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Abstract
Angle-resolved photoemission spectroscopy with nanoscale spatial resolution (Nano-ARPES) is a powerful tool for the investigation of electronic structures of materials and their spatial configurations. In order to capture the area of interest in Nano-ARPES measurements effectively, an optical microscope can be used to provide real space optical images as a reference. In this work, a new type of optical microscope for Nano-APRES spectrometer with a large tilt angle of ∼30 degrees and a long focal length of ∼12 mm has been designed. Large magnifications by 7 × to 20 × and a spatial resolution of 3 um have been achieved, which can effectively assist optical alignment for Nano-ARPES. In addition, the strong boundary sensitivity observed in such a tilt design demonstrates its special capability in detecting the fine features of surface coarseness.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Optical and electronic microscopies are among the most commonly used tools in observing details of microregions of matter. The state of the art of an optical microscopy has reached a resolution of tens of nanometers by using a microsphere [1–5]. Most optical microscopies of very large magnifications exhibit similar characteristics and configurations, functioning by directly looking downwards onto the sample surface with rather small focal lengths to ensure a large numerical aperture (NA). The electronic microscope could reach even better resolution. However, the preparation for scanning in real space and especially zooming into the specific microscopic region are very time consuming. Electronic microscopes with extra assisting optical devices in ultrahigh vacuum (UHV) could greatly improve the measurement efficiency. To achieve this goal, an optical microscope can be incorporated, whereas optical measurements need to be carried out at a large tilt angle with a long focal length, to avoid clashing with the sample surface.
Such a tilt microscope can be realized by various methods. A digital microscope - tilt model with annular dark-field (ADF) has been introduced by Olympus to observe the latent fingerprints on metal, which is dedicated to distinguish the coarseness features that are absent at the vertical view of the imprints [6]. The tilt mode electronic microscope, such as ADF scanning transmission electron microscope (STEM), exemplifies an approach of electronic tilt tomography to obtain the three-dimensional (3D) morphology of nanoscale objects. Ideally, it is possible to obtain tilted images covering the entire angular range of ±90° [7–10]. Unfortunately, due to the very limited space in most UHV systems, the ADF methods based on the illumination mechanism can hardly be applied as a side assisting optical microscope.
Nano-ARPES has become a powerful tool in directly investigating the electronic band structure of various micro-size sample systems nowadays, including exfoliated two-dimensional materials and multiphase single crystals [11–18]. For a conventional Nano-ARPES spectrometer, the real space mapping, is realized by scanning through moving the multi-axis piezo-motor sample stage. Before investigating the specific region of interest, it usually takes much effort and time to target the area by scanning the whole region to collect photoelectrons. Moreover, the image contrast of the Nano-ARPES mapping can be weak for some materials. In contrast, optical microscope can be employed to effectively target the region of interest, and thus function as a good assisting tool for a Nano-ARPES facility. However, the design and realization of an extra optical microscope may face many difficulties. First, the space available to accommodate a conventional optical microscope inside a UHV chamber is very limited. Many existing assisting microscopes were mounted on a flange of the vacuum chamber far away from the sample surface and therefore the magnifications were not large enough. Second, in the Nano-ARPES sample-detector configuration, the big sample holder together with the cooling head are installed at the focus point of the photoelectron analyzer, with the space between them being less than 50 millimeters. The method of direct downward-looking microscope is not available. Therefore, the assisting optical microscope has to be amounted at a tilt angle of at least 25 degrees. To date, only one type of assisting optical microscope for Nano-ARPES system exists (the end station at Elettra synchrotron in Italy) [19–21], which greatly helps the Nano-ARPES experiments. In that system, the photoelectron analyzer is home-made and thus is small and could rotate inside a large vacuum main chamber. Such a configuration makes the direct view of the microscope possible. However, the energy resolution has been consequently sacrificed. To the best of our knowledge, in other Nano-ARPES setups with standard sizes of analyzers, the side assisting optical microscope is still lacking.
In this paper, a side assisting optical microscope for Nano-ARPES has been designed, which combines a tilt mode microscope and a telescope. The microscope is designed with a long focal length of 12 mm, which allows light to illuminate the sample at a maximum incident angle of 30 degrees, and the optical magnification from 7 × to 20 × could be achieved with only one objective lens inside the vacuum chamber. The detector has been amounted meters away outside the vacuum system to avoid interfering with other UHV components. A gold electrode with microscopic structures has been used to test the performance of this microscope, and a mathematical model has been formulated to analyze the images. In addition, the boundary sensitivity observed at large tilt angles demonstrates its distinct advantage in the detection of fine features of surface coarseness. Tiny contaminants which are absent at direct downward-looking mode can now be clearly observed at a large tilt angle. This new type of tilt mode microscopy could be applied to many other electronic microscopies, for example the photoemission electronic microscopy (PEEM) [22], and tip-enhanced Raman spectroscopy (TERS) [23].
2. Objective lens configuration
In order to achieve high adaptability of the side assisting optical microscope for Nano-ARPES, the most important step is to design a proper objective lens configuration. Generally, most optical microscopes adopt Kohler illumination. However, when incident light is tilted to large angles, their zeroth-order diffraction light could not return, resulting in a sharp decrease of illumination brightness. Therefore, the illumination way has to be decided as critical lighting. Two possible objective configurations for the side assisting optical microscope are introduced, as shown in Figs. 1(a) and 1(b), both of which could realize a large tilt angle and a long focal length with only one objective lens inside the vacuum chamber. The major difference between these two designs is that the lens is parallel to the sample (Fig. 1(a)) or vertical to the optical axis (Fig. 1(b)). Considering the influence of these two configurations on the imaging efficiency, a simple mode is introduced to analyze the illumination and the observation path of these two configurations, respectively. For the objective lens parallel to the sample as shown in Fig. 1(c), the advantage is that the whole sample lies on the front focal plane, with the illuminated areas being off-axis of the focal plane. Therefore, the main optical aberrations are curvature and astigmatism, which have been well corrected in many commercial objective lenses. However, due to the limitation of outer frame and the numerical aperture, the illumination can't completely pass through the objective lens, leading to the image loss at a large tilt angle. As for the secondary configuration shown in Fig. 1(d), the illumination could completely pass through the objective lens, providing the best lighting conditions. However, due to the tilt angle, only a strip of the sample is on focus, and the different degrees of defocusing in the rest regions make aberration correction difficult. In order to quantitatively evaluate the difference in return area ${S_{1,2}}$ (1,2 for parallel and perpendicular configurations, shown in Fig. 1(c) and Fig. 1(d), respectively) of zeroth-order diffraction light, the relational expression based on geometrical optics between ${S_{1,2}}$ and the tilt angle $\theta $ is derived as
Fig. 1. Objective lens configurations. (a) and (b) Two possible configurations of objective lens, being parallel to the sample and orthogonal to the optical axis, respectively. (c) and (d) The processing of illumination and observation. (e) and (f) ${S_{1,2}}$ (black) and their derivative ${S_{1,2}}^{\prime}$ (red) with respect to θ for two configurations respectively.
Comparing the above two configurations, although it requires low-cost for the first configuration to correct aberrations, the return illumination of zeroth-order diffraction light is only 2.5% of the other one, and the impossibility of larger tilt angle limits the application to other sorts of electronic microscopies. (Section 1 in Supplementary Materials). Therefore, the prototype setup of the objective lens we would like to choose is the configuration shown in Fig. 1(b).
3. Prototype setup
In order to realize the new type microscope we proposed, a prototype setup is designed and built. Figure 2 is the schematic drawing of the system which contains four functional components: an LED collimation stage, a beam shaping stage, a large tilt focusing part, and an imaging compensation part. Firstly, the divergent beam emitted from an LED light source with a central wavelength of 620 nm (Daheng Optics, GCI-060401) is converged by a lens L1 (f = 75 mm) to form a virtually 16-mm-diameter wide beam. Then lenses L2 (f = 200 mm) and L3 (f = 100 mm) are set to nearly collimate and narrow the beam diameter to 8 mm to match the aperture of the objective lens for maximizing the illumination power. To reduce the size of light spot in defocusing and enhancing the illumination efficiency in focus, a set of cylindrical lenses L4 (f = 150 mm) and L5 (f = 75 mm) is used as the beam shaping stage, compressing the lateral dimension of the beam by half to form an elliptical spot on the sample surface. Then, a splitter mirror M1 (50%) guides the elliptical beam into the objective lens, and the beam is focused to the sample surface at a tilt angle. The sample, upon which the beam is reflected before passing through objective lens, M1 and a reflecting mirror M2, is fixed on a five-axis motorized stage. Considering the very limit space in vacuum chamber of Nano-ARPES, the distance between objective lens and M1 has to be at least one meter in length to install other optical components outside the vacuum chamber and to avoid the clashing of other vacuum accessories. Finally, to avoid the influence of distortion for heavily tilted observation axes in this system to a certain extent, an actively tilted zoom lens (the tilt angle is determined by Scheimpflug principle [24]) is placed in front of the CMOS camera, to compensate the depth of field of the system. According to the Scheimpflug adjustment mechanism, a constant focus can be achieved over the entire sample size, as shown in Fig. 2(c), where the plane, the subject lens plane and the image plane intersect in a straight line. The objective lens needs to be mounted close to the sample surface inside the vacuum chamber, which is required to be vacuum-compatible. Furthermore, due to the space limitation in Nano-ARPES chamber, a long focal length is needed and the total length of the objective has to be properly designed, which limits the choice of high NA objectives. As a result, we select a commercial lens (Foctek photonics, M12-12IR) with a resolution up to 3 megapixels, a focal length of 12 m and the total length of 16.9 mm. It is as light as 5 grams and features high transmission at 620 nm wavelength. In addition, the full field optical distortion of this objective is only -4.44%.
Fig. 2. Principle and scheme of the side assisting microscope. (a) Principal optical setup including four parts: (1) LED collimation stage, (2) beam shaping, (3) large tilt focusing optic, (4) imaging compensation part based on Scheimpflug principle in (b). (c) Photo of the tilt focusing part.
Cameras with high dynamic range and quantum efficiency are required. A CMOS with 5680 × 3648 pixels, a pixel size of 2.4 µm × 2.4 µm, and a maximum resolution frame rate of 22 fps is selected in the camera. It has a high quantum efficiency of QE ≈ 90% at a wavelength of 620 nm and the dynamic range of 73 dB is sampled with a bit depth of 8 or 12 bit. To realize imaging with different magnifications under fixed objective lens, we use a zoom lens (Tamron, A025) with high contrast in the full focus section. It has a large aperture of F/2.8 and the focal length of 70-200 mm. Therefore, our microscope can achieve continuous optical amplification from 7 × to 20 ×.
4. Experimental results
To test the imaging ability of our setup, a device is prepared with specific gold electrode pattern of parallel micro-line structures. The image of the device is provided in the Fig. 3(a) as a reference, it has an overall size of 1.5 mm × 1.5 mm with the gold-plated white area and the blue area of silicon dioxide substrate. The part in the red outlined region of the sample is selected as the target area, where the zooming-in image is shown in the upper-right insets (Fig. 3(b)). Targeting and resolving this area could well showcase the performance of our microscope.
Fig. 3. Experimental results and quantitative analysis. (a) A conventional optical microscope image at 5 ×. (b) Region for experimenting. (c) Image of normal incidence. (d1) to (d3) Results at tilt angles of 10, 20 and 30 degrees, respectively. (e1) to (e3) The corresponding Fourier transform diagrams. (f) and (g) Intensity profiles along the two vertical yellow lines at each angle, representing central and fringe FOV respectively. The inserts in (f) and (g) show the Fourier transform of the intensity. (h) Calculation of longitudinal distortion in central and fringe FOV. (j) and (i) Intensity profiles along the two horizontal green lines at each angle, representing central and fringe FOV, respectively. The inserts in (i) and (j) show the derivative of the intensity with respect to lateral position at 0 deg. (k) Calculation of lateral distortion in central and fringe FOV.
Firstly, the imaging result of normal incidence observed at the magnification of 10 × is shown in Fig. 3(c). The impact of the uneven LED light source, which is the main disadvantage of critical lighting, has been diminished through the LED collimation stage in the system. The textures of the electrode are clearly visible, the lateral FOV could be realized as wide as 120 µm and 160 µm for the longitudinal. Then, we collect images from different tilt angles (Section 2 in Supplementary Materials), Figs. 3(d1) to (d3) show the performances of our microscope (intervals of 10 degrees), and the corresponding Fourier transfer spectrums are shown in Fig. 3(e1) to (e3). The image at the tilt angle of 10 degrees shows agreement with the 0 deg incident image despite the reduction of brightness. With the tilt angle increased by another 10 degrees, it is obvious to see that the lateral textures are distributed sporadically and the brightness of middle gold-plated areas show a sharp decrease. On the contrary, the edges of the gold-plated areas are still clearly visible. This is probably caused by the height difference in the gold plating process. When the tilt angle increases to 30 degrees, the lateral FOV can be achieved as wide as 150 µm and 195 µm for the longitudinal. In addition, similar boundary sensitivity phenomenon appears in the image, and the white outlined regions in the figure shows bright sharp spots, which may be some tiny contaminate particles on the sample surface. Furthermore, through comparing Fourier spectrograms of different angles, it could be clearly seen that the reduction of the low frequency parts corresponds to the absence of the images in the middle areas. In addition, the longitudinal high frequency parts diminish with the increase of tilt angle, which means the boundary sensitivity phenomenon is related to the orientation of the illumination light to the sample. The images obtained above are all raw without any digital processing. Although only the sample boundary of the image could be seen at large tilt angle, it is enough to assist the Nano-ARPES to observe the extremely flat samples.
To characterize the spatial resolution and distortion of our microscope, both in longitudinal (Y) and lateral (X) directions, the intensity distributions are plotted via the two vertical yellow lines and horizontal green lines at each angle (limited by the size of the FOV, the position of the lines may be different), investigating differences between center and fringe of the FOV. The longitudinal results of central and fringe FOV are shown in Fig. 3(f), (g), respectively, clearly showing the expected period of 6 µm, as also confirmed by the Fourier transformation (see the insets in Fig. 3(f), (g)), though the absence of peaks exist in fringe FOV at 30 degrees due to the weak reflected light. These results indicate that the longitudinal feature of the 3 µm half-pitch can be well resolved by our setup. Besides, since our work is concerned with the relative position of the feature in the sample, the distortion can be defined as
where ${z_0}$ is length of adjacent extreme points without distortion and ${z_{m ean}}$ is the mean length of the adjacent extreme value point. As shown in Fig. 3(h), although the longitudinal distortion becomes larger with increasing tilt angle, it can be well controlled within -4%, both in the center and fringe of the FOV. Next, the intensity profiles of central and fringe FOV along the horizontal green lines are shown in Fig. 3(i), (j), respectively. Due to the boundary sensitivity phenomenon and inclination of large angle, multiple main intensity peaks and secondary peaks with middle depressions can be clearly seen at 20, 30 degrees, and the intensity of the peaks are still high and even better than at 0 deg, both in center and fringe (yellow circles). Though the lateral resolution is difficult to measure under the influence of boundary sensitivity at large tilt angles, it can be seen from the images where the resolution is little sacrificed. Then, the derivative of the intensity with respect to lateral position at 0 deg is used to measure the lateral resolution (see the inserts in Fig. 3(i), (j)). The full width at half maximum (FWHM) is 2.42 µm in center of the FOV and 3.53 µm in fringe of the FOV, indicating that the lateral spatial resolution can be better than 3.53 µm. As shown in Fig. 3(k), the lateral distortion is almost independent of the tilt angle and can be controlled within -2% in the center and -5% in the fringe, which confirms the validity of our design to Nano-ARPES.5. Model and discussion
Finally, in order to analyze the imaging results of the prototype, a mathematical model based on Fourier optics is developed. J. Wang et al have established a microscope model for Kohler illumination [25], which took a slant angle between the optical axis and the observed surface into account. As for the critical illumination, C. J. R. Sheppard et al developed a microscope model without tilt [26–28]. Based on these models, the influence of tilted sample is considered below.
For a microscope shown in Fig. 4(a), the objective and the condenser are the same lens ${L_0}$, ${d_1}$ and ${d_2}$ are image distance and object distance, respectively. The image intensity for an object with amplitude reflectivity $R({x,y} )$ can be expressed as
where ${h_{1,2}}$ are the spread functions for the convergence lens and collection lens, which are in general complex. For lenses that have equal circular apertures, the optical coordinates are introduced [26]: where k is the wave number, $\alpha$ is the semi-angular aperture, z is the distance in object space from the focal plane, and $r^{\prime}$ is the radial distance in object space from the optic axis. The u characterizes the axial response of object plane and the $\upsilon$ represents the range of exit pupil. Considering total reflection of a single point object ($R({x,y} )= 1$), the image can be expressed asFig. 4. Mathematical model. (a) Geometry of the model developed in Ref. (22). (b) Geometry of a tilt model. (c) Intensity I of axial amplitude for a tilt model
According to the Kirchhoff's diffraction theory, when the sample is tilted, as shown in Fig. 4(b), the optical field can be expressed as
Here, $\lambda$ is wavelength, $U^{\prime}({x,y} )$ is the incident optical field, and $({{n},{r}} )$ is the angle between optical axis ${n}$ and incident direction ${r}$. According to geometric relation
Then, introducing optical coordinates (Eq. (6) and Eq. (7)), the axial amplitude can be expressed as
Here, s is the ratio of the return light area to the exit pupil area under the tilting illumination.
According to this model, the intensity profiles are shown in Fig. 4(c). Under the oblique illumination, each point object in the illumination area has different degrees of defocus, the intensity of which can be well reflected by the different u in the axial amplitude profiles. As the profiles show that the defocus will cause rapid decrease of intensity, which explains the decline of brightness in the direction perpendicular to the incident light. Besides, it can be seen that the intensity drops sharply with increasing tilt angle, and drops by approximately 50% from the normal incidence to 10 degrees and even 10% to 30 degrees for in-focus image ($u = 0$). It's the reason why the apparent loss of details can be observed in the experimental results. Considering the height differences between the sample and the substrate, these side boundaries are parallel to the illumination light under normal incidence and will not appear in the image. Whereas, the oblique illumination will cause these boundaries to reflect some light, and the intensities of them are gradually higher than the sample surface with the increasing tilt angle, resulting in the boundary sensitive phenomenon at a large tilt angle. Furthermore, this phenomenon can quickly separate structures with different height differences in materials by adjusting the inclination angle, which can play a significant role in the field of roughness detection of materials. And in Nano-ARPES, it renders an effective approach to direct measure the sample quality and the sample cleave.
6. Conclusion and outlook
In conclusion, we have designed and built a side assisting optical microscope for Nano-ARPES, which is ready to be installed at the S2 beamline (BL07U)’s Nano-ARPES end station of Shanghai Synchrotron Radiation Faculty (SSRF). According to our experimental results, the longitudinal resolution can reach 3 µm both in the center and fringe of the FOV, and the lateral resolution can be finer than 3.53 µm. Furthermore, the raw image without digital processing can achieve less than -4% longitudinal distortion both in the center and fringe of the FOV, and can be controlled within -2% in the center and -5% in the fringe in terms of lateral distortions. Noticeably, our results show extremely high boundary sensitivity, which can play a significant role in observing fine surface coarseness features.
Funding
National Natural Science Foundation of China (11774427).
Acknowledgments
The design and manufacture of the optical microscopy in this work is supported from BL07U beamline of SSRF. We thank the staffs of Nano-ARPES end station for their technical support and assistance in designing.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
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