In this investigation, a low cost Si wafer metrology system based on low coherence interferometry using NIR light is proposed and verified. The whole system consists of two low coherence interferometric principles: low coherence scanning interferometry (LCSI) for measuring surface profiles and spectrally-resolved interferometry (SRI) to obtain the nominal optical thickness of the double-sided polished Si wafer. The combination of two techniques can reduce the measurement time and give adequate dimensional information of the Si wafer. The wavelength of the optical source is around 1 μm, for which transmission is non-zero for undoped silicon and can be also detected by a typical CCD camera. Because of the typical CCD camera, the whole system can be constructed inexpensively.
©2013 Optical Society of America
A silicon (Si) wafer is very important as a substrate of semiconductor products such as integrated circuit (IC) chips, light emitting diodes (LEDs), solar cells and MEMS devices. In case of manufacturing semiconductor products based on Si wafers by lithography, chemical vapor deposition (CVD) or laser scribing process, the critical parameters are the surface and thickness profiles of a Si wafer for uniformity and reliability of layers deposited on the substrate. Even, the importance of knowing the size of a Si wafer has increased according to the industrial demands for high throughput, and therefore the surface and thickness profiles of a Si wafer should be precisely inspected not only locally at a few points on the wafer but also over entire wafer surface for successful performances of the products.
In current wafer metrology, two types of inspection technologies based on capacitive sensors  and optical interferometry [2–7] have been widely used. A capacitive sensor is very easy to use in order to measure the gap between the probe and the wafer surface by detecting the capacitance variation. Although this sensor has high sensitivity measuring the electrical signals, it is fundamentally a kind of point measurements and the precise stage should be incorporated for the whole surface profile measurement.
On the other hand, optical interferometry is suitable for measuring the entire wafer surface as it is typically used in surface metrology. One of drawback is that optical interferometry with visible light cannot analyze the Si wafer thickness without the replica on the other side, which makes the measuring system complicated [3,4]. Near infrared (NIR) light, which goes through an undoped Si wafer, can be used to overcome this drawback but the video camera is very expensive in this wavelength region and also laser interferometry can only detects the thickness variations without any special techniques [5–7].
In this investigation, we propose a low cost Si wafer metrology system based on low coherence interferometry using NIR light. The whole system consists of two low coherence interferometric principles; low coherence scanning interferometry (LCSI) for measuring surface profiles [8,9] and spectrally-resolved interferometry (SRI)  to obtain the nominal optical thickness of the Si wafer. The wavelength of the optical source is around 1 μm, for which transmission is non-zero for undoped silicon and also detectable by the typical CCD camera. The main advantage of the proposed system is that it can measure surface profiles of both sides and the optical thickness of the Si wafer, double-side polished at once. Moreover, it does not need any expensive NIR cameras.
2. Optical characteristics of a Si wafer and a CCD camera
In general, a Si wafer is not transparent in the visible range but it is partially transparent beyond 1 μm wavelength as shown by a blue line in Fig. 1, which is the transmittance curve of 600 μm thickness undoped Si wafer as a function of wavelengths .
It shows that NIR light can be successfully applied for wafer metrology. The red curve in Fig. 1 indicates the wavelength dependent sensitivity of a typical CCD camera. As known in Fig. 1, the light in the range of 1-1.1 μm can go through the wafer and also be detected at the CCD camera. Even though the transmittance of a Si wafer and the CCD sensitivity are not so high in this wavelength region, they are enough to be used in wafer metrology, especially low coherence interferometry.
3. Low coherence interferometry for a Si wafer metrology
Figure 2 shows the optical configuration of the combined measurement system which adopts two low coherence interferometric principles; LCSI and SRI. LCSI allows for the measurements of surface profiles of the Si wafer of both sides while SRI can determine the nominal optical thickness of the wafer. Then, the surface and thickness profiles of the Si wafer, double-side polished, can be simultaneously obtained.
As an optical source, a super luminescence diode (SLD) at 1050 nm with 50 nm bandwidth is used and the light is incident to the Michelson-type interferometer. Then, two reflected beams from a reference mirror and a wafer are recombined and split again into two; one goes to the CCD camera for LCSI and the other is detected by an optical spectrum analyzer or a spectrometer for SRI.
(1) Low coherence scanning interferometry (LCSI) for measuring a Si wafer
LCSI has been an attractive tool for measuring 3D surface profile of a sample because it can avoid the well-known 2-pi ambiguity problem [8,9]. By using low coherence characteristic of a light source, LCSI can obtain a localized correlogram when the optical path difference (OPD) between reference and measurement arms becomes near zero by adjusting one of two path lengths. In this investigation, MR should be scanned in Fig. 2 until two correlograms corresponding to the front and rear sides of the wafer are obtained. In order to confirm the transmission of the SLD light and the detection of two correlograms, a point measurement was performed with the Si wafer, which has approximately 0.5 mm thick and for which both sides are polished. Figure 3 shows the experimental result of LCSI when MR was scanned with 50 nm step size in the range of 2 mm.
As shown in Fig. 3, two correlograms were detected successfully and the position of each correlogram peak indicates each height position of the Si wafer surface. An interesting feature is that the second correlogram is broader (23 μm, FWHM) than the first correlogram (9 μm, FWHM), caused by the dispersion of the Si wafer. In LCSI, of course, the optical thickness of the Si wafer can be obtained from the gap between two peak positions of the correlograms as 1866.3 μm, which leads to the geometrical thickness of 484.3 μm with the group refractive index of Si (3.854) at 1050 nm . However, the measurement time becomes too long to determine the gap between two correlograms in LCSI, and even the position error of the scanning stage may be accumulated in the result. Moreover, the intensity acquisition in the range between the two correlograms is not necessary. In order to improve the limitations of LCSI, another thickness measurement technique (SRI) can be combined with LCSI and the whole system can measure surface profiles and thickness simultaneously without any time loss because the scanning stage should move quickly to reduce the scanning time.
(2) Spectrally-resolved interferometry (SRI) for measuring the Si wafer thickness
Before LCSI obtains two correlograms as shown in Fig. 2, an optical spectrum analyzer (OSA) detects the spectral interferogram in SRI, where the spectral phase, ϕ(ν) is related to the geometrical thickness of the Si wafer, t such as 
As a result of the point measurement, the spectral interferogram of the Si wafer was captured by the OSA in SRI as shown in Fig. 4(a), where the modulation term caused by the spectral interference was added to the original spectrum of the SLD (the red line). In this case, the reference mirror (MR) was placed beyond the maximum measurable range of SRI , so the interference between MR and the Si wafer could be avoided. Figure 4(b) represents the Fourier transformation result of the spectral interferogram, and then the optical thickness of the Si wafer can be obtained from the peak position of the Fourier amplitude as 1864.6 μm. The main advantage of SRI is that it does not need any moving parts to determine the optical thickness of the Si wafer, but it only measures the thickness at a point. If the illumination light has a finite spot size, SRI gives the nominal thickness value of the illuminated area.
4. Experiment and result
The whole procedure to measure the surface and thickness profile of the Si wafer starts with the SRI measurement result. SRI determines the optical thickness of the Si wafer for the measurement to the necessary scanning range of LCSI in order to reduce the scanning range and time. Then, LCSI obtains two correlograms pixel by pixel of the CCD camera, which can be used reconstruct two surface profiles of both wafer sides. Also, the thickness profile can be calculated with the nominal thickness determined by SRI and thickness variations obtained by LCSI. In the experiment, the Si wafer, which has nominally 475 μm ± 25 μm thick and was polished on both sides, was aligned with two clips as shown in Fig. 5(a) and the measurement area was set as the red circle with the diameter of 2.96 mm.
The measurement of SRI yielded a nominal optical thickness of the Si of 1864.6 μm and this value was used to determine the skip range between two correlograms in LCSI. In LCSI, two correlograms were detected while the scanning stage moved with 50 nm step size near the location of each correlogram and the height maps were calculated with the phase peak detection method of LCSI . Figure 5(b) shows the measurement results of LCSI, where two surface profiles were successfully obtained. Figures 6(a) and 6(c) shows surface profiles of front side and rear side, respectively, and then the thickness variation profile was calculated from two profiles as Fig. 6(e). In the data analysis, the group refractive index of Si was assumed as 3.854 over entire wafer and the P-V values of the front, rear and thickness profiles were 58 nm, 108 nm and 69 nm, respectively.
In order to speed up the measurement, the step size was adjusted as 650 nm much larger than the Nyquist sampling limit (1050/4 = 262.5 nm) and the measurement time was significantly reduced as approximately 13 times shorter. Then, the correlograms were sub-sampled but the phase peak detection method was still valid to reconstruct the surface profiles . Figures 6(b), 6(d) and 6(f) show the measurement results of the front, rear and thickness profiles of the Si wafer, respectively, at the same region corresponding to data of (a), (c) and (e). Compared to the 50 nm step size case, the detailed surface texture could not be seen because of the poor resolution caused by the larger step size, but the whole surface shapes were as same as those of the previous case. The P-V values of the front, rear and thickness profiles were 51 nm, 121 nm and 95 nm, respectively.
The main reason for the flipped surface profiles of the wafer as shown in Fig. 6 is that the wafer was fixed with two clips and the measurement area was located in the middle. Because of the force caused by the clips, the wafer seems to be bent a little bit but not much so that PV values have the order of magnitude of sub-micrometers. In order to avoid the surface warp, a Si wafer was put on the optical table and the same experiment was performed vertically. Figure 7 shows the experimental results of front, rear surface profiles in two step size cases. As expected, the measured surface was not flipped over opposed to the previous results.
On the other hand, the waviness appeared in the height maps in Figs. 6(a) and 6(c) was attributed to the error caused by the non-equidistant step size during the reference mirror scanning. The scanning stage used in the experiment was a stepping motorized stage with 50 nm position resolution of one step. Although the step size was 50 nm in the experiment, the actual scanning step size was deviated from the command value and it generated the distortion of the measured surface profile. It also appeared in Figs. 7(a) and 7(c) but the direction was changed according to the interference fringe. The same errors can be also introduced in the 650 nm step size case, but the number of appearing the waviness decreases due to the averaging the position deviation errors of the single step (50 nm) over 13 steps (650 nm / 50 nm = 13).
In order to estimate the performance, the repeatability was calculated from the average value of standard deviation maps between 10 consecutive height maps and the mean height map (not shown) corresponding to the front and rear surface profiles in the 650 nm step size case, which did not involve the waviness on the surfaces. As the result, they were 8.3 nm and 22.1 nm, respectively.
In this investigation, NIR light was used for measuring an undoped Si wafer with the transmittance characteristic as shown in Fig. 1. However, highly doped Si wafers are not applicable to this measurement because they become highly absorptive to the NIR light due to band gap shifts, which affect phonon-assisted absorption and free-carrier absorption . In order to measure heavily doped Si wafers, the doping level should be adjusted as low or the wafer thickness should be thinned for the successful transmission of NIR light. In addition, the wafer to be measured needs to be double-side polished.
Another consideration is that the correlogram can be distorted by the dispersion as broadening and reshaping of the peak and reduction of the contrast when measuring the rear side of the wafer. This dispersion effect gives rise to measurement errors to determine the envelope peak or the phase peak in LCSI, but they can be compensated with the theoretical model of the correlogram of LCSI with optical properties of the material . Moreover, it can be used for the refractive index measurement if the group refractive index and the geometrical thickness are separated from the optical thickness . In this investigation, however, the dispersion effect was not compensated because the group refractive index of Si was adopted from Ref.  and assumed as constant in the measurement region. It alleviated the measurement accuracy to measure the rear surface profile of the wafer. The further research to compensate this dispersion effect and measure the refractive index profile of a Si wafer needs to be investigated.
In this paper, we investigated a low cost Si wafer metrology system based on low coherence interferometry using NIR light. The whole system consists of two low coherence interferometric principles; low coherence scanning interferometry (LCSI) for measuring surface profiles and spectrally-resolved interferometry (SRI) to obtain the nominal optical thickness of the Si wafer. The wavelength of the optical source is around 1 μm, which can be transparent to the Si wafer and also detected by the typical CCD camera. Because of using the typical CCD camera, the whole system can be constructed inexpensively and it can give most of dimensional information of the Si wafer at once. In the experiment, the front and rear surface profiles as well as the nominal thickness and thickness variation of the Si wafer were simultaneously obtained.
This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2012R1A1A1001842)
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