Abstract

We propose a new type of photothermal spectroscopic technique. The experimental setup is simple and the experiment can be readily carried out, even in the difficult environments that are often required for optical and surface studies of materials. Features of the method proposed here are nondestructive and noncontact; in addition, the simplicity of our design enables us easily to make the system resistant to vibration and drift, which leads to a high signal-to-noise ratio of the photothermal signal. A few experiments have been conducted to demonstrate the utilization of the method, e.g., a quantum-radiative efficiency of surface polaritons in an air–Ag film–BK-7 prism geometry has been evaluated.

© 1992 Optical Society of America

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  1. A. C. Boccara, D. Fournier, J. Badoz, “Thermo-optical spectroscopy: detection by the “mirage effect”,” Appl. Phys. Lett. 36, 130–132 (1980).
    [CrossRef]
  2. M. A. Olmsted, N. M. Amer, S. Kohn, “Photothermal displacement spectroscopy: an optical probe for solids and surfaces,” Appl. Phys. A 32, 141–154 (1983).
    [CrossRef]
  3. M. A. Olmstead, N. M. Amer, “A new probe of the optical properties of surfaces,” J. Vac. Sci. Technol. B 1, 751–755 (1983).
    [CrossRef]
  4. J. Opsal, A. Rosencwaig, D. L. Willenborg, “Thermal-wave detection and thin-film thickness measurements with laser beam deflection,” Appl. Opt. 22, 3169–3176 (1983).
    [CrossRef] [PubMed]
  5. L. C. M. Miranda, “Photodisplacement spectroscopy of solids: theory,” Appl. Opt. 22, 2882–2886 (1983).
    [CrossRef] [PubMed]
  6. H. Dersh, N. M. Amer, “Direct method for the investigation of nonradiative recombination in semiconductors,” Appl. Phys. Lett. 47, 292–294 (1985).
    [CrossRef]
  7. P. Cielo, G. Rousset, L. Bertrand, “Photoacoustic and photothermal evaluation of stratified materials,” Appl. Opt. 25, 1327–1334 (1986).
    [CrossRef] [PubMed]
  8. J. T. Fanton, G. S. Kino, “High-sensitivity laser probe for photothermal measurements,” Appl. Phys. Lett. 51, 66–68 (1987).
    [CrossRef]
  9. E. L. Lasalle, F. Lepoutre, J. P. Roger, “Probe beam size effects in photothermal deflection experiments,” J. Appl. Phys. 64, 1–5 (1988).
    [CrossRef]
  10. T. Inagaki, Y. Nakagawa, E. T. Arakawa, D. J. Aas, “Photoacoustic determination of radiative quantum efficiency of surface plasmons in silver films,” Phys. Rev. B 26, 6421–6430 (1982).
    [CrossRef]
  11. Y. Naoi, M. Fukui, “Intensity of surface-plasmon polariton energy emitted into the air side in an air/Ag-film/prism configuration,” Phys. Rev. B 42, 5009–5012 (1990).
    [CrossRef]

1990

Y. Naoi, M. Fukui, “Intensity of surface-plasmon polariton energy emitted into the air side in an air/Ag-film/prism configuration,” Phys. Rev. B 42, 5009–5012 (1990).
[CrossRef]

1988

E. L. Lasalle, F. Lepoutre, J. P. Roger, “Probe beam size effects in photothermal deflection experiments,” J. Appl. Phys. 64, 1–5 (1988).
[CrossRef]

1987

J. T. Fanton, G. S. Kino, “High-sensitivity laser probe for photothermal measurements,” Appl. Phys. Lett. 51, 66–68 (1987).
[CrossRef]

1986

1985

H. Dersh, N. M. Amer, “Direct method for the investigation of nonradiative recombination in semiconductors,” Appl. Phys. Lett. 47, 292–294 (1985).
[CrossRef]

1983

L. C. M. Miranda, “Photodisplacement spectroscopy of solids: theory,” Appl. Opt. 22, 2882–2886 (1983).
[CrossRef] [PubMed]

J. Opsal, A. Rosencwaig, D. L. Willenborg, “Thermal-wave detection and thin-film thickness measurements with laser beam deflection,” Appl. Opt. 22, 3169–3176 (1983).
[CrossRef] [PubMed]

M. A. Olmsted, N. M. Amer, S. Kohn, “Photothermal displacement spectroscopy: an optical probe for solids and surfaces,” Appl. Phys. A 32, 141–154 (1983).
[CrossRef]

M. A. Olmstead, N. M. Amer, “A new probe of the optical properties of surfaces,” J. Vac. Sci. Technol. B 1, 751–755 (1983).
[CrossRef]

1982

T. Inagaki, Y. Nakagawa, E. T. Arakawa, D. J. Aas, “Photoacoustic determination of radiative quantum efficiency of surface plasmons in silver films,” Phys. Rev. B 26, 6421–6430 (1982).
[CrossRef]

1980

A. C. Boccara, D. Fournier, J. Badoz, “Thermo-optical spectroscopy: detection by the “mirage effect”,” Appl. Phys. Lett. 36, 130–132 (1980).
[CrossRef]

Aas, D. J.

T. Inagaki, Y. Nakagawa, E. T. Arakawa, D. J. Aas, “Photoacoustic determination of radiative quantum efficiency of surface plasmons in silver films,” Phys. Rev. B 26, 6421–6430 (1982).
[CrossRef]

Amer, N. M.

H. Dersh, N. M. Amer, “Direct method for the investigation of nonradiative recombination in semiconductors,” Appl. Phys. Lett. 47, 292–294 (1985).
[CrossRef]

M. A. Olmstead, N. M. Amer, “A new probe of the optical properties of surfaces,” J. Vac. Sci. Technol. B 1, 751–755 (1983).
[CrossRef]

M. A. Olmsted, N. M. Amer, S. Kohn, “Photothermal displacement spectroscopy: an optical probe for solids and surfaces,” Appl. Phys. A 32, 141–154 (1983).
[CrossRef]

Arakawa, E. T.

T. Inagaki, Y. Nakagawa, E. T. Arakawa, D. J. Aas, “Photoacoustic determination of radiative quantum efficiency of surface plasmons in silver films,” Phys. Rev. B 26, 6421–6430 (1982).
[CrossRef]

Badoz, J.

A. C. Boccara, D. Fournier, J. Badoz, “Thermo-optical spectroscopy: detection by the “mirage effect”,” Appl. Phys. Lett. 36, 130–132 (1980).
[CrossRef]

Bertrand, L.

Boccara, A. C.

A. C. Boccara, D. Fournier, J. Badoz, “Thermo-optical spectroscopy: detection by the “mirage effect”,” Appl. Phys. Lett. 36, 130–132 (1980).
[CrossRef]

Cielo, P.

Dersh, H.

H. Dersh, N. M. Amer, “Direct method for the investigation of nonradiative recombination in semiconductors,” Appl. Phys. Lett. 47, 292–294 (1985).
[CrossRef]

Fanton, J. T.

J. T. Fanton, G. S. Kino, “High-sensitivity laser probe for photothermal measurements,” Appl. Phys. Lett. 51, 66–68 (1987).
[CrossRef]

Fournier, D.

A. C. Boccara, D. Fournier, J. Badoz, “Thermo-optical spectroscopy: detection by the “mirage effect”,” Appl. Phys. Lett. 36, 130–132 (1980).
[CrossRef]

Fukui, M.

Y. Naoi, M. Fukui, “Intensity of surface-plasmon polariton energy emitted into the air side in an air/Ag-film/prism configuration,” Phys. Rev. B 42, 5009–5012 (1990).
[CrossRef]

Inagaki, T.

T. Inagaki, Y. Nakagawa, E. T. Arakawa, D. J. Aas, “Photoacoustic determination of radiative quantum efficiency of surface plasmons in silver films,” Phys. Rev. B 26, 6421–6430 (1982).
[CrossRef]

Kino, G. S.

J. T. Fanton, G. S. Kino, “High-sensitivity laser probe for photothermal measurements,” Appl. Phys. Lett. 51, 66–68 (1987).
[CrossRef]

Kohn, S.

M. A. Olmsted, N. M. Amer, S. Kohn, “Photothermal displacement spectroscopy: an optical probe for solids and surfaces,” Appl. Phys. A 32, 141–154 (1983).
[CrossRef]

Lasalle, E. L.

E. L. Lasalle, F. Lepoutre, J. P. Roger, “Probe beam size effects in photothermal deflection experiments,” J. Appl. Phys. 64, 1–5 (1988).
[CrossRef]

Lepoutre, F.

E. L. Lasalle, F. Lepoutre, J. P. Roger, “Probe beam size effects in photothermal deflection experiments,” J. Appl. Phys. 64, 1–5 (1988).
[CrossRef]

Miranda, L. C. M.

Nakagawa, Y.

T. Inagaki, Y. Nakagawa, E. T. Arakawa, D. J. Aas, “Photoacoustic determination of radiative quantum efficiency of surface plasmons in silver films,” Phys. Rev. B 26, 6421–6430 (1982).
[CrossRef]

Naoi, Y.

Y. Naoi, M. Fukui, “Intensity of surface-plasmon polariton energy emitted into the air side in an air/Ag-film/prism configuration,” Phys. Rev. B 42, 5009–5012 (1990).
[CrossRef]

Olmstead, M. A.

M. A. Olmstead, N. M. Amer, “A new probe of the optical properties of surfaces,” J. Vac. Sci. Technol. B 1, 751–755 (1983).
[CrossRef]

Olmsted, M. A.

M. A. Olmsted, N. M. Amer, S. Kohn, “Photothermal displacement spectroscopy: an optical probe for solids and surfaces,” Appl. Phys. A 32, 141–154 (1983).
[CrossRef]

Opsal, J.

Roger, J. P.

E. L. Lasalle, F. Lepoutre, J. P. Roger, “Probe beam size effects in photothermal deflection experiments,” J. Appl. Phys. 64, 1–5 (1988).
[CrossRef]

Rosencwaig, A.

Rousset, G.

Willenborg, D. L.

Appl. Opt.

Appl. Phys. A

M. A. Olmsted, N. M. Amer, S. Kohn, “Photothermal displacement spectroscopy: an optical probe for solids and surfaces,” Appl. Phys. A 32, 141–154 (1983).
[CrossRef]

Appl. Phys. Lett.

A. C. Boccara, D. Fournier, J. Badoz, “Thermo-optical spectroscopy: detection by the “mirage effect”,” Appl. Phys. Lett. 36, 130–132 (1980).
[CrossRef]

H. Dersh, N. M. Amer, “Direct method for the investigation of nonradiative recombination in semiconductors,” Appl. Phys. Lett. 47, 292–294 (1985).
[CrossRef]

J. T. Fanton, G. S. Kino, “High-sensitivity laser probe for photothermal measurements,” Appl. Phys. Lett. 51, 66–68 (1987).
[CrossRef]

J. Appl. Phys.

E. L. Lasalle, F. Lepoutre, J. P. Roger, “Probe beam size effects in photothermal deflection experiments,” J. Appl. Phys. 64, 1–5 (1988).
[CrossRef]

J. Vac. Sci. Technol. B

M. A. Olmstead, N. M. Amer, “A new probe of the optical properties of surfaces,” J. Vac. Sci. Technol. B 1, 751–755 (1983).
[CrossRef]

Phys. Rev. B

T. Inagaki, Y. Nakagawa, E. T. Arakawa, D. J. Aas, “Photoacoustic determination of radiative quantum efficiency of surface plasmons in silver films,” Phys. Rev. B 26, 6421–6430 (1982).
[CrossRef]

Y. Naoi, M. Fukui, “Intensity of surface-plasmon polariton energy emitted into the air side in an air/Ag-film/prism configuration,” Phys. Rev. B 42, 5009–5012 (1990).
[CrossRef]

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Figures (13)

Fig. 1
Fig. 1

Reflection of Gaussian beams from (a) a flat surface and (b) a disturbed surface. Although the directions of the incident light and the reflected light are drawn not to be normal to the sample surface, the light is directed to be almost normal to the sample surface in actual experiments. This is also true for the probe light depicted in Figs. 5 and 6.

Fig. 2
Fig. 2

Spatial distributions of (a) reflected light intensities and (b) a PTD intensity.

Fig. 3
Fig. 3

Reflection of light from a disturbed surface.

Fig. 4
Fig. 4

Reflection of light from a disturbed surface when the maximum point of intensity of the incident light coincides with that of u(x).

Fig. 5
Fig. 5

Experimental setup for metal films. Refer to information on the probe light described in the caption of Fig. 1.

Fig. 6
Fig. 6

Experimental setup for semiconductors. Refer to information on the probe light described in the caption of Fig. 1.

Fig. 7
Fig. 7

PTD intensity versus x for a Ag film.

Fig. 8
Fig. 8

Power density dependence of PTD intensity for a Ag film.

Fig. 9
Fig. 9

Surface displacement δ as a function of power density for a Ag film.

Fig. 10
Fig. 10

PTD intensity as a function of chopping frequency for a Ag film. The solid line denotes the 1/f characteristic.

Fig. 11
Fig. 11

Surface displacement versus chopping frequency for a Ag film. The solid line has the same meaning as that in Fig. 10.

Fig. 12
Fig. 12

Normalized PTD intensity (solid curve) and absorptance (Ab) (dots) versus angle of incidence of the pump light. The sample is a Ag film that is 50-nm thick.

Fig. 13
Fig. 13

Cross-sectional view of an attenuated-total-reflection configuration for calculating surface displacement of a Ag film.

Tables (1)

Tables Icon

Table I List of Parameters Employed in the Calculation of δ in the Air–Ag–BK-7 Prism Geometry

Equations (51)

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u ( x ) = δ exp ( - a x 2 ) .
z = D - u ( x 1 ) x p 1 - x 1 x + u ( x 1 ) x p 1 - D x 1 x p 1 - x 1 .
z = x 1 - x u ( x 1 ) + u ( x 1 ) .
ϕ 1 = tan [ 1 u ( x 1 ) ] - tan - 1 [ D - u ( x 1 ) x p 1 - x 1 ] .
D - u ( x 1 ) - ( x p 1 - x 1 ) tan ( π 2 - 2 ϕ 1 ) = 0.
y 0 r 2 [ 1 - ( 1 - C r ) exp ( - a x p 0 ) 2 ] ,
I u = pinhole I i d x d y ,
I i = I 0 exp [ - b ( x 2 + y 2 ) ] ,
I d = x 1 x 2 d x - y 0 y 0 d y I i .
P = I u - I d .
P = ( 1 - r 2 / x p 10 2 ) I u .
x p 10 r + D tan 2 ϕ .
tan 2 ϕ 2 tan ϕ = 2 u ( r ) = 4 a r δ exp ( - a r 2 ) .
x p 10 r + 4 a D r δ exp ( - a r 2 ) .
P 8 a D I u δ exp ( - a r 2 ) .
4 a D I u δ exp ( - a r 2 ) .
γ = 1 - normalized PTD signal A p ,
Q ( x ) = α I 0 β exp ( - 2 α x ) [ 1 + exp ( j w t ) ] ,
2 T f x 2 = 1 λ f T f t - α I 0 β κ s × exp ( - 2 α x ) [ 1 + exp ( j w t ) ]             for - 1 f x 0 ,
2 T p x 2 = 1 λ p T p t             for 0 x 1 p ,
2 T a x 2 = 1 λ a T a t             for x - 1 f ,
T p ( 1 p , t ) = 0 ,
T p ( 0 , t ) = T f ( 0 , t ) ,
T a ( - , t ) = 0 ,
T a ( - 1 f , t ) = T f ( - 1 f , t ) ,
κ p T p x ( 0 , t ) = κ f T f x ( 0 , t ) ,
κ a T a x ( - 1 , t ) = κ f T f x ( - 1 f , t ) .
T p ( x , t ) = T p 0 exp ( - σ p x ) exp ( j w t ) ,
T p 0 = - ( 1 + g ) ( 1 + r ) exp ( σ f l f ) + ( 1 - g ) ( 1 - r ) exp ( - σ f l f ) + 2 ( r + g ) exp ( 2 α l f ) ( 1 + g ) ( 1 + h ) exp ( σ f l f ) - ( 1 - g ) ( 1 - h ) exp ( - σ f l f ) T f 0 ,
T f 0 = I 0 β α / κ f ( 4 α 2 - σ f 2 ) ,
T f ( x , t ) = [ T f ( + ) exp ( σ f x ) + T f ( - ) exp ( - σ f x ) - T f 0 exp ( - 2 α x ) ] exp ( j w t ) ,
T f ( + ) = T f 0 = T f ( - ) + T p 0 ,
T ( - ) = ( 1 - g ) ( h - r ) exp ( - σ f l f ) + ( g + r ) ( 1 + h ) exp ( 2 α l f ) ( 1 + g ) ( 1 + h ) exp ( σ f l f ) - ( 1 - g ) ( 1 - h ) exp ( - σ f l f ) T f 0 .
2 R p x 2 - ρ p B p 2 R p t 2 = - ρ p α t h , p 2 t 2 T p ( x , t )             for 0 x 1 p ,
2 R f x 2 - ρ f B f 2 R f t 2 = - ρ f α t h , f 2 t 2 T f ( x , t )             for - 1 f x 0 ,
R p ( 1 p ) = 0 ,
R f ( - 1 f ) = 0 ,
R f ( 0 ) = R p ( 0 ) = 0.
R p ( x , t ) = { D p T p 0 2 A p [ b 1 exp ( A p x ) + b 2 exp ( - A p x ) ] - D p T p 0 A p 2 - σ p 2 exp ( - σ p x ) } exp ( j w t )             for 0 x 1 p ,
R f ( x , t ) = { D f 2 A f [ C 1 exp ( A f x ) + C 2 exp ( - A f x ) ] - D f A f 2 - σ f 2 [ T f ( + ) exp ( - σ f x ) + T f ( - ) exp ( - σ f x ) ] + D f T f 0 A f 2 - 4 α 2 exp ( - 2 α x ) } exp ( j w t )             for - 1 f x 0 ,
b 1 = 2 A [ exp ( - σ p 1 p ) - exp ( - A p 1 p ) ] ( A p 2 - σ p 2 ) [ exp ( A p 1 p ) - exp ( - A p 1 p ) ] ,
b 2 = - b 1 ( A p A p ) ,
C 1 = 1 [ exp ( - A f 1 f ) - exp ( A f 1 f ) ] ( 1 4 L 1 { T f ( + ) [ exp ( - σ f 1 f ) - exp ( A f 1 f ) ] + T f ( - ) [ exp ( σ f 1 f ) - exp ( A f 1 f ) ] } - L 2 T f 0 [ exp ( 2 α 1 f ) - exp ( A f 1 f ) ] ) ,
C 2 = - C 1 ( L 1 , 2 - L 1 , 2 , A f - A f ) ,
L 1 = 2 A f A f 2 - σ f 2 ,
L 2 = 2 A f A f 2 - 4 α 2 ,
A i 2 = - ρ i ω 2 B i ( i = p , f ) ,
D i 2 = ρ i α t h , i ω 2 ( i = p , f ) .
δ = [ 1 ω 2 ρ f R f ( x ) x ] x = - 1 f + [ 1 ω 2 ρ p R p ( x ) x ] x = 0 = ( δ f + δ p ) exp ( j w t ) ,
δ f = D f ω 2 ρ f { 1 2 [ C 1 exp ( - A f 1 f ) - C 2 exp ( A f 1 f ) ] - σ f A f 2 - σ f 2 × [ T f ( + ) exp ( - σ f 1 f ) - T f ( - ) exp ( σ f 1 f ) ] - 2 α A f 2 - 4 α 2 T f 0 exp ( 2 α 1 f ) } ,
δ p = D p T p 0 ω 2 ρ p ( b 1 - b 2 + σ p A p 2 - σ p 2 ) .

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