The conversion efficiency of short-wavelength light to long-wavelength light by a wavelength - converter (X-converter) material is determined by two distinct factors, namely (i) the external quantum efficiency of the X-converter and (ii) the inherent quantum-mechanical-energy loss incurred in wavelength conversion.

The external quantum efficiency of the converter material, next, is given by

П _ number of photons emitted into free space by X-converter per second (211) ^ext number of photons absorbed by X-converter per second

The external efficiency originates in the internal efficiency and the extraction efficiency of the converter material according to next = ninternal Пе^асйоп. Note that the internal quantum efficiency depends on the inherent efficiency of the material whereas the extraction efficiency depends on the spatial distribution of the X-converter material. Generally, thin films have high extraction efficiencies whereas lumpy aggregations of converter materials have lower extraction efficiency due to reabsorption. It is therefore desirable to employ X-converter materials in the form of thin layers.

The inherent wavelength-conversion loss (sometimes called quantum deficit or Stokes shift)

incurred when converting a photon with wavelength X1 to a photon with wavelength X2 (X1 < X2) is given by

a ^ hc hc _,

AE _ hv - hv2 _ --------------------- - ----- . (212)

X1 X2

Thus the wavelength-conversion efficiency is given by

n _ _Xk (21 3)

'IX - conversion _ 7 _ л ^lJ)

h v1 X2

where X1 is the wavelength of the photon absorbed by the phosphor and X2 is the wavelength of the photon emitted by the phosphor. Note that wavelength-conversion loss is fundamental in nature. The loss cannot be overcome with conventional X-converter materials.

However, quantum-splitting phosphors allow one to convert one short-wavelength photon into two longer-wavelength photons so that hv1 = hv2 + hv3, where hv1 is the energy of the photon absorbed by the phosphor and hv2 and hv3 are the energies of the photons emitted by the phosphors. Several quantum-splitting phosphors have been reported (Justel et al., 1998; Wegh et al., 1999; Srivastava and Ronda, 2003; Srivastava, 2004). The possibility of quantum efficiencies approaching 200% for Eu3+-doped LiGdF4 has been proposed (Wegh et al., 1999). The quantum - splitting phosphor YF3:Pr3+ at room temperature has a quantum efficiency of about 140% for 185 nm excitation (Justel et al., 1998). However, viable quantum phosphors suitable for commercial applications have not yet been demonstrated.

The power-conversion efficiency of a wavelength converter is the product of Eqs. (21.1) and (21.3)

nX-converter _ ЛХ-conversion next. (21.4)

The inherent wavelength-conversion loss is the reason that X-converter-based white LEDs such as phosphor-based white LEDs have a fundamentally lower efficiency limit than white-light sources based on multiple LEDs.

The wavelength-conversion loss is highest for wavelength conversion from the UV to the red. For example, the conversion from UV (405 nm) to red (625 nm) can have a X-conversion efficiency of at most 65%. The low X-conversion efficiency represents a strong driving force to employ red LEDs (rather than red phosphors) in highly efficient lighting systems.

Most white-light emitters use an LED emitting at short wavelength (e. g. blue) and a wavelength converter. Some of the light emitted by the blue LED is absorbed in the converter material and then re-emitted as light with a longer wavelength. As a result, the lamp emits at least two different wavelengths. The types and characteristics of wavelength-converter materials will be discussed below.

The possibility that white light can be generated in different ways raises the question as to which is the optimum way to generate white light? There are two parameters that need to be considered: Firstly, the luminous efficiency and, secondly, the color-rendering index. For signage applications, the luminous efficiency is of primary importance and the color-rendering index is irrelevant. For illumination applications, both the luminous efficiency and the color - rendering index are important.

White-light sources employing two monochromatic complementary colors result in the highest possible luminous efficacy. However, the color-rendering index of such a dichromatic light source is lower than that of broad-band emitters.

The maximum luminous efficacy of radiation, attainable for white light created by two complementary monochromatic colors was calculated by MacAdam (1950). MacAdam showed that luminous efficacies exceeding 400 lm/W can be attained using a dichromatic source for white-light generation. The work of MacAdam (1950) was further refined by Ivey (1963) and Thornton (1971). These authors showed that dichromatic white-light sources have high luminous efficacy but low color-rendering properties, making them perfectly suitable for display applications but unsuitable for daylight illumination applications. In addition, Thornton (1971) showed that trichromatic white-light sources, i. e. sources creating white light by additive mixing of three discrete colors, have a color-rendering index suited for most applications. Thornton reported on an experiment in which 60 observers judged the color rendition of meat, vegetables, flowers, complexions, etc., when illuminated with a trichromatic light source with peak wavelengths at 450, 540, and 610 nm. The color rendition in this experiment was found to be “very good, if not excellent” illustrating the suitability of trichromatic white-light sources as potent daylight illumination sources.

A white-light source duplicating the sun’s spectrum would have good color-rendering capability. However, the radiation efficacy of such a light source would be lower than what is possible with other spectral distributions, e. g. a trichromatic distribution. The sun’s spectrum has strong emission near the boundaries of the visible spectrum (390 and 720 nm) where the eye sensitivity is very low. Thus exact duplication of the sun’s spectrum is not a viable strategy for high-efficiency light sources.

21.1 Wavelength-converter materials There are several types of converter materials including phosphors, semiconductors, and dyes. Converter materials have several parameters of interest, including the absorption wavelength, the emission wavelength, and the quantum efficiency. A good converter has near 100% quantum efficiency. The overall power-conversion efficiency of a wavelength converter is given by

П _ next(V Ч) (215)

where next is the external quantum efficiency of the converter, X1 is the wavelength of photons absorbed by the phosphor, and X2 is the wavelength of photons emitted by the phosphor. Even if the external quantum efficiency is unity, there is always energy loss associated with the wavelength-conversion process, so that the power-conversion efficiency of a wavelength converter is always less than unity.

The most common wavelength-converter materials are phosphors and they will be discussed in greater detail in the following section. The optical absorption and emission spectrum of a
commercial phosphor is shown in Fig. 21.2. The phosphor displays an absorption band and a lower-energy emission band. The emission band is rather broad, making this particular phosphor suitable for white-light emission. Phosphors are very stable materials and can have quantum efficiencies close to 100%. A common phosphor used for white LEDs is cerium-doped (Ce - doped) YAG phosphor (Nakamura and Fasol, 1997). For Ce-doped phosphors, quantum efficiencies of 75% have been reported (Schlotter et al., 1999).

Finally, semiconductors are another type of wavelength converter. Semiconductors are

Dyes are another type of wavelength converter. Many different dyes are commercially available. An example of a dye optical absorption and emission spectrum is shown in Fig. 21.3. Dyes can have quantum efficiencies close to 100%. However, dyes, as organic molecules, lack the long-term stability afforded by phosphors and semiconductors.

characterized by narrow emission lines with linewidths of the order of 2 kT. The spectral emission linewidth of semiconductors is narrower than the linewidth of many phosphors and dyes. Thus, semiconductors allow one to tailor the emission spectrum of a semiconductor wavelength converter with good precision.

As for phosphors and dyes, semiconductors can have internal quantum efficiencies near 100%. The light escape problem in semiconductor converters is less severe than it is in LEDs due to the fact that semiconductor converters do not need electrical contacts that could block the light.

“Italics” = indirect gap “Roman” = direct gap О hexagonal structure 9 cubic structure

AIN О

T= 300 к

6.0

Diamond

AIN 0

BNO

5.0

MgS

>  1) 5 о ZJ Сц C3 ZU •o

4.0

.. . „ /.nSO (ia • GaN_0 - C’dSO-r,7r ZnSeO — ' — A„>0 CdS0--------------------

MgSe

znsa

Ultra­violet 4H-SiC.

MgTe

С 3.0

Fig. 21.4. Room - temperature bandgap energy versus lattice constant of common elemental and binary compound semicon­ductors.

liiyL Ji^A-.Cdslo____

с 2.0

InNQ)

red __ Infra­ red

сз CC

InNO'

CdSc О

GaAs

AlSb *CdTe

InP

1.0

Si

InAs *.GaSb>sb 1 і і і і і і і і і І і і і і і і і і і І і і і і і і і і і 1< і і і* і і і і

Ge

I 1 I » I 1 1 « 1

2.0

3.0 4.0 5.0 Lattice constant a (angstroms)

6.0

7.0

Similar to phosphors and dyes, a great variety of semiconductors is available. Figure 21.4 shows elemental and binary compound semiconductors versus the semiconductor lattice constant. Using ternary or quaternary alloys, wavelength converters operating at virtually any visible wavelength can be fabricated.