3.1.

BPRA Fabrication

Due to their deterministic binary character, BPR test surfaces are easy to specify for standard micro- and nanofabrication processes. For the purpose of MTF measurement, an ideal surface based on a BPR pattern is determined as a set of rectangular grooves of binary height levels with grooves and peaks corresponding to values of 1 and 0 in the BPR sequence or array [Fig. 1]. The optimal height, h₀, and fundamental element size (pitch), Δ, depend on the specifics of the instrument under calibration.³⁷

In order to carry out MTF calibration of an interferometer, an optimal BPRA sample should have i. a fundamental element size smaller than the highest lateral resolution available with the instrument; ii. the height step should be smaller than the light wavelength, h₀ < λ, and iii. the test pattern should fill a relatively large area of the instrumental field of view.

In the case of the 6-in Zygo™-GPI interferometer under test, the lateral resolution can be varied from about 0.4 mm down to approximately 0.09 mm depending on the optical magnification. Therefore, for an adequate BPRA test sample according to condition i., we choose a fundamental element size of 20 μm that provides a sufficient higher spatial frequency bound.

Conditions ii. and iii. lead to a relatively stringent requirement that the figure error of the BPRA substrate be less than [TeX:] ${\lambda \mathord{/ {\vphantom {\lambda {20}}} \kern-\nulldelimiterspace} {20}}$ $\lambda /20$ over a clear aperture of about 150 mm. In addition to the high price of such substrates, they are also rather thick, 3/4 to 1 in., making it difficult to use them in conventional microlithography machines and processes. For this reason, the first prototype BPRA samples (with 4027 × 4029 elements with 20-μm fundamental element size) for MTF calibration of the Zygo™-GPI interferometer were fabricated by conventional microlithography with chromium deposition on a standard 4 in. silicon wafer with a thickness of 4 mm.

Figure 2 shows the higher spatial frequency topography of a 1.25 mm × 0.94 mm sub-area of a total 80.54 mm × 80.58 mm pattern of the fabricated BPRA as it was seen with the MicroMap™-570 interferometric microscope equipped with a 10× objective. The resolution of the microscope (∼2 μm) is adequate for examination of the quality of the profile of the BPRA elements obtained with the used microlithography process. Based on the consideration of the effect of the BPRA fabrication imperfections on the MTF correction given in Refs. 38 and 39, we conclude that the observed irregularity of the profile of the array elements is negligible, perturbing the inherent BPRA PSD distribution at higher spatial frequencies by less than 1%. The BPRA's geometrical parameters were measured with an atomic force microscope to be h₀≅100 nm and Δ≅20 μm, exactly as desired.

Fig. 2

(a) Height distribution measurement over 1.25 mm × 0.94 mm sub-area of the developed BPRA test sample performed with the Micromap™-570 interferometric microscope equipped with a 10× objective. (b) Measurement of the BPRA sample height distribution over the entire area with a Zygo™-GPI with the 1× magnification. The BPRA surface structure is almost invisible due to the figure (low spatial frequency) variation of the sample's surface.

As it was expected with a low budget substrate used for fabrication of the BPRA, the residual curvature and low frequency variations of the wafer are significantly worse than that which is required for an ideal substrate, ≪h₀, according to condition ii. above. Measurements with the Zygo™-GPI with 1× magnification [Fig. (2)] revealed that the fabricated BPRA test surface has a curvature on the order of 1000 m, which masks the appearance of the BPRA features, even at a larger magnification of the interferometer. The measured peak-to-valley variation of ∼5 μm is much larger than the BPRA height h₀≅100 nm.

Note that a similar problem was encountered during the calibration of the MicroMap™-570 interferometric microscope when using the smaller magnifications, e.g., 2.5 and 5× objectives.^{37, 38} In these cases, waviness of the substrate tended to distort the measured PSDs from the PSDs expected to result from the mathematical properties of the BPRA. The solution to this problem was to etch the BPRAs into a superpolished silicon substrate. Because the largest field of view with the MicroMap™-570 microscope is only 2.51 mm × 1.88 mm, a suitable substrate is relatively inexpensive, and the corresponding developments are currently in progress at the Advanced Light Source Optical Metrology Laboratory.

In the case of the Zygo™-GPI, two mutually supplemental alternatives to starting with a BPRA test sample on an excessively expensive substrate have been employed. First, the overall lower spatial frequency variations of the substrate could be accurately fitted and subtracted using Zernike polynomials or filtered out with the Zygo software's data filtering options. An ideal fitting/filtering procedure would remove all low frequency irregularities without disturbing the higher spatial frequency structure of the measured PSD spectra. Second, the range of substrate figure variations can be significantly decreased if the MTF calibration is applied to the Zygo™-GPI interferometer with the maximum magnification (nominally 6×). Such proof-of-principle MTF measurements are the focus of the present work (see Sec. 3.2).

3.2.

MTF Measurements with Zygo™-GPI Interferometer

The BPRA test sample was mounted in the front of the Zygo™-GPI interferometer on a rotatable kinematic mount and visually aligned to the grid of the interferometer's CCD. The small value of the fundamental period of the BPRA (20 μm) allows for the measurement of the MTF of the Zygo™-GPI with maximum magnification, i.e., when the nominal pixel size of the CCD detector is about 90 μm. However, even at the maximum magnification, the BPRA surface figure measured over the whole field of view (640 × 480 pixels) still exhibits significant low frequency variations. Neither detrending with the Zernike polynomials or astigmatic (cylindrical) surfaces, nor using a fast Fourier transform (FFT) filter with a low frequency cutoff, available in the Zygo software, fully removed these variations.

Nevertheless, Zygo MTF tests were still possible using a reduced field of view of approximately 215 × 215 CCD pixels (a 19.4 mm × 19.4 mm area) and measuring the central portion of the test surface, which had the least amount of curvature. The data were then filtered using a FFT filter, available with the Zygo MetroPro Version 7.6.1 software, with three different low frequency cutoffs of 0.025, 0.25, and 0.5 mm⁻¹. Note that when filtering of this type is used, the size of the data set is necessarily reduced because points along the perimeter of the field of view are excluded by the Zygo software.

Figure 3 depicts 2D height distribution measured with the 6-in aperture Zygo™-GPI under test over 19.4 mm × 19.4 mm sub-area of the BPRA sample developed and shown with higher resolution in Fig. 2 as measured with the MicroMap™-570 interferometric microscope. The different plots in Fig. 3 are presented to visualize the effects of filtering the data compared with detrending with the best fitted astigmatic (cylindrical) surface. Detrending removes a significant amount of the substrate's saddle like shape, but filtering clearly provides a better means for removing other low frequency variations.

Fig. 3

Two-dimensional height distribution plots of the BPRA measured with a Zygo 6-in. Fizeau interferometer equipped with the nominal 6× magnification over 19.4 mm × 19.4 mm sub-area of the BPRA sample developed. (1) No filtering or detrending applied; (2) detrended with the best fit astigmatic (cylindrical) surface; (3), (4), and (5) data filtered using an FFT filter with low frequency cutoffs of 0.025, 0.25, and 0.5 mm⁻¹, respectively.

Throughout the present work, the recorded surface height distributions (as well as the SEM and TEM intensity distributions) are transformed to 2D PSD distributions by using the calculation procedure described in detail in Refs. 17, 18, 19, and briefly outlined in Sec. 1. The corresponding 1D PSDs are obtained by a direct integration (discrete summing) of the 2D PSDs. No additional filter or windowing to the data (except the filters with the Zygo software described above) is used for the PSD calculation.

A comparison of the PSDs from the unprocessed data, the detrended data, and the filtered data indicates positive results, Fig. 4. Both the tangential and sagittal PSDs before detrending or filtering demonstrate an inverse-power–like (a negative slope on a log–log scale) character. Detrending the data significantly reduces the PSD level at the lower spatial frequencies, but there is still a significantly raised lower frequency tail. As filtering is applied with increasing cutoff frequency, however, the raised low frequency tail starts to flatten out and the PSDs start to exhibit precisely the expected characteristics for a BPRA test surface. That is, the PSD is largely flat across the lower frequency range before it begins to roll off in the higher frequency range, which is primarily an effect of the instrumental MTF. Note that the low frequency filtering does not cause any noticeable perturbations to the PSD at the higher frequency range (limited by the roll-off at the Nyquist frequency), interesting from the point of view of MTF measurement. Thus, FFT filtering is a suitable method for removing inherent waviness of the substrate and recovering the desired BPRA height distribution, which can then be used for MTF calibration.

Fig. 4

One-dimensional PSDs obtained from BPRA test sample height distribution measured with a Zygo 6-in. Fizeau interferometer equipped with the nominal 6× magnification. (1) No filtering or detrending applied; (2) detrended with the best fit astigmatic (cylindrical) surface; (3), (4) and (5) data filtered using an FFT filter with low frequency cutoffs of 0.025, 0.25, and 0.5 mm⁻¹, respectively.

The major result from the Zygo™-GPI MTF measurements is that the instrument's Nyquist frequencies, easily identified by visual inspection of the 1D PSDs, in the tangential and sagittal directions are significantly different. To determine the source of this asymmetry, the BPRA test surface was rotated 90° from its original orientation and re-measured. Comparison of the measurements with and without rotation has confirmed that the asymmetry is inherent to the Zygo MetroPro Version 7.6.1 software that processes the data from rows and columns of the CCD in different ways. Note that a similar asymmetry of the tangential and sagittal PSD spectra has also been observed with another phase measuring Fizeau-type interferometer.⁵⁹

The observed asymmetry is remarkably analogous to a discovery regarding how the MicroMap™-570 processes data.^{17, 19} In the case of the MicroMap™-570, a detailed investigation of the origin of the anisotropy problem has been performed.¹⁷ The problem appears when a two field interlaced camera is used.⁶⁰ One field consists of odd pixel lines, another includes the even lines. Both fields are collected simultaneously but are read out alternately. Such a read-out process leads to a systematic distortion between alternate detector outputs, corresponding to two fields. This distortion is reduced by averaging (summing) alternate outputs with the instrumental software. The averaging eliminates the distortion but also reduces the image resolution (Nyquist frequency) in the sagittal direction, and, therefore, the spatial frequency bandwidth of the instrument. Note that in the case of the MicroMap™-570, the latest (fifth) version of the microscope software accounts for the asymmetry by applying an additional averaging over two neighboring columns.

4.1.

Fabrication of BPR Multilayer Test Samples

Here we describe the details of the development of BPRML test samples suitable for measurements with scanning and transmission electron microscopes. First, we create a multilayer structure consisting of two materials, WSi₂ and Si (marked with indexes 0 and 1, respectively) with significantly different contrasts when observed with an electron microscope. In order to serve as a test sample for MTF calibration of an SEM or TEM, the 1010 layers of the two materials have thicknesses pseudorandomly distributed according to a binary pseudorandom sequence of 2047 total elements. The thickness of a particular layer of the material with index 0 (1) is equal to the elementary thickness of the multilayer, Δt = 3 nm, multiplied by the number of adjacent 0's (1's) in the BPR sequence used for the multilayer generation. The thickest deposited layer in the stack is 33 nm, which corresponds to 11 of the same (0's or 1's) adjacent elements. The specified total thickness of the multilayer deposited is 6141 nm. The first layer of 33 nm of WSi₂ is on the substrate, while the top layer of 6 nm of Si is exposed to air. The overall size of the sample multilayer deposited on 0.5-mm thick Si (100) substrate is approximately 25 mm × 12.5 mm.

The BPR sequence of 2047 elements was generated using parameters⁴⁴ n = 11 and M = 83. Unfortunately, the recursion coefficient M = 83 was used mistakenly (instead of M = 43); it does not correspond to a recursion coefficient which produces an ideal MLPRS. Although the fabricated BPRML samples do not correspond to an ideal BPR distribution, the samples were found to be still suitable for MTF measurements with an SEM. As verified analytically, the autocorrelation function of the sequence is very close to a one-element delta-function expected for the corresponding BPR sequence (e.g., with M = 43); and the inherent PSD spectrum is a white noise one, however, with a noticeable level of noise. A new BPR multilayer with the ideal BPR distribution of layers and with even smaller elementary thickness (1.5 nm) and larger total number of elementary layers (4095) is in progress.

The BPR multilayer was fabricated with solid-source targets of B-doped Si and hot-pressed WSi₂ using modified 3-in. direct-gas injection cathodes⁶¹ in a turbopumped rotary deposition system. The target to sample distance was 78 mm, with a process gas pressure of Ar held at a constant 2.3 MT by an upstream dual-MFC feedback control. The average gas flow through each cathode was ∼9 SCCM. Deposition was carried out at a constant power of 170 W for both guns. The proper thickness for each individual layer is produced by raster-scanning the substrate over figured apertures by varying both the number of passes over this aperture and the rotational velocity. Due to the inherent nature of the magnetron deposition growth rate to decay over time, a compensation factor is included during the growth, which adjusts the velocity appropriately as is used for growth of other types of thick multilayers.^{62, 63}

Test sample preparation and the SEM and TEM measurements with the samples were performed at Evans Analytical Group, Inc.⁶⁴ The BPRMLs were loaded in and processed with a Dual Beam FIB (focused ion beam)/SEM instrument (Helios NanoLab,™ FEI Company). The instrument integrates imaging capabilities of a field emission SEM and the capability for preparation of a precise thin sample cross-section using a focused ion beam. In order to avoid rounding of the top surface edge of the sample cross section in the course of FIB etching, the area of the BPRML used for the SEM measurements was preliminary coated with a thin, about 1.5-μm thick, layer of Pt.

For the SEM measurements, the BPRML was cross-sectioned by etching with the FIB/SEM technique — Fig. 5. After careful FIB flattening of the side wall of the dimple shown in Fig. 5, the dissected BPR multilayer cross-section was measured with a SEM — Sec. 4.2.

Fig. 5

(a) Photomicrograph of the BPRML with a dimple etched with the FIB. In the course of FIB etching, deposition of the etched material leads to overgrowth of the sides of the dimple. The sample was used for SEM measurements discussed in Sec. 4.2. (b) Photomicrograph of the BPRML with sample multilayer section detached from the Si substrate by FIB etching and undercutting across the Si substrate cross-section. The sample was used for TEM measurements discussed in Sec. 4.3. (c) Photomicrograph of the multilayer test sample piece under super-polishing to approximate 80-nm thickness suitable for TEM imagining.

The process for fabrication of a test sample suitable for measurements with a TEM consisted in FIB etching out of a thin sample from the BPRML – Figs. 4, 5. The TEM sample preparation was performed with the multilayer piece shown in Fig. 5 when it was completely detached from the multilayer. In this step, in order to hold the piece, a sharp transporting needle was Pt ion-beam welded to the free, right-hand side of the piece. After that, the piece was cut out from the rest of the BPRML and attached to a pin of a standard TEM sample holder, Fig. 5. Finally, in order to decrease the test sample piece thickness to ∼60 to 100 nm and make the thickness uniform, both sides of the ML piece at its free end were processed with “super-polishing” at extremely low FIB current.

Figure 5 shows an SEM image of the BPRML TEM sample prepared using the FIB/SEM process described above. Because SEM imaging is associated with a noticeable ablation of the sample material, the last SEM measurement was carried out just before the last cycle of the FIB “super-polishing.” After the FIB/SEM preparation of the BPRML TEM sample was completed, the FIB/SEM vacuum chamber was vented and the holder with the sample was moved to a clean glass dish. In this way the sample was brought to a TEM lab.

4.2.

SEM Measurements of the BPRML Cross-Section

SEM measurements of the multilayer cross section [Fig. 5] prepared with the FIB technique were performed with an electron beam tilted by 52° with respect to the surface normal. This led to a distortion of the vertical scale of the SEM photomicrograph of the cross sections of the samples. The distortion should be accounted for when estimating the thickness of the layers and calculating the PSD spectra. Figure 6 shows an SEM image of a cross-section of the BPRML sample obtained with 35,000× magnification. The vertical bar in the image is placed in order to provide a corrected vertical scale that accounts for the 52º tilt of the electron beam.

Fig. 6

(a) SEM image of a cross section of the BPRML [see Fig. 5] obtained with 35,000× magnification. (b) SEM image of a cross section of the BPRML obtained with 200,000× magnification. (c) Power spectral densities calculated for the top third (blue dashed line), middle third (red dashed–dotted line), and bottom third (black solid line) of the image shown in (a). The defocusing effect is clearly seen as a lower spatial frequency shift of the PSD spectra for the bottom third part of the image. (Color online only.)

Magnification of 35,000× is suitable for acquiring an image of the entire ML cross-section; however, it is too low to resolve the thinnest layers of the BPRML structure. SEM images of the BPRML samples measured with a significantly increased magnification (200,000×) are shown in Fig. 6. It still seems that magnification of 200,000× is not enough to resolve the thinnest layers of the BPRML structure. Images with significantly higher resolution were obtained using FIB/TEM technology (Sec. 4.3).

As an example of the valuable information that can be obtained with the developed BPRML test samples, in Fig. 6 we show how the measurements of the BPRML lead to understanding of the limitations of FIB/SEM analysis. Figure 6 presents 1D PSDs calculated for the “top third,” (dashed line), “middle third” (dashed-dotted line), and “bottom third” (solid line) of the BPRML image obtained with 35,000× magnification [Fig. 6]. The observed differences of the spectra suggest that the SEM images performed at a tilt angle of 52° suffer from a limited focal depth of the instrument. As a result, for a vertically lengthy sample, such as our BPRML cross-section, the image resolution varies significantly in the vertical direction.

In order to obtain PSD distributions from the SEM measurements [Fig. 6], the images in tiff-format [as ones shown in Figs. 6, 6] were analyzed by converting the image brightness profiles to 1D PSD distributions. We used the following PSD processing. First, in order to avoid a contribution to the PSD spectrum from a gate-like function associated with the averaged image brightness, an original 2D brightness distribution was detrended by subtracting the best fitted plane surface. As a result, the averaged brightness of the detrended image is equal to zero (a negative brightness value is now allowed). Second, after detrending, 1D PSD distributions were calculated for each column and averaged to decrease random spectral variation in the way described, e.g., in Refs. 17, 18, 19. The PSD spectra at this stage have a characteristic high frequency roll-off that is due to the limited resolution of the SEM. The spectra flatten at significantly high frequencies where a contribution of the instrumental random noise exceeds the PSD magnitude inherent to the image of the structure. Finally, the random noise spectrum is removed by subtracting a minimum PSD value of the flat tail. In this way, we avoid obtaining a negative PSD value that is unphysical.

4.3.

TEM Measurements with the BPRML Sample Prepared with SEM/FIB Technique

The structure of the BPRML TEM sample was investigated with a Tecnai™ TEM instrument (FEI, Co.). The instrument is capable of high-resolution transmission electron and scanning transmission electron microscopy. With electron energies of about 300 keV and with ultrathin samples, the TEM image resolution is on the order of 1 to 2 Å. Compared to SEM, the TEM has better spatial resolution, and is capable of additional analytical measurements, but requires significantly more sample preparation, as described above.

Figure 7 shows the TEM images of the BPRML sample piece [Fig. 5] obtained with different magnifications. The resolution of the image, obtained at a rather low electron energy of 2.3 keV [Fig. 7], is noticeably higher than that of the image obtained with the SEM and shown in Fig. 6. There is a noticeable contrast variation from top to bottom of the image that is due to the variation of the sample thickness. The contrast variation of a TEM image can be significantly improved by detrending the image with a 2D low order polynomial distribution. The specified relative accuracy of distance measurements with the SEM and TEM is 2% to 3%. This can explain the difference of the thickness values obtained with the instruments [compare the scale lines in Figs. 6, 7]. Note that in the TEM images we do not see any noticeable imperfection of the multilayer structure. This is in contrast to a few of the measurements with the SEM in which we saw waviness in the layers.

Fig. 7

(a) TEM images of a cross section of the BPRML sample piece obtained: at an electron energy of (a) 2.3 keV, (b) 17.5 keV, and (c) and (d) 255 keV. The contrast variation from top to bottom of the low magnification image (a) is due to the variation of the sample thickness. The images in (b) and (c) were taken over areas at the top of the BPRML test sample. The image in (d) approximately corresponds to the bottom part of the sample.

The measurement in Fig. 7 was performed at an electron energy of 17.5 keV. The corresponding resolution is high enough to provide high contrast separation, even for the thinnest layers with 3-nm thickness. High resolution (at 255 keV electron energy) TEM measurements of the BPRML test sample are shown in Figs. 7, 7. The TEM resolution is about 2 Å, allowing for the observation of the interlayers of the ML coating. Moreover, in Fig. 7 an amorphous layer of Pt deposition is visible on the top of the sample, and a layer of oxidized Si is clearly seen on the top of the Si substrate [bottom of Fig. 7]. Note the very high contrast between the WSi₂ and Si layers. The observed high stability of the measurements allows for effective and reliable stitching of multiple images taken along the sample cross-section. Processing of TEM measurements with stitching will be reported elsewhere. The major conclusion from the presented data is that the TEM measurements testify to the high quality of fabrication of the BPR multilayer with a structure exactly corresponding to the binary sequence that was used.

Similar to the PSD treatment of the SEM images applied in Sec. 4.2, the images in tiff-format obtained with TEM (Fig. 7) were analyzed by converting the image brightness profiles to 1D PSD distributions. Figure 8 shows the resulting 1D PSD distribution along the vertical direction of the BPRML sample [Fig. 5] obtained by averaging of six PSDs of the image files measured with 17.5 keV electron energy, as shown in Fig. 7.

Fig. 8

(a) 1D PSD of the BPRML sample obtained from the average of the PSDs obtained from 6 individual image files as measured with an electron energy of 17.5 keV [Fig. 7]. (b) Histogram of intensity values obtained from a single TEM image measured with 17.5 keV electron energy.

In the PSD distribution in Fig. 8, there is a noticeable spike occurring at about 350 μm⁻¹. This is most likely due to diffraction related to the nominal 3-nm fundamental layer thickness. In fact, after calibrating the length scale of the images, it was found that the fundamental layer thickness is about 2.8 nm, which would exactly correspond to a diffraction peak at 350 μm⁻¹. A similar diffraction peak has been observed in scatterometer measurements with a BPR array, when the wavelength of the scattered light was smaller than a fundamental size of the array.³⁷

The PSD measurements with the TEM suggest a number of questions related to a metrological interpretation of the data. One such question is about the high frequency behavior of the PSD spectra in Fig. 8. Indeed, because the magnified pixel size is about 1 nm, and the BPRML fundamental thickness is about 3 nm, the TEM measurements are oversampled. In this case, one would expect the high frequency behavior of the PSDs to resemble a Sinc squared function. This is not the case for the spectra shown in Fig. 8.

Another question is about the frequency distribution of different intensities in the TEM images recorded with 8-bit resolution. Figure 8 shows a histogram of intensity values obtained from a TEM image spread over 2⁸ intensity intervals. For the BPR sequence used here, the distribution of the BPRM contrasts (transmissions) should have two equal intensity frequency peaks corresponding to the low and high transmission materials. However, the histogram in Fig. 8 demonstrates a significant asymmetry in the appearance of the low and high intensities.

Figure 8 illustrates one more problem with TEM data presentation via tiff-files. The surprising (at first glance) spikes in the intensity histogram are probably related to the well known effect of double compression in the TIFF (MPEG) format.^{65, 66}

Therefore, in order to use TEM data for a reliable metrological characterization of a sample under test, one should first address the listed problems. An investigation of these problems and the appropriate way to handle them are currently in progress.