Laser apparatus and method for measuring stress in a thin film using multiple wavelengths

In accordance with the present invention, an apparatus and a method for measuring the radius of curvature of a surface using laser beams of multiple wavelengths are provided. The present invention avoids poor measurement due to destructive interference of the beams reflected at a thin film's upper and lower surfaces. The present invention is applicable to laser reflection stress measurement apparatuses of both scanning and beam-splitting types.

FIELD OF THE INVENTION 
This invention relates to the use of lasers to measure the radii of 
curvature of reflective structures. In particular, this invention relates 
to the use of lasers to measure stress in a thin film formed on top of a 
substrate, by measuring the change in local radius of curvature of the 
substrate due to the presence of the thin film. 
BACKGROUND OF THE INVENTION 
Thin films of various materials are often used in the fabrication of 
semiconductor structures. The use of a laser to measure the radius of 
curvature of the surface of a semiconductor structure underneath a thin 
film is known in the art. Such a measurement is useful because the degree 
to which a thin film deforms the surface of a semiconductor structure, 
i.e. changes the local radius of curvature of the semiconductor structure, 
is indicative of the stress in the thin film. Thus, the measurement of the 
radius of curvature of a semiconductor structure is common, for example, 
in inspection of incoming wafers, as a monitor of the stability of a 
fabrication process, and for measurement of stress in a thin film. 
The "cantilever beam" model, which is well known in the art, relates stress 
in a thin film to the material properties of the substrate (e.g. Young's 
modulus), the radius of curvature of the substrate, and the dimensions 
(e.g. thickness) of the thin film. Many techniques for measuring stress 
have been developed based on the cantilever beam model. Among these 
techniques are x-ray diffraction and laser reflection. A description of an 
x-ray diffraction technique may be found in an article entitled "Automatic 
x-ray diffraction measurement of the lattice curvature of substrate wafers 
for the determination of linear strain patterns" by A. Segmuller et al, 
J.Appl.Phys., volume 51, no. 12, December 1980, pp. 6224-30. 
There are two principal types of laser reflection 
apparatuses--beam-splitting and scanning--for measuring radii of 
curvature. In either apparatus type, the radius of curvature is derived by 
measuring the angles of reflection of an incident laser beam at two or 
more points of known separation on the surface of the substrate. 
In a beam-splitting type laser reflection apparatus, the laser beam is 
split optically into two or more beams directed at the two or more points 
at which angles of reflection are measured. An example of stress 
measurement performed with a beam-splitting type laser reflection 
apparatus is given in the article entitled "In situ stress measurements 
during thermal oxidation of silicon," E. Kobeda and E. A. Irene, 
J.Vac.Sci.Techno.B 7(2), Mar/Apr., 1989, pp. 163-66. 
In a scanning type laser reflection apparatus, either the laser beam or the 
surface under measurement is moved from point to point in order that the 
angle of reflection may be measured at each selected point. Each of the 
following articles discusses stress measurements performed using a 
scanning type laser reflection apparatus: 
i) "Principles and Applications of Wafer Curvature Techniques for Stress 
Measurements in Thin Films," P.A. Flinn in "Thin Films: Stresses and 
Mechanical Properties", MRS Proceedings, vol. 130, ed. Bravman, Nix, 
Barnett, Smith, 1989, pp. 41-51. 
ii) "In situ stress measurement of refractory metal silicides during 
sintering," J.T. Pan and I. Blech, J.Appl.Phys. 55(8), April 1984, pp. 
2874-80. 
iii) "Thermal stresses and cracking resistance of dielectric films (SiN, 
Si.sub.3 N.sub.4, and SiO.sub.2) on Si Substrates," A. K. Sinha et al., 
J.App.Phys. 49(4), April 1978, pp. 2423-26. 
The references cited above are also illustrative of the method of stress 
measurement. 
Because a monochromatic (i.e., one single wavelength) laser is used in 
either type of laser reflection stress measurement apparatuses, an 
apparatus in the prior art is unable to provide a reliable measurement 
under certain conditions. These conditions are illustrated in FIG. 1. 
FIG. 1 shows a thin film t under measurement bounded by media 1 and 2 at 
the upper and lower surfaces of the thin film. Reflected beams a and b of 
incident laser beam I are shown to reflect respectively from the upper and 
lower interfaces (i.e. the interfaces between medium 1 and thin film t, 
and between medium 2 and thin film t). The reflected beams a and b will 
destructively interfere with each other, i.e., cancel each other, when the 
following conditions are satisfied: (i) the thin film's index of 
refraction .mu..sub.t is close to the quantity .sqroot..mu..sub.1 
.mu..sub.2, which is the geometrical mean of media 1 and 2's individual 
indices of refraction (.mu..sub.1, .mu..sub.2 ; and, (ii) the thickness of 
the film is such that the two beams reflected from its two interfaces with 
the bounding media are out of phase by one-half wavelength. Condition (ii) 
is satisfied when 
EQU d=(.lambda./n)/4+m(.lambda./n)/2 (1) 
where .lambda. is the wavelength of the incident beam in air, 
d is the thickness of the thin film, 
n is the index of refraction of the thin film, and 
m is any integer greater than or equal to zero. 
When both conditions (i) and (ii) are satisfied, the reflected beams at the 
interfaces destructively interfere or cancel each other resulting in 
either no intensity detectable or substantially diminished intensity 
detectable in the reflected beams. 
For example, a thin film particularly difficult to measure in practice is 
silicon nitride, which has a refractive index of about 2, when bounded by 
air (refractive index of 1) and silicon (refractive index of about 4). In 
this example, since the index of refraction for silicon nitride is about 
2, beams a and b at the respective air/silicon nitride and silicon 
nitride/silicon interfaces cancel each other in the manner described 
above, when the thickness of the thin film is one-quarter of the 
wavelength of the incident beam in silicon nitride, or at one-half 
wavelength increments thereof. 
Thus, an apparatus and method capable of avoiding poor measurement of the 
angle of reflection due to destructive interference over a wide range of 
thicknesses using existing laser technology is desired. 
SUMMARY OF THE INVENTION 
In accordance with the present invention, an apparatus and a method for 
measuring the radius of curvature of a surface using laser beams of 
multiple wavelengths are provided. The present invention avoids poor 
measurement due to destructive interference of the beams reflected at a 
thin film's upper and lower surfaces. The present invention is applicable 
to laser reflection stress measurement apparatuses of both scanning and 
beam-splitting types. 
The present invention is better understood after considering the following 
detailed description in conjunction with the accompanying drawings.

DETAILED DESCRIPTION 
The present invention is applicable to both scanning and beam-splitting 
types of laser reflection stress measurement apparatuses. 
According to equation (1) discussed in the "Background of the Invention" 
section, the thickness of the thin film at which destructive interference 
or cancellation occurs in the reflected beams is dependent upon both the 
wavelength of the incident laser beam and the refractive indices of the 
thin film and the bounding media. This effect is illustrated in FIG. 2. In 
FIG. 2, which assumes a silicon nitride index of refraction to be 2.2, the 
first and second minimum reflected intensities for the laser beam 
.lambda..sub.1 (wavelength in silicon nitride=0.305 microns) are seen at 
film thicknesses of 0.076 microns (a.sub.1.sup.0) and 0.228 microns 
(a.sub.1.sup.1). Likewise, the first and second minimum intensities for 
the laser beam .lambda..sub.4 (wavelength in silicon nitride=0.59 microns) 
are seen at film thicknesses 0.148 microns (a.sub.4.sup.0) and 0.443 
microns (a.sub.4.sup.1). However, when minimum intensity is measured for 
laser beam .lambda..sub.1 at a thin film thickness of 0.076 microns, the 
reflected intensity of laser beam .lambda..sub.4 is measured to be 0.21 of 
the incident beam, which is sufficient intensity for the purpose of 
measuring the angle of reflection. Therefore, if the incident laser beam 
comprises more than one wavelength, the intensity of the reflected beam is 
likely to be adequate for the purpose of measuring the angle of 
reflection, unless the thickness of the thin film is a minimum intensity 
point for each of the component wavelengths. Minimum intensity points of 
different wavelengths may coincide because, as can be seen from equation 
(1) above, the thicknesses at which destructive interference occur are 
periodic. When the minimum intensity points of the different wavelengths 
coincide, the problem of no reflected intensity or substantially 
diminished reflected intensity results. However, by choosing a combination 
of wavelengths, sufficient intensity for measuring an angle of reflection 
is assured over a broad range of thicknesses. 
FIG. 3 shows a first embodiment of the present invention. As shown in FIG. 
3, two monochromatic lasers L.sub.1 and L.sub.2, having wavelengths 
.lambda..sub.1 and .lambda..sub.2 respectively, are positioned 
orthogonally such that their individual beams B.sub.1 and B.sub.2 are 
combined by optical element P (e.g. a beam-splitter prism) to form laser 
beam B.sub.3, which is incident on sample S. The reflected beam B.sub.R is 
detected by a photodetector (not shown) to determine the angle of 
reflection at laser beam B.sub.3 's point of incidence. If either the 
sample S or the apparatus (i.e. optical element P and lasers L.sub.1 and 
L.sub.2) is capable of being repositioned for measurement over multiple 
points on the surface of sample S, this first embodiment constitutes a 
scanning type laser reflection stress measurement apparatus. 
Alternatively, if the combined laser beam B.sub.3 is split into multiple 
beams by a beam-splitter element P (not shown but of well known design) to 
be incident on multiple points on the surface of sample S, so as to allow 
the measurement of multiple angles of reflection at the same time, this 
first embodiment constitutes a beam-splitting type laser reflection stress 
measurement apparatus. 
FIG. 4 shows a second embodiment of the present invention. As shown in FIG. 
4, a laser L.sub.1 is used to provide a laser beam B.sub.1 having 
component radiations of at least wavelengths .lambda..sub.1 and 
.lambda..sub.2. In general laser L.sub.1 is capable of providing a beam 
comprising component radiations of two or more wavelengths. An optical 
element P (e.g. a prism) is used to direct laser beam B.sub.1 onto the 
surface of sample S, which reflects the incident laser beam B.sub.1 as 
reflected beam B.sub.R. Laser beam B.sub.R is detected by a photodetector 
(not shown) to determine the angle of reflection at laser beam B.sub.1 's 
point of incidence. If either the sample S or the apparatus (i.e. optical 
element P and laser L.sub.1) is capable of being repositioned for 
measurement over multiple points on the surface of sample S, this second 
embodiment constitutes a scanning type laser reflection stress measurement 
apparatus. Alternatively, if the combined laserbeam B.sub.R is split into 
multiple beams by a beam-splitter element (not shown) to be incident on 
multiple points on the surface of sample S, so as to allow the measurement 
of multiple angles of reflection at the same time, this second embodiment 
constitutes a beam-splitting type laser reflection stress measurement 
apparatus. Because the laser source in this second embodiment provides a 
multiple wavelength beam in the first instance, the second embodiment is 
more suitable as a beam-splitting laser reflection stress measurement 
apparatus. At the time of filing this application, however, even though a 
gas laser source (e.g. a helium-neon laser) providing a beam of multiple 
wavelengths is available, a solid state laser providing such beam is not 
commercially available. Therefore, an embodiment such as the first 
embodiment is more preferable because of size and cost considerations but 
the invention can be implemented with any source of multiple wavelengths 
whether available at the time of filing this application or in the future. 
FIG. 5 shows an embodiment of the present invention in a scanning laser 
reflection stress measurement apparatus. As shown in FIG. 5, this 
embodiment comprises photodetector assembly DA, laser assemblies LA.sub.1 
and LA.sub.2, cube beam-splitter assembly PA, and mirror assembly MA 
mounted on a carriage plate CP. Carriage plate CP is mounted directly 
above a wafer table WT, on which the sample wafer (the surface W of which 
is shown) is located. Carriage plate CP is movable back and forth along 
the direction A indicated, driven by a stepping motor (not shown) which 
allows the carriage plate CP to move 10 microns per step relative to the 
sample wafer. Inside laser assemblies LA.sub.1 and LA.sub.2 are, 
respectively, lasers L.sub.1 and L.sub.2 not shown). In this embodiment, 
the wavelengths of the lasers are 670 nm and 750 nm. As mentioned before, 
depending upon the range of thicknesses of the thin film, other 
wavelengths may also be used. The shorter wavelength laser in this 
embodiment is obtainable from Power Technology Inc., Arkansas and the 
longer wavelength laser is obtainable from D.O. Industries, New York. A 
position-sensitive photodetector D, obtainable from Silicon Detector Inc., 
California, is contained in the photodetector assembly DA. (Other 
position-sensitive photodetectors may also be used as desired). In this 
embodiment, photodetector D provides two output voltages (positional 
signals) V1 and V2. The position at which a light beam is detected by 
photodetector D is given by the value VA=(V2-V1)/(V2+V1). The 
correspondence between this voltage Va and actual angle of reflection is 
established by a calibration step when the apparatus is set up. 
As shown in FIG. 5, laser beams B.sub.1 and B.sub.2 from lasers L.sub.1 and 
L.sub.2 respectively are combined at beam-splitting cube P, and the 
combined beam B.sub.3 strikes the wafer surface W at the point where the 
angle of reflection is to be measured. The angle at which the beam B.sub.3 
strikes the wafer surface is designed to be as normal to the wafer surface 
as possible. In this embodiment, this angle is calibrated to ensure the 
reflected beam B.sub.R misses laser assembly LA.sub.1, in order that 
reflected beam B.sub.R may pass by and beyond the laser assembly LA.sub.1 
to strike mirror M.sub.1, which directs the laser beam B.sub.R at the 
position-sensitive photodetector D. The light rays BL.sub.1 and BL.sub.2 
shown in FIG. 5 illustrate the positional limits between which a reflected 
beam can be detected by photodetector D. 
FIG. 6 shows the disassembled view of the embodiment shown in FIG. 5. As 
shown in FIG. 6, the lasers L.sub.1 and L.sub.2 are mounted respectively 
on laser mounts LM.sub.1 and LM.sub.2 by screws S.sub.1 and S.sub.6 to 
form laser assemblies LA.sub.1 and LA.sub.2. Laser mount LM.sub.1 is 
attached to carriage plate CP by screw S.sub.2. Laser mount LM.sub.2 is 
attached to carriage plate CP by screw S.sub.5, and the spring and 
retainer rings R.sub.1 and R.sub.2. The beam-splitter P is mounted by set 
screw S.sub.8 on beam-splitter mount PM, which is in turn mounted on 
carriage plate CP by two screws (only screw S.sub.4 is shown). The 
beam-splitter mount PM, and laser mounts LM.sub.1 and LM.sub.2 are 
positioned such that laser L.sub.1 's beam, which travels downward, and 
laser L.sub.2 's beam, which travels substantially horizontally, are 
combined at beam-splitter P with the combined beam emerging downward from 
beam-splitter P. The detector D is mounted on the detector mount DM by two 
screws (only screw S.sub.10 is shown). The detector mount DM is in turn 
mounted as shown on carriage plate CP by screw S.sub.9. Mirror assembly MA 
is mounted by screw S.sub.7 directly above the beam-splitter P and 
oriented such that the reflected beam from the sample is reflected again 
at mirror M1 approximately 90 degrees to strike the photodetector D. 
Carriage plate CP is secured onto stage ST by three screws (only screw S3 
is shown). Stage ST is driven by a step motor MR, which provides mobility 
to the stage ST over the range of the scan. 
FIG. 7 shows a electrical wiring diagram of the embodiment shown in FIG. 5. 
As shown in FIG. 7, external 110V AC power is transformed by power supply 
module 704 into internal supply voltages++12V, -12V and 5V. These supply 
voltages are provided to laser power supplies 702 and 703 of lasers 
L.sub.1 and L.sub.2 respectively, and to the dual channel pre-amplifier 
705, which amplifies the positional signals V1 and V2 of the 
position-sensitive photodetector D (See description of output voltages V1 
and V2 in the discussion above). The positional signals V1 and V2 are 
provided to an external computer (not shown) for processing. The lasers 
L.sub.1 and L.sub.2 are cooled by a fan 707, which is provided 110V AC 
power The stepping motor MR (FIG. 6) and its control 701 are also provided 
110V AC power. An interlock switch, which turns off the power supply 
module 704 when the housing containing the apparatus is open, is provided 
as a safety feature. 
The above detailed description is intended to illustrate the specific 
embodiments of the present invention and is not limiting. A skilled person 
in the art will be able to provide modifications and variations within the 
scope of the present invention, as set forth in the following claims, upon 
consideration of the above detailed description in conjunction with the 
accompanying drawings.