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Abstract
We present a femtosecond laser-based interferometry for step-structure surface measurement with a large field of view. A height axial scanning range of 348 µm is achieved by using the method of repetition frequency scanning with reference to the Rb atomic clock and the optical path length difference design for 21 times of the pulse interval. A combined method, which includes the envelope peak positioning method for rough measurement, synthetic-wavelength interferometry for connection, and carrier wave interferometry for fine measurement, is proposed to reconstruct the surface. A three-step specimen with heights of approximately 20, 50, and 70 µm was successfully measured with a height precision of 7 nm, and the accuracy was verified by a commercial white light interferometer. The diameter of the field of view that was demonstrated was 17.3 mm, which could be much larger owing to the high spatial coherence of the femtosecond laser. The results show that the femtosecond laser system combines the step-structure measurement performance of white light interferometry and the high-precision large-field performance of phase shifting interferometry, indicating its potential for widespread use in ultra-precision manufacturing of micro/nano-devices, such as semiconductor chips, integrated circuits, and micro-electro-mechanical systems.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
In recent years, micro/nano-devices such as semiconductor chips, integrated circuits, diffractive optical elements, and micro-electro-mechanical systems (MEMS) have been widely demanded in scientific research and industrial fields such as telecommunications, microelectronics, aerospace, and high-precision engineering [1–5]. Micro/nano-structure surfaces that cover large areas are typical in these devices, and the surface topography has a great influence on device performance. For example, for MEMS chips, the lateral size could range from a few micrometers to hundreds of millimeters, and the vertical size of the structure could range from a few nanometers to millimeters. The surface topography with step height information affects its electromechanical properties such as the capacitance, voltage, and electric field distribution [6,7]. In addition, the finer morphological features of the surface on each layer, such as the peak-to-valley (PV) value, the root-mean-square (RMS) value, and the presence of scratches also reflect the hardness, residual stress, contact stiffness, and fatigue strength of the materials [8]. Furthermore, these properties may directly influence the final performance and yield of a MEMS device. Therefore, high-precision measurement of the step-structure surface over a large area is of great significance for quality control in ultra-precision manufacturing of micro/nano-devices.
In the field of micro/nano-surface measurements, optical methods are widely used because they offer the advantages of non-contact and high-precision measurements. These methods include phase shifting interferometry, white light interferometry, wavelength scanning interferometry, and holography [9–12]. Among these methods, phase shifting interferometry offers high vertical resolution and large lateral field-of-view (FOV) owing to the high coherence of the laser light source, but the existence of 2π phase-ambiguity limits its application to surfaces of which the discontinuities exceed half a wavelength [13]. Two-wavelength phase shifting interferometry is adopted to overcome the phase ambiguity problem. The principle is that by measuring the phase of the surface at two wavelengths, λ1 and λ2, a phase map corresponding to a longer equivalent synthetic-wavelength given by ${\mathrm{\lambda}_{\textrm{syn}}} = {\lambda _1}{\lambda _2}/|{{\lambda_1} - {\lambda_2}} |$ is obtained, thus increasing the ambiguity-free range from half a single-wavelength to half a synthetic-wavelength [14,15]. Further extension of the range requires additional wavelengths to be provided individually in sequence, which is not a cost-effective approach [16,17]. Therefore, the most widely used method for discontinuous surface measurements is white light interferometry. Owing to the short coherence length of white light, high-contrast interference fringes appear only at the position at which the optical path length difference (OPD) is close to zero. Scanning the reference arm along the optical axis enables the distribution of the zero OPD position, which represents the topography of the measured surface to be obtained [18–20]. However, the low spatial coherence of the white light, such as the halogen lamps, light emitting diode and thermal sources, restricts the FOV below to a few square millimeters [21]. Measurement of a surface with a larger area can only be achieved by multiple measurements on different lateral parts followed by stitching [22]. The superluminescent light-emitting diode (SLD) is a great broadband light source with high spatial coherence, but the randomness of the frequency phase limits its precision to reach the nanometer level as single longitudinal mode laser does [20,23–25]. Therefore, with conventional approaches, it is not easy to realize discontinuous micro/nano-surface topography with both high vertical precision and large lateral FOV.
During the last decade, femtosecond lasers have significantly advanced the surface measurement fields owing to their superior characteristics with high spatial coherence and periodical low temporal coherence, and compared to SLD, it offers higher stability of multi-frequency modes traceable to atomic clock [26,27]. Several femtosecond-laser-based approaches for full-field surface measurement have been proposed, including femtosecond laser based coherence scanning interferometry [28], phase shifting interferometry and low coherence interferometry by sweeping the repetition rate [29–31], multi-wavelength interferometry based on wavelength generation from the frequency comb [32,33], and spectral interferometry based on a chirped frequency comb [34,35]. Among these methods, low coherence interferometry based on repetition rate sweeping adopts the basic principle of white light interferometry and achieves microelectronic step-structures surface measurement with nanoscale height precision and an FOV of hundreds of square millimeters [30]. The envelope peak positioning of the interferogram (IGM) could overcome the 2π phase-ambiguity, and thus, carrier phase peak extraction offers a higher precision for height measurement [30,36]. However, with respect to the bridge of the envelope peak and the phase peak results, systematic problems related to fringe order determination may occur. For example, the pulse broadening effect caused by long fiber transmission flattens the envelope peak, which reduces the positioning precision of the envelope peak. Batwing effects at sharp edges and the slope effects at locally tilted surface areas, which have often been discussed in white light interferometry methods, also arise in a femtosecond laser system because they are the result of diffraction and dispersion errors [15,36]. All these effects may lead to so-called ghost steps. Specifically, when the height precision obtained by the envelope peak position does not reach a quarter wavelength, the fringe order of the carrier phase cannot be correctly determined, resulting in ghost steps that are half a wavelength high or an integer multiple thereof [36,37].
In this paper, we demonstrate a full-field high-precision interferometer for step-structures surface topography using a femtosecond laser. The laser beams were expanded and a Twyman-Green interferometer was adopted to reach a large FOV with hundreds of square millimeters. For vertical scanning, we revisited the repetition rate sweeping method to acquire low coherence IGM, which is expressed as a sinusoidal carrier inside the pulse envelope. The envelope peak positioning (EPP) method was used to obtain rough measurement results for step surface topography. In addition, carrier wave interferometry (CWI) was employed to attain higher precision based on single wavelength phase extraction. We overcame the problems presented by ghost steps by employing synthetic-wavelength interferometry (SWI) as a bridge to connect the EPP and CWI methods. As a result, the precision of the step height measurement was enhanced to the nanoscale, and the continuous surfaces of each step layer were also precisely reconstructed.
2. System configuration
Figure 1 shows a schematic of the interferometric surface measurement system based on a femtosecond laser. The light source is a mode-locked Er-doped fiber laser with a central wavelength of 1558 nm and spectral bandwidth of 46 nm, and the optical spectrum is shown in the inset in Fig. 1(a). The repetition frequency frep is 63.804 MHz, and it can be scanned precisely by adjusting the resonant cavity length of the femtosecond laser and detected by a frequency counter with reference to the Rb atomic clock. Adjustment of the laser cavity length is based on two-stage modulation with different mechanisms: the first is a moving stage with a scanning range of 20 mm, resulting in frep changing by 271.4 KHz; and the second is a piezoelectric transducer (PZT), which is affixed to part of the fiber cavity for a scanning range of 33.2 µm, resulting in frep changing by 450 Hz. The pulse train from the light source is divided into two paths by a 50:50 fiber coupler, naturally becoming the reference pulses and measurement pulses, respectively. A long fiber delay line consisting of a single-mode fiber (SMF) and a dispersion compensation fiber (DCF) is inserted in the measurement path, together with the subsequent spatial delay line consisting of a retroreflector prism (RP) and a mirror (M1) to extend the OPD to 98.67 m, which is 21 times the pulse interval. After it is transformed into space light beams by the fiber collimators, the pulses of the two paths are adjusted to be polarization perpendicular to each other with half-wavelength plates (HWP), polarization beam splitters (PBS), and quarter-wavelength plates (QWP), thus constructing a polarization multiplexing system. A beam expander, which is composed of a micro-objective, a pinhole, and a collimating lens, was built to expand the reference and measurement beams simultaneously at a magnification of 10. Then, the expanded beams enter the polarized Twyman-Green interferometer, are separated again at PBS3 and are incident to the reference mirror surface and the measurement surface, respectively. To prevent unnecessary interference fringes caused by light leakage from the PBS and reflections from unwanted surfaces, the interferometer is designed to be asymmetric with a deliberate path difference of ∼5 mm (considerably larger than the pulse width) between the two arms. The measurement pulses with the wavefront carrying information about the target surface and the reference pulses may encounter interference at the polarization plate (P) and the interference images are recorded by a high-speed infrared camera (Allied Vision, G-033). To compensate for the wavefront error caused by the expanded aberration, we use a compensate mirror as the measurement surface first to obtain the inherent aberration between the reference and measurement wavefronts. Two band-pass filters (BPF) with different central wavelengths are alternatively inserted to construct the subsequent synthetic-wavelength interferometry. The filtered spectra are illustrated in the inset Fig. 1(b).
Fig. 1. Schematic of the experimental setup of a large-field interferometer based on a femtosecond laser: CP (coupler), FC (fiber collimator), SMF (single mode fiber), DCF (dispersion compensation fiber), HWP (half wavelength plate), PBS (polarized beam splitter), RP (retroreflector prism), M (mirror), QWP (quarter wavelength plate), OL (objective lens), CL (collimator lens), P (polarizer), BPF (band-pass filter). (a) Optical spectrum of the light source. (b) Filtered optical spectra after BPFs.
3. Principles of repetition frequency scanning
To simulate the femtosecond laser based interferometric system, we set up a theoretical model to illustrate the basic principles of repetition frequency scanning. The frequency spectrum of a femtosecond laser consists of a series of discrete longitudinal optical modes, and the nth optical mode can be expressed in terms of repetition frequency frep and offset frequency fceo as fn=n frep+ fceo. Thus, the electric field of the original pulse train can be described as a superposition of frequency components as $E(t )= \mathop \sum \nolimits_n {A_n}\cdot {\exp}({i\cdot 2\pi {f_n}t} )$, where An represents the amplitude of the nth frequency components, which is equivalent to the optical spectrum and theoretically to a Gaussian function [38,39]. Assuming that the optical length of the reference path and measurement path are x0 and x1, respectively, and both the paths have the same intensity, the electric field of the reference and measurement pulse trains can be expressed as follows:
Fig. 2. Principle of repetition frequency scanning for relative time delay between the measurement and reference pulses to generate inteferograms. The distance offset between the dark blue and light blue pulse trains represent twice the step height of the specimen.
4. Data processing for surface reconstruction
According to the theoretical model of the repetition frequency scanning principle in Section 3, we can reconstruct the measurement surface by extracting the envelope peak position and the initial carrier phase from the IGMs. To obtain the complete IGMs, we first scan the moving stage in the resonant cavity of the femtosecond laser to approximately locate the interference position, and then apply a linearly varying voltage to the PZT to precisely scan the frep. Although the tuning speed of PZT can reach 10 mm/s, the final scanning speed is mainly limited by the frame rate of the camera, which is 200 fps in our experiment. According to the Nyquist limits, the sampling rate should be more than twice as large as the carrier frequency. Hence, the sampling step is calculated to be less than half of the carrier wavelength, which is 779 nm, and the maximum scanning speed is 155.8 µm/s (maximum sampling step × frame rate). Here, we set the repetition frequency scanning range and one-way scanning time based on PZT to approximately 300 Hz and 14 s, respectively. These values correspond to the final scanning speed of ∼33.6 µm/s, and the scanning step is 168 nm, which means that there are approximately 10 sampling points in a cosine period of the IGM. Figure 3(a) shows the time-resolved IGM of one surface point recorded by the camera and the repetition frequency simultaneously recorded by the frequency counter. Because of the nonlinear voltage response of PZT and transmission nonlinearity between PZT and the fiber, the IGM is distorted to a certain extent. Therefore, we first need to preprocess the signal to obtain the scanning-distance-resolved IGM using the relationship $\mathrm{\Delta }{l_{\textrm{pp}}} = c\cdot \mathrm{\Delta }{f_{\textrm{rep }}}/f_{\textrm{rep}}^2$, as shown in Fig. 3(b). Figure 3(c) shows a magnified view of the horizontal axis near the envelope peak in Fig. 3(b).
Fig. 3. Data processing of the envelope peak positioning method. (a) Time-resolved interferogram and repetition frequency increment. (b) Interferogram and repetition frequency increment transformed as a function of the scanning distance. (c) Magnified view of the horizontal axis near the envelope peak. (d) Extracted envelope and the Gaussian fitting results thereon.
After obtaining the scanning-distance-resolved IGM of each pixel in the FOV, the target distance D, which is linear to the corresponding pixel height H, is measured in three steps. First, EPP method is applied to find the position that the envelope peak of the IGM appears, reaching a precision of micrometer level. Second, SWI is used to obtain the interferometric phase of the synthetic wavelength, whose integer order is determined by EPP results. This step improves the precision to submicron level. Finally, the carrier phase of the IGM derived from CWI, whose integer order is determined by SWI results, is used to calculate D with nanometer level. Following are the details.
To obtain the position of the envelope peak, we process the preprocessed signal by a Fourier transformation, filter out the fundamental frequency components, and then perform an inverse Fourier transform to extract the envelope. Thereafter, Gaussian fitting is adopted to position the envelope peak, and the results are recorded as DEPP. This is the processing flow of EPP method. And the fitting result for the extracted envelope is shown in Fig. 3(d). At the same time, the argument of the maximum frequency in the Fourier spectrum, which is exactly the carrier phase ${\varphi _\textrm{c}}$ of the central wavelength, is also extracted as a partial result of the CWI. The complete expression of the precise result of CWI is ${D_{\textrm{CWI}}} = ({{N_\textrm{c}} + {\varphi_\textrm{c}}/2\mathrm{\pi}} )\cdot {\mathrm{\lambda }_\textrm{c}}/2$, where the integer order Nc could only be determined with a high degree of certainty when the precision of DEPP is below λc/4 [36]. However, the IGM indicates that the envelope peak is relatively flat compared to the carrier wavelength and that at least 10 cosine periods with approximately the same amplitude exist near the peak, which means that it is difficult to reach a precision of λc/4. To resolve this problem, we use synthetic-wavelength interferometry to bridge the EPP method and CWI.
To generate the synthetic-wavelength, we insert two band-pass filters with different central wavelengths, measured as λ1=1528.7 nm and λ2=1579.4 nm, as mentioned in the system configuration. Thus, the two carrier phases, ${\varphi _1}$ and ${\varphi _2}$, are obtained by detecting the IGMs at two optical wavelengths by scanning the repetition frequency in a very small range that covers the carrier wavelength. Then, the two interference signals can be written as $\textrm{cos}({2\mathrm{\pi}\textrm{M}{l_{\textrm{pp}}}/{\mathrm{\lambda }_1} - {\varphi_1}} )$ and $\textrm{cos}({2\mathrm{\pi}\textrm{M}{l_{\textrm{pp}}}/{\mathrm{\lambda }_2} - {\varphi_2}} )$. Therefore, the equivalent synthetic signal can be derived as $\textrm{cos}({2\mathrm{\pi}\textrm{M}{l_{\textrm{pp}}}/{\mathrm{\lambda }_{\textrm{syn}}} - {\varphi_{\textrm{syn}}}} )$, where the phase of the synthetic-wavelength can be calculated by ${\varphi _{\textrm{syn}}} = {\varphi _2} - {\varphi _1}$, and the synthetic-wavelength is calculated as 47.62 µm by ${\mathrm{\lambda }_{\textrm{syn}}} = {\lambda _1}{\lambda _2}/({{\lambda_2} - {\lambda_1}} )$, which is much larger than the carrier wavelength. The result derived from the SWI method is expressed as ${D_{\textrm{SWI}}} = ({{N_{\textrm{syn}}} + {\varphi_{\textrm{syn}}}/2\mathrm{\pi}} )\cdot {\mathrm{\lambda }_{\textrm{syn}}}/2$. Therefore, step-by-step conveyance of the precision is possible under two conditions, as illustrated in Fig. 4: First, the precision of DEPP should be higher than λsyn/4, which is calculated as 11.905 µm, to determine the integer order Nsyn in the expression of the SWI results. Second, the precision of DSWI should be higher than λc/4, which is calculated as 389.5 nm, to determine the integer order Nc in the expression of the CWI results [44–47]. The precision of DEPP and DSWI are measured as 1.478 µm and 125 nm through experiments, and details are described in the next section. Figure 5 shows the complete data processing flow chart, demonstrating all the processing steps mentioned above.
Fig. 4. Principle of the combined method for surface reconstruction. Synthetic-wavelength interferometry is used to connect the envelope peak-positioning method and carrier wave interferometry. The EPP result (DEPP) determines the integer order Nsyn of the synthetic-wavelength, and the SWI result (DSWI) determines the integer order Nc of the carrier wavelength.
5. Experiments and results
5.1 Verification of conveyance conditions with SWI
The compensation mirror was first measured as the sample and the surface was reconstructed with the combined methods mentioned in Section 4. This measurement is conducted for two reasons: on the one hand, the reconstruction results are used, as system aberrations mainly resulted from the beam expansion to compensate for the wavefront errors in the subsequent measurements; on the other hand, the precision of the EPP method, SWI, and CWI is obtained from 15 consecutive measurements to verify the two conditions. Figure 6 shows the surface measurement results of the mirror. The results of the height reconstruction using the EPP method and the distribution of the standard deviation (STD) over repetitive measurements are shown in Fig. 6(a), from which we can deduce that the maximum STD of the EPP height δDEPP is 1.478 µm. This is greater than λc/4, but much smaller than λsyn/4, indicating that the precision of the EPP method for this system is insufficiently high to directly determine the integer order Nc of CWI; however, it is sufficient to determine the integer order Nsyn of SWI. This verifies that the first transfer condition is satisfied. Figures 6(b) and 6(c) show the carrier phase distribution at the central wavelengths of 1528.7 nm and 1579.4 nm, which were measured by using the CWI method, and also the STD distribution of the phase. The precision of the phase measurement can be derived as $\delta {\varphi _1} \le 0.025\; \textrm{rad}$ and $\delta {\varphi _2} \le 0.022\; \textrm{rad}$. According to the expression of DSWI, the precision of SWI can be estimated with the equation
Fig. 6. Results of 15 measurements for the compensated mirror surface. The (a-1) reconstructed height distribution and (a-2) STD of the height obtained by the EPP method. The (b-1) phase distribution and (b-2) STD of the phase by CWI based on the central wavelength of 1528.7 nm. The (c-1) phase distribution and (c-2) STD of the phase by CWI based on the central wavelength of 1579.4 nm. The (d-1) reconstructed height distribution and (d-2) STD of the height by SWI, calculated with the two carrier phase data in (b) and (c).
5.2 Measurements of optical surface based on CWI
To demonstrate the precision and accuracy of the proposed method on full-field continuous surfaces, a glass slide surface with an area of 7.5×10.5 mm2 was measured based on the CWI method. Figure 7(a) shows the reconstructed height distribution of the surface. Based on the results of 10 repetitive experiments, it was concluded that the PV value is 0.765 µm with a standard deviation of 4.1 nm, and the RMS value is 0.253 µm with a standard deviation of 0.9 nm. To validate the accuracy of the results, a commercial Fizeau interferometer was used to perform a comparative experiment with the same specimen, and the reconstruction result is shown in Fig. 7(b). The PV and RMS values measured by the Fizeau interferometer are 0.802 µm and 0.254 µm, respectively, which are essentially consistent with the results generated by the femtosecond laser system. The maximum height difference of the sectional profiles along the line AA’ is 79 nm, as illustrated in Fig. 7(c), and the residual for the entire surface is displayed in Fig. 7(d). The difference in surface height is mainly due to the different stresses on the glass surface resulting from the different fixtures we used in the two experiments. However, the consistency of the surface shape could indicate that the performance for full-field continuous surface measurement of the femtosecond laser system maintains the same level with the commercial Fizeau interferometer.
Fig. 7. Reconstruction results of the glass slide surface with (a) the femtosecond laser system, (b) the commercial Fizeau interferometer. (c) Height comparison of the sectional profiles between the two methods along the line AA’. (d) Distribution of the residual error for the entire surface.
5.3 Measurements of large-step structures
To demonstrate the capability of the combined methods we proposed for full-field step surface measurement, a three-step specimen composed of three standard gauge blocks with heights of 1.01, 1.03, and 1.08 mm was measured as an example. The height differences among the three blocks are approximately 20, 50, and 70 µm. The repetition frequency is scanned by PZT with a range of 430 Hz. Figure 8(a) displays selected interference images captured by the camera. Here we adjusted the interferometer to set the angle between the reference wavefront and measurement wavefront close to zero, and therefore, the interference fringes on a single image are not obvious. Moreover, the frep-resolved interference signals of two points P and Q from the different step surfaces are shown in Fig. 8(b), from which we can clearly see the distance offset between the two IGMs due to the difference in the step height.
Fig. 8. (a) Selected interference frames captured by CCD camera during repetition frequency scanning. The dark horizontal and vertical bars are the gap among the gauge blocks. (b) The frep-resolved IGMs of two points P and Q from the different step surfaces, which are marked on the frames. The middle one shows the complete IGM with the frep scanning range of 430 Hz. The upper one is a magnified view of the horizontal axis at Δfrep from 84 to 89 Hz, where the IGM of point P has a high contrast whereas point Q does not. The lower one is a magnified view of the horizontal axis at Δfrep from 261 to 265.5 Hz, where the IGM of point Q has a high contrast whereas point P does not.
After acquiring the IGMs of all the pixels in the interference field, the step-structure surface was firstly reconstructed using the EPP method, shown in Fig. 9(a-1). The sectional profiles along lines A1A2 and B1B2 are illustrated in Fig. 9(a-2). Because of the existence of a gap width of approximately 0.5 mm among the gauge blocks, these data were removed. The results clearly show the oscillation at the edges of the surface, the so-called batwing effects caused by diffraction. The step height of the single line is calculated with the average values of the upper and lower heights. We repeated the experiment 15 times, and the measurement results of the step height HA are demonstrated in Fig. 9(a-3), with the repeatability σEPP of 1.820 µm. Then, the methods of SWI and CWI are used to reconstruct the surface, and Figs. 9(b) and 9(c) shows the results similarly organized as those in Fig. 9(a), respectively. The batwing effect is obviously gradually weakened without resulting in ghost steps. Furthermore, the height repeatability is improved to σSWI of 0.209 µm with SWI, and finally to σCWI of 7 nm with CWI, indicating that the precision for height measurement with the combined methods reaches the nanometer level.
Fig. 9. Three-step surface reconstruction and height repeatability over 15 measurements. Results from the EPP method: (a-1) 3D reconstructed height distribution, (a-2) sectional profiles along lines A1A2 and B1B2, (a-3) measurement repeatability of step height HA of 1.820 µm. Results from the SWI: (b-1) 3D reconstructed height distribution, (b-2) sectional profiles along lines A1A2 and B1B2, (b-3) measurement repeatability of step height HA scales down to 0.209 µm. Results from the CWI: (c-1) 3D reconstructed height distribution, (c-2) sectional profiles along lines A1A2 and B1B2, (c-3) measurement repeatability of step height HA finally improved to 7 nm.
To validate the height accuracy, we also conducted a comparative experiment with a commercial white light interferometer (Bruker, Contour GT-IM) with a step height accuracy of 0.75%. As shown in Fig. 10(a), the step heights corresponding to the two reference lines are 51.571 µm and 71.102 µm, respectively. Figure 10(b) shows the results obtained from the femtosecond laser system. Considering the reference lines at the same position, the step heights are 51.737 µm and 70.869 µm, respectively, which are consistent with the results of the comparison. It should be noted that the area of FOV in our system is approximately 50 times larger than the commercial white light interferometer.
Fig. 10. Comparison of reconstruction results between the commercial white light interferometer and femtosecond laser interferometer. Results from the white light interferometer: (a-1) reconstructed surface, (a-2) x section profile with length of 1.2559 mm, (a-3) y section profile with length of 0.9414 mm. Results from the femtosecond laser interferometer: (b-1) reconstructed surface, (b-2) x section profile with length of 7.883 mm, (b-3) y section profile with length of 7.586 mm.
5.4 Wide FOV measurement for step-structure with letterings on surface
A femtosecond laser can achieve a very large FOV for measurement owing to its high spatial coherence. Theoretically, it can be expanded to several meters [27,31] and still create high-contrast interference fringes, which is exceedingly difficult for other broadband light sources. In this experiment, we adopted a collimating lens with a larger focal length, expanding the FOV to 17.3 mm, and measured another step-structure specimen composed of two gauge blocks with heights of 1.08 mm and 1.09 mm. The letterings on the surface of the blocks are clearly visible in the field of view, shown in Fig. 11(a). The full-field reconstructed results are demonstrated in Fig. 11(b), and the step height at the central line is measured to be 10.062 µm, which coincides with the value of 10.065 µm measured by the white light interferometer, which was used for comparison. In addition to the step height information, we also obtained the high-precision morphological information for the step surface of each layer at the same time, shown with the height axial magnified view of the upper and lower surfaces in Fig. 11(c) and Fig. 11(d). Therefore, both the step height and fine morphological information within a large FOV can be obtained in a single measurement, which is almost not possible with the traditional interferometers alone such as a Fizeau interferometer or white light interferometer. These experimental results demonstrate the strong potential of using the proposed method in industrial applications, such as step measurement and scratch detection for large-scale integrated circuit chips and MEMS chips.
Fig. 11. Reconstruction results of step-structure sample with letterings on step surface. (a) Image of the surface captured by the camera. (b) 3D reconstructed height distribution with FOV of 17.3 mm diameter. (c) Height axial magnified view of the lower step surface with letterings of “1.09” thereon. (d) Height axial magnified view of the upper step surface with letterings of “1.08” thereon.
6. Conclusion
We demonstrated a large-field, high-precision interferometer to measure the surfaces of step-structures with a femtosecond laser. A polarization-multiplexing unequal-path interferometer was designed and configured for the purpose of this measurement. Precise scanning along the height axis of the specimen was achieved by scanning the repetition frequency with reference to the Rb atomic clock. The scanning range by PZT modulation is approximately 450 Hz, corresponding to a height measurement range of 348 µm, with maximum extension to 210 mm with the moving stage in the laser cavity. For the surface reconstruction process, we proposed a combined method, which includes the EPP method for rough measurement, the SWI for connection, and the CWI for fine measurement. The SWI proved to be effective for overcoming the problem associated with the insufficient precision of the EPP method for determining the integer order of the carrier wave results, as well as the problem of batwing effects. However, SWI needs to switch BPFs during the measuring process, which increases the measurement time, so the system is not suitable for the rapid or on line detection of step-surface specimen. This problem can be solved by adding a camera to capture IGMs under two wavelengths at the same time. It is not achieved due to cost reasons, which will be improved in the future. We used the combined method to reconstruct a three-step specimen with step heights of approximately 20, 50, and 70 µm. The precision of the height measurement is enhanced from 1.820 µm with the EPP method to 7 nm with the CWI method, and the accuracy is also verified by comparison with a commercial white light interferometer. For the measurement of continuous surfaces, a glass slide surface morphology is obtained with CWI, and the PV and RMS values agree well with those obtained by the commercial Fizeau interferometer. Finally, we expanded the field of view to 17.3 mm to simultaneously realize the step height measurement and surface morphological detection for the step-structure specimen with lettering on each of the surfaces, indicating that the femtosecond laser system combines the functions of the traditional white light interferometer and phase shifting interferometer. All these measurement capabilities of the femtosecond-laser-based topography system demonstrate its potential for wide applications in the ultra-precision manufacturing field for micro/nano-devices, such as semiconductor chips, integrated circuits, and micro-electro-mechanical systems.
Funding
Natural Science Foundation of Beijing Municipality (3182011); National Key Research and Development Program of China (2016YFF0101804); National Natural Science Foundation of China (51835007, 61575105).
Disclosures
The authors declare no conflicts of interest.
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