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A new scanning microscope scheme which can map both phase and amplitude change of the probe beam is introduced. We will show that the true surface structure can be imaged by using the results of phase measurements while the amplitude image represents the map of the magnitude of the effective local reflection coefficient (ELRC). Relation between the surface structure and the ELRC is discussed. Spatial resolution is 0.67µm which is limited by diffraction and the precision for measuring point-to-point variation of the average height of the surface structure is a few nanometers. Potential of this microscopy on surface diagnostics is discussed.
©2008 Optical Society of America
1. Introduction
Optical diagnostics is very important in both fundamental academic researches and industrial applications in spite of its relatively poor spatial resolution, limited by diffraction, then that of a scanning probe microscope [1–12]. Among many optical diagnostic techniques, scanning two-beam interferometer (STBI) scheme is very important because it can provide a 3-dimensional image of the surface under test (SUT) with extremely good depth resolution. Various STBI schemes for imaging the surface structure have been proposed [1–8, 10–13]. In the STBI scheme, one of the two beams is used for probing the surface, a probe beam (PB), and the other beam is used as the reference beam (RB). In a homodyne interferometer, the two beams have the same frequency while there is a frequency difference, typically in the range of 10s or 100s of MHz, in a heterodyne interferometer.
In the STBI operating with a reflection mode, the PB is focused onto a SUT by using a focusing lens. The reflected beam is recollimated by the same lens and injected back to the interferometer along the same path. Scanning of the PB on a SUT results in phase modulation on PB, in which the phase difference between two neighboring scanning points is proportional to the geometrical path length between them. The modulated phase is directly converted to the base band signal for a homodyne interferometer, but the relative phase between PB and RB must be biased properly by a feedback control loop to maintain an optimum phase demodulation condition while scanning [1–5]. In the case of a heterodyne interferometer, the modulated phase is down converted to the intermediate frequency and requires another RF demodulation process to measure the phase change [6]. It has been shown that a phase-locked-loop (PLL) is a very effective demodulation technique, because it does not requires a complicated feedback control of the optical path length of one arm of the interferometer, which is unavoidable in the homodyne scheme [8,9]. Cho et al. applied this heterodyne scheme to obtain the map of the local slope of the SUT [8]. The 3-D image of the surface structure was reconstructed by use of the local slope of the scanning points. Mazzoni et al. applied this interferometer scheme to map the local electric filed distribution in the GaAs substrate produced by a micro-strip line [9].
In addition to the phase modulation, while scanning the SUT, the amplitude of the PB is also modulated because of defocusing of the PB due to height change and scattering of the PB at the surface structure. Moreover, local reflection coefficient can also be changed if the SUT is inhomogeneous. Therefore, in general, the PB is both phase modulated and amplitude modulated in the scanning process. Slow change in amplitude can be compensated for by use of an rf-automatic gain control (AGC) stage in the PLL. The amplitude change, however, is as fast as phase change in most of surface structures and may not be compensated for by using an AGC. Therefore, in practice, the image obtained by use of a conventional STBI may not provide the true topography of the SUT.
Both amplitude and phase of the PB provide very useful information for surface diagnostics if they can be measured separately and simultaneously. Jeong et. al, had shown that a scanning homodyne in-phase and quadrature (I/Q-) interferometer, which can measure both the amplitude and the phase of the probe beam at the same time, can be used for complex analysis of a surface. Optical arrangement of the homodyne I/Q-interferometer used in this pioneering work, however, is not simple and requires a tedious alignment procedure [2].
In this paper, we are introducing a scanning heterodyne I/Q-interferometer scheme which can map the phase and the amplitude change simultaneously while scanning the PB over the surface. We will show that the phase image represents the true 3D structure of the surface, while the amplitude image represents the map of the magnitude of the ELRC. I/Q-demodulation is a well known technology in rf-communications and we applied this technique for demodulating the heterodyne beat signal. The technique may have been used in various sensor applications [14,15]. However, to the best of our knowledge, it is the first time that this technique has been applied for obtaining maps of the phase and amplitude change of the PB in the scanning heterodyne interferometry. Although we did not use a proper aperture in the image plane, we will show that, as a first order approximation, the amplitude image can be regarded as a confocal image. Therefore, the proposed microscope scheme can provide both confocal amplitude image and true topographical structure of the surface.
2. The Experiment
The schematic of the optical arrangement is shown in Fig. 1. A homemade dual-frequency, dual-polarization, stabilized He-Ne laser is used for a light source of the scanning interferometer. Frequency difference between the two modes is 680MHz and heterodyne beat measurements ensure us that the frequency stability of each polarization mode is as stable as a commercial stabilized single frequency laser. Output light from the laser is split into two paths by a beam splitter, BS1. Two polarization modes in the reflected beam from the BS1 are mixed by the use of an analyzing polarizer oriented at 45° to the polarization modes and a high speed photodiode, PD1. AC component of the beat signal from the PD1 is used as the LO in the RF mixing. Two polarization modes of the transmitted beam from the BS1 are split into two paths by using the PBS1. As shown in Fig. 1, the transmitted beam from the PBS1 is used as the PB of the scanning heterodyne interferometer while the reflected beam is used as the reference beam of the heterodyne interferometer. An OI is used in the path of the PB to prevent any stray reflections from tracing back to the laser. A HWP is used to let the probe beam transmitted through the PBS2. A QWP is inserted into the path of the PB so that the plane of polarization of the returning beam from a SUT is rotated by 900 and reflected at the PBS 2. The PB is focused onto the surface by using a OL and the reflected beam from the SUT is re-collimated by the same OL. The numerical aperture of the MOL is 0.8 and the focused beam size is approximately 0.67µm. The SUT is mounted on a 3-axes, precision, computer controlled step-motor stage. The PB is scanning over the SUT by moving the translation stage in two directions orthogonal to the propagation direction of the probe beam. Reflected beam from the PBS2 is mixed with the reference beam at the beam splitter, BS2, and the intensity of the mixed beam is detected by a fast photodiode PD2.
Fig. 1. Schematic of experimental arrangement. In the figure, BS’s are beam splitters, PBS’s are polarizing beam splitters, HWP’s are half-wave plates, QWP is a quarter-wave plate, OLis a microscope objective lens, PD’s are photodiodes, OI is an optical isolator, and LO and RF are local oscillator and rf-input port of a I/Q-demodulator.
The optical path length of the PB can be decomposed into two parts: the average length determined by the average height of the structure of the SUT and the difference between the average height and the actual height of the structure, h(x,y), at the scanning position (x,y). The former results in a quasi-static phase term φ 0 and the latter results in phase modulation which can be represented as φm(x,y). The amplitude of the PB reflected from the SUT is determined
AC component of the output signal from the PD2, which is the beat signal, νbeat, between the PB and RB, carries the phase modulation φm(x,y) and amplitude modulation AS(x,y) induced by the surface structure while scanning. Therefore, the beat signal is position dependent and can be written as
where R, AP and Δω=ω 2-ω 1 are the responsivity of the photodetector, amplitude of the PB, and the frequency difference between the SB and PB, respectively. The LO signal, the AC component of the output signal from PD1 is given by
where PLO and φLO are the optical power received at PD1 and the phase between two polarization modes, respectively.
The beat signal and LO are mixed at a commercial broad band I/Q-demodulator, which consists of two mixers. Both the beat signal and LO are divided into two and drive the corresponding ports of the two mixers, for which the LO phase of one of the two mixers is shifted by 90°. After low-pass filtering, the output intermediate frequency (IF) signal from each mixer can be written as,
and
where Δφs=φ 0-φLO is a quasi-static phase difference between the beat signal and LO signal. The phase modulation induced by the surface structure can be obtained by
and the amplitude modulation can be demodulated by the relation:
Along the scanning direction, say x direction, the phase difference between two neighboring scanning points can be converted to the height difference:
where Δx, λ, n, and h(x,y) are the scanning step size, wavelength of the PB, refractive index of air, and height of the structure at the scanning position (x,y).
In a conventional two-beam interferometer in which the output signal can be represented as Eq. (3), the phase and amplitude cannot be measured simultaneously. Therefore, it cannot be distinguished if the optical path length and the amplitude of the PB vary at the same time. In order to measure the height of the structure, for a conventional interferometer, correct response function must be obtained by a calibration using a standard structure [15]. In our new scheme, however, the absolute value the height can be directly obtained by using Eq. (5) and (7).
We did not use a proper confocal arrangement in this preliminary study. However, since the RB can select the specific field components of PB for which the propagation vectors are parallel to each other in the mixing procedure, and we are using a small size photodiode with 500µm diameter, as a first order approximation, the amplitude image obtained in our scheme can be regarded as a confocal.
The output signals from the I/Q-demodulator in each scanning point are digitized by the multi-channel 12-bit A/D converter and stored in the computer. Our own algorithm for accumulating the change in phase value, which will not be discussed in this paper, can effectively follow the phase change between two consecutive scanning points unless there is an abrupt change larger than ±π. The height variation of the surface structure between two neighboring scanning points was obtained by processing the data by using Eq. (7). The image of the surface structure obtained from the phase measurements, which is very close to the true topographical structure because the phase value is independent of amplitude of the PB. Since the focused beam has a finite size, ~0.67nm in our current arrangement, the phase value or the surface structure is given by the geometrical average of the path length over the focused region. The ambiguity caused by an abrupt change is much relaxed if the scanning step size is smaller than the focal size. As mentioned earlier, scanning the SUT results in amplitude modulation and a complete map of the local changes in amplitude can be obtained by processing the stored data with Eq. (6). The amplitude of the reflected beam from the surface is determined by the ELRC of the focused area.
In theory, if a coherent source is used, the sensitivity of measuring phase difference between two beams in the interferometer is limited by shot noise [16]. It can be shown that the minimum detectable phase difference between the PB and RB is given by
where P/hν, Δf, and η represent the number of photons, detection bandwidth, and quantum efficiency of the photodiode, respectively [16]. In this calculation, we took into account losses at the BS1, BS2, and I/Q-demodulation process. For a 1.7mW He-Ne laser and silicon photodiode (η~0.8), the minimum detectable phase difference is . Therefore, if the optical path length of the RB remains at constant value, the minimum OPL change of the PB which can be measured by a two beam interferometer is . Sensitivity close to the shot noise limit has been reported by many authors [8,9,16,17]. There are additional noises caused by environmental effects such as acoustic noise, vibrations, temperature change, and so forth. In order to minimize these environmental noises, the interferometer was installed in a constant temperature/humidity environment. In order to minimize interferences caused by floor vibrations and acoustic noises, the interferometer was mounted on the 300 mm thick optical table and enclosed in an acoustically shielded box. In addition, a quasi-static drift in phase can be rejected by using a low pass filtering of the data.
In order to measure the sensitivity of our interferometer, we used a vibrating mirror mounted on a PZT stage, in which the response of the PZT had been calibrated carefully. Applied AC voltage to the PZT was 1.5 Vrms at 40Hz and the corresponding RMS displacement of the mirror along the z-direction was approximately 0.22 µm. The output signal was processed in the computer and the result of the FFT of phase measurements is shown in Fig. 2. Assuming the noise level at the middle value of the noise floor, -40 dB(rad) or equivalently 10-4 rad, the signal to noise ratio is given approximately 39dB. Therefore, from the signal to noise ratio, the minimum displacement which can be measured in our interferometer is approximately 0.01 nm. It can also be shown that, from the mid value of the phase noise, -40 dB(rad), the measurable minimum displacement is approximately 0.014 nm. It is natural that these two calculations are in good agreement because the experimental data in phase measurements represent true phase value induced in the PB by the vibrating mirror. It is an experimental evidence that this new interferometer scheme does not require any calibrations for measuring displacement. Regarding the other parameters such as bandwidth of the receiver, number of average performed in each measurement, and so forth, it is reasonable to say that the precision for measuring the displacement is limited by the resolution of the 12-bit A/D-converter, which is approximately 0.1 nm. From this indirect evidence we can say that, in principle, the precision for measuring the height difference between two scanning points is approximately 0.1 nm. It will be shown from our actual scanning results that, in our present work, the precision for measuring the height variation of the surface is a few nanometers.
Fig. 2. The FFT spectra of phase measurements. The signal was modulated at 40 Hz and the term ‘dB rad’ stands for 10 log (phase change in radian).
In order to demonstrate the operation principle of this new microscope scheme, we used a patterned gold film as a SUT. The gold film was deposited on a strip pattern of photoresist (PR) to make a surface structure materially homogeneous. The cross-sectional view of the mesa structure of the strip line is shown in Fig. 3(a) and the conventional microscope image of the structure is shown in Fig. 3(b). The image show that the mesa structure has a gradual slope and there are a few hill structures in the bottom plane, which may be resulted from an imperfect patterning process.
Fig. 3. The cross-sectional view of the strip line structure (a), the conventional microscope image of the structure (b).
3. Measurement Results and Discussion
Three dimensional (3D) plot of the surface topography and the amplitude of the PB the scanning area are shown in Fig. 4(a) and (b), respectively. The height and width of the strip line obtained from the topography image are in good agreement with those measured by using a commercial stylus profiler. The amplitude image, which is equivalent to the local reflection coefficient map, shows that there is a significant loss on the edges of the structure.
Fig. 4. 3D plot of the surface structure (a), and amplitude of the PB (b) obtained by use of our proposed scanning I/Q-heterodyne scheme.
Height and amplitude image along one scanning line are shown in Fig. 5 as a blue and red line, respectively. The actual height obtained in this line scan result is in good agreement with both AFM and stylus measurements. The undulating structure in the lower part of the height scan image is also shown in the AFM measurement. Although the height is much larger than the theoretical limit of the precision in height measurement, this result ensures us that our new scheme can provide at least a few nanometer precision in height measurements of a surface without elaborated calibration procedure.
Fig. 5. Line scan images of the height and amplitude. The red and the blue trace represent the amplitude and the height variation along the scanning line, respectively.
It can be seen from the line scan images in Fig. 5 that the phase and amplitude measurements exhibit different responses. The amplitude image starts to decrease before the height changes at both the rising and falling edge of the strip and the slope of the height change is steeper than that of the amplitude. The width measured by using the topography image is narrower than the value obtained by using the amplitude image. These relationships can be explained qualitatively as follows: As shown in Fig. 6, if the focus is located at the edge of the strip, marked as FA1 in the figure, a part of the PB is reflected away from the side of the strip and it gives loss of the PB. There is a back scattered light from the illuminated region but it gives negligible contribution to the amplitude measurement. However, in the case of phase measurement, since it does not depend on the amplitude of the PB, the contribution from the backscattered light has the equal weight as the PB reflected back to the collecting lens from the top plane of the structure in Fig. 6. This is the reason why the amplitude of the PB decreases before the height or the phase changes. If the focus is located at the side of the mesa structure, marked as FA2 in Fig. 6, most of the light is reflected away which results in maximum loss in the amplitude of the returning PB. In the phase measurement, the average height in the focused area is given by the backscattered light and this is the reason why the minimum amplitude occurs in the approximately midway in the height change. The width of the strip line may be defined as the distance between the minimum amplitude points or half maximum width of the topography image. The phase image shows the hill structures in the bottom plane which can be seen in Fig. 4(b).
Two-dimensional (2D) contour plots of the surface structure and the amplitude are shown Fig. 7(a) and (b), respectively. As mentioned above, relationship between the topography and amplitude changes is clear in the vicinity of the edges of the strip structure, in which the loss mechanism of the PB is obvious. In the other areas, however, although we can say there is a subtle relationship between the topography and the amplitude image, it is difficult to find an exact correlation between them. We believe that an uneven surface structure results in different reflection geometries and it is the reason why we cannot fine exact correlations between two images. We can also see from Fig. 7(b) that there is no significant difference between the average amplitude of the reflected lights from the top and bottom area of the structure. It is reasonable to have this result because the strip line is not high enough (~70nm) to introduce a significant amplitude change. It should be pointed out that, although we did not use a lens-aperture assembly in front of the PD2 to clean up the spatial noise on the PB in this preliminary work, since only the collimated component of the returning beam gives a significant contribution to the beat signal, the image obtained by using the amplitude measurement scheme may be regarded as a confocal microscope image. Our experimental results show that it is difficult to observe a fine detail of the surface structure by use of the amplitude microscope or confocal microscope. In order to observe the true surface structure, the phase microscopy must be employed.
4. Conclusions
In this paper, we have introduced a scanning heterodyne I/Q-interferometer, which can simultaneously measure both phase and amplitude change of the PB. From the results of the phase measurements, we have been able to map the 3D structure of the SUT. It should be emphasized that this image represents the true topographical surface structure because the phase measurement is independent of the amplitude change of the PB during the scanning. We also have been able to obtain the map of the amplitude of the PB, which is equivalent to the map of the ELRC. To the best of our knowledge, using a scanning heterodyne interferometry, it is the first time that the true phase and amplitude images are obtained simultaneously. Although, we did not use a proper aperture in the image plane in this preliminary study, as a first order approximation, the amplitude image can be regarded as a confocal. Therefore, the proposed microscope scheme can provide both the confocal amplitude image and the surface topography, which can provide very useful information for a SUT. We believe that this new microscope scheme is very useful in diagnostics of a structure which is not homogenous in material. The spatial resolution is 0.67µm, which is limited by diffraction. We have shown that, in principle, the precision for measuring height difference by using our new interferometer scheme is ~0.1nm. In our present work, for a sample used in our measurement, the actual precision for measuring height difference of the surface structure was a few nanometers.
Acknowledgement
This research was supported by Korea Science and Engineering Foundation grant funded by Korea government (NO R01- 2006-000-11374-0) and Seoul Research and Business Development Program (10816).
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