Light is perceived as white light if the three types of cones located on the retina of the human eye are excited in a certain ratio, namely with similar intensity. For the case of white light, the tristimulus values are such that the location of the chromaticity point is near the center of the chromaticity diagram.

The generation of white light can be accomplished with a huge number of possible spectra. The creation of white light out of monochromatic visible-spectrum emitters can be based on dichromatic, trichromatic, or tetrachromatic approaches, as shown in Fig. 20.1, or on approaches of higher chromaticity. The optical sources can be classified in terms of their luminous efficacy

of radiation, luminous source efficiency, and color-rendering properties.

Whereas high luminous efficacy and high luminous efficiency are always desirable properties of high-power light sources, color rendering depends strongly on the application. Generally, high-quality daylight illumination applications, e. g. illumination in museums, homes, offices, and stores, require a high color-rendering capability.

(a) Di­chromatic white source (b) Tri­chromatic white source

(c) Tetra - chromatic white source

However, there are numerous applications where the color rendering capability is of lower priority, for example in the illumination of streets, parking garages, and stairwells. Finally, in signage applications, color rendering is irrelevant. Such signage applications include white pedestrian traffic lights, displays, and indicator lights.

There is a fundamental trade-off between the luminous efficacy of radiation and color rendering capability of a light source. Generally, dichromatic white light has the highest luminous efficacy and the poorest color-rendering capabilities. A trichromatic white source can have very acceptable color-rendering properties (CRI > 80) and luminous efficacies greater than 300 lm/W. Tetrachromatic sources can have color-rendering indices greater than 90.

20.1 Generation of white light by dichromatic sources White light can be generated in several different ways. One way of generating white light is the use of two narrow emission bands, called complementary wavelengths or complementary colors. Two complementary colors, at a certain power ratio, result in tristimulus values that are perceived as white light. The wavelengths of complementary colors are shown in Fig. 20.2.

Fig. 20.2. Monochromatic complementary wavelengths resulting in the perception of white light at a certain power ratio (after Wyszecki and Stiles, 1982).

	1 1 1		■
	Complementary wavelengths CIE Standard Illuminant D55 CIE 1931 Standard Observer			■	■
			■ ■	■
						■ ■ ■ /	■
						■ ■ /	■
				_ ^			■
	-	.	■	.	■	,

£ 660 с

640

ы 620

600 ГЗ I 580 с. S о U

560

380 400 420 440 460 Short wavelenth Л| (nm)

480

500

The numerical values for monochromatic complementary wavelengths are given in Table 20.1. The table also gives the power ratio required to attain the same chromaticity coordinate as Illuminant D65.

Table 20.1. Wavelengths h and X2 of monochromatic complementary colors with respect to CIE Illuminant D65 and the CIE 1964 Standard Observer. Also given is the required power ratio. Illuminant D65 has chromaticity coordinates xD65 = 0.3138 and yD65 = 0.3310 (after Wyszecki and Stiles, 1982).

Complementary wavelengths	Power ratio
h (nm)	X2 (nm)	P(X2) / p(xd
380	560.9	0.000642
390	560.9	0.00955
400	561.1	0.0785
410	561.3	0.356
420	561.7	0.891
430	562.2	1.42
440	562.9	1.79
450	564.0	1.79

Complementary wavelengths	Power ratio
h (nm)	h (nm)	P(X2) / p(xd
460	565.9	1.53
470	570.4	1.09
475	575.5	0.812
480	584.6	0.562
482	591.1	0.482
484	602.1	0.440
485	611.3	0.457
486	629.6	0.668

Next we analyze the luminous efficacy of radiation of a source with two complementary emission lines. It is assumed that the two lines are thermally broadened to a full-width at half­maximum of AE. Emission lines of AE = 2 kT to 10 kT have been found experimentally for the GaInN system at room temperature (kT = 25.9 meV at 300 K). A gaussian distribution is assumed for the two emission lines, so that the spectral power density is given by

2

1 (x-xL

1

1

P(X) = Pl

(20.1)

+ P2

e

e

1 <3i4bK

1 f X-X2 j 2 I CT2 J

where PL and P2 are the optical powers of the two emission lines, and XL and X2 are the peak wavelengths of the source. The gaussian standard deviation a is related to the full-width at half­maximum of an emission spectrum, AX, by

/[2V2

(20.2)

a = AX

ln 2

= AX/2.355 .

The peak emission wavelengths XL and X2 are chosen from Table 20.1. The table also gives the required power ratio of the two light sources. Although the table applies to strictly monochromatic sources (AX ^ 0), the data can be used, as an excellent approximation, for sources exhibiting moderate spectral broadening such as LEDs.

The luminous efficacy of radiation of a dichromatic source is shown in Fig. 20.3. The figure reveals that the highest luminous efficacy of 440 lm/W occurs at a primary wavelength of XL = 445 nm for AE = 2 kT. The very high value of the efficacy shows the great potential of dichromatic sources.

Several approaches for the generation of white light by mixing two complementary colors have been demonstrated (Guo et al., 1999; Sheu et al., 2002; Dalmasso et al., 2002; Li et al.,

2003). One possibility uses the mixing of light emitted by two LEDs, one emitting in the blue and the other one in the yellow spectral region. Another possibility, demonstrated by Guo et al. (1999), generates white light by using a GaN-based blue LED and a second semiconductor, AlGaInP, as a wavelength converter. Sheu et al. (2002) demonstrated a codoped single active region quantum well white LED. The active region is doped with both Si and Zn. Blue light emission originates from quantum well band-to-band transitions, whereas a wide yellowish emission originates from donor-acceptor-pair (D-A) transitions. Because the D-A transition is spectrally wide, the codoped approach has the advantage of good color rendering. A dichromatic monolithic LED has also been reported by Dalmasso et al. (2002), who employed two closely spaced GaInN active regions within the pn-junction region. A strong dependence of the emission spectrum on the injection current was found.

Li et al. (2003) reported a monolithic GaInN based LED with two active regions separated by a thin GaN layer. The device was designed for emission at 465 nm and 525 nm. The device structure is shown in Fig. 20.4.

layer

Fig. 20.4. Structure of a mono­lithic dichromatic LED with two active regions (after Li et al., 2003).

Photoluminescence results are shown in Fig. 20.5 (a). The spectra exhibit two emission bands one centered at about 465 nm and one at 525 nm. As the excitation density is varied, the two peak positions do not change. However, the ratio of the two peak intensities changes with the excitation power density of the laser. The excitation-density-dependent emission ratio can be explained by the competition of different recombination paths (Li et al., 2003). Neglecting non - radiative recombination, possible recombination paths of an electron in the blue quantum well (QW) are either direct radiative recombination in the blue QW or tunneling to the green QW with subsequent radiative recombination. Electrons and holes can tunnel from the blue QW to

Wavelength X (nm) Wavelength X (nm) Fig. 20.5. Room temperature (a) photoluminescence and (b) electroluminescence spectra of monolithic dichromatic LED with two active regions (after Li et al., 2003).

the green QW and recombine there radiatively. However, once in the green QW, carriers cannot tunnel back to the blue QW due to the higher energy of this QW.

Electroluminescence (EL) spectra of the device are shown in Fig. 20.5 (b). Two emission peaks are clearly observed with center wavelengths at about 450 nm and 520 nm. The blue peak is more intense than the green peak which can be attributed to the higher quantum efficiency of blue QWs compared with green QWs. In addition, holes are injected from the blue side (i. e. the side of the high-energy, blue-emitting QWs), whereas electrons are injected from the green side. As holes have a lower mobility and a higher effective mass, they are less likely to reach the green QWs, which can explain the higher intensity of the blue emission.

For current injection, holes are injected into the blue QWs, whereas electrons are injected into the green QWs. This is very different from optical excitation, where both types of carriers are injected from both sides of the active region. For the structure discussed here, the optical absorption length is longer than the distance between the active regions and the surface. This can explain the marked difference between the results for photoluminescence and electroluminescence (Li et al., 2003).

Room temperature I-V curves of the double-active region LED exhibit excellent forward voltages < 3.0 V at small contact diameters of 100 |j, m indicating high-quality ohmic contacts. The increase in forward voltage for contacts with larger diameters was attributed to an increased voltage drop in the n-type buffer layer, because, at a given current density, the current in the buffer layer scales with the area of the contact A, but the access resistance through the n-type

1/2

buffer layer scales with the circumference A. In addition, the current crowding effect leads to non-uniform current injection particularly in large-diameter contacts and thus to an increased forward voltage.

20.2 Generation of white light by trichromatic sources Whereas high-quality white light suitable for illumination applications cannot be generated by additive mixing of two complementary colors, such high-quality white light can be generated by mixing of three primary colors or more than three colors. In a detailed analysis, Thornton (1971) showed that mixing of discrete emission bands with peak wavelengths near 450 nm, 540 nm, and 610 nm resulted in a high-quality source. Thornton (1971) reported experiments with 60 human subjects who judged the quality of a trichromatic source in terms of its color rendition capability of meat, vegetables, flowers, and complexion, to be “very good, if not excellent”. Thornton (1971) also reported that, for high-quality color rendition of trichromatic sources, the use of emitters near 500 nm and 580 nm should be avoided.

Although Thornton (1971) established that trichromatic sources can have high quality, the individual emission bands used in the experiments had a broad spectral width: The full-widths at half-maximum of the phosphor emitters employed in the study exceeded 50 nm. Semiconductors, with typical spectral widths < 50 nm, have much narrower emission lines than phosphors.

The trichromatic emission spectrum of a white-light source made out of three types of LEDs emitting at 455 nm, 525 nm, and 605 nm is shown in Fig. 20.6 (a). The experimentally determined full-width at half-maximum of the spectra at room temperature (20 °C) is 5.5 kT,
7.9 kT, and 2.5 kT for the GaInN blue, GaInN green, and AlGaInP orange emitter, respectively, where kT = 25.25 meV. The expression of the full-width at half-maximum in terms of kT is very useful, as it can be easily related to the theoretical full-width at half-maximum of a thermally broadened emission band of a semiconductor, which is 1.8 kT. Using the full-width at half­maximum given in the figure and

AX

(AE /eV) ,

(20.3)

(X / nm)2 1239.8

the full-widths at half-maximum of the blue, green, and orange sources are 23.2 nm, 44.3 nm, and 18.6 nm, respectively. Note that the green emission line is particularly broad, which can be attributed to alloy broadening and the formation of quantum-dot-like InN-rich regions within the high-In-content GaInN.

Also shown in the figure are gaussian fits to the experimental spectra. The gaussian fits match the experimental spectra well. Note that the gaussian curves (equations were given earlier in this chapter) are symmetric in terms of wavelength. Asymmetric gaussian distributions, which have a more pronounced long-wavelength tail, have been employed for phosphors (Ivey, 1963). The use of such asymmetric gaussian distributions does not appear to be warranted for semiconductors as their spectral power distribution is quite symmetric when plotted versus wavelength.

A photograph of the light source assembled from a large number of LEDs is shown in Fig. 20.6 (b). The power ratio of the orange, green, and blue emitters is adjusted to match the chromaticity of a planckian radiator with color temperature 6500 K. The LED source, assembled from standard commercial devices, has a luminous efficacy of radiation of 319 lm/W, a luminous source efficiency of 32 lm/W, and a color-rendering index of 84 (Chhajed et al., 2005).

There are a large number of possible wavelength combinations for trichromatic sources. To attain a high efficacy of radiation, sources near the fringes of the visible spectrum (deep red and deep violet) should be avoided. Contour plots of the luminous efficacy of radiation and of the color rendering index of a trichromatic source with color temperature of 6500 K are shown in Fig. 20.7 for a full-width at half-maximum for each emission line of 5 kT. Inspection of the figure reveals that X = 455 nm, X2 = 530 nm, and = 605 nm are particularly favorable in terms of the color-rendering index. The CIE general CRI is about 85 for this wavelength combination with the luminous efficacy of radiation being 320 lm/W.

The figure also reveals that the CRI depends very sensitively on the exact peak positions. For

example, changing the red peak wavelength from 605 nm to 620 nm decreases the CRI from 85 to 65. Similarly, changing the green wavelength from 530 nm to 550 nm decreases the CRI to values less than 60.

Wavelength A-2 (nm) Fig. 20.7. Contour plot of luminous efficacy of radiation and CIE color-rendering index of white trichromatic LED source with color temperature 6500 К as a function of the three wavelengths for a linewidth (FWHM) of 5kT (after Chhajed et al., 2005).

Contour plots of the luminous efficacy of radiation and of the color-rendering index of a trichromatic source with color temperature of 6500 K are shown in Fig. 20.8 for a full-width at half-maximum for each emission line of 8 kT. A higher CRI results from the broader emission lines. A very favorable combination in terms of a high CRI is obtained for X = 450-455 nm, X2 = 525-535 nm, and X3 = 600-615 nm, where a CRI in the range 90-95 is obtained.

20.3 Temperature dependence of trichromatic LED-based white-light source The relatively small range of wavelengths that enables a high color-rendering capability raises the question as to the stability of trichromatic sources with respect to junction and ambient

temperature. It is known that emission power (P), peak wavelength (X, eak), and spectral width (AX) depend on temperature, each of these quantities having a different temperature coefficient.

The optical output power of LEDs is temperature dependent in a manner that can be described by an exponential function and a characteristic temperature, T1. The light output power of an LED is then given by

Wavelength Ал (nm) Fig. 20.8. Contour plot of luminous efficacy of radiation and CIE color-rendering index of white trichromatic LED source with color temperature 6500 К as a function of the three wavelengths for a linewidth (FWHM) of 8kT (after Chhajed et al., 2005).

As a result of these temperature dependences, the chromaticity point of a multi-LED white - light source changes with temperature. Consider a white-light source consisting of three types of emitters emitting in the red, green, and blue. For such LEDs, the temperature coefficients of the peak emission wavelength, spectral width, and emission power have been measured and are

Table 20.2. Experimentally determined temperature coefficients for peak wavelength, spectral width, and emission power for blue, green, and red LEDs. Blue Green Red d^peak/dT 0.0389 nm / °C 0.0308 nm / °C 0.156 nm / °C dM /dT 0.0466 nm / °C 0.0625 nm / °C 0.181 nm / °C T 1 characteristic 493 K 379 K 209 K

Wavelength X (nm)

given in Table 20.2 (Chhajed et al., 2005).

Consider further that the three currents feeding the red, green, and blue LEDs are adjusted in such a way that the resulting chromaticity point equals that of Illuminant D65 when the device temperature is 20 °C. The optical spectrum of such a trichromatic white source is shown in Fig. 20.9.

Fig. 20.9. Emission spectrum of trichromatic white LED source for different ambient temperatures (junction heating neglected). Opti­cal power, linewidth, and peak wavelength change with tempera­ture. As a result of these changes, the color temperature of the source increases (after Chhajed et al., 2005).

However, as the device temperature increases, the chromaticity point of the trichromatic source changes due to the temperature dependences of the emission power, peak wavelength, and spectral width. This shift of the chromaticity point is shown in Fig. 20.10. Inspection of the figure reveals that the chromaticity point shifts towards higher color temperatures. This can be explained by the stronger temperature dependence of the red LED emission power. At high temperatures, the red component of the light source decreases more strongly (due to low T1 value) than the green component, and the blue component, which is particularly stable.

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 x - chromaticity coordinate

Fig. 20.10. Change in chromaticity of trichromatic white LED-based source. The source color tempera­ture is 6500 К when devices are at room temperature. Due to the de­pendence of emission power, peak wavelength, and linewidth on tem­perature, the chromaticity point mi­grates off the planckian locus as the device temperature increases (after Chhajed et al., 2005).

Figure 20.11 shows the chromaticity shift of the trichromatic source on a magnified scale in the CIE 1931 (x, y) chromaticity coordinate system as well as in the CIE 1976 (U, v') uniform
chromaticity coordinate system along with the planckian locus. At Tj = 50 °C, the chromaticity point is 0.009 units away from the original point, and at 80 °C, it is shifted 0.02 units from the original point. This shift causes a clearly noticeable change in color appearance and exceeds the deviation limit of 0.01 units ("0.01 rule”) commonly used in the lighting industry (Duggal, 2005).

The shift in chromaticity can be eliminated by adjusting the relative power ratio of the three LED sources. There are two possible implementations for adjusting the power ratio. In one implementation, the spectrum of the light source is constantly measured and a feedback control is used to adjust the optical power of the three components. In an alternative implementation, the device temperature is monitored and the optical power of the three components is adjusted using the known temperature dependence of the different types of emitters. The second method is easier due to the simplicity of a temperature measurement. However, the second method does not enable a compensation for device-aging effects.

20.4 Generation of white light by tetrachromatic and pentachromatic sources Tetrachromatic and pentachromatic white sources use four and five types of LEDs, respectively (Zukauskas et al., 2002a; Schubert and Kim, 2005). The color-rendering index of polychromatic sources generally increases with the number of sources. However, the luminous efficacy generally decreases with increasing number of sources. Thus, the color-rendering index and the luminous efficacy of tetrachromatic sources are generally higher and lower than those of trichromatic sources, respectively. However, the specifics depend on the exact choice of the emission wavelengths. Due to the greater number of wavelength choices, the color temperatures of such sources can be adjusted more liberally without compromising the color-rendering capability of the source.