We propose and demonstrate a new method which employs time-of-flight detection of femtosecond laser pulses for precise height measurement of large steps. By using time-of-flight detection with fiber-loop optical-microwave phase detectors, precise measurement of large step height is realized. The proposed method shows uncertainties of 15 nm and 6.5 nm at sampling periods of 40 ms and 800 ms, respectively. This method employs only one free-running femtosecond mode-locked laser and requires no scanning of laser repetition rate, making it easier to operate. Precise measurements of 6 μm and 0.5 mm step heights have been demonstrated, which show good functionality of this method for measurement of step heights.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
With the rapid development of the microelectronic industry, precise measurement of large-step structures in semiconductor devices, flat panel displays, and photovoltaic products becomes increasingly important for quality assurance. Commercial contacting profilers are powerful tools in step measurements. However, they may impose damage on the surface of the structures. Optical methods, which are noncontact, can overcome this problem. However, the step heights to be dealt with usually fall in the scale from micrometers to sub-millimeters, which is challenging for conventional optical profilers based on a monochromatic laser, since ambiguity in phase unwrapping exists when step height exceeds half of the wavelength . In order to get rid of the phase ambiguity problem, varieties of methods have been explored, including multi-wavelength interferometry [2,3], wavelength sweeping interferometry , and low-coherence scanning interferometry .
The optical pulse time-of-flight (TOF) detection has been intensively investigated in the past decades, which resulted in providing powerful tools in absolute distance measurements. Earlier TOF methods have been based on detection of optical pulses by electronic instruments  and can make absolute measurements of very long distance. However, due to the precision and resolution of electronic devices, the best of which is around picosecond level, the resolution of this scheme is limited to millimeter scale. Hence, such TOF methods are not suitable for measurement of steps in the microelectronic industry. For sub-micrometer resolution, optical TOF detection methods have been developed. In 2004, a stabilized femtosecond mode-locked laser (MLL) for high-resolution distance measurement was proposed, which combined the TOF and interference-fringe analysis . Several experiments were conducted based on this idea, showing precision comparable to the theoretical predictions [8–11]. Further efforts were made with an optical cross-correlation technique for TOF detection , which also showed good precision [13,14]. However, in these methods employing a single comb [7–14], the distance could be determined only when the two pulses were overlapped. As a result, additional work of adjusting laser repetition rate or the optical delay line was essential. This problem could be overcome by dual-comb-based methods [15–18]. The key feature of this kind of method was the creation of the Vernier effect in the time domain, realized by slight difference in repetition periods of the two combs. This detuning could generate a rapid scan of the entire range. The principle is also known as asynchronous optical sampling (ASOPS) [19,20]. By using dual combs, rapid and precise distance measurement is possible, but the requirement of two femtosecond MLLs and the phase lock system adds cost and complexity .
In this Letter, we propose a new method with the capability for precise height measurement of large steps, which employs TOF detection of femtosecond laser pulses. The new method enables precise TOF measurement with only one free-running femtosecond MLL, which helps reduce the cost and complexity. Figure 1 shows the principle. The output of MLL is divided into the reference pulses and interrogating pulses. First, a microwave signal is tightly synchronized with the reference laser pulse train. The interrogating pulses are incident on the target and then reflected to determine the time delay. Here, the time delay refers to the temporal position difference between the interrogating laser pulses and the zero crossings of the synchronized microwave. In order to achieve precise measurement, high-resolution timing detection and synchronization between the optical pulse train and the microwave signal are necessary. For this purpose, we employ sub-femtosecond-resolution fiber-loop optical-microwave phase detectors (FLOM-PDs) , which were also recently used for detecting strain of the fiber delay element in Ref. . When MLL pulses and a microwave signal with a multiple of the MLL repetition rate are fed to the FLOM-PD, the output error signal is proportional to the phase difference between the laser pulse position and the microwave signal zero crossing. The measured residual error (integrated in the 1 Hz–100 kHz Fourier frequency range) is down to 8.99 μrad (i.e., 179 as at 8 GHz) , which enables precise TOF measurement. Note that, due to the ultralow timing jitter property of typical free-running femtosecond Er-fiber MLLs [24,25], precise synchronization and TOF measurement are possible. Unlike the approach of optical sampling by cavity tuning (OSCAT) employed in lidar , the proposed method requires no repetition-rate scanning, and therefore it eliminates the need for the cavity tuning part (e.g., piezoelectric transducer) in MLLs.
In this method, the output error signal of FLOM-PD can be actually interpreted as the result of the optical pulse sampling the microwave. When the optical pulse samples beyond the linear range of the microwave, the sensor output does not uniquely correspond to the time difference between the optical pulse and the microwave zero crossing. Therefore, the proposed approach has a non-ambiguity range (NAR). The NAR in this method is related to the microwave frequency. Typically, the microwave applied to FLOM-PD ranges from 1 GHz to 10 GHz, and thus the corresponding NAR varies from 7.5 mm to 75 mm. Such NAR well suits the demand for large step measurement (usually from micrometers to sub-millimeters) in the microelectronic industry, which is challenging for conventional optical profilers based on a monochromatic laser.
To demonstrate the functionality of the proposed method for height measurement of large steps, we conduct the following proof-of-principle experiments. Figure 2 shows the schematic of the experimental setup. The 250-MHz pulse train generated from a free-running femtosecond Er-fiber MLL comb source (MenloSystems GmbH, FC1500-250-ULN) is divided into two paths, namely, the reference pulses and the interrogating pulses, with optical power of and , respectively. The reference pulses are for synchronization. They are fed to FLOM-PD 1, and the phase error signal between the pulse train and the 8-GHz microwave signal () generated from a voltage-controlled oscillator (VCO, Hittite HMC-C200) can be obtained. This error signal is fed to a home-built proportional-integral (PI) board to regulate the VCO. With the high-resolution FLOM-PD and precise PI control, tight synchronization between the VCO and the MLL can be achieved. The interrogating pulses are for TOF detection. They are coupled to free space by a fiber collimator. Since the sample to be measured is of small size, the beam size of the interrogating pulses is reduced by a pair of lenses. After reflection by the sample, the laser pulses are coupled into the fiber and fed to FLOM-PD 2 to detect the temporal position difference between the interrogating laser pulses and the zero crossings of the microwave generated by the synchronized VCO.
To get the distance-voltage response over the entire NAR, the error signal from the FLOM-PD 2 is recorded by a 16-bit 50 kS/s data acquisition card (National Instruments, USB-6002) when the VCO is not synchronized with the reference pulse train. In this situation, the frequency of the microwave does not equal the integer multiple of the MLL repetition rate, so the laser pulses will not stay stationary relative to the zero crossings of the microwave, but move one after another. As a consequence, they cover all the temporal positions over the entire period of the microwave. Therefore, the error signal from FLOM-PD 2 here is, in fact, the collection of all the possible voltages that will appear in TOF measurement. This approach can easily get the FLOM-PD response curve over the entire NAR, avoiding the relatively complex process of that in . In the experiment, the MLL repetition rate is read by a spectrum analyzer (Rohde & Schwarz, FSL18) in counter mode, which is 249.695800281 MHz, and the frequency of the synchronized microwave can be calculated by multiplying with a factor of 33, which results in 8.239961409273 GHz. Then the distance-voltage response curve (shown in Fig. 3) is attained by polynomial fitting of the data from the data acquisition card with the known NAR of 9.102 mm calculated from the microwave frequency. Once the error signal from the FLOM-PD is obtained, the distance can be determined by this curve. Note that, different from the TOF detection in just the linear range , this work employs the entire range of the NAR, which is beneficial for large step measurements. For precise measurement of the distance, we employ a low-noise data logger (Keysight, 34970A) for acquisition of FLOM-PD error signal with a sampling rate of 25 Hz for 5 1/2-digit resolution after a 30-Hz low-pass filter.
For this method, the ultimate uncertainty of the measurement is determined by how precise the timing detection and synchronization can be achieved between the optical pulse train and the microwave signal. This can be calculated by the out-of-loop residual phase noise power spectral density (shown in Fig. 4) when synchronization between them is achieved with the help of FLOM-PD. Note that, since we use a 30-Hz low-pass filter, we do not have to consider the phase noise above 30 Hz. Therefore, the calculated integrated timing jitter is 51 as, which determines the ultimate uncertainty of 7.7 nm.
To evaluate the system performance, a mirror is used as the sample. We first test the stability of the system with different averaging times while the mirror is fixed. As plotted in Fig. 5(a), the Allan deviation  varies with different averaging times: 15 nm for 40 ms, 9.5 nm for 400 ms, and 6.5 nm for 800 ms, which is consistent with the ultimate uncertainty of 7.7 nm calculated from the measured phase noise spectrum. Then the mirror is moved by the translation stage (driven by a stepper motor actuator with minimum incremental movement of 60 nm, Thorlabs, DRV001) with a step of 0.2 mm, and 10 displacement points are measured with an averaging time of 400 ms. As Fig. 5(b) illustrates, the residuals range from to 99 nm. Note that the p-value for the F-test of the linear fit between the measured distance and the true distance is calculated to be much smaller than 0.05, which indicates good significance.
In the microelectronic industry, the large step to be measured usually falls on the scale from micrometers to sub-millimeters. We first measure a step of micrometers. A microstructure with a step height of 6.0621 μm is employed as the specimen, which is confirmed by a commercial contacting profiler (Bruker Dektak XT) with 0.4 nm repeatability. As displayed in Fig. 6(a), the measured result is 6.049 μm, showing good performance, which benefits from the high-quality synchronization and high-resolution TOF detection. The repeatability over 10 measurements is 7.75 nm (). To further explore the applications in large step measurements, we increase the step height to sub-millimeters. A large step composed by two grade-K gauge blocks (Mitutoyo) is under test to examine the performance of this method. The two gauge bocks with thicknesses of 1 mm and 1.5 mm are stuck to an optical plane, so the nominal height of the step is 0.5 mm. As shown in Fig. 6(b), the measured height is 0.499984 mm, which is in good agreement with the nominal value, when considering the tolerance of the grade-K gauge blocks. The repeatability over 10 measurements is 11.5 nm ().
In summary, a new method that employs the TOF detection of femtosecond laser pulses for precise height measurement of large steps has been proposed and experimentally demonstrated. There is no requirement for laser repetition-rate scanning and only one free-running femtosecond MLL is needed, which makes it easier to operate. Meanwhile, this method also shows good measurement capabilities. It shows an uncertainty of 15 nm for a single measurement, which corresponds to 40 ms averaging time. The uncertainty can be further reduced to 9.5 nm for 400 ms and 6.5 nm for 800 ms. By using the tightly synchronized microwave phase as the timing ruler, precise measurement of large steps ranging from micrometers to sub-millimeters can be achieved. With these significant advantages, it is expected to find wider applications in the dimensional metrology field.
National Natural Science Foundation of China (NSFC) (61322509); National Research Foundation of Korea (NRF) (2013M1A3A3A02042273, 2018R1A2B3001793).
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