1. Introduction

As the size of flat panel displays (FPDs) is getting larger, the technique for high speed and non-contact measurement of nano structures over large area is highly required by the FPD industry. Among various techniques, three major techniques for profile measurement of nano structures are white light scanning interferometry (WSI), confocal microscopy (CM), and phase shifting interferometry (PSI) [1-3]. WSI is widely being used in the manufacturing lines for semiconductors and liquid crystal display panels. However, since it uses mechanical scanning of the probe head or the specimen stage, high speed measurement is not available with WSI. Similarly, CM also requires mechanical scanning of the probe head or the sample stage, thus being limited for high speed measurement.

PSI, on the other hand, does not necessarily require a mechanical scanning, since there are several methods to produce phase shifts to the interferometric fringes. Apart from the typical method of using a piezoelectric transducer, phase shifts could be achieved by changing the refractive index of air, scanning the laser frequency, or using optical elements to make spatially phase shifted interferograms. The change of refractive index of air could be made by adjusting air pressure inside the interferometer, but the pressure change also causes deformation to the interferometer optics which results in measurement error. Two methods to provide four phase shifted interferograms simultaneously were proposed [4-5]. One method uses a diffractive optical element and two micro polarizer sheets fabricated by using lithography technique [4]. Another method uses bulk optical elements to spatially provide four phase shifted interferograms [5]. Both methods are very powerful in that they can make a one shot measurement which is insensitive to vibration from the environment. However, they face degradation in spatial resolution because four phase shifted images are acquired by a single charge-coupled device (CCD) array. Phase shifting by scanning the laser frequency, which does not require a sacrifice of spatial resolution was introduced [6,8], but these techniques are not applicable to high speed measurements.

This paper proposes a new technique to realize a high speed PSI which is based on frequency scanning method and uses injection locking of laser frequency to the resonant modes of a Fabry Perot cavity (FPC). In Section 2, the overall scheme of the high speed PSI is presented, and in Section 3, the evaluation result on the phase steps and the experimental result showing the insensitiveness of the interferometer to vibration are given.

2. Principle of the high speed PSI

The schematic diagram of the high speed PSI is depicted in Fig. 1. The laser diode (LD) which has a power of 10 mW operates in single mode, and is tunable about 25 GHz without mode hopping around 635 nm. The FPC is made of ultra-low-expansion (ULE) glass, and has a confocal configuration. The cavity length and the radius of curvature of the spherical surfaces of the FPC are designed as 20 mm so that the free spectral range (FSR) of the FPC would be

where c is the speed of light in vacuum, n is the refractive index of ULE glass, and l is the cavity length of FPC.

Laser beam emitted from the LD undergoes a spatial filtering and passes a lens, L₂. This lens is used to mode match the laser to the confocal FPC. The beam which is transmitted through the beam splitter (BS₁) enters the confocal FPC, while the beam being reflected by the BS₁ is headed to the interferometer and to the frequency monitoring system. If we linearly scan the applied current to the LD, whenever the laser frequency matches one of the resonant frequencies of the FPC, the beam from the FPC is seeded back to the LD. By injection locking, the LD frequency is locked to the resonant frequency of FPC [7]. When the current is linearly changed, LD will be locked to successive resonant frequencies of the FPC whose frequency differences are equal to the FSR of the FPC. To confirm the locking of laser frequency, a frequency monitoring system which consists of a Fabry-Perot etalon (FPE) is used. The FPE is a 5 mm thick parallel glass plate whose surfaces are uncoated, so that the FSR is wide enough compared to that of the confocal FPC. When the incident laser frequency is linearly scanned, the intensity of light reflected from the FPE changes nearly sinusoidally. The locking of the laser frequency can be monitored by this system because when the laser frequency is injection locked, the laser intensity reflected from the FPE no longer varies sinusoidally but stands still until the frequency of the LD cavity is beyond the locking range. This monitoring system is only used during the system setup, and is not necessary for surface profile measurements. Frequencies of equal step can be used for producing equal step phase shifts in the PSI, especially for the Carré algorithm [8]. Since the LD current can be modulated in high speed, and injection locking occurs in a sufficiently short time, four equally phase shifted interferograms can be acquired and processed rapidly in a short time with high repetition rate. The speed limit is mostly determined by the speed of the CCD camera and the processor of the computer. To be able to always scan the laser frequency from a specific resonant frequency of the FPC, temperature and current of the LD were controlled within ±1 mK and ±0.01 mA, respectively, by using the LD driver (ILX Lightwave, LDX-3220) and a TEC controller (ILX Lightwave, LDT-5948), so that the frequency variation due to the temperature and current fluctuation would be small enough compared to the FSR. Since the thermal expansion coefficient of ULE glass is about 3×10^-8 /K, the ambient temperature fluctuation of ±0.1 K contributes less than 3×10^-9 to the relative standard uncertainty of the laser frequency. Although the Carré algorithm can be applied with an arbitrary phase step except multiple of π, we used the phase step of 110° which is known to minimize the influence of the random intensity noises [9].

 

Fig. 1. Schematic diagram of the high speed phase-shifting interferometry. LD: laser diode; L₁,L₂, L₃, L₄: lens; PH: pinhole; BS₁, BS₂, BS₃: beam splitter; OI: optical isolator; CFPC: confocal Fabry-Perot cavity; PD₁, PD₂, PD₃: photo detector; FCL₁, FCL₂: fiber collimating lens; FBS: fiber-optic beam splitter; FPE: Fabry-Perot etalon; CL: collimating lens; M: mirror; RM: reference mirror; A: aperture.

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Since the frequency step is determined by the FPC, the length difference, ΔL , between the reference arm and the test arm of the interferometer is set to be

where c is the speed of light in vacuum, n is the refractive index of ULE glass, and Δf is the frequency step which is equal to the FSR of the FPC.

Laser intensity transmitted through the FPC is monitored while linearly scanning the LD current, and when it reaches a specific level, a trigger signal is sent to the high speed CCD camera (MIKROTRON, MC1310) after a certain time delay. When setting the triggering intensity level, the difference in peak intensities of the modes was taken into account. The camera shutter is opened in the manner that the central part of the mode is used for the image acquisition. The LD current was modulated with a saw tooth function whose amplitude is 1 mA, so that four equally phase shifted interferometric fringes could be acquired within a period. Figure 2 shows the applied LD current, laser frequency, laser intensity transmitted through the confocal FPC, and the trigger signal for the image acquisition, measured with modulation frequency of 100 Hz. It can be seen from the second graph of Fig. 2 that even the LD current is linearly changed, whenever the frequency of the LD cavity is within the locking range, the laser frequency is kept constant as the result of injection locking. This was tested with various modulation frequencies, and it was possible to produce four equally phase shifted images over 250 Hz, i.e., within 4 ms. Carré algorithm is applied to these images for phase reconstruction.

3. Experimental evaluation of the high speed PSI

Repeatability of the locked frequency was evaluated by measuring the laser frequency with a wavelength meter while repeatedly scanning the LD current with a saw tooth function of frequency 1 Hz for 60 s. Since the response of the wavelength meter (HighFinesse, Wavelengthmeter WSU30) is not fast enough, a mechanical shutter (UNIBLITZ, LS3ZM2-108) was placed between the laser and the wavelength meter. While monitoring the laser intensity transmitted through the confocal FPC, a trigger signal was sent to the shutter when the intensity reached a specific level just as in the case of image acquisition. The shutter was opened for 9 ms during which the laser frequency was measured. The standard deviation of the locked frequency of a specific resonant mode of the laser was measured to be 2.4 MHz.

 

Fig. 2. LD current, laser frequency, transmitted intensity after FPC, and the trigger signal.

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The standard deviations of three frequency steps measured during 60 s were 3.0 MHz, 3.4 MHz, and 3.3 MHz, respectively, which corresponds to about 0.1° in phase step. This phase step error gives rise to length measurement uncertainty of about 0.2 nm.

High speed PSI has an advantage of being insensitive to vibration. To verify this property, profile of a flat mirror was measured with two different conditions. At first, the surface profile of a test mirror was measured with the interferometer on a vibration isolated optical table. Next, we released the air of the optical table so that vibration from the environment could be transferred to the interferometer. For each measurement, the modulation frequency of 20 Hz was used. The difference of two profiles is shown in Fig. 3, and the root mean square of the difference is calculated to be 0.5 nm. On the other hand, the standard deviation of 10 repeated measurements made on the vibration isolated optical table was calculated to be 0.4 nm. Comparing these two values, it can be concluded that the high speed PSI is insensitive to vibration.

 

Fig. 3. Difference between two surface profiles measured with and without vibration isolation.

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4. Conclusions

We have presented a high speed PSI which utilizes self injection locking property of a frequency tunable LD. Since the LD frequency is locked to the resonant modes of the FPC, equal phase steps can be provided to the interferometric fringes by varying the LD current linearly, and these images are ideal to be analyzed by the Carré algorithm. As the LD current can be modulated in high speed, and injection locking occurs in a sufficiently short time, we could realize a high speed PSI which takes only 4 ms for a single measurement which acquires four equally phase shifted images with 640×480 pixels in size. The repeatability of the self locked frequency of the laser was evaluated to be 2.4 MHz, and the standard deviation of the frequency steps was measured to be about 3 MHz, which corresponds to 0.1° in phase. This phase step error gives rise to length measurement uncertainty of about 0.2 nm. High speed measurement has the advantage of being insensitive to vibration, and this was verified by experiment. The proposed high speed PSI could be applied as a microscopic interferometer in the fields which require fast measurement of micro or nano structures on a large area with high repetition rate.