BRIEF DESCRIPTION OF THE DRAWINGS
[FIGS. 1(a) to 1(d)] Transmittance spectrum for a substrate and a thin film on-substrate, in normal incidence.
[FIG. 2] An on-incident-angle dependence of S and P polarization transmittance and reflectance, on incident angle.
[FIG. 3] An S-polarization transmittance spectrum form in the case incident angle is changed.
[FIGS. 4(a) and 4(b)] (a) An on-incident-angle dependence of absolute transmittance spectrum for a substrate and a thin film on the substrate, and (b) An on-incident-angle dependence of relative transmittance spectrum determined from those spectrums.
[FIG. 5] S-polarization reflectance spectrum form in the case incident angle is changed.
[FIGS. 6(a) and 6(b)] FIG. 6(a) A dependence of absolute reflectance spectrum for a substrate and on-substrate thin film upon incident angle, and FIG. 6(b) A dependence of relative reflectance spectrum determined from those spectrums upon incident angle.
[FIGS. 7(a) and 7(b)] FIG. 7(a) A dependence of a relative reflectance spectrum for a substrate and on-substrate thin film upon a thin-film extinction coefficient, and FIG. 7(b) A plotting of a spectrum minimum value determined from those spectra, regarding a distinction coefficient.
[FIGS. 8(a) and 8(b)] FIG. 8(a) A dependence of a relative reflectance spectrum of a substrate and a thin film on the substrate upon a thin-film refractive index, and FIG. 8(b) A plotting of a spacing of between the spectrum maximum and minimum values determined from those spectra, regarding a refractive index.
[FIGS. 9(a) and 9(b)] FIG. 9(a) A dependence of a relative reflectance spectrum for a substrate and a thin film on the substrate upon a thin-film thickness, and FIG. 9(b) Plotting of a spacing of between the spectrum maximum and minimum values determined from those spectrums, relative to a thin-film thickness.
[FIG. 10] A concept view of a complex dielectric-constant measuring apparatus due to light transmission (embodiment 1).
[FIG. 11] A drawing of a best fitting with a relative-transmittance measurement result in the case of S-polarization at an incidence of 70 degrees.
[FIG. 12] A drawing of a relative transmittance measurement result of S-polarization in the case incident angle is changed.
[FIGS. 3(a) and 13(b)] FIG. 13(a) is a relative transmittance measurement result at an incident angle of 85 degrees in the case measuring point is changed on a sample surface of FIG. 13(b).
[FIG. 14] A concept view of a complex dielectric-constant measuring apparatus due to light reflection (embodiment 2).
FIGS. 15(
a) and 15(b)] FIG. 15(a) A figure showing a reflection power at an incident angle of 70 degrees, by a 700-μm thick silicon substrate and a 20-μm thick SiO2 film on the substrate, and FIG. 15 (b) a figure showing a relative reflection spectrum for the above spectrum.
DESCRIPTION OF REFERENCE NUMERALS AND SIGNS
10 Complex dielectric-constant measuring apparatus
11 Sample
12 Light source
13 Photodetector
14 Mechanical chopper
15, 17, 20, 22 Lens
16, 18, 19, 21 Aperture
23 polarizer and light-power attenuator
30 Incident system
31 Light-receiving system
BEST MODE FOR CARRYING OUT THE INVENTION
The best mode for carrying out the invention will be shown in the below.
Embodiment 1
<Embodiment Based on Light Transmission>
With reference to the figures, explanation is made on an embodiment of a complex-dielectric-constant measurement based on light transmission according to the invention.
FIG. 10 is a conceptual view of a complex-dielectric-constant measuring apparatus 10. The CW light exits a light source 12 (backward millimeter-wave tube (BWO), in the figure) and is intensity-modulated by a mechanical chopper 14. The light passes a lens 15, and an aperture 16 turns the light into a plane wave. In front of a sample 11, focusing is made onto a surface of the sample by a lens 17 and an aperture 18. A polarizer (not shown in the figure) and light-power attenuator (not shown in the figure) is inserted, as required, in the incident system 30. Only a part of the light is transmitted through the sample. This light is received by a lens 20 and an aperture 19 and changed into a plane wave. The light is received by a lens 22 and aperture 21 and collected onto a photodetector 13 (Golay Cell, in the figure). The intensity signal of the light is converted into an electric signal by the photodetector, and the electric signal is forwarded to a measuring instrument (not shown in the figure). The section of the apparatus from the sample to the photodetector is referred to as a light-receiving system 31. The light source, the sample, the photodetector, etc. are arranged nearly on a line. The propagating direction of the light is taken as z-axis. The light source is placed on an x-y auto stage (not shown in the figure) in order to desirably change the incident point upon the sample. The sample rests on an autorotation stage (not shown in the figure) in order to change the incident angle and is free to rotate about the vertical axis (y-axis). The photodetector is placed on an x-y-z auto stage (not shown in the figure) and an autorotation stage (not shown in the figure) so as to be set up at the optimal position. A sample holder (not shown in the figure) is devised so as not to block the incoming light even if entering obliquely. Furthermore, a radio-wave absorber (not shown in the figure) is attached on the sample holder in order to prevent the light that is not transmitted through the sample from entering the light-receiving system. When collimated light is incident upon the sample, the lenses 17, 20 are not used.
Ten-μm thick thermal oxide films (SiO2) were formed on a main surface and a back surface of a silicon substrate having a diameter of 4 inches and a thickness of 700 μm. Then, the thermal oxide films, in the same positions on the main and back surfaces, were removed completely so that the oxide films on the main and the back surfaces have a semilunar form, thus preparing a sample exposed at its silicon surfaces. The sample was set up on the FIG. 10 sample holder. S-polarized light was irradiated obliquely (at an incident angle of 70 degrees) to the surface where the thermal oxide film remains (the upper half surface) and to the surface where is the oxide film was removed (the lower half surface), to measure transmission spectrums at each time. The transmission spectrums are referred to as T(SiO2/Si) and T(Si), respectively. Here, a ratio of a transmission spectrum through the on-substrate-film sample to a transmission spectrum through the substrate was determined (relative transmittance=T(SiO2/Si)/T(Si)). The result is shown by the solid line in FIG. 11. The “curve where the maximum and minimum values are adjacent” represented in the figure is qualitatively well matched to the FIG. 4(b) calculation result. Next, the equations, expressing a transmittance spectrum form provided by S-polarized light incident upon a (multi-layer) parallelepiped plate sample, are found in many books on optics (e.g. “Non-patent Document 4” in paragraph [0023]). With those equations, a transmittance spectrum for the substrate only (Ts(Si)) was calculated by using a silicon optical constant (ns=3.4155 and ks=0) and a substrate thickness (ds=700 μm). A transmittance spectrum for the sample formed by the substrate and the thin film (Ts(SiO2/Si)) was best-fit to the FIG. 11 measurement result (solid line) by using a thin-film thickness (df=20 μm) and substrate optical constant while taking a thin-film optical constant as an unknown number (nf and kf), the result of which is shown with solid circles in FIG. 11. The complex refractive index of the thin film thus determined is nf=2.00 and kf=0.08. From these, if using the paragraph [0011] relational expression, the complex dielectric constant of the SiO2 thin film at 65 GHz is determined as ε1=3.994 in its real part and ε2=0.32 in its imaginary part.
Using the same sample as in paragraph [0050], measurement was made at a changing incident angle. The result is shown in FIG. 12. In the measurement result, there is almost no difference in the relative transmittance at an incident angle of 0 to 40 degrees whereas there is a growth in the structure appearing in the relative transmittance as the incident angle is increased as 60, 70, 80 and 85 degrees. The dependence upon incident angle is also well matched to the FIG. 4(b) calculation result.
A silicon substrate having a uniform thickness 700 μm (bare substrate sample without forming a thin film) was put on the FIG. 10 sample holder, and an incident angle of the sample was set to 85 degrees. Then, while rotating the sample about the axis normal to the sample surface and passing the center thereof, a transmission spectrum through the sample upper half surface and a transmission spectrum through the sample lower half surface was made in order to calculate a ratio of those spectra (relative transmittance). The result is shown in FIG. 13(a). If the silicon wafer were a perfect parallelepiped plate, there could not be a structure where the maximum and minimum values are adjacent that is similar to FIG. 4(b). However, in FIG. 13(a), a structure appears where the maximum and minimum values are adjacent. In FIG. 13(a), the origin of sample rotation angle was selected as an angle at which the maximum and minimum values of relative transmittance spectrum have a height assuming a lowest curve (i.e. most flat curve). On the positive angle side, the relative transmittance spectrum is in a form similar to FIG. 4(b) wherein the minimum and maximum values increase in height as the angle increases toward 45 degrees. Meanwhile, the relative transmittance spectrum, on the negative angle side, is nearly in a mirror reflection of the positive-angle-side relative transmittance spectrum with respect to a relative transmittance spectrum at an angle of 0 degrees. From the measurement results, the commercially-available silicon wafers used today in the semiconductor industry are considered as “wedge-like disks” as typically shown in FIG. 13(b). The silicon wafer has a thickness deviation (difference in thickness between the maximum and the minimum) estimated to be 2 μm. In this manner, the “sample complex-dielectric-constant measuring apparatus based on optical spectral measurement” of the invention is capable of measuring the flatness of a sample as well.
Embodiment 2
<Embodiment Based on Light Reflection>
With reference to the figures, explanation is made with respect to an embodiment for measuring a complex dielectric constant based on light reflection according to the invention.
FIG. 14 is a conceptual view of a complex-dielectric-constant measuring apparatus 10. The CW light exits a light source 12 and is intensity-modulated by a mechanical chopper 14. The light passes a lens 15, and an aperture 16 turns the light into a plane wave. In front of a sample 11, focusing is made onto a surface of the sample by a lens 17 and an aperture 18. A polarizer and light-power attenuator (23 in the figure) is inserted, as required, in the incident system 30. Only a part of the light is reflected by the sample. This light is received by a lens 20 and an aperture 19 and is changed into a plane wave. The light is received by an aperture 21 and a lens 22 and is collected onto a photodetector 13. The intensity signal of light the is converted into an electric signal by the photodetector. The electric signal is forwarded to a measuring instrument (not shown in the figure). The section of the measuring apparatus from the sample to the photodetector is referred to as a light-receiving system 31. The sample is rested upon an x-y auto stage (not shown in the figure) in order to desirably change the incident position of light upon the sample. Furthermore, the sample is placed on an autorotation stage (not shown in the figure) in order to change the incident angle. Thus, the sample is free to rotate about the vertical axis (y-axis). The photodetector is placed on an x-y-z auto stage (not shown in the figure) and an autorotation stage (not shown in the figure) so as to be set up in the optimal position. A sample holder (not shown in the figure) is devised so as not to block the incoming light even if entering obliquely. Furthermore, a radio-wave absorber (not shown in the figure) is attached on the sample holder in order to prevent the light reflected upon the sample holder from entering the light-receiving system. When collimated light is incident upon the sample, the lenses 17, 20 are not used.
Ten-μm thick thermal oxide films (SiO2) were formed on a main surface and a back surface of a silicon substrate having a diameter of 4 inches and a thickness of 700 μm. Then, the thermal oxide films, in the same positions on the main and back surfaces, were removed so that the oxide films on the main and the back surfaces have a semilunar form, thus preparing a sample exposed at its silicon surfaces. The sample was put on the FIG. 14 sample holder. S-polarized light was irradiated obliquely (at an incident angle of 70 degrees) to the surface where the thermal oxide film remains (the upper half surface) and to the surface where the oxide film was removed (the lower half surface), to measure reflection power at that time. The reflection powers are referred to as R(SiO2/Si) and R(Si), respectively. The measurement result is shown in FIG. 15(a). In this figure, the solid line represents R(SiO2/Si) while the dotted line represents R(Si). Both curves have minimum values at around 65 GHz. Although the dotted line is greater than the solid line at a lower frequency than 65 GHz, the relationship in magnitude is inverted at a higher frequency than 65 GHz. This result is well matched to the FIG. 6(a). Next, a ratio of a reflection spectrum upon the a thin film on the substrate (R(SiO2/Si)) sample to a reflection spectrum upon substrate (R(Si)) sample was determined. (i.e., relative reflectance=R(SiO2/Si)/R(Si)). The result is shown in FIG. 15(b). The “curve where the maximum and minimum values are adjacent” represented in the figure is qualitatively well matched to the FIG. 6(b) calculation result.
Description is made of a method to determine a complex dielectric constant from the measurement result FIGS. 15(a) and 15(b). Firstly, in FIG. 15(a), the reflection power upon the sample having the on-substrate (Si) thermal oxide film (SiO2) is equal in valley value to the reflection power upon the sample having only the substrate (Si). From the result, paragraph [0042] and FIG. 7(a), the thin film can be estimated having an extinction coefficient of zero (k=0). Then, from FIG. 15(b), the “distance between the minimum and maximum values” was determined to be 0.5 GHz. Because valley frequency, substrate thickness, substrate refractive index, incident angle and thin-film thickness are known in (Equation 6), the thin film is determined having a refractive index (nf) of nf=1.3. From the relationship between these results and paragraph [0011], the SiO2 thin film is determined having a complex dielectric constant having ε1=1.69 in its real part and ε2=0 in its imaginary part.
Patent Application
20080013070
