Detection of inter-layer and internal defects in semiconductor silicon (Si) wafers by non-contact, non-destructive and depth-resolving techniques with a high lateral and depth resolution is one of the challenging tasks in modern semiconductor industry. In this paper, we report that nonlinear optical harmonic generation can be of great virtue therein because it enables non-invasive inspection of inter-layer defects with sub-micrometer depth resolution in extensive penetration depth over several millimeters. Compared to existing inspection methods for inter-layer defects, such as ultrasound, photoacoustic and photothermal imaging, the proposed technique provides higher lateral and depth resolution as well as higher interfacial selectivity. For in-depth understanding of nonlinear harmonic generation at Si wafer surfaces, the spectral power distributions of third and fifth harmonics from Si wafers with various crystal orientations and dopants were carefully analyzed under different incident polarizations and excitation depths using a near-infrared (NIR) femtosecond laser as the excitation light source. We finally demonstrated that inter-layer defects inside stacked Si wafers, such as delamination or stacking faults, can be inspected with a high lateral and depth resolution in a non-contact and non-destructive manner. These findings will pave the way for nonlinear optical harmonic generation to the fields of interfacial studies of crystalline materials, high-resolution detection of sub-diffraction-limit surface defects, and high-resolution imaging of internal structures in stacked semiconductor devices.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
CorrectionsYi Gao, Hyub Lee, Jiannan Jiao, Byung Jae Chun, Seungchul Kim, Dong-Hwan Kim, and Young-Jin Kim, "Surface third and fifth harmonic generation at crystalline Si for non-invasive inspection of Si wafer’s inter-layer defects: erratum," Opt. Express 27, 38028-38028 (2019)
Silicon (Si) is the most widely used base material in the semiconductor industry. The requirement for high-quality Si wafers has drastically increased as the minimum feature size has decreased to a few nanometers in the semiconductor manufacturing. The higher density integration requested in semiconductor products has attracted significant interest in three-dimensional memory and data storage devices . As a result, non-destructive inspection of internal and inter-layer defects in Si wafers has become more important to realize higher productivity with higher process reliability. While the surface defects, such as micro-scratches, micro-cracks, and crystal originated particles, can be detected by traditional optical inspection techniques based on light scattering [2,3], the internal or inter-layer defects beneath the Si wafer surfaces have remained difficult to detect with depth and lateral resolution down to sub-micrometer-scale utilizing traditional transmission-based inspection techniques, even with NIR light [4–6]. Existing non-destructive defect inspection techniques mainly rely on ultrasonic, thermal, or high-energy electromagnetic radiations . Ultrasonic inspection requires intermediate media for wave propagation and provides a relatively low sub-millimeter resolution due to long wavelength . Thermal inspection is known to be slow due to the slow nature of heat transfer process and the inspection images are disturbed by thermal blurring effects . Although high-energy radiations provide a high lateral resolution down to a few nanometers, high-energy radiation sources generating X-rays or gamma-rays should be involved which are highly dangerous to human beings. Recent advances in internal defect inspection have been made by utilizing photoacoustic or photothermal effects excited by short laser pulses [9–11]; due to the high directionality of laser beam and high NIR transmission of Si wafers, these techniques do not require any physical contact between the detection probe and sample, nor the ionizing radiation sources. However, they still provide limited performance regarding the spatial and depth resolution (20 µm in the lateral and 50 µm in the depth domain), as well as the layer selectivity along the depth direction . Linear low-coherence interferometry using a broadband NIR femtosecond laser was applied to the detection of small gaps between two stacked Si wafers , where super-continuum generation, low-NIR-sensitivity of Si CCD camera, and their vibration sensitivity have limited their wide-spread applications. Therefore, a non-contact, non-destructive, and depth-resolving internal defect inspection techniques with high lateral and spatial resolution has been highly demanded so as to improve the manufacturing productivity in semiconductor manufacturing processes.
Nonlinear optical harmonic generation could be a novel solution candidate for internal defect inspection of Si wafers enabling non-contact, non-destructive, high-resolution, and depth-selective measurement . Optical harmonic generation occurs when an intense laser beam passes through an optical medium, leading to the generation of higher energy photons at the integer multiples of input photon energy while maintaining the very high coherence with the incident laser . Second harmonic generation (SHG) is the most widely reported nonlinear optical phenomena but its efficiency is known to be very low in cubic-symmetry material like Si. Instead, the odd orders of harmonics, including third harmonic (TH) and fifth harmonic (FH), are efficiently generated in Si, because they are not strongly dependent on the asymmetry of materials [14,15]. Interestingly, third harmonic generation (THG) and fifth harmonic generation (FHG) are surface phenomena so their conversion efficiency is significantly higher at material interfaces where bulk symmetry is broken . Therefore, TH and FH intensities are strong at the surfaces and drastically decay within a skin depth of a few micrometers . Great efforts have been addressed to enhance odd-order harmonics at the surfaces of a various of substrates [18,19]. However, in-depth optical characterization of surface THG in crystalline Si wafers and its applications in internal or inter-layer defect inspection have remained unexplored to date. Surface FHG has barely been studied even with higher potential imaging resolution due to the limited photon numbers after the conversion.
In this report, we characterized crystalline Si as a nonlinear optical medium for surface THG and FHG by focusing NIR femtosecond laser pulses under different input polarization states and excitation depths. After the characterization, inter-layer structural defect inspection of the stacked Si wafers was demonstrated in a non-contact, non-destructive, and depth-selective manner. Firstly, the spectral positions, bandwidths, and power conversion efficiencies of THG and FHG were measured to confirm the wavelength conversion mechanism. Secondly, polarization dependencies and crystal orientation effects were checked; four-fold polarization dependency was found for both THG and FHG; the different crystal orientation made the changes in conversion efficiencies by ~35 and 50%. Thirdly, the depth resolutions for THG and FHG were evaluated to be 46.8 and 11.1 μm when NIR femtosecond pulses were focused by a 40 × objective lens. Finally, to demonstrate the technological feasibility of inter-layer defect inspection, the inter-layer delamination in stacked Si wafers was measured and reconstructed by monitoring the transmitted power at the fundamental wavelength with a depth resolution of 121 nm at an averaging time of 1 s. These results suggest that nonlinear optical harmonic generation can be applied to the non-contact, non-destructive, high-resolution, and depth-selective inspection of the internal defects in Si wafers.
2. Third and fifth harmonic generation at crystalline Si: optical layout and sample preparation
Semiconductor Si wafers are known to be opaque because Si has a low optical transmittance over the whole visible wavelength from 400 to 850 nm (See Figs. 1(a) and 1(b)). Therefore, the internal and inter-layer defect inspection of Si semiconductor products has remained difficult with existing optical inspection systems. If we shift the spectral range of our interest to NIR regime having longer wavelengths than 1,100 nm, Si wafers are partially transparent; the transmittance through a 5.0 mm Si wafer is about 52% (See Fig. 1(b)), which is high enough for efficient inspection of internal structures. The other remaining inspection issue is the depth selectivity when measuring multi-layer stacked wafers. Because the NIR light transmits through the stacked wafers, all the layer images will be overlapped. Thus, in order to check the inter-layer stacking faults, depth selectivity is essential, which cannot be realized with traditional optical inspection methods. Therefore, we introduced nonlinear THG and FHG here for depth-resolved and layer-sensitive multi-layer inspection.
Figure 1(c) shows the optical layout for Si wafer characterization and defect inspection. A NIR mode-locked Er-doped fiber femtosecond pulse laser (Toptica, FemtoFiber Pro NIR) having a central wavelength of 1,595 nm was selected as the inspection light source considering the high NIR transmittance of Si wafer and high optical power required for efficient THG and FHG. The pulse repetition rate and the pulse duration were set to ~83 MHz and ~400 fs, respectively. For in-depth characterization of THG and FHG at Si wafers, five double-side polished Si wafers having different crystal orientations and doping conditions were tested, including intrinsic, P-doped and N-doped ones with either (100) or (111) crystalline orientation. All Si wafers utilized here had the same thickness of 500 μm and diameter of 4 inches. A half-wave plate (Thorlabs WPH10M-1550) rotated the polarization state of the linearly polarized input laser beam. Before the focusing objective lens, the laser beam was firstly long-pass-filtered to remove the background noise at shorter wavelength range than 1,200 nm. This is because the short wavelength noise can be generated during the power amplification in an Er-doped fiber amplifier and subsequent power delivery through the optical single mode fiber. The laser beam was then focused into a small spot of 7.6 μm diameter using a 40 × objective lens (Newport LI-40X) having a numerical aperture of 0.65; the power density at the focus was 1.1 × 109 W·cm−2. Nonlinear optical harmonics generated from the Si sample were collected by another 40 × objective lens (Olympus UPlan 40X) with the same numerical aperture. They were delivered to a broadband spectrometer (Andor’s Shamrock 193i) with a highly-sensitive electron-multiplying charge coupled device (EMCCD; Andor’s IXon Ultra) for the spectral analysis and an amplified photo-detector (PD; Thorlabs, PDA10CF) for the power analysis in the frequency domain. For highly sensitive detection of relatively weak FH pulses, a 400 nm short-pass filter (Ruiqi Optoelectronics SPF-400) was installed to suppress the relatively strong background noise at longer wavelengths.
When the intense NIR laser pulses are focused onto the internal or inter-layer defects in Si wafers, TH and FH are generated at the defects; this energy conversion to shorter wavelength induces the optical power decrease at the fundamental NIR wavelength following the energy conservation law. Because TH and FH generated inside the wafers are directly absorbed back to Si, they cannot be directly detected by the EMCCD nor photodetector. Therefore, TH and FH cannot be used for Si wafer inter-layer inspection. Instead, we monitored the transmitted optical power at the fundamental NIR wavelength over different focal depths to reconstruct the interfaces among different layers and also to detect the internal defects with a high lateral and depth resolution.
Figure 1(d) shows the conceptual diagram for THG and FHG at an intrinsic (100) Si wafer. Because Si is a typical face-centered diamond cubic crystalline material, the atomic structures of the Si along with the polarization states of the incident laser beam should be different with different crystalline faces . For example, while the (100) plane of single crystalline Si has a 90° symmetry cell with the edge length of 0.54 nm , the (111) plane has a hexagonal bi-dimensional cell having the edge length of 0.76 nm . The cell’s edge length affects the dipole strength, which determines THG and FHG efficiencies under different polarization states of the incident laser beam . The different cell symmetry also results in the difference in harmonic spectrum [14,22]. Because the doping rate changes with the energy band structures, its variation also changes the power conversion efficiencies in harmonic generation .
3. THG and FHG: spectral peak position, conversion efficiency, and spectral bandwidth
TH and FH were generated at the lower surfaces of the Si wafers as shown in Fig. 2(a). Figure 2(b) shows the energy diagram involved in THG and FHG. Three photons at the fundamental wavelength are combined at the Si wafer into one new photon having three times higher photon energy in THG, while five photons are involved in FHG resulting in five times higher photon energy. As the fundamental wavelength of the laser used in the experiments is 1,595 nm, the resulting TH emission should be theoretically in the visible wavelength at 531 nm, while FH in the UV wavelength at 319 nm. The typical output spectra including the fundamental laser beam, TH, and FH are shown in Fig. 2(c). Figures 2(d) and 2(g) show the experimental spectra of third and fifth harmonics from various sets of Si wafers with different doping and crystalline axis. Clear TH peaks are observed at ~531 nm as in Fig. 2(d) with minor deviations of less than 3.2 nm for different samples; these minor deviations could come from the imperfect angular alignment among optical axis of the optical components in the free-space optical setup during the sample unloading and reloading. It is worth to note that the fundamental laser’s NIR spectrum around 1,595 nm was measured using an optical spectrum analyzer (OSA, Yokogawa AQ6370D) instead of the EMCCD due to the low spectral sensitivity of Si-based detectors at longer wavelength than 1,000 nm. The absolute power of TH was measured at the maximum average pump power of 56.3 mW using a high-sensitivity photomultiplier tube (PMT; Thorlabs, PMT1001M); the conversion efficiency was calculated to be 9.9 × 10−8. FH peaks are observed around 330 nm, which is slightly higher than one-fifth of the excitation laser wavelength, ~319 nm. This deviation comes from the contribution of multiple photoluminescence at high pump peak intensity. Multiple photoluminescence also results in higher emission yield and boarder spectra as in Figs. 2(h) and 2(i), which will be discussed in the later section. The absolute power of FH could not be directly measured due to the low signal level even with the high quantum efficiency of PMT; the conversion efficiency was indirectly estimated by using the relative power ratio of fifth and third order harmonics detected by EMCCD. Note that the power ratio between TH and FH was calculated by considering the transmittance and quantum efficiencies of all optical components, spectroscope, and EMCCD. The estimated FHG efficiency is then calculated to be around 1.2 × 10−9.
The emission yields of TH and FH are evaluated by the linear-fitted slopes of the harmonic-intensity vs. pump power density relations as shown in Figs. 2(e) and 2(h). For THG, the slopes are 2.94, 2.92, 2.93, 2.96 and 2.86 for intrinsic-(100) (hereafter, this will be abbreviated to un-(100)), P-(100), N-(100), intrinsic-(111) (hereafter, this will be abbreviated to un-(111)) and P-(111) Si wafers with standard errors of 0.028, 0.034, 0.029, 0.026 and 0.024, respectively. All these slopes are very close to 3.0 within 3% deviation, which agrees well with the nonlinear power dependence, ITHG ∝ Pn in nonlinear perturbative harmonic generation, where n is 3 for THG and 5 for FHG. FH slopes are 7.16, 7.15, 7.38, 7.67 and 6.54 with standard errors of 0.26, 0.75, 0.76, 0.90 and 0.18 for un-(100), P-(100), N-(100), un-(111) and P-(111) Si wafers. These emission yields are higher than 5.0 for all wafers, suggesting that there are additional power contributions from other mechanisms, which could be attributed to multiphoton luminescence. There has not been a report about the multiphoton luminescence from bulk Si but was reported in Si quantum dots and similar semiconducting materials such as GaAs [24,25]. The relatively larger standard errors are expected to come from the low power conversion efficiency of FHG; because of this lower efficiency, FH is more vulnerable to spectral background noise than TH.
The spectral bandwidths of TH and FH are analyzed as in Figs. 2(f) and 2(i). The bandwidths of TH and FH are converted from wavelength domain to photon energy domain, then, normalized by dividing the photon energy spectra by harmonic orders, which is 3 for TH and 5 for FH. The resulting spectra for both TH and FH make a good agreement with the original spectral profile in the fundamental wavelength (See Figs. 2(f) and 2(i)); theoretically, the normalized harmonic spectral bandwidth is same as that of the fundamental beam. The bandwidths of TH spectra with different wafers are all ~0.005 eV in full-width-half-maximum (FWHM), slightly smaller than that of fundamental laser spectrum of 0.008 eV. This smaller TH bandwidth is expected to come from the spectral characteristics of the optical components in the imaging path, spectrographs, and EMCCD. The material dispersions of all focusing and imaging optical components could also contribute to this spectral bandwidth reduction. For FHG, the normalized spectra show ~0.021 eV bandwidths in FWHM, which is wider than that of the fundamental laser (0.008 eV). This broader bandwidth and its different spectral shape (See Fig. 2(i)) cannot be simply explained by the harmonic generation mechanism; this peak broadening could come from weak multiple photoluminescence from Si. It should be noted that the spectral resolution of the EMCCD-based spectrograph system is 0.47 nm (this corresponds to 0.005 eV in photon energy), so the wider FH bandwidth does not come from the spectral resolution. The spectral power of the multiphoton luminescence around TH is much weaker compared to TH, so we could not observe this trend in TH. However, FH has two orders of magnitudes lower power conversion efficiency than TH at the pump power density of 187 kW/cm2, which makes the multiple photoluminescence more significant at FH. No clear differences have been observed in spectral domain for Si wafers with different doping conditions.
4. Polarization-dependency of THG and FHG: crystallographic orientation effect
The yield dependence of THG and FHG to different incident polarization states was tested as shown in Fig. 3(a). The conversion efficiency of nonlinear perturbative harmonic generation process is strongly dependent on the crystalline structure due to the variation of energy bands at different electron oscillation directions as shown in Fig. 3(b) . Normalized THG and FHG spectra at different incident polarization states from 0 to 360° for un-(100), P-(100), N-(100), un-(111) and P-(111) wafers are shown in Figs. 3(c)-3(l). In all polarization states, THG shows a distinct peak around 531 nm with the deviation of less than 3.2 nm; this deviation is expected to come from the optical axis misalignment in the excitation pathway. Note that breaks are inserted into the horizontal axis of Figs. 3(c)-3(g) to clarify that SHG signal was not observed in all polarization and doping conditions. For all the samples except P-(111), clear four-fold symmetry is observed with ~35% modulation depths. No clear polarization dependence is observed in P-(111) Si wafer, which is because the P-type ions are randomly doped into Si crystal so break the symmetric structure of Si lattice. The longer atomic distance between nearby Si atoms in the <111> crystal plane results in weaker electric dipole formation when exposed to the laser field . As a result, the dopants play a crucial role in determining the dipole strength when excited by the polarized light . Due to the random distribution of the dopants in Si crystal, the overall intensity of electric dipoles is not dependent on the polarization state of the excitation laser field . This explains the weaker polarization dependence of THG yield for P-(111) Si wafer. In (100) Si wafer, the shorter distance to nearby Si atoms on the lattice plane creates a stronger electric dipole when exposed to the polarized laser field and it also weakens the counter effect made by randomly distributed dopants in Si crystal. These lead to the stronger polarization dependence of THG in doped (100) Si wafers. Similar trends are observed in FHG. For Si wafers other than P-(111), clear four-fold symmetry is observed with a modulation depth of ~50%. This higher polarization dependence for FHG can be explained by the higher sensitivity of the electron restoration forces in higher-order nonlinear optical processes [18,22]. These results indicate that the doping conditions and crystalline orientation of Si wafers can be characterized based on the polarization dependence of TH and FH.
5. Surface THG and FHG: a study on excitation depth dependence
THG and FHG are both surface phenomena so they provide high power conversion efficiency selectively at the interfaces between two materials having different refractive indices . In-depth studies on this excitation depth effect have been addressed as shown in Fig. 4. A high-resolution 3-axis translational stage (Thorlabs RB13M) was used to adjust the height of a focusing objective lens with a step size of 5.0 μm as shown in Fig. 4(a). Figures 4(c)-4(g) show the resultant TH intensity distribution at different excitation depths for all five Si wafers with different doping concentrations and cutting planes. The polarization angle was chosen to be 280° for the optimization of TH and FH intensity. The TH intensity reaches its maximum at the Si-air interface and drastically decreases at both the air and bulk Si part. In the air side, TH cannot be excited due to the low density of molecules in the atmospheric air. In the bulk Si side, the lower TH intensity can be explained by the Gouy phase shift which leads to π/2 phase shift of the generated TH beam ; as the result, the two TH beams, one generated before the focal point and the other generated after the focal point, interfere with each other in destructive way so as to decrease the resultant intensity to zero . This occurs at all cutting planes, indicating no dependence on crystal orientation. By fitting the TH intensities at different focusing depths using Gaussian profile, it was found that FWHM of TH intensity decreases to 50% at 23.4, 20.1, 15.6, 18.5 and 12.3 μm from the air-Si interface for un-(100), P-(100), N-(100), un-(111) and P-(111) wafers, respectively; the intensity decreases to zero at 52.1 μm for all Si samples. This suggests that the simultaneous excitation of TH at both top and bottom surfaces of Si would be possible for the wafers thinner than 52.1 μm. Compared to THG, FHG was found to be more sensitive to the excitation depth. The FH spectra from different excitation depths are shown in Figs. 4(h)-4(l). The maximum FHG is also found to be located at the exact excitation depth for maximum THG. The full-widths FH intensity decreases to 50% are 6.1, 5.5, 5.2, 5.0 and 5.4 μm, respectively. The FH intensity decreases to zero at the excitation depth of 34.6 μm away from the Si-air interface to both bulk Si and air side. No clear relationship is identified among the doping condition, crystalline orientation and the excitation depth of TH and FH.
6. Non-contact, non-destructive, and interface-selective detection of inter-layer defects in Si wafers
Because nonlinear optical phenomena are highly selective to the presence of interfaces, THG and FHG can be promising tools for efficient detection of the internal and inter-layer defects in Si wafers. When the intense femtosecond pulses are focused onto internal or inter-layer defects in Si wafers, the resulting TH and FH intensities increase significantly due to the breakage of local symmetry at boundary atoms and end unit cells. This process is governed by the energy conservation law in nonlinear optical processes, which is described by the equation, , where , , and are the energies of transmitted, incident, reflected, and absorbed photons, respectively. The absorbed photon energy can be described as where is the Planck constant, ∑n, ∑3 and ∑5 are the sum of the photons absorbed in fundamental, TH, and FH wavelengths; and are the optical frequencies of the fundamental beam, TH and FH; ∑i is the sum over the material excitations created in the elementary quantum process; describes the energy of an elementary material excitation, for example, a phonon or an exciton . This equation on energy conservation implies that TH and FH generated at the defects with energy of and will result in the decrease of the transmitted intensity at the fundamental wavelength, , which newly enables the efficient inspection of internal and inter-layer defects of Si wafers. Although TH and FH are at visible and ultra-violet wavelength regime where Si has extremely low transmission of around 0.0001%, the intensity decrease at the fundamental NIR wavelength can be efficiently monitored using amplified InGaAs photodetectors thanks to the high transmission of Si wafers in the NIR range. Besides, the presence of material excitations in the elementary quantum process make the power decrease of the fundamental wavelength even higher than the simple sum of the energy of TH and FH, so improves the inspection resolution. Based on this energy conservation law in nonlinear harmonic generation, we demonstrated non-contact, non-destructive, and interface-selective detection of internal or inter-layer defects in stacked Si wafers with high resolution as shown in Fig. 5. Three un-(100) Si wafers of 280 ± 10 μm thickness were stacked together to imitate a stacked Si wafers with a thickness of ~840 μm and two inter-layer defects, one at ~280 μm and the other at ~560 μm, respectively (See Figs. 5(a) and 5(b)). The focal depth of a NIR femtosecond laser was scanned along the depth direction over the stacked Si wafers to measure TH intensity profile for the reconstruction of the inter-layer structures; the focusing objective lens was gradually shifted up with a 5 µm step size. The wavelength was selected to 1,595 nm considering the high transmission window of silicon wafers (1,400~2,000 nm), short depth-of-focus and available femtosecond lasers. At the interface between Si wafers, TH and FH are generated, which leads to sudden power decreases at fundamental wavelength (See Fig. 5(c)). The location of the interfaces can be calculated from the focusing depth by considering the refractive index of Si at 1,595 nm, which was 3.47 in this experiment . For highly sensitive signal detection with minimal background noise, we introduced frequency-selective signal detection which is generally used in the field of optical communication. For the purpose, the intensity of incident beam was detected by a PD and analyzed by a radio frequency (RF) spectrum analyzer (Rigol DSA875) with a resolution bandwidth of 1 kHz and a span from 83.3345 to 83.3350 MHz. A distinct RF peak is identified at 83.33 MHz, which matches well with the repetition rate of incident femtosecond laser beam; this indicates that the coherence, linewidth, and mode spacing of the femtosecond laser is successfully maintained during THG (See the RF spectrum in linear and logarithm scale in Figs. 5(d) and 5(e)). The signal-to-noise ratio is higher than 55 dB, which means the signal strength is ~320,000 times higher than the background noise thanks to the frequency selective nature of RF spectrum analyzer; this is significantly higher than traditional non-frequency-sensitive analysers such as oscilloscope, data analyzers, or EMCCD. The background noise was further suppressed to 0.36 mV by optimizing the data averaging time (to 1 s) and resolution bandwidth (RBW; to 1 kHz), which leads to a better depth resolution of 121 nm; the depth resolution was determined here as the smallest excitation depth change which makes the detectable power decrease at the fundamental wavelength. The accumulated RF spectrum along the depth scanning shows the interior interfacial structure of the stacked wafers as shown in Fig. 5(f). Three clear gaps can be recognized around 287.3, 652.4, and 926.5 μm from the back surface of the overall stacked wafers, indicating the precise locations of the two Si-Si interfaces between stacked Si wafers intimating the inter-layer delamination and the top Si-air interface of the Si wafer stack. The yellow dots on the right side of Fig. 5(f) show the peak intensity of RF spectra at different Si wafer depths, three clear dips can be clearly identified and match well with the positions of the interfaces. Note that these dips are created by the nonlinear optical absorption, not by other linear optical phenomena such as multiple reflections at the Si-air-Si interfaces. This is experimentally evidenced by the dip at the excitation depth of 926.5 μm at the Si-air interface (See Fig. 5(f)), where multiple reflection does not take place. Theoretically, the intensity decrease made by the multiple reflections was calculated to be about 0.05% based on the Fresnel equations , which is two orders of magnitude lower than the experimental result of 3%. Due to the high incident-power dependence of nonlinear optical harmonic generation, TH and FH generated by the multiple reflected light is negligible. Besides, linear absorption was also negligible in the experiment due to the low absorption coefficient of Si at 1,595 nm (~10−9 cm−1).
This proposed method provides a non-contact, non-destructive inspection technique for internal defects in Si wafers with a high depth resolution of 121 nm, which is higher than that of current standard methods such as ultrasonic and photothermal based techniques . The lateral resolution in this paper is ~1.0 μm which is limited by lateral scanning mechanism. By utilizing nano-positioners for the lateral scanning, sub-diffraction-limit high resolution imaging can be realized due to the nonlinear optical imaging capabilities of THG and FHG. The data acquisition time is dependent on the averaging time for noise reduction; with a fast 3D scanning stage, the full scanning time requested for covering a 3-inch wafer is estimated to ~1 s based on previous reports based on similar optical configurations [32,33], which is suitable for in-line Si wafer inspection. The scanning speed and resolution can be further improved by utilizing integrated optical devices, motor-controlled scanning platforms and objective lens with higher numerical aperture and working distance. This technique can be applied to the materials where the fundamental wavelength can transmit through because odd-order optical harmonic generation is an extensive phenomenon in most materials. This nonlinear harmonic generation can be a promising tool to achieve non-contact, non-destructive, on-line inspection of internal defects with high lateral and depth resolution for any wafers with good transmission at incident laser wavelength such as Si, gallium arsenide and gallium nitride.
To conclude, we demonstrated depth-selective optical inspection of stacked Si wafers using nonlinear THG and FHG at interfacial surfaces. In-depth optical characterization was firstly addressed for understanding THG and FHG in crystalline Si wafers by focusing mode-locked femtosecond pulses to the Si wafers with different crystalline orientation, doping ratio, and excitation depths. With different crystalline Si of intrinsic, P-doped, and N-doped wafers, TH and FH intensities were changed by 35% and 50%, respectively, whereas the crystalline intensity dependence was much weaker in P-doped (111) wafer. For non-contact, non-destructive, interface-selective detection of inter-layer defects inside the Si wafers, the focal depth of the incident NIR laser beam was scanned along the depth direction of the stacked Si wafers and detected the Si-Si interfaces intimating the internal defects at the depths of 287.3 and 652.4 μm, by monitoring the optical power decrease at the fundamental wavelength based on the energy conservation in nonlinear optical harmonic generation. By introducing frequency-selective RF peak detection and background noise suppression, the depth resolution was improved to 121 nm at an averaging time of 1 s. This scheme can serve as an excellent tool for surface and inter-layer studies in material sciences and nonlinear photonics as well as mass production of semiconductor devices.
Singapore National Research Foundation (NRF) (NRFF2015-02); National Research Foundation of Korea (NRF-2017M3D1A1039287).
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