Abstract

Interference effects, including multiple-beam and wide-angle, associated with luminescence from within a thin film are described. A simple geometrical model is used to calculate the s- and p-polarized luminescent light assuming electric-dipole radiation. The luminescence exhibits fringes when measured both as a function of the film thickness and as a function of the wavelength of the light. In the latter case the fringes can also show a beating effect. The model is applied to several experimental examples of cathodoluminescence in SiO2 and an example of photoluminescence in a-Si.

© 1982 Optical Society of America

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References

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  1. W. Lukosz, R. E. Kunz, Opt. Commun. 31, 251 (1979).
    [CrossRef]
  2. K. H. Drexhage, Prog. Opt. 12, 165 (1974). See references therein.
  3. J. P. Mitchell, D. G. Denure, Solid-State Electron. 16, 825 (1973).
    [CrossRef]
  4. Lj. D. Zekovic, V. V. Vrosevic, Thin Solid Films 78, 279 (1981).
    [CrossRef]
  5. H. O. McMahon, J. Opt. Soc. Am. 40, 376 (1950).
    [CrossRef]
  6. A. Marek, A. A. Jaecklin, J. Cornu, IEEE Trans. Electron Devices ED-21, 54 (1974).
    [CrossRef]
  7. G. A. N. Connell, R. J. Nemanich, C. C. Tsai, Appl. Phys. Lett. 36, 31 (1980).
    [CrossRef]
  8. W. Lukosz, J. Opt. Soc. Am. 71, 744 (1981).
    [CrossRef]
  9. R. K. Wangsness, Electromagnetic Fields (Wiley, New York, 1979).
  10. M. V. Klein, Optics (Wiley, New York, 1970), p. 205.
  11. Note that rij(p) as defined here equals −rij(s,p) as defined in Ref. 8.
  12. C. E. Jones, D. Embree, J. Appl. Phys. 47, 5365 (1976);in The Physics of SiO2and Its Interfaces, S. T. Pantelides, Ed. (Pergamon, New York, 1978), p. 289.
    [CrossRef]
  13. S. W. McKnight, E. D. Palik, J. Non-Cryst. Solids 40, 595 (1980).
    [CrossRef]
  14. H. Koyama, K. Matsubara, M. Mouri, J. Appl. Phys. 48, 5380 (1977).
    [CrossRef]
  15. G. H. Sigel, J. Non-Cryst. Solids 13, 372 (1973).
    [CrossRef]
  16. J. A. Gledhill, J. Phys. A: Math. Nucl. Gen. 6, 1420 (1973).
    [CrossRef]
  17. J. R. Young, J. Appl. Phys. 28, 524 (1957).
    [CrossRef]
  18. S. W. McKnight, Proc. Soc. Photo-Opt. Instrum. Eng. 276, 39 (1981).
  19. S. W. McKnight, in The Physics of MOS Insulators, G. Lucovsky, S. T. Pantelides, F. L. Galeener, Eds. (Pergamon, New York, 1980), p. 137.
  20. R. C. Weast, Ed., Handbook of Chemistry and Physicss (CRC Press, Cleveland, 1965).
  21. D. E. Aspnes, J. A. Theeten, J. Electrochem. Soc. 127, 1359 (1980).
    [CrossRef]
  22. S. G. Bishop, Naval Research Laboratory; private communication.
  23. D. E. Gray, Ed., American Institute of Physics Handbook (McGraw-Hill, New York, 1972).
  24. R. C. Chittick, J. Non-Cryst. Solids 3, 255 (1970).
    [CrossRef]

1981 (3)

Lj. D. Zekovic, V. V. Vrosevic, Thin Solid Films 78, 279 (1981).
[CrossRef]

W. Lukosz, J. Opt. Soc. Am. 71, 744 (1981).
[CrossRef]

S. W. McKnight, Proc. Soc. Photo-Opt. Instrum. Eng. 276, 39 (1981).

1980 (3)

D. E. Aspnes, J. A. Theeten, J. Electrochem. Soc. 127, 1359 (1980).
[CrossRef]

S. W. McKnight, E. D. Palik, J. Non-Cryst. Solids 40, 595 (1980).
[CrossRef]

G. A. N. Connell, R. J. Nemanich, C. C. Tsai, Appl. Phys. Lett. 36, 31 (1980).
[CrossRef]

1979 (1)

W. Lukosz, R. E. Kunz, Opt. Commun. 31, 251 (1979).
[CrossRef]

1977 (1)

H. Koyama, K. Matsubara, M. Mouri, J. Appl. Phys. 48, 5380 (1977).
[CrossRef]

1976 (1)

C. E. Jones, D. Embree, J. Appl. Phys. 47, 5365 (1976);in The Physics of SiO2and Its Interfaces, S. T. Pantelides, Ed. (Pergamon, New York, 1978), p. 289.
[CrossRef]

1974 (2)

A. Marek, A. A. Jaecklin, J. Cornu, IEEE Trans. Electron Devices ED-21, 54 (1974).
[CrossRef]

K. H. Drexhage, Prog. Opt. 12, 165 (1974). See references therein.

1973 (3)

J. P. Mitchell, D. G. Denure, Solid-State Electron. 16, 825 (1973).
[CrossRef]

G. H. Sigel, J. Non-Cryst. Solids 13, 372 (1973).
[CrossRef]

J. A. Gledhill, J. Phys. A: Math. Nucl. Gen. 6, 1420 (1973).
[CrossRef]

1970 (1)

R. C. Chittick, J. Non-Cryst. Solids 3, 255 (1970).
[CrossRef]

1957 (1)

J. R. Young, J. Appl. Phys. 28, 524 (1957).
[CrossRef]

1950 (1)

Aspnes, D. E.

D. E. Aspnes, J. A. Theeten, J. Electrochem. Soc. 127, 1359 (1980).
[CrossRef]

Bishop, S. G.

S. G. Bishop, Naval Research Laboratory; private communication.

Chittick, R. C.

R. C. Chittick, J. Non-Cryst. Solids 3, 255 (1970).
[CrossRef]

Connell, G. A. N.

G. A. N. Connell, R. J. Nemanich, C. C. Tsai, Appl. Phys. Lett. 36, 31 (1980).
[CrossRef]

Cornu, J.

A. Marek, A. A. Jaecklin, J. Cornu, IEEE Trans. Electron Devices ED-21, 54 (1974).
[CrossRef]

Denure, D. G.

J. P. Mitchell, D. G. Denure, Solid-State Electron. 16, 825 (1973).
[CrossRef]

Drexhage, K. H.

K. H. Drexhage, Prog. Opt. 12, 165 (1974). See references therein.

Embree, D.

C. E. Jones, D. Embree, J. Appl. Phys. 47, 5365 (1976);in The Physics of SiO2and Its Interfaces, S. T. Pantelides, Ed. (Pergamon, New York, 1978), p. 289.
[CrossRef]

Gledhill, J. A.

J. A. Gledhill, J. Phys. A: Math. Nucl. Gen. 6, 1420 (1973).
[CrossRef]

Jaecklin, A. A.

A. Marek, A. A. Jaecklin, J. Cornu, IEEE Trans. Electron Devices ED-21, 54 (1974).
[CrossRef]

Jones, C. E.

C. E. Jones, D. Embree, J. Appl. Phys. 47, 5365 (1976);in The Physics of SiO2and Its Interfaces, S. T. Pantelides, Ed. (Pergamon, New York, 1978), p. 289.
[CrossRef]

Klein, M. V.

M. V. Klein, Optics (Wiley, New York, 1970), p. 205.

Koyama, H.

H. Koyama, K. Matsubara, M. Mouri, J. Appl. Phys. 48, 5380 (1977).
[CrossRef]

Kunz, R. E.

W. Lukosz, R. E. Kunz, Opt. Commun. 31, 251 (1979).
[CrossRef]

Lukosz, W.

W. Lukosz, J. Opt. Soc. Am. 71, 744 (1981).
[CrossRef]

W. Lukosz, R. E. Kunz, Opt. Commun. 31, 251 (1979).
[CrossRef]

Marek, A.

A. Marek, A. A. Jaecklin, J. Cornu, IEEE Trans. Electron Devices ED-21, 54 (1974).
[CrossRef]

Matsubara, K.

H. Koyama, K. Matsubara, M. Mouri, J. Appl. Phys. 48, 5380 (1977).
[CrossRef]

McKnight, S. W.

S. W. McKnight, Proc. Soc. Photo-Opt. Instrum. Eng. 276, 39 (1981).

S. W. McKnight, E. D. Palik, J. Non-Cryst. Solids 40, 595 (1980).
[CrossRef]

S. W. McKnight, in The Physics of MOS Insulators, G. Lucovsky, S. T. Pantelides, F. L. Galeener, Eds. (Pergamon, New York, 1980), p. 137.

McMahon, H. O.

Mitchell, J. P.

J. P. Mitchell, D. G. Denure, Solid-State Electron. 16, 825 (1973).
[CrossRef]

Mouri, M.

H. Koyama, K. Matsubara, M. Mouri, J. Appl. Phys. 48, 5380 (1977).
[CrossRef]

Nemanich, R. J.

G. A. N. Connell, R. J. Nemanich, C. C. Tsai, Appl. Phys. Lett. 36, 31 (1980).
[CrossRef]

Palik, E. D.

S. W. McKnight, E. D. Palik, J. Non-Cryst. Solids 40, 595 (1980).
[CrossRef]

Sigel, G. H.

G. H. Sigel, J. Non-Cryst. Solids 13, 372 (1973).
[CrossRef]

Theeten, J. A.

D. E. Aspnes, J. A. Theeten, J. Electrochem. Soc. 127, 1359 (1980).
[CrossRef]

Tsai, C. C.

G. A. N. Connell, R. J. Nemanich, C. C. Tsai, Appl. Phys. Lett. 36, 31 (1980).
[CrossRef]

Vrosevic, V. V.

Lj. D. Zekovic, V. V. Vrosevic, Thin Solid Films 78, 279 (1981).
[CrossRef]

Wangsness, R. K.

R. K. Wangsness, Electromagnetic Fields (Wiley, New York, 1979).

Young, J. R.

J. R. Young, J. Appl. Phys. 28, 524 (1957).
[CrossRef]

Zekovic, Lj. D.

Lj. D. Zekovic, V. V. Vrosevic, Thin Solid Films 78, 279 (1981).
[CrossRef]

Appl. Phys. Lett. (1)

G. A. N. Connell, R. J. Nemanich, C. C. Tsai, Appl. Phys. Lett. 36, 31 (1980).
[CrossRef]

IEEE Trans. Electron Devices (1)

A. Marek, A. A. Jaecklin, J. Cornu, IEEE Trans. Electron Devices ED-21, 54 (1974).
[CrossRef]

J. Appl. Phys. (3)

C. E. Jones, D. Embree, J. Appl. Phys. 47, 5365 (1976);in The Physics of SiO2and Its Interfaces, S. T. Pantelides, Ed. (Pergamon, New York, 1978), p. 289.
[CrossRef]

J. R. Young, J. Appl. Phys. 28, 524 (1957).
[CrossRef]

H. Koyama, K. Matsubara, M. Mouri, J. Appl. Phys. 48, 5380 (1977).
[CrossRef]

J. Electrochem. Soc. (1)

D. E. Aspnes, J. A. Theeten, J. Electrochem. Soc. 127, 1359 (1980).
[CrossRef]

J. Non-Cryst. Solids (3)

G. H. Sigel, J. Non-Cryst. Solids 13, 372 (1973).
[CrossRef]

R. C. Chittick, J. Non-Cryst. Solids 3, 255 (1970).
[CrossRef]

S. W. McKnight, E. D. Palik, J. Non-Cryst. Solids 40, 595 (1980).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Phys. A: Math. Nucl. Gen. (1)

J. A. Gledhill, J. Phys. A: Math. Nucl. Gen. 6, 1420 (1973).
[CrossRef]

Opt. Commun. (1)

W. Lukosz, R. E. Kunz, Opt. Commun. 31, 251 (1979).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

S. W. McKnight, Proc. Soc. Photo-Opt. Instrum. Eng. 276, 39 (1981).

Prog. Opt. (1)

K. H. Drexhage, Prog. Opt. 12, 165 (1974). See references therein.

Solid-State Electron. (1)

J. P. Mitchell, D. G. Denure, Solid-State Electron. 16, 825 (1973).
[CrossRef]

Thin Solid Films (1)

Lj. D. Zekovic, V. V. Vrosevic, Thin Solid Films 78, 279 (1981).
[CrossRef]

Other (7)

R. K. Wangsness, Electromagnetic Fields (Wiley, New York, 1979).

M. V. Klein, Optics (Wiley, New York, 1970), p. 205.

Note that rij(p) as defined here equals −rij(s,p) as defined in Ref. 8.

S. W. McKnight, in The Physics of MOS Insulators, G. Lucovsky, S. T. Pantelides, F. L. Galeener, Eds. (Pergamon, New York, 1980), p. 137.

R. C. Weast, Ed., Handbook of Chemistry and Physicss (CRC Press, Cleveland, 1965).

S. G. Bishop, Naval Research Laboratory; private communication.

D. E. Gray, Ed., American Institute of Physics Handbook (McGraw-Hill, New York, 1972).

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Figures (10)

Fig. 1
Fig. 1

(a) Coordinate system used to calculate the electric field E at observation point A due to dipole p located at the origin. The orientation of the dipole is given by the polar angle θ and the azimuthal angle ϕ. The direction of observation is in the x-z plane and is given by the angle α. The angle between the dipole and the direction of observation is β. (b) Decomposition of electric field E into s- and p-polarized components with respect to the x-z plane. ψ is the dihedral angle between planes AOB and AOC (which contains E).

Fig. 2
Fig. 2

Dipole p located a distance h from the top of a film with thickness d. D and R are the direct and indirect beams with the s- and p-polarized components indicated. Only the first of the transmitted components, excluding phase factors, is shown.

Fig. 3
Fig. 3

Calculated emission spectra I(s) = I(p) for normal emission vs relative optical-film thickness n0d/λ. The relative luminescent-layer thickness n0H/λ is much larger (smaller) than unity in a(b). The optical constants of the substrate and film are given in the text.

Fig. 4
Fig. 4

Calculated emission spectra I(s) = I(p) for normal emission vs inverse wavelength in units of 1/n0d. In (a) H = 0.1d, and in (b) H = 0.3d. Optical constants are the same as in Fig. 3. The beating effect due to the wide-angle interference is clearly evident.

Fig. 5
Fig. 5

Room-temperature cathodoluminescence spectrum of an SiO2 film (d = 82.5 nm) on an Si substrate for Vb = 0.8 kV and Ib = 37 μA. The correction for spectrometer efficiency has not been made. The interference fringes are so far apart that their effect is not obvious.

Fig. 6
Fig. 6

(a) Electron-energy loss in SiO2 for three beam voltages Vb for constant-beam current Ib at normal incidence. Electron range Re is obtained by extrapolation of the leading edge of the curves as indicated by the dashed lines. A triangular approximation to this energy-loss distribution used in the calculations is illustrated in the inset for 55° incidence, (b) Electron range Re in SiO2 as a function of beam voltage Vb.

Fig. 7
Fig. 7

(a) Calculated fit (dashed line) to the SiO2 cathodoluminescent data of Mitchell and Denure (solid line) as a function of film thickness. (b) Individual s- and p-polarized spectra whose sum is the dashed line in (a).

Fig. 8
Fig. 8

Experimental (circles) and calculated (lines) cathodoluminescence signal at λ = 290 nm as a function of SiO2 film thickness for four beam voltages: (a) Vb = 2.8 kV, Ib = 50 μA; (b) Vb = 1.6 kV, Ib = 50 μA; (c) Vb = 0.8 kV, Ib = 40 μA; and (d) Vb = 0.4 kV, Ib = 20 μA. The electron range and, therefore, the light-layer thickness are indicated by the rectangle along the abscissa. A 10-nm dead layer was used in the fits with s = 0.1 in (a) and (d) and with s = 0.3 in (b) and (c). The dashed line in (a) is the fit without a dead layer. Note the increase in fringe contrast as Vb decreases.

Fig. 9
Fig. 9

Experimental (solid lines) and calculated (dashed lines) cathodoluminescence spectra for a thick (d = 1.67 μm) SiO2 film as a function of wavelength for three beam voltages: (a) Vb = 3 kV, Ib = 0.11 μA; (b) Vb = 1.6 kV, Ib = 0.14 μA; and (c) Vb = 0.5 kV, Ib = 0.35 μA. The spectrum in (d) for a thin SiO2 film (d = 125 nm) with Vb = 1.6 kV was taken to be the band shape in the absence of interference effects. The fits included a dead layer with s = 0.2 and t = 15 nm.

Fig. 10
Fig. 10

(a) Experimental photoluminescence spectrum of an a-Si film with d = 2.0 μm on an Al substrate, (b) Calculated spectrum.

Equations (19)

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E k 2 p 0 4 π ε 0 n 2 r sin β ,
E ( s ) = E sin ψ ,
E ( p ) = E cos ψ ,
E ( s ) k 2 p 0 4 π ε 0 n 2 r sin θ sin ϕ ,
E ( p ) k 2 p 0 4 π ε 0 n 2 r ( cos θ sin α sin θ cos α cos ϕ ) .
cos ρ = sin α cos θ cos α sin θ cos ϕ .
P ( s ) = 3 n 1 3 cos 2 α 1 2 π n 0 ( n 1 cos α 1 + n 0 cos α 0 ) 2 × sin 2 θ sin 2 ϕ { 1 + [ ρ 02 ( s ) ] 2 + 2 ρ 02 ( s ) cos σ ( s ) } 1 + [ ρ 01 ( s ) ρ 02 ( s ) ] 2 2 ρ 01 ( s ) ρ 02 ( s ) cos Δ ( s ) ,
P ( p ) = 3 n 1 3 cos 2 α 1 2 π n 0 ( n 1 cos α 0 + n 0 cos α 1 ) 2 × 1 1 + ( ρ 01 ( p ) ρ 02 ( p ) ) 2 2 ρ 01 ( p ) ρ 02 ( p ) cos Δ ( p ) × { cos 2 θ sin 2 α 0 { 1 2 ρ 02 ( p ) cos σ ( p ) + [ ρ 02 ( p ) ] 2 } + sin 2 θ cos 2 α 0 cos 2 ϕ { 1 + 2 ρ 02 ( p ) cos σ ( p ) + [ ρ 02 ( p ) ] 2 } sin 2 θ sin 2 α 0 cos ϕ { 1 [ ρ 02 ( p ) ] 2 } / 2 } ,
σ ( s , p ) = 2 k z ( d h ) + δ 02 ( s , p ) ,
Δ ( s , p ) = 2 k z d + δ 01 ( s , p ) + δ 02 ( s , p ) ,
k z = 2 π ( n 0 / λ ) cos α 0 ,
r i j ( s ) = ρ i j ( s ) exp [ i δ i j ( s ) ] = n i cos α i n j cos α j n i cos α i + n j cos α j , r i j ( p ) = ρ i j ( p ) exp [ i δ i j ( p ) ] = n i cos α j n j cos α i n i cos α j + n j cos α i
P i ( s ) = n 1 3 cos 2 α 1 { 1 + [ ρ 02 ( s ) ] 2 + 2 ρ 02 ( s ) cos σ ( s ) } 2 π n 0 ( n 1 cos α 1 + n 0 cos α 0 ) 2 { 1 + [ ρ 01 ( s ) ρ 02 ( s ) ] 2 2 ρ 01 ( s ) ρ 02 ( s ) cos Δ ( s ) } ,
P i ( p ) = n 1 3 cos 2 α 1 { 1 + [ ρ 02 ( p ) ] 2 + 2 ρ 02 ( p ) cos 2 α 0 cos σ ( p ) } 2 π n 0 ( n 1 cos α 0 + n 0 cos α 1 ) 2 { 1 + [ ρ 01 ( p ) ρ 02 ( p ) ] 2 2 ρ 01 ( p ) ρ 02 ( p ) cos Δ ( p ) } .
I ( s , p ) = 0 H L ( h ) E ( h ) P i ( s , p ) d h ,
L ( h ) E ( h ) = { C 0 h H , 0 H h d ,
I ( s ) = n 1 3 cos 2 α 1 C H { 1 + [ ρ 02 ( s ) ] 2 + 2 ρ 02 ( s ) k z H cos [ k z ( 2 d H ) + δ 02 ( s ) ] sin ( k z H ) } 2 π n 0 ( n 1 cos α 1 + n 0 cos α 0 ) 2 { 1 + [ ρ 01 ( s ) ρ 02 ( s ) ] 2 2 ρ 01 ( s ) ρ 02 ( s ) cos Δ ( s ) } ,
I ( p ) = n 1 3 cos 2 α 1 C H { 1 + [ ρ 02 ( p ) ] 2 + 2 ρ 02 ( p ) cos 2 α 0 k z H cos [ k z ( 2 d H ) + δ 02 ( p ) ] sin ( k z H ) } 2 π n 0 ( n 1 cos α 0 + n 0 cos α 1 ) 2 { 1 + [ ρ 01 ( p ) ρ 02 ( p ) ] 2 2 ρ 01 ( p ) ρ 02 ( p ) cos Δ ( p ) } .
L ( h ) = s h t , L ( h ) = 1 h > t ,

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