Abstract

Calculations have been made for the color and luminous efficiency of single phosphors and of blends of such phosphors. In the latter case, all the emission is assumed to come from the phosphors so that the results apply to cathode-ray tubes or to electroluminescent lamps, but not to fluorescent lamps. In these calculations it is considered that (1) real phosphors have somewhat asymmetrical spectral emission distributions of appreciable width, and (2) phosphors are quantum emitters so that the energy output from a red emitter will be lower than that of a blue emitter of equal quantum efficiency. In the case of phosphors to be used in blends, two preferred peak wavelengths at 445 and 570–590 mμ, as well as an unfavorable region at 500–505 mμ, are found. The existence of these special regions can be explained on the basis of the CIE tristimulus functions.

© 1963 Optical Society of America

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References

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  1. D. L. MacAdam, J. Opt. Soc. Am. 40, 120 (1950).
    [Crossref]
  2. H. W. Leverenz, J. Opt. Soc. Am. 30, 309 (1940).
    [Crossref]
  3. R. T. Ellickson, J. Opt. Soc. Am. 36, 261 (1946).
    [Crossref]
  4. W. L. Brewer and F. R. Holly, J. Opt. Soc. Am. 38, 858 (1948).
    [Crossref] [PubMed]
  5. G. F. J. Garlick, in Handbuclh der Physik, edited by S. Flügge (Springer-Verlag, Berlin, 1958), Vol. 26, p. 1; C. C. Klick and J. H. Schulman, in Solid State Physics, edited by F. Seitz and D. Turnbull (Academic Press Inc., New York, 1957), Vol. 5, p. 17.
    [Crossref]
  6. S. T. Henderson, Proc. Roy. Soc. (London) A173, 323 (1939); K. H. Butler, J. Electrochem. Soc. 93, 143 (1948).
    [Crossref]
  7. C. Vlam, Brit. J. Appl. Phys. 5, 443 (1954).
    [Crossref]
  8. P. W. Randy, D. H. Mash, and S. T. Henderson, Brit. J. Appl. Phys. Suppl. 4, 18 (1955); S. T. Henderson, P. W. Ranby, and M. B. Halstead, in Solid State Physics in Electronics and Telecommunications, edited by M. Desirant and J. L. Michiels (Academic Press Inc., New York, 1960), Vol. 4, p. 714.
  9. D. A. Patterson and C. C. Klick, Phys. Rev. 105, 401 (1957).
    [Crossref]
  10. M. H. Aven and R. M. Potter, J. Electrochem. Soc. 105, 135 (1958).
    [Crossref]
  11. W. Lehmann, J. Electrochem. Soc. 110, 754 (1963).
    [Crossref]
  12. Eν~λ2Eλ and Nν~λ3Eλ.
  13. D. L. Dexter, Phys. Rev. 96, 615 (1954).
    [Crossref]
  14. D. Curie, Luminescence Cristalline (Dunod Cie, Paris, 1960); Compt. Rend. 246, 404 (1958); Compt. Rend. 250, 834 (1960); Luminescence in Crystals (John Wiley & Sons, Inc., New York, 1963).
  15. A. E. Hardy, RCA Rev. 8, 554 (1947).
  16. F. A. Kröger, A. Bril, and J. A. M. Dikhoff, Philips Res. Rept. 7, 241 (1952).
  17. It should be noted that the value of 0.36 eV given by Lehmann11 is the separation of the two half-amplitude points. Δν corresponds to the distance from λ0−1 to the corresponding points where the amplitude has fallen to 1/e or 37% of the maximum value. In terms of the usual plot as a function of wavelength, these two wavelengths are given byλ1,2=λ0/(1±λ0Δν)andλ2-λ1=2λ02Δν/[1-(λ0Δν)2]≃2λ02Δν.Thus for constant Δν, as for the (Zn,Cd)S:Cu family, the bandwidth for the usual type of plot increases as λ0 increases.
  18. H. F. Ivey, Electroluminescence and Related Effects (Academic Press Inc., New York, 1963).
  19. H. F. Ivey, IRE Trans. Component Parts CP4, 114 (1957); Proc. Natl. Electronics Conf. 13, 583 (1957).
    [Crossref]
  20. A. Bril and H. A. Klasens, Philips Res. Rept. 7, 401 (1952).
  21. A. Bril, in Luminescence of Organic and Inorganic Materials, edited by H. P. Kallmann and G. M. Spruch (John Wiley & Sons, Inc., New York, 1962), p. 479.
  22. G. F. J. Garlick, Brit. J. Appl. Phys. 13, 541 (1962).
    [Crossref]
  23. J. Tregellas-Williams, J. Electrochem. Soc. 105, 173 (1958).
    [Crossref]
  24. The effect of the emission wavelength on the efficiency has been included in a paper by C. W. Jerome [J. Electrochem. Soc. 100, 586 (1953)] concerning the application of phosphors to fluorescent lamps.
    [Crossref]
  25. The writer is indebted to G. Kemeny, G. R. Hagen, and D. W. Morgan for computer programming.
  26. A. C. Hardy, Handbook of Colorimetry (Technology Press, Cambridge, Massachusetts, 1936); Committee on Colorimetry, Optical Society of America, The Science of Color (The Thomas Y. Crowell Company, New York, 1953).
  27. Only Cu gives electroluminescent phosphors.
  28. Cu can introduce two different emission bands (of equal width) in ZnS. Space does not permit further discussion of this point.
  29. H. W. Leverenz, An Introduction to the Luminescence of Solids (John Wiley & Sons, Inc., New York, 1950), p. 199.

1963 (1)

W. Lehmann, J. Electrochem. Soc. 110, 754 (1963).
[Crossref]

1962 (1)

G. F. J. Garlick, Brit. J. Appl. Phys. 13, 541 (1962).
[Crossref]

1958 (2)

J. Tregellas-Williams, J. Electrochem. Soc. 105, 173 (1958).
[Crossref]

M. H. Aven and R. M. Potter, J. Electrochem. Soc. 105, 135 (1958).
[Crossref]

1957 (2)

H. F. Ivey, IRE Trans. Component Parts CP4, 114 (1957); Proc. Natl. Electronics Conf. 13, 583 (1957).
[Crossref]

D. A. Patterson and C. C. Klick, Phys. Rev. 105, 401 (1957).
[Crossref]

1955 (1)

P. W. Randy, D. H. Mash, and S. T. Henderson, Brit. J. Appl. Phys. Suppl. 4, 18 (1955); S. T. Henderson, P. W. Ranby, and M. B. Halstead, in Solid State Physics in Electronics and Telecommunications, edited by M. Desirant and J. L. Michiels (Academic Press Inc., New York, 1960), Vol. 4, p. 714.

1954 (2)

C. Vlam, Brit. J. Appl. Phys. 5, 443 (1954).
[Crossref]

D. L. Dexter, Phys. Rev. 96, 615 (1954).
[Crossref]

1953 (1)

The effect of the emission wavelength on the efficiency has been included in a paper by C. W. Jerome [J. Electrochem. Soc. 100, 586 (1953)] concerning the application of phosphors to fluorescent lamps.
[Crossref]

1952 (2)

A. Bril and H. A. Klasens, Philips Res. Rept. 7, 401 (1952).

F. A. Kröger, A. Bril, and J. A. M. Dikhoff, Philips Res. Rept. 7, 241 (1952).

1950 (1)

1948 (1)

1947 (1)

A. E. Hardy, RCA Rev. 8, 554 (1947).

1946 (1)

1940 (1)

1939 (1)

S. T. Henderson, Proc. Roy. Soc. (London) A173, 323 (1939); K. H. Butler, J. Electrochem. Soc. 93, 143 (1948).
[Crossref]

Aven, M. H.

M. H. Aven and R. M. Potter, J. Electrochem. Soc. 105, 135 (1958).
[Crossref]

Brewer, W. L.

Bril, A.

A. Bril and H. A. Klasens, Philips Res. Rept. 7, 401 (1952).

F. A. Kröger, A. Bril, and J. A. M. Dikhoff, Philips Res. Rept. 7, 241 (1952).

A. Bril, in Luminescence of Organic and Inorganic Materials, edited by H. P. Kallmann and G. M. Spruch (John Wiley & Sons, Inc., New York, 1962), p. 479.

Curie, D.

D. Curie, Luminescence Cristalline (Dunod Cie, Paris, 1960); Compt. Rend. 246, 404 (1958); Compt. Rend. 250, 834 (1960); Luminescence in Crystals (John Wiley & Sons, Inc., New York, 1963).

Dexter, D. L.

D. L. Dexter, Phys. Rev. 96, 615 (1954).
[Crossref]

Dikhoff, J. A. M.

F. A. Kröger, A. Bril, and J. A. M. Dikhoff, Philips Res. Rept. 7, 241 (1952).

Ellickson, R. T.

Garlick, G. F. J.

G. F. J. Garlick, Brit. J. Appl. Phys. 13, 541 (1962).
[Crossref]

G. F. J. Garlick, in Handbuclh der Physik, edited by S. Flügge (Springer-Verlag, Berlin, 1958), Vol. 26, p. 1; C. C. Klick and J. H. Schulman, in Solid State Physics, edited by F. Seitz and D. Turnbull (Academic Press Inc., New York, 1957), Vol. 5, p. 17.
[Crossref]

Hagen, G. R.

The writer is indebted to G. Kemeny, G. R. Hagen, and D. W. Morgan for computer programming.

Hardy, A. C.

A. C. Hardy, Handbook of Colorimetry (Technology Press, Cambridge, Massachusetts, 1936); Committee on Colorimetry, Optical Society of America, The Science of Color (The Thomas Y. Crowell Company, New York, 1953).

Hardy, A. E.

A. E. Hardy, RCA Rev. 8, 554 (1947).

Henderson, S. T.

P. W. Randy, D. H. Mash, and S. T. Henderson, Brit. J. Appl. Phys. Suppl. 4, 18 (1955); S. T. Henderson, P. W. Ranby, and M. B. Halstead, in Solid State Physics in Electronics and Telecommunications, edited by M. Desirant and J. L. Michiels (Academic Press Inc., New York, 1960), Vol. 4, p. 714.

S. T. Henderson, Proc. Roy. Soc. (London) A173, 323 (1939); K. H. Butler, J. Electrochem. Soc. 93, 143 (1948).
[Crossref]

Holly, F. R.

Ivey, H. F.

H. F. Ivey, IRE Trans. Component Parts CP4, 114 (1957); Proc. Natl. Electronics Conf. 13, 583 (1957).
[Crossref]

H. F. Ivey, Electroluminescence and Related Effects (Academic Press Inc., New York, 1963).

Jerome, C. W.

The effect of the emission wavelength on the efficiency has been included in a paper by C. W. Jerome [J. Electrochem. Soc. 100, 586 (1953)] concerning the application of phosphors to fluorescent lamps.
[Crossref]

Kemeny, G.

The writer is indebted to G. Kemeny, G. R. Hagen, and D. W. Morgan for computer programming.

Klasens, H. A.

A. Bril and H. A. Klasens, Philips Res. Rept. 7, 401 (1952).

Klick, C. C.

D. A. Patterson and C. C. Klick, Phys. Rev. 105, 401 (1957).
[Crossref]

Kröger, F. A.

F. A. Kröger, A. Bril, and J. A. M. Dikhoff, Philips Res. Rept. 7, 241 (1952).

Lehmann, W.

W. Lehmann, J. Electrochem. Soc. 110, 754 (1963).
[Crossref]

Leverenz, H. W.

H. W. Leverenz, J. Opt. Soc. Am. 30, 309 (1940).
[Crossref]

H. W. Leverenz, An Introduction to the Luminescence of Solids (John Wiley & Sons, Inc., New York, 1950), p. 199.

MacAdam, D. L.

Mash, D. H.

P. W. Randy, D. H. Mash, and S. T. Henderson, Brit. J. Appl. Phys. Suppl. 4, 18 (1955); S. T. Henderson, P. W. Ranby, and M. B. Halstead, in Solid State Physics in Electronics and Telecommunications, edited by M. Desirant and J. L. Michiels (Academic Press Inc., New York, 1960), Vol. 4, p. 714.

Morgan, D. W.

The writer is indebted to G. Kemeny, G. R. Hagen, and D. W. Morgan for computer programming.

Patterson, D. A.

D. A. Patterson and C. C. Klick, Phys. Rev. 105, 401 (1957).
[Crossref]

Potter, R. M.

M. H. Aven and R. M. Potter, J. Electrochem. Soc. 105, 135 (1958).
[Crossref]

Randy, P. W.

P. W. Randy, D. H. Mash, and S. T. Henderson, Brit. J. Appl. Phys. Suppl. 4, 18 (1955); S. T. Henderson, P. W. Ranby, and M. B. Halstead, in Solid State Physics in Electronics and Telecommunications, edited by M. Desirant and J. L. Michiels (Academic Press Inc., New York, 1960), Vol. 4, p. 714.

Tregellas-Williams, J.

J. Tregellas-Williams, J. Electrochem. Soc. 105, 173 (1958).
[Crossref]

Vlam, C.

C. Vlam, Brit. J. Appl. Phys. 5, 443 (1954).
[Crossref]

Brit. J. Appl. Phys. (2)

C. Vlam, Brit. J. Appl. Phys. 5, 443 (1954).
[Crossref]

G. F. J. Garlick, Brit. J. Appl. Phys. 13, 541 (1962).
[Crossref]

Brit. J. Appl. Phys. Suppl. (1)

P. W. Randy, D. H. Mash, and S. T. Henderson, Brit. J. Appl. Phys. Suppl. 4, 18 (1955); S. T. Henderson, P. W. Ranby, and M. B. Halstead, in Solid State Physics in Electronics and Telecommunications, edited by M. Desirant and J. L. Michiels (Academic Press Inc., New York, 1960), Vol. 4, p. 714.

IRE Trans. Component Parts (1)

H. F. Ivey, IRE Trans. Component Parts CP4, 114 (1957); Proc. Natl. Electronics Conf. 13, 583 (1957).
[Crossref]

J. Electrochem. Soc. (4)

M. H. Aven and R. M. Potter, J. Electrochem. Soc. 105, 135 (1958).
[Crossref]

W. Lehmann, J. Electrochem. Soc. 110, 754 (1963).
[Crossref]

J. Tregellas-Williams, J. Electrochem. Soc. 105, 173 (1958).
[Crossref]

The effect of the emission wavelength on the efficiency has been included in a paper by C. W. Jerome [J. Electrochem. Soc. 100, 586 (1953)] concerning the application of phosphors to fluorescent lamps.
[Crossref]

J. Opt. Soc. Am. (4)

Philips Res. Rept. (2)

A. Bril and H. A. Klasens, Philips Res. Rept. 7, 401 (1952).

F. A. Kröger, A. Bril, and J. A. M. Dikhoff, Philips Res. Rept. 7, 241 (1952).

Phys. Rev. (2)

D. L. Dexter, Phys. Rev. 96, 615 (1954).
[Crossref]

D. A. Patterson and C. C. Klick, Phys. Rev. 105, 401 (1957).
[Crossref]

Proc. Roy. Soc. (London) (1)

S. T. Henderson, Proc. Roy. Soc. (London) A173, 323 (1939); K. H. Butler, J. Electrochem. Soc. 93, 143 (1948).
[Crossref]

RCA Rev. (1)

A. E. Hardy, RCA Rev. 8, 554 (1947).

Other (11)

D. Curie, Luminescence Cristalline (Dunod Cie, Paris, 1960); Compt. Rend. 246, 404 (1958); Compt. Rend. 250, 834 (1960); Luminescence in Crystals (John Wiley & Sons, Inc., New York, 1963).

It should be noted that the value of 0.36 eV given by Lehmann11 is the separation of the two half-amplitude points. Δν corresponds to the distance from λ0−1 to the corresponding points where the amplitude has fallen to 1/e or 37% of the maximum value. In terms of the usual plot as a function of wavelength, these two wavelengths are given byλ1,2=λ0/(1±λ0Δν)andλ2-λ1=2λ02Δν/[1-(λ0Δν)2]≃2λ02Δν.Thus for constant Δν, as for the (Zn,Cd)S:Cu family, the bandwidth for the usual type of plot increases as λ0 increases.

H. F. Ivey, Electroluminescence and Related Effects (Academic Press Inc., New York, 1963).

A. Bril, in Luminescence of Organic and Inorganic Materials, edited by H. P. Kallmann and G. M. Spruch (John Wiley & Sons, Inc., New York, 1962), p. 479.

Eν~λ2Eλ and Nν~λ3Eλ.

G. F. J. Garlick, in Handbuclh der Physik, edited by S. Flügge (Springer-Verlag, Berlin, 1958), Vol. 26, p. 1; C. C. Klick and J. H. Schulman, in Solid State Physics, edited by F. Seitz and D. Turnbull (Academic Press Inc., New York, 1957), Vol. 5, p. 17.
[Crossref]

The writer is indebted to G. Kemeny, G. R. Hagen, and D. W. Morgan for computer programming.

A. C. Hardy, Handbook of Colorimetry (Technology Press, Cambridge, Massachusetts, 1936); Committee on Colorimetry, Optical Society of America, The Science of Color (The Thomas Y. Crowell Company, New York, 1953).

Only Cu gives electroluminescent phosphors.

Cu can introduce two different emission bands (of equal width) in ZnS. Space does not permit further discussion of this point.

H. W. Leverenz, An Introduction to the Luminescence of Solids (John Wiley & Sons, Inc., New York, 1950), p. 199.

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Figures (13)

Fig. 1
Fig. 1

Contours of maximum luminous efficiency (lm/W) on CIE trichromatic diagram as calculated by MacAdam,1 without consideration of quantum effects, with superimposed Planckian locus (temperature indicated in hundreds of Kelvin degrees).

Fig. 2
Fig. 2

Normalized spectral energy distributions for four typical phosphors. The crosses are experimental points while the curves are calculated “asymmetrical Gaussian” distributions [Eq. (1)].

Fig. 3
Fig. 3

Chromaticity plot for phosphors with “asymmetrical Gaussian” spectral distributions [Eq. (1)]. The solid lines correspond to constant bandwidth (Δν), while the dashed lines correspond to constant peak wavelength (λ0).

Fig. 4
Fig. 4

Luminous efficiency factor, η′, for phosphors with “asymmetrical Gaussian” spectral distributions [Eq. (1)] of various widths as a function of peak wavelength.

Fig. 5
Fig. 5

Contours of maximum luminous efficiency (lm/W) on CIE trichromatic diagram for monochromatic emitters (Δν=0), taking into account the fact that phosphors are quantum emitters. Planckian locus is superimposed (temperature indicated in hundreds of Kelvin degrees).

Fig. 6
Fig. 6

Contours of maximum luminous efficiency for phosphors with “asymmetrical Gaussian” spectral distributions [Eq. (1)] and Δν=0.1 μ−1.

Fig. 7
Fig. 7

Contours of maximum luminous efficiency for phosphors with “asymmetrical Gaussian” spectral distributions [Eq. (1)] and Δν=0.2 μ−1.

Fig. 8
Fig. 8

Contours of maximum luminous efficiency for phosphors with “asymmetrical Gaussian” spectral distributions [Eq. (1)] and Δν=0.3 μ−1.

Fig. 9
Fig. 9

Maximum luminous efficiency of Planckian blends of phosphors with “asymmetrical Gaussian” spectral distributions [Eq. (1)] of various emission bandwidths. Color temperature in °K.

Fig. 10
Fig. 10

Illustrative example of effect of selection of peak wavelength on characteristics of Planckian blend (T=4500°K) of phosphors with “asymmetrical Gaussian” spectral distributions (Δν=0.2 μ)−1.

Fig. 11
Fig. 11

Values of optimum wavelength for shorter wavelength component in binary blends of monochromatic emitters for maximum luminous efficiency.

Fig. 12
Fig. 12

Comparison of various “figures of merit” for high efficiency in blends consisting of monochromatic emitters, showing preferred wavelengths near 445 and 580–590 mμ.

Fig. 13
Fig. 13

“Figure of merit” for phosphors with “asymmetrical Gaussian” spectral distributions of various emission bandwidths in blends.

Tables (6)

Tables Icon

Table I Parameters for emission spectra of various phosphors (Eq. 1).

Tables Icon

Table II Summary of calculations for asymmetrical Gaussian spectral distributions.

Tables Icon

Table III Results for optimum blends of emitters with asymmetrical Gaussian distributions.a

Tables Icon

Table IV Optimum Planckian blends of asymmetric Gaussian emitters.

Tables Icon

Table V Results for blends (T=3500°K) of phosphors with asymmetrical Gaussian distributions of different width.

Tables Icon

Table VI Calculated luminous efficiency factors for sulfide phosphor blends (see text).

Equations (21)

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E λ = exp { - [ ( λ - 1 - λ 0 - 1 ) / Δ ν ] 2 } ,
680 y ¯ ( λ ) · ( 400 / λ ) lm / W ,
E = 680 E λ y ¯ ( λ ) d λ / E λ ( λ / 400 ) d λ .
η = E λ y ¯ ( λ ) d λ / E λ d λ ,
η = E λ y ¯ ( λ ) d λ / E λ ( λ / 400 ) d λ = η / λ ¯
λ ¯ = E λ λ d λ / 400 E λ d λ
Y ¯ 2 = Y 2 / ( Y 1 + Y 2 ) , etc .
Ē 2 = [ 1 + ( Y 1 η 2 / Y 2 η 1 ) ] - 1 ,
Q ¯ 2 = [ 1 + ( Y 1 λ ¯ 1 η 2 / Y 2 λ ¯ 2 η 1 ) ] - 1 ,
η 0 = Y 1 + Y 2 Q 1 + Q 2 = Y 1 + Y 2 ( Y 1 λ ¯ 1 / η 1 ) + ( Y 2 Y ¯ 2 / η 2 ) ,
η 0 = η 1 Q ¯ 1 / Y ¯ 1 = η 2 Q ¯ 2 / Y ¯ 2 .
x 0 = x 1 ( Y 1 / y 1 ) + x 2 ( Y 2 / y 2 ) ( Y 1 / y 1 ) + ( Y 2 / y 2 ) ,
y 0 = Y 1 + Y 2 ( Y 1 / y 1 ) + ( Y 2 / y 2 ) ,
1 = Y 1 λ ¯ 1 η 1 + Y 2 λ ¯ 2 η 2 = Y 1 η 1 + Y 2 η 2 .
Y 0 = y 0 [ ( Y 1 / y 1 ) + ( Y 2 / y 2 ) ] ,
Y 0 = ( y 0 / x 0 ) [ x 1 ( Y 1 / y 1 ) + x 2 ( Y 2 / y 2 ) ] .
M 1 = η / y = η / λ ¯ y             or             M 2 = η x / y = η x / λ ¯ y .
M 3 = η ( x + 1 2 ) / y             and             M 4 = η ( x + 1 3 ) / y ,
M 1 = ( 400 / λ ) ( x ¯ + y ¯ + z ¯ ) , M 3 = ( 400 / 2 λ ) ( 3 x ¯ + y ¯ + z ¯ ) , M 2 = ( 400 / λ ) x ¯ , M 4 = ( 400 / 3 λ ) ( 4 x ¯ + y ¯ + z ¯ ) .
λ1,2=λ0/(1±λ0Δν)
λ2-λ1=2λ02Δν/[1-(λ0Δν)2]2λ02Δν.