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Laser reflectance relaxation spectroscopy: Determination of thermal diffusivity in thin films of gold
Solid State Communications,
Vol. 13, PP. 1845—1849, 1973.
Pergamon Press.
Printed in Great Britain
LASER REFLECTANCE RELAXATION SPECFROSCOPY: DETERMINATION OF THERMAL DIFFUSIVITY IN THIN FILMS OF GOLD Y. Yeh and F. Wooten Department of Applied Science, University of California, Davis, California 95616, U.S.A. and T. Huen Lawrence Livermore Laboratory, University of California, Livermore, California 94550, U.S.A. (Received 21 August 1973 by S. Lundqvist)
The technique of thermal modulation is applied to the study of transient thermal properties of thin films of Au. Relaxation spectra as seen in the reflected laser light give a value the thermal diffusivity Au as 2!sec, comparable to for previous data for the bulk of metal. 1.2 cm Versatility and potentials of the laser reflectance relaxation spectroscopy are discussed.
RELAXATION spectroscopy is widely used as a powerful technique for obtaining rate information on systems as they approach equilibrium irreversibly. In the present experiment, we have applied a version of the temperature jump technique’ to study thermal diffusion in thin films of gold. The essence of the experiment can be explained with the help of Fig. 1. A gold film having the shape of an H is evaporated onto a glass substrate. A square wave current is passed through the gold film between the electrode contacts. The result is a sequence of heat pulses and a periodic variation of temperature of the film between the electrodes. The process of redistribution of heat results in a series of heat pulses along the crossbar of the gold film. This redistribution is governed by the thermal conductivity and thermal diffusivity of the film. Since the optical reflectance of the gold film is temperature dependent, shining light onto the film provides a modulated reflected light signal which serves as a very sensitive monitor of both the steady
coherent, it can be localized on the surface to the size of an Airy disc,2 A2, where A is the laser wavelength. Then the measured reflectance from specific regions of the surface provides an accurate probe of the local thermal response of the gold film. Thus, if the reflectance of the gold film is monitored at, say, point a in Fig. 1, it is found that the reflectivity varies in magnitude at the same frequency as the square wave heating current. At points b, c, and so on along the crossbar, the reflectance also varies at the same frequency but with a reduced magnitude and delayed in time because of heat losses through the glass substrate and the finite thermal diffusivity of the gold film. Analysis of the data permits determination of the thermal diffusivity. To see how one determines thermal diffusivity, we begin by considering the temperature dependence of reflectance. The incident and reflected electric fields, E 1 and E7., respectively, are related by the equation
state and transient thermal behavior of the gold film. When the light is provided by a laser so that it is
— —
*
()~J j,
Work performed under the auspices of the U.S.
where p() is the complex reflection coefficient and
Atomic Energy Commission.
e is the dielectric constant of the material. If the 1845
1846 Laser
DETERMINATION OF THERMAL DIFFUS1VITY IN THIN FILMS OF GOLD Vol. 13, No. 11
Signal
~
~
~ \L~J
r
To the the firstcontribution order in temperature variation, 2 term. we may ignore of the (&p(T)) Equation (3), in its approximate form, is that commonly encountered in thermal modulation experiments.3’4 In particular, ifIfto = 1 0R is the steady state reflected intensity, then
_________ ________
J
[mcrnitc~
8p\
(~)~ = 2&p(T)
film
_______
Syn.
i
___________
I nhance
~Sw1tch ________
Power
~a’ ~aT1
(~~
2 —)~—)~T =
______________
Po
Po
(4)
necessary to determine 5p(T, r, t). Equation (2) will In order to examine transient effects, it is be replaced by
ap
Electrode
6px(T,r,t)
—
ae~(r)\ ~
—
_____
)
~T(r,
t).
(5)
note that Here, filmthe homogeneity specification hasofbeen wavelength assumed.is We important also
-
because e and p are strong functions of A. Electrode
_______________________
_________________________
FIG. 1. Schematic diagTam of reflection relaxation spectrometer. A square wave current of 8A and having a 50% duty cycle was passed through the gold film. Reflection data from points a, b, c, etc., were taken along the z-axis (Insert). The glass substrate was attached to a copper block with a heat sink adhesive so as to make good thermal contact. reflection coefficient is temperature dependent because of a temperature dependent dielectric constant, then p(e) ~p(e(T))_~p0(e(To))
/8p\ be
T E Po + ~p(T)
Since all time dependence is embodied in the variations of z~ T, we see that the local thermal behavior of the surface significantly affects the observed 6p~(T,r, t). To study the problem quantitatively, consider an infinitesimally narrow strip of metallic film deposited on some suitable substrate. Upon application of a pulse of heat to one end of this strip, z = 0, we ask for the response of the strip at z >0 to such an impulse of heat. Basically, one has to solve the temperature diffusion equation subject to an initial heat impulse applied at one end (z = 0) and an appropriate heat leak to the substrate below. This problem is best solved by examining the two-dimensional flow of heat along the film and into the substrate, assuming the temperature across the depth of the film, 1, is to be constant. If the substrate is thick relative to the film, it can be considered to extend to + oo along the y-direction.
(2)
where ~ T = T T0. The magnitude of the temperature effect depends on (ap/ae) (ac/aT) and the local temperature differential, ~ T. Upon detection by a photosensitive det. tor the photocurrent is IR(T) = 1 2Po &p(T) + (6p(T))2) (3) where 0(R + ‘R (T) = I E, 12,10 = I E~12, R = IPo 12. —
The appropriate diffusion equation for the film along the z-direction is given by 2 T(z,t) I aT(z,r) = 0 (6) —
a az2
K
at
where K is the thermal diffusivity of the film and its temperature is T(z, t).
DETERMINATION OF THERMAL DIFFUSIVITY IN THIN FILMS OF GOLD
Vol. 13, No. 11
Assuming perfect thermal contact at thefilm substrate interface, the heat dissipation into the substrate,y-direction, evaluated at y = 0, is given by ~
K’aT loT
=0,
-___________________________________
4
(7)
3-
where K’ arid K are the thermal conductivities of the substrate and the film respectively. Here the temperature of the substrate is assumed to equal T at y = 0 consistent with our assumptions.
2 ~ x
=
Temperature Pulse (r).
~
c
(8)
Even though the applied voltage pulse is accurately represented as a step function, the resultant temperature pulse is modified by the thermal leak rate into the substrate even at z = 0. It is possible to show that for thin films, when the voltage pulse is a step function, that A0! Temperature Pulse (0, t) =
-~-
A/E~.
(9)
The solution to equation (6), subject to the conditions where A0 is the applied power density and K’ is the thermal diffusivity of the substrate, described above, can be found using Lapi~cetransform techniques. On the surfacey = 0,
T~z,t) ~ T(0, t) 2ierfc
( ) I
z
-
1-
At the one end of the film, z = 0, T(0, t)
1847
-l
-
-2
-
—3
—
‘S ‘S
2.0
‘S —
‘S
—
I 2.1
I 2.2
I 2.3
I 2.4 2.5
I 2.6
I 2.7 2.8
Photon energy (eV) FIG. 2. (IR)ac/IRO vs hv(eV). Measurements were made at the six laser wavelengths 5145 A (2.44 eV), 5017 A (2.47 eV) 4965 A (2.52 eV), 4880 A (2.56 eV), 4765 A (2.62 eV), 4579 A (2.74eV). Scouler’s curve (---) is approximated from reference 5. I
48bu vine
0.7—
\
(10)
2~t
5 proportional Since diffusivity the change ofto thethe in film reflection chai~ge can beindetermined temperature, coefficient by is the directly knowing thermal where 2ierfc (x) can be found in standa;d texts. the reflectance at z = 0 and z> 0.
U VS
0.5 04 0 0.~ -
0
000~
0 00
~ 0.2
In the present experiment, no attempt was made to measure the absolute temperature of the film, instead, all of the measurements were normalized to a fixed value of ‘RO• An Ar~laser, capable of providing 6 wavelengths near the band edge of Au was used as the light source. The focused spot on the surface of the film was imaged on an SD 100 photodiode. Signal averaging was accomplished through the use of an SAI-42 100 channel correlation analyzer operating in the digital enhancement mode. The differentiated driving pulse also provided the external synchronization for a display of the 100 ms period,
0.1 00
5
10
~ io2 (sec)
15
20
FIG. 3. Time dependence of the temperature of the film at the film-substrate interface. The circles are experimental values. An initial experiment was performed to confirm equation (4) and to corroborate the results of Scouler5 on the temperature modulated reflectance of gold at
1848
DETERMINATION OF THERMAL DIFFUSIVITY IN THIN FILMS OF GOLD
1 20°K.Our experiments were all room temperature studies. For a fixed current of 8 A through the sample and a fixed reflection location, the six laser wavelengths were used to establish a plot of (ZR )aJIRo vs photon energy (Fig. 2). The results are shown in comparison with Scouler’s data. All (JR)~~ values used were steady state, approximately 25 msec after pulse application. The agreement with Scouler is good, and a well defined zero (lR)~was seen at 2.50 ±0.01 eV. There is apparently little change in the spectra from 120°C to room temperature. Similar experiments have been reported for HgTe using a CO 7 2 laser. In order to determine the thermal diffusivity of the film, it is necessary to first determine T(0,t). Using the laser excitation at 4880 A, where a maximum of (IR)~was observed, we examine the reflectance vs time profile. In Fig. 3, the first 17.5 msec of the transient response at z = 0 is plotted against t”2. The slope of this straight line curve is proportional to the magnitude of the applied current and to the thermal conductivity and diffusivity of the glass substrate. In the absence of absolute measurements of ~5p,it was not possible to check the various quantitive values involved, however, equation (9) is verified. Upon knowing T(0, t) the experiment was performed at four different z values. From the ratios T(z, r/2)/T(0, r/2) one obtainsR = 2ierfc(z/2~,/KT/2). Here r/2 is the terminus of the applied square pulse. In Fig. 4, such a plot of R (z) vs z is shown together with the fits to the theoretical arguments of 2ierfc (x). It is seen that our data fits well to a diffusivity value between ~ = 1.0 and K 1.5. From Carsiaw and Jaeger,5 the bulk value for Au is ~ 1.2 cm2!sec. It is interesting to note that at z = 1 mm, the observed value of temperature or reflectance rise far exceeds that predicted. This is because th~finite breadth of the film allows a certain amount of fringing field with a component directed along the z-axis. It should also be noted that in fitting the data to the theoretical results of equation (10), we have assumed a single pulse transient response. Since the actual experiment is conducted with repetitive pulsing of heat, a more accurate analysis must take that into consideration. We have shown here that laser reflectance relaxation spectroscopy can be used to obtain
Vol. 13, No. 11
1.
I
2/sec
1.5 cm
1.0
1.0 cm2/sec ,~
0.5
0.5 cm2/sec
-
-
I
I
I
2
3
4
5
z FIG. 4. R(z) vs z. The five experimental points correspond to R(z) = T(z, r/2)/T(O, r/2). Theoretical curves of R(z) 2ierfc(z/2s,/Kr/2) are shown for three values of ~. The large deviation from theory of the measured point at 1 mm arises from fringing field effects, meaningful values ofK and K for thin films of metals. It is possible to extend the measurements to semiconductors and semimetals, as well as to many other methods of reflectance changes, e.g., electric field modulation, pressure modulation, or anisotropy modulation.4 The present technique can also be of immense importance for determining heat dissipation properties of solar reflectors as proposed in solar farm configurations.8 In that case, pulse laser heating9 and localized laser monitoring would have to be incorporated. In principle, therefore, the present technique can provide accurate in situ measurements of surface properties necessary for the prediction of lifetimes of these collectorsand reflectors, whether those lifetimes are due to thermal deterioration or chemical ~ Finally, this use of a laser reflectance monitor as a zero heat capacity probe would be
Vol. 13, No. 11
DETERMINATION OF THERMAL DIFFUSIVITY IN THIN FILMS OF GOLD
significantly more advantageous than present methods which are generally limited to measurements on bulk
1849
samples because of the use of thermocouple probes’1 having a significant inherent heat capacity.
REFERENCES I.
EIGEN M. and DEMAEYER L., Relaxation methods in Techniques ofOrganic Chemistry VII—2, (Edited by FRIESS S.L., LEWIS E.S. and WEISSBERGER A., ) Interscience Publishers (1963), p. 895.
2. 3.
SIEGMAN A.E., An Introduction to Lasers and Masers, p. 316 McGraw-Hill,New York (1971). CAIWONA M., Temperature modulation in Modulation Spectroscopy, p. 117 Academic Press New York (1969). First mt. Conf on Modulation Spectroscopy, Tuscon, Arizona, November, 1972. Proceesings to be published.
4.
6. 7.
CARSLAW H.S. and JAEGER J.C., Conduction ofHeat in Solids, c.f. ch. 1, ch. 12. Clarendon Press, Oxford, (1959). SCOULERW.J.,Phys. Rev. Lett. 18,445(1967). RAYMOND F. and VERIE C., Infrared laser modulation spectroscopy (in Reference 4).
8.
MEINEL A.B. and MEINEL M.P., Phys. Today 25,44(1972).
5.
9. 10. 11.
SCHRIEMPH J.T., High Temp-High Pres. 4, 411(1972). JASPERSON S.N., BARGE D.K. and O’HANDLEY R.C., a modulated ellipsometer for studying thin films, optical properties, and surface dynamics (in Reference 4). DANIELSON G.C. and SIDLES P.H., thermal diffusivity and other non-steady-state methods, Thermal Conductivity, p. 149, (Edited by TYE R.P., Academic Press (1969).
Das Verfahren thermischer Modulation wird in der Untersuchung der thermischen Eigenschaften von dünner Gold Filmer augewandt. Relaxationsspektra gemessen an der reflektierten Laser.strahlung orgeben für die thernilsche Diffusivität einen Wert von ~ = 1.2 cm2/sec. ahnlich dem früher gemessenen Wert fur Festmassen. Verschiedene Anwendungen und Vorteile der Laser-Reflesionspektroskopie werden diskutiert.
Vol. 13, PP. 1845—1849, 1973.
Pergamon Press.
Printed in Great Britain
LASER REFLECTANCE RELAXATION SPECFROSCOPY: DETERMINATION OF THERMAL DIFFUSIVITY IN THIN FILMS OF GOLD Y. Yeh and F. Wooten Department of Applied Science, University of California, Davis, California 95616, U.S.A. and T. Huen Lawrence Livermore Laboratory, University of California, Livermore, California 94550, U.S.A. (Received 21 August 1973 by S. Lundqvist)
The technique of thermal modulation is applied to the study of transient thermal properties of thin films of Au. Relaxation spectra as seen in the reflected laser light give a value the thermal diffusivity Au as 2!sec, comparable to for previous data for the bulk of metal. 1.2 cm Versatility and potentials of the laser reflectance relaxation spectroscopy are discussed.
RELAXATION spectroscopy is widely used as a powerful technique for obtaining rate information on systems as they approach equilibrium irreversibly. In the present experiment, we have applied a version of the temperature jump technique’ to study thermal diffusion in thin films of gold. The essence of the experiment can be explained with the help of Fig. 1. A gold film having the shape of an H is evaporated onto a glass substrate. A square wave current is passed through the gold film between the electrode contacts. The result is a sequence of heat pulses and a periodic variation of temperature of the film between the electrodes. The process of redistribution of heat results in a series of heat pulses along the crossbar of the gold film. This redistribution is governed by the thermal conductivity and thermal diffusivity of the film. Since the optical reflectance of the gold film is temperature dependent, shining light onto the film provides a modulated reflected light signal which serves as a very sensitive monitor of both the steady
coherent, it can be localized on the surface to the size of an Airy disc,2 A2, where A is the laser wavelength. Then the measured reflectance from specific regions of the surface provides an accurate probe of the local thermal response of the gold film. Thus, if the reflectance of the gold film is monitored at, say, point a in Fig. 1, it is found that the reflectivity varies in magnitude at the same frequency as the square wave heating current. At points b, c, and so on along the crossbar, the reflectance also varies at the same frequency but with a reduced magnitude and delayed in time because of heat losses through the glass substrate and the finite thermal diffusivity of the gold film. Analysis of the data permits determination of the thermal diffusivity. To see how one determines thermal diffusivity, we begin by considering the temperature dependence of reflectance. The incident and reflected electric fields, E 1 and E7., respectively, are related by the equation
state and transient thermal behavior of the gold film. When the light is provided by a laser so that it is
— —
*
()~J j,
Work performed under the auspices of the U.S.
where p() is the complex reflection coefficient and
Atomic Energy Commission.
e is the dielectric constant of the material. If the 1845
1846 Laser
DETERMINATION OF THERMAL DIFFUS1VITY IN THIN FILMS OF GOLD Vol. 13, No. 11
Signal
~
~
~ \L~J
r
To the the firstcontribution order in temperature variation, 2 term. we may ignore of the (&p(T)) Equation (3), in its approximate form, is that commonly encountered in thermal modulation experiments.3’4 In particular, ifIfto = 1 0R is the steady state reflected intensity, then
_________ ________
J
[mcrnitc~
8p\
(~)~ = 2&p(T)
film
_______
Syn.
i
___________
I nhance
~Sw1tch ________
Power
~a’ ~aT1
(~~
2 —)~—)~T =
______________
Po
Po
(4)
necessary to determine 5p(T, r, t). Equation (2) will In order to examine transient effects, it is be replaced by
ap
Electrode
6px(T,r,t)
—
ae~(r)\ ~
—
_____
)
~T(r,
t).
(5)
note that Here, filmthe homogeneity specification hasofbeen wavelength assumed.is We important also
-
because e and p are strong functions of A. Electrode
_______________________
_________________________
FIG. 1. Schematic diagTam of reflection relaxation spectrometer. A square wave current of 8A and having a 50% duty cycle was passed through the gold film. Reflection data from points a, b, c, etc., were taken along the z-axis (Insert). The glass substrate was attached to a copper block with a heat sink adhesive so as to make good thermal contact. reflection coefficient is temperature dependent because of a temperature dependent dielectric constant, then p(e) ~p(e(T))_~p0(e(To))
/8p\ be
T E Po + ~p(T)
Since all time dependence is embodied in the variations of z~ T, we see that the local thermal behavior of the surface significantly affects the observed 6p~(T,r, t). To study the problem quantitatively, consider an infinitesimally narrow strip of metallic film deposited on some suitable substrate. Upon application of a pulse of heat to one end of this strip, z = 0, we ask for the response of the strip at z >0 to such an impulse of heat. Basically, one has to solve the temperature diffusion equation subject to an initial heat impulse applied at one end (z = 0) and an appropriate heat leak to the substrate below. This problem is best solved by examining the two-dimensional flow of heat along the film and into the substrate, assuming the temperature across the depth of the film, 1, is to be constant. If the substrate is thick relative to the film, it can be considered to extend to + oo along the y-direction.
(2)
where ~ T = T T0. The magnitude of the temperature effect depends on (ap/ae) (ac/aT) and the local temperature differential, ~ T. Upon detection by a photosensitive det. tor the photocurrent is IR(T) = 1 2Po &p(T) + (6p(T))2) (3) where 0(R + ‘R (T) = I E, 12,10 = I E~12, R = IPo 12. —
The appropriate diffusion equation for the film along the z-direction is given by 2 T(z,t) I aT(z,r) = 0 (6) —
a az2
K
at
where K is the thermal diffusivity of the film and its temperature is T(z, t).
DETERMINATION OF THERMAL DIFFUSIVITY IN THIN FILMS OF GOLD
Vol. 13, No. 11
Assuming perfect thermal contact at thefilm substrate interface, the heat dissipation into the substrate,y-direction, evaluated at y = 0, is given by ~
K’aT loT
=0,
-___________________________________
4
(7)
3-
where K’ arid K are the thermal conductivities of the substrate and the film respectively. Here the temperature of the substrate is assumed to equal T at y = 0 consistent with our assumptions.
2 ~ x
=
Temperature Pulse (r).
~
c
(8)
Even though the applied voltage pulse is accurately represented as a step function, the resultant temperature pulse is modified by the thermal leak rate into the substrate even at z = 0. It is possible to show that for thin films, when the voltage pulse is a step function, that A0! Temperature Pulse (0, t) =
-~-
A/E~.
(9)
The solution to equation (6), subject to the conditions where A0 is the applied power density and K’ is the thermal diffusivity of the substrate, described above, can be found using Lapi~cetransform techniques. On the surfacey = 0,
T~z,t) ~ T(0, t) 2ierfc
( ) I
z
-
1-
At the one end of the film, z = 0, T(0, t)
1847
-l
-
-2
-
—3
—
‘S ‘S
2.0
‘S —
‘S
—
I 2.1
I 2.2
I 2.3
I 2.4 2.5
I 2.6
I 2.7 2.8
Photon energy (eV) FIG. 2. (IR)ac/IRO vs hv(eV). Measurements were made at the six laser wavelengths 5145 A (2.44 eV), 5017 A (2.47 eV) 4965 A (2.52 eV), 4880 A (2.56 eV), 4765 A (2.62 eV), 4579 A (2.74eV). Scouler’s curve (---) is approximated from reference 5. I
48bu vine
0.7—
\
(10)
2~t
5 proportional Since diffusivity the change ofto thethe in film reflection chai~ge can beindetermined temperature, coefficient by is the directly knowing thermal where 2ierfc (x) can be found in standa;d texts. the reflectance at z = 0 and z> 0.
U VS
0.5 04 0 0.~ -
0
000~
0 00
~ 0.2
In the present experiment, no attempt was made to measure the absolute temperature of the film, instead, all of the measurements were normalized to a fixed value of ‘RO• An Ar~laser, capable of providing 6 wavelengths near the band edge of Au was used as the light source. The focused spot on the surface of the film was imaged on an SD 100 photodiode. Signal averaging was accomplished through the use of an SAI-42 100 channel correlation analyzer operating in the digital enhancement mode. The differentiated driving pulse also provided the external synchronization for a display of the 100 ms period,
0.1 00
5
10
~ io2 (sec)
15
20
FIG. 3. Time dependence of the temperature of the film at the film-substrate interface. The circles are experimental values. An initial experiment was performed to confirm equation (4) and to corroborate the results of Scouler5 on the temperature modulated reflectance of gold at
1848
DETERMINATION OF THERMAL DIFFUSIVITY IN THIN FILMS OF GOLD
1 20°K.Our experiments were all room temperature studies. For a fixed current of 8 A through the sample and a fixed reflection location, the six laser wavelengths were used to establish a plot of (ZR )aJIRo vs photon energy (Fig. 2). The results are shown in comparison with Scouler’s data. All (JR)~~ values used were steady state, approximately 25 msec after pulse application. The agreement with Scouler is good, and a well defined zero (lR)~was seen at 2.50 ±0.01 eV. There is apparently little change in the spectra from 120°C to room temperature. Similar experiments have been reported for HgTe using a CO 7 2 laser. In order to determine the thermal diffusivity of the film, it is necessary to first determine T(0,t). Using the laser excitation at 4880 A, where a maximum of (IR)~was observed, we examine the reflectance vs time profile. In Fig. 3, the first 17.5 msec of the transient response at z = 0 is plotted against t”2. The slope of this straight line curve is proportional to the magnitude of the applied current and to the thermal conductivity and diffusivity of the glass substrate. In the absence of absolute measurements of ~5p,it was not possible to check the various quantitive values involved, however, equation (9) is verified. Upon knowing T(0, t) the experiment was performed at four different z values. From the ratios T(z, r/2)/T(0, r/2) one obtainsR = 2ierfc(z/2~,/KT/2). Here r/2 is the terminus of the applied square pulse. In Fig. 4, such a plot of R (z) vs z is shown together with the fits to the theoretical arguments of 2ierfc (x). It is seen that our data fits well to a diffusivity value between ~ = 1.0 and K 1.5. From Carsiaw and Jaeger,5 the bulk value for Au is ~ 1.2 cm2!sec. It is interesting to note that at z = 1 mm, the observed value of temperature or reflectance rise far exceeds that predicted. This is because th~finite breadth of the film allows a certain amount of fringing field with a component directed along the z-axis. It should also be noted that in fitting the data to the theoretical results of equation (10), we have assumed a single pulse transient response. Since the actual experiment is conducted with repetitive pulsing of heat, a more accurate analysis must take that into consideration. We have shown here that laser reflectance relaxation spectroscopy can be used to obtain
Vol. 13, No. 11
1.
I
2/sec
1.5 cm
1.0
1.0 cm2/sec ,~
0.5
0.5 cm2/sec
-
-
I
I
I
2
3
4
5
z FIG. 4. R(z) vs z. The five experimental points correspond to R(z) = T(z, r/2)/T(O, r/2). Theoretical curves of R(z) 2ierfc(z/2s,/Kr/2) are shown for three values of ~. The large deviation from theory of the measured point at 1 mm arises from fringing field effects, meaningful values ofK and K for thin films of metals. It is possible to extend the measurements to semiconductors and semimetals, as well as to many other methods of reflectance changes, e.g., electric field modulation, pressure modulation, or anisotropy modulation.4 The present technique can also be of immense importance for determining heat dissipation properties of solar reflectors as proposed in solar farm configurations.8 In that case, pulse laser heating9 and localized laser monitoring would have to be incorporated. In principle, therefore, the present technique can provide accurate in situ measurements of surface properties necessary for the prediction of lifetimes of these collectorsand reflectors, whether those lifetimes are due to thermal deterioration or chemical ~ Finally, this use of a laser reflectance monitor as a zero heat capacity probe would be
Vol. 13, No. 11
DETERMINATION OF THERMAL DIFFUSIVITY IN THIN FILMS OF GOLD
significantly more advantageous than present methods which are generally limited to measurements on bulk
1849
samples because of the use of thermocouple probes’1 having a significant inherent heat capacity.
REFERENCES I.
EIGEN M. and DEMAEYER L., Relaxation methods in Techniques ofOrganic Chemistry VII—2, (Edited by FRIESS S.L., LEWIS E.S. and WEISSBERGER A., ) Interscience Publishers (1963), p. 895.
2. 3.
SIEGMAN A.E., An Introduction to Lasers and Masers, p. 316 McGraw-Hill,New York (1971). CAIWONA M., Temperature modulation in Modulation Spectroscopy, p. 117 Academic Press New York (1969). First mt. Conf on Modulation Spectroscopy, Tuscon, Arizona, November, 1972. Proceesings to be published.
4.
6. 7.
CARSLAW H.S. and JAEGER J.C., Conduction ofHeat in Solids, c.f. ch. 1, ch. 12. Clarendon Press, Oxford, (1959). SCOULERW.J.,Phys. Rev. Lett. 18,445(1967). RAYMOND F. and VERIE C., Infrared laser modulation spectroscopy (in Reference 4).
8.
MEINEL A.B. and MEINEL M.P., Phys. Today 25,44(1972).
5.
9. 10. 11.
SCHRIEMPH J.T., High Temp-High Pres. 4, 411(1972). JASPERSON S.N., BARGE D.K. and O’HANDLEY R.C., a modulated ellipsometer for studying thin films, optical properties, and surface dynamics (in Reference 4). DANIELSON G.C. and SIDLES P.H., thermal diffusivity and other non-steady-state methods, Thermal Conductivity, p. 149, (Edited by TYE R.P., Academic Press (1969).
Das Verfahren thermischer Modulation wird in der Untersuchung der thermischen Eigenschaften von dünner Gold Filmer augewandt. Relaxationsspektra gemessen an der reflektierten Laser.strahlung orgeben für die thernilsche Diffusivität einen Wert von ~ = 1.2 cm2/sec. ahnlich dem früher gemessenen Wert fur Festmassen. Verschiedene Anwendungen und Vorteile der Laser-Reflesionspektroskopie werden diskutiert.