Optics: measuring and testing – Material strain analysis – By light interference detector
Reexamination Certificate
2000-04-12
2002-10-15
Kim, Robert H. (Department: 2882)
Optics: measuring and testing
Material strain analysis
By light interference detector
C356S496000, C356S511000, C356S512000
Reexamination Certificate
active
06466308
ABSTRACT:
FIELD OF THE INVENTION
The present invention is related to a method for measuring a thermal expansion coefficient of a thin film by using phase shifting interferometry, and more particularly to a method for measuring a thermal expansion coefficient, intrinsic stress and an elastic modulus of a thin film simultaneously by using phase shifting interferometry.
BACKGROUND OF THE INVENTION
Tantalum pentoxide (Ta
2
O
5
) dielectric film has a high refractive index in the visible region with a wide transmission range extending from 300 nm to about 10 &mgr;m. Ta
2
O
5
coatings are widely used in both optical and electronic applications. Some of these applications are as antireflection coatings, optical waveguides, metal oxide semiconductor (MOS) devices, insulator in electronic devices, and as narrow-bandpass filters. The temperature stability of optical coatings has become more and more important, especially for optical telecommunications. Narrow-bandpass filters (NBF) are the key components in the elimination of noise in fibre amplifiers and for wavelength selection in high-density wavelength-division-multiplexed systems. One of the key design parameters in the NBF is the coefficient of thermal expansion (CTE). In general, thermal effects provide important contributions to film stress. Films prepared at an elevated temperature and cooled to room temperature will be thermally strained.
For a thin film deposited on a substrate, a stress of the thin film will cause the substrate deflect downward or upward. The deflection is downward for a tensile stress and upward for a compressive stress. In either case, the thin film might detach from the substrate when the stress is too large. The stress of the thin film is composed of two components, which are intrinsic stress, &sgr;
i
, and thermal stress, &sgr;
T
, if no external stress is exerted thereon. The intrinsic stress is a result of interaction between the growth modes and the microstructure of the thin film, and the thermal stress is caused by different values of thermal expansion coefficients between the thin film and the substrate. The thermal stress can be represented by the following formula:
σ
T
=
(
α
s
-
α
f
)
E
f
(
1
-
v
f
)
(
T
2
-
T
1
)
wherein &agr;
s
is the thermal expansion coefficient of the substrate, &agr;
f
and E
f
are the thermal expansion coefficient and Young's modulus of the thin film, respectively, &ngr;
f
is Poisson's ratio of the thin film, T
1
is a deposition temperature of the thin film. It can be understood from the above formula, the thermal stress, &sgr;
T
, at a measuring temperature, T
2
, can be calculated if &agr;
s
, &agr;
f
and
E
f
(
1
-
v
f
)
are known. The stress of the thin film at measuring temperature, T
2
, can also be obtained if the intrinsic stress, &sgr;
i
, is known. Briefly, the &agr;
f
and
E
f
(
1
-
v
f
)
so measured will enable a person calculate, in advance, a stress of the thin film deposited on the substrate at a pre-determined temperature.
A number of techniques for measuring the thermal expansion coefficients of thin films have been developed, such as the interference fringe method, the optical levered laser technique, the bending beam technique and the capacitance cell method. In these techniques, the principle of measurement is detecting the deflections caused by the stress of the thin film at different temperatures, and calculating th hermal expansion coefficient, intrinsic stress and elastic modulus,
E
f
(
1
-
v
f
)
,
by using the relationship between the stress of the thin film and the temperatures. One suitable method for measuring the deflections of the thin film deposited on a substrate is the interferometric technique [A.E. Ennos, “Stress developed in optical film coatings”, Appl. Opt. Vol 5, No. 1, pp.51-61, 1966; K. Roll and H. Hoffmann, “Michelson interferometer for deformation measurements in an UHV system at elevated temperatures”, Rev. Sci. Instrum., Vol 47, No. 9, pp.1183-1185, 1976.] The above interferometric technique is somewhat elaborate, and inaccurate because the difference of the number of fringe in two fringe patterns is required to be an integer.
SUMMARY OF THE INVENTION
The present invention disclose a method for measuring a thermal expansion coefficient of a thin film, in which the thin film is first deposited on two substrates having different thermal expansion coefficients under the same conditions. For each of the two deposited substrates, a relationship between the thin film stresses and the measuring temperatures is established by using a phase shifting interferometry technique, in which the stresses in the thin films are derived by comparing the deflections of the substrates prior to and after the deposition. Based the two relationships the intrinsic stress, thermal expansion coefficient, and elastic modulus,
E
f
(
1
-
v
f
)
,
can be calculated. Alternatively, the stresses of the thin films deposited on two different substrates are plotted against the stress measuring temperatures, showing a linear dependence. From the slopes of the two lines in the stress versus temperature plot, the intrinsic stress, thermal expansion coefficient and elastic modulus of the thin film is determined, simultaneously. The present method is relatively simple and convenient and can be extended to varying-temperature applications without damaging the thin film.
The method for measuring a thermal expansion coefficient of a thin film deposited on a substrate by phase shifting interferometry accomplished in accordance with the present invention comprises the following steps:
a) measuring a phase function of a target surface of a first substrate at a first measuring temperature;
b) depositing a thin film on said target surface of said first substrate;
c) measuring a phase function of said thin film by using the same conditions as those in step a);
d) calculating one or more relative heights of one or more points with respect to a central point of said substrate prior to and after the deposition in step b) by using the phase functions obtained in steps a) and c), respectively, and calculating a difference of the relative heights at a same point prior to and after the deposition in step b) for each of said one or more points;
e) calculating a stress of said thin film for each of said one or more points by using said difference from step d) and calculating an average stress of said thin film therefrom;
f) obtaining another one or more average stresses of said thin film of another one or more measuring temperatures by repeating steps a), c), d) and e) except that said first measuring temperature is replaced by said another one or more temperatures, and obtaining a first set of data of said average stresses versus said measuring temperatures with respect to said first substrate;
g) measuring a phase function of a target surface of a second substrate at a second measuring temperature, wherein the second substrate has a thermal expansion coefficient different from that of said first substrate;
h) depositing a thin film on said target surface of said second substrate with the conditions same as those in step b);
i) measuring a phase function of said thin film in step h) by using the same conditions as those in step g);
j) calculating one or more relative heights of one or more points with respect to a central point of said substrate prior to and after the deposition in step h) by using the phase functions obtained in steps g) and i), respectively, and calculating a difference of the relative heights at a same point prior to and after the deposition in step h) for each of said one or more points;
k) calculating a stress of said thin film of step h) for each of said one or more points by using said difference from step j) and calculating an average stress of said thin film of step h) therefrom;
l) obtaining another one or more average stresses of said thin film of step h) of another one or more measuring temperatures by repeating steps g), i), j) and k) except that said second measuring temperature is replaced by said another o
Ho Ing-Jer
Jaing Cheng-Chung
Lee Cheng-Chung
Tien Chuen-Lin
Bacon & Thomas PLLC
Kim Robert H.
Precision Instrument Development Center, National Science Counci
Wang George
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