectrum are much lower. If it is assumed that solid-state-lighting research will improve efficiencies, then reaching an efficacy of 200 lm/W (6500 K) would require laser efficiencies of only 50 percent.

If laser diode efficiencies are improved even further into the range targeted by the Super High Efficiency Diode Source program — say, 80 percent — then the maximum attainable efficacy rises to 320 lm/W. This would represent a remarkable improvement over what is attainable with low-pressure sodium technology.

What are the color rendering properties of a bichromatic light source? Monte Carlo results (n = 250,000) show very interesting behavior for this type of light source. The maximum color rendering index of 38 is achievable at unrealistically low correlated color temperatures (CCTs) of 1000 K. Because this would appear as a highly saturated red, results are further restricted to CCT = 2800 to 7000 K. Using these boundaries, the maximum attainable color rendering index falls to 34 at CCT = 2940 K, with a theoretical efficacy of 452 lm/W.

The exceedingly low color rendering index of a bichromatic light source by itself would render it unsuitable for anything other than industrial lighting applications. Adding wavelengths generally improves the color rendering index, so addition of a third laser source should yield better rendering performance. But does it improve performance to a level that would be acceptable for business or residential use? Indeed it does.

A third wavelength results in a remarkable improvement in color rendering index, as it now allows for CRI >80 over the entire target range of correlated color temperature values. Maximum CRI = 84 was found at 2820 K with a theoretical efficacy of 331 lm/W. Large gains in efficacy can be obtained from slight sacrifices in the color rendering index. The highest efficacy (restricted to CRI ≥80) was calculated at 392 lm/W, CCT = 2806 K.

For these trichromatic systems, efficacy and color rendering index are very sensitive functions of wavelength and intensity. Adding a fourth wavelength reduces the sensitivity, although this would obviously add complexity to the resulting lighting system as well as redundancy in terms of color rendering properties. The color rendering index now can be increased above 90, which allows use in specialty lighting applications. Interestingly, the maximum efficacy increases because wavelengths can more closely approach the V(λ) maximum of 555 nm. The maximum CRI is 91 for a CCT of 4468 K with a theoretical efficacy of 358 lm/W. The highest efficacy was found to be 450 lm/W at a CCT of 3415 K with a CRI of 81 (Table 1).


Table 1. The maximum color rendering index results (n = 250,000) are summarized for various laser diode light sources.

Because of the high current densities in their active regions, and other operational issues, laser diodes typically have lifetimes one to two orders of magnitude below those of comparable-wavelength LEDs. A large portion of the expected economic benefit of solid-state lighting sources is related to long lifetime (hence, low maintenance); therefore, it does not seem realistic for laser diode systems to meet the goals and demands for solid-state lighting.

Other issues associated with the epitaxial structures, yields, fabrication costs and cooling requirements also point to LED-based light sources as the most plausible route to achieving the established targets for solid-state lighting. The broader spectral power distribution of LEDs also would be expected to dramatically improve the color rendering index (Table 2).


Table 2. The maximum efficacy results (n = 250,000) are shown for various laser diode light sources.

LED efficiency assumptions

For laser diodes, the assumptions used for efficiency are straightforward, but for LEDs, the situation is much more complex.

One reason is the power source. Because commercial power is distributed as an AC, high-voltage source, and LEDs require low-voltage DC power, power conversion is required. Using a transformer to reduce the voltage followed by rectification inevitably leads to some loss of power. Although common systems have efficiencies of 60 to 70 percent, high-efficiency systems are rated at about 90 percent. There is obviously a price penalty associated with performance, but it is assumed that the high volume required for solid-state lighting inevitably will drive down the price to competitive levels.

Looking next at LED operation, there are inherent electrical losses associated with contact resistance, the bulk resistivity of the semiconductor layers themselves and band bending effects that must be overcome to transport electrons and holes into the active region where they recombine to produce photons. The most obvious impact of the sum of these effects is that the forward voltage of LEDs exceeds the photon energy. For example, a typical blue LED with a nominal emission wavelength of 460 nm will have a forward voltage between 3.1 and 3.6 V. Comparing this with the 2.7-eV energy of photons with a wavelength of 460 nm reveals internal electrical efficiencies of 75 to 87 percent. The more mature technologies associated with AlInGaP LEDs allow higher internal electrical efficiencies in excess of 90 percent. For simplicity, a single factor of 90 percent was assumed.

There is also the internal quantum efficiency of LEDs, which is a measure of the fraction of photons produced for each electron injected into the device. Internal quantum efficiencies of nearly 100 percent have already been reported for longer-wavelength (AlInGaP) LEDs. Efficiencies for InGaN LEDs are much lower and are believed to be caused by high defect densities that result from a lack of suitable lattice-matched substrates. For this study, a quantum efficiency of 90 percent was assumed regardless of wavelength.

The final issue with LED efficiency is an optical problem directly resulting from the high refractive index of the compound semiconductor materials used to make LEDs. This leads to large reflective losses at the interface between the LED die and the encapsulating medium. Reflective losses can be calculated from R = [(n1 – n2)/(n1 + n2)]2. For most compound semiconductor materials n = 2.4 to 4.0, so it is easy to see why light extraction is difficult. Various schemes either have been or are in the process of being developed to reduce these reflective losses. Again, for simplicity, I am assuming that the combination of existing and future technologies will allow extraction efficiencies of 90 percent.

The LED outlook

The overall efficiency of any LED is the product of all of these factors, or 90 percent × 90 percent × 90 percent × 90 percent = 65.61 percent. Although many assumptions have gone into the calculation of this efficiency factor and many solid-state-lighting road maps call for even higher efficiencies, it should be noted that the highest recorded wall plug efficiency for any LED is 45 percent, so increasing efficiency to 65.6 percent at all wavelengths would be an achievement. This efficiency is used as the criterion for the practical efficacy of LED systems.

A slightly less optimistic but possibly more realistic approach would be to assume that the overall efficiency is a function of emission wavelength. Currently significant differences in efficiency are noted with respect to wavelength for both AlInGaP and InGaN LEDs. In general, efficiency decreases for InGaN LEDs as emission wavelength increases. The opposite behavior is noted for AlInGaP LEDs. Unfortunately the lowest efficiencies occur near the photopic maximum at 555 nm. Thus, perhaps the most realistic assumption would be based on maximum efficiencies of 65 percent for both short (λp≤460 nm) and long (λp≥630 nm) wavelengths, with efficiencies dropping by a factor of two at middle wavelengths (Figure 1).


Figure 1. LED wall plug efficiency is shown as a function of peak wavelength. The nominal assumption is that InGaN materials will be used for peak wavelengths <580 nm, and AlInGaP materials will be used for peak wavelengths >580 nm.

Following the path outline for true monochromatic emitters above, I investigated using two different wavelength LEDs. I modified the output of the simulation software to include full rendering values for all indexes outlined in CIE 13.3.

Because this represents a significantly larger volume of data, simulations were limited to n = 125,000. This detailed data in turn will enable much more stringent future evaluations of the simulated light sources because it can allow constraints to be placed on certain rendering values, especially those associated with skin tones (R13, R15).

For binary LED systems, color rendering performance is not significantly better than that of the binary laser systems studied above. The maximum color rendering index of 44 occurred at a CCT of 6313 K, with a theoretical efficacy of 326 lm/W. The maximum efficacy occurred at a CCT of 3576 K at an efficacy of 403 lm/W, with a CRI of 31.

The results showed that the color rendering index had a weak function of correlated color temperature and varied inversely with correlated color temperature. Efficacy was found to have a stronger correlation with correlated color temperature with the theoretical maximum decreasing from about 400 to about 350 over the range of 2800 to 6500 K. Because the highest color rendering values were significantly below those required for residential lighting, no further analysis is required for this system.

Ternary LED systems present a much more interesting scenario. Although it is common knowledge that RGB LED systems can produce a wide gamut of chromaticities, it is not always understood that significant penalties are paid in terms of color rendering if a true red/green/blue system is used. Because of the way that color rendering is calculated, using an orange-amber LED in place of red produces a higher color rendering index; however, this results in a deficiency of red wavelengths that affects the perceived color of red objects and, more importantly, skin tones. For ternary LED systems, color rendering performance can, in fact, be quite good when judged on the basis of the general color rendering index by itself.


Figure 2. Here, maximum CRI is shown as a function of chromaticity coordinates (CIE 1931 2° Standard Observer) for a ternary LED SSL system. Note that the coordinates for highest CRI values lie above the Planckian locus and would appear as greenish- or yellowish-white.

The results from this system help to illustrate the arcane nature of color rendering, which allows for light sources having chromaticities well off the Planckian locus to achieve high CRI values. (It is also possible, though not for this system, for light sources with chromaticity coordinates that fall directly on the Planckian locus to achieve negative CRI values) (Figure 2). Thus, the best achievable results as measured by CRI may actually be poor choices for light sources because of their chromaticity values alone. In a similar fashion, for laser diodes, the assumptions used for efficiency are straightforward, but for LEDs, the situation is much more complex.

As has been reported elsewhere, the color rendering index values for this system can exceed 90 over a wide range of correlated color temperature values (2800 to 7000 K) (Table 3). Unfortunately, the chromaticity values corresponding to maximum color rendering index lie above the Planckian locus and actually appear as greenish-white colors. Note that the region of highest efficacy does not correspond to the region of highest color rendering index.


Table 3. The maximum CRI results (n = 125,000) are shown for various LED SSL systems.

Again, adding a fourth color should improve color rendering, enabling an index of 96 at 4363 K, with a theoretical efficacy of 329 lm/W (Tables 4 and 5, Figure 3).


Table 4. The maximum efficacy (CRI ≥80) results (n = 125,000) are shown for various LED SSL systems.


Table 5. The maximum practical efficacy results (n = 125,000) are shown for various LED SSL systems. Results for three- and four-LED systems are constrained to CRI ≥80.


Figure 3. On the left, the maximum theoretical efficacy for a four-laser SSL lighting system as a function of CRI and CCT is shown. There is a general trend for higher efficacy at lower CCT values. For CCT ≥4500 K, efficacy decreases with increasing CRI. On the right, the calculated theoretical efficacy limits are shown for a quaternary LED SSL system as a function of CRI and CCT. The LED efficiencies shown in Figure 1 were used.

Using the wavelength-dependent efficiencies outlined above, the maximum projected efficacies will obviously be lower and are detailed below. This data was not presented in the tables above because the ideal wavelengths are significantly different.

Many questions still remain about how best to improve the efficiency of LED devices, but it may be unrealistic to assume that the efficiency will be high and constant across all wavelengths, especially when two very different material systems (InGaN and AlInGaP) are used for state-of-the-art high-brightness LEDs. Given this fact alone, it is doubtful that all LED systems would simultaneously achieve high color rendering and efficacies >200 lm/W. The most realistic limits would appear to be in the range of 150 to 200.

Meet the author

Eric Bretschneider is assistant sales manager of Toyoda Gosei Co. of Irvine, Calif.; e-mail:eric.bretschneider@toyodagosei.com.




Achieving maximum efficiency in LED luminary and LCD backlight designs

Donald Schelle, Texas Instruments

AUGUST 04, 2014

Figure 1: The 1988 photopic curve defines the visible spectrum as containing wavelengths between 380 – 780 nm. Alternate limits between 400 – 700 nm contain 99.93% of the total visible optical energy.

Calculating maximum efficacy from a spectral density curve
Chromaticity coordinates [1] and maximum efficacy can be calculated after normalizing the total energy beneath the spectral density curve. Once normalized, multiplying the Y coordinate by 683 lm/W yields the maximum efficacy of the light source.

The spectral density curve in Figure 2 can be digitized using a number of free software tools [2]. Once digitized, the resulting data is then normalized (green curve) such that the sum of the power underneath the curve totals 1. Chromaticity coordinates are calculated using the normalized data.

Figure 2: Digitized data is indexed, smoothed, and normalized before calculating chromaticity coordinates and maximum efficacy.

Calculated chromaticity coordinates for this particular LED (Nichia NNSW208CT) are x = 0.2989 and y = 0.2952, which correlate closely with the published coordinates in the datasheet for the binned selection sbj26. The calculated maximum efficacy is 296.36 lm/W and is dependent on the shape of the spectral distribution.

The calculated typical efficacy of the LED at a specified operating point of 20 mA is 150.00 lm/W, which is obtained by using a few common datasheet parameters (VF, IF, and ΦF). Dividing the typical efficacy into the theoretical maximum efficacy yields an efficiency of 50.61%.

Just over half of the electrical power injected into the LED is converted into light energy within the visible spectrum. By mixing two monochromatic sources (dichromatic) it is possible to create a light source yielding the same chromaticity coordinates, but yielding a much higher efficacy. The maximum dichromatic efficacy at these chromaticity coordinates is 382.71 lm/W.

Calculating maximum efficacy of dichromatic light
In 1949 David MacAdam postulated that the maximum efficiency of any colored light could be created in only one way: by mixing two monochromatic sources at suitable intensities.[3] MacAdam’s original data (Figure 3) was digitized from a copy of his original submission. While his theory and calculated curves are widely known, little is known on the method MacAdam used to obtain the data.

Figure 3: Maximum possible luminous efficiency (lumens per watt) shown on CIE 1931 chromaticity diagram (MacAdam)

Replicating MacAdam’s results is relatively easy using modern computer processing power and a simple brute force calculation method. CIE chromaticity coordinates can be calculated by using two monochromatic light sources at varying wavelengths and intensities. Ensuring that the intensities of the monochromatic sources sum to a value of one, an apples-to-apples comparison across the entire color loci can be ascertained. A sweep of all monochromatic wavelengths between 360 – 830 nm blankets the color loci with calculated xyY values. For each pair of monochromatic sources, the intensity of the first monochromatic source is swept from 0 to 1 in increments of 0.0001.

The intensity of the second monochromatic source is fixed at 1 minus the intensity of the first source. As an iterative process, xyY values are calculated, compared against previously calculated values (if any), and stored in a large matrix memory array. Calculated xy values are rounded to the nearest 0.0001 increment. The corresponding Y value is compared against the existing value. If the newly calculated Y value is larger, the xyY contents of that matrix cell are replaced.

Calculations generate xyY coordinates along a line between the two monochromatic sources used to generate the target color. Using monochromatic sources spaced at 5 nm increments (Figure 4) leaves a substantial number of uncalculated holes in the color loci.

Decreasing the spacing between monochromatics to 1 nm improves the calculated results substantially. The 5 nm CIE color-matching tables are available directly from CIE. However, 1 nm tables are more difficult to find. They are available in print [4], and are also available for download [5] in Excel format from various third-party websites.

The 1-nm monochromatic wavelength spacing produces results good enough to prove the concept, but to achieve results that rival MacAdam’s 1949 paper, smaller intervals are required. Interpolation is the key. CIE recommends linear interpolation. Results displayed in Figures 5 – 7 use monochromatics spaced at 0.01 nm increments.

Figure 4: Accurate results depend on adequate coverage by dichromatic calculation lines. Using 5 nm increments, as illustrated here, does not provide the required coverage. Note that 0.01 nm increments are required to produce comprehensive results.

Figure 5: Maximum possible luminous efficiency (lumens per watt) shown on CIE 1931 chromaticity diagram (Schelle).


Filed in: LED & Light Sources, Technology

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