Thomas Dieing

) is a transition metal dichalcogenide (TMDC) that belongs to a class of nanomaterials with potential in optoelectronic device applications. Several characteristics that define the electronic, optical, and thermal properties of these two-dimensional (2D) crystals are thickness, crystal symmetry changes, and growth defects. The combination of various techniques for investigating the same WSe

 flake sample shows that various processes involved in producing the photoluminescence (PL) signal are correlated with the localized strain. The WSe

 flake samples are observable by confocal Raman imaging and topographic homogeneity can be determined by atomic force microscopy (AFM). The edge of the flake shows strong variations, which could be explained by the correlation of the various techniques. In addition, second harmonic generation (SHG) measurements identify grain boundaries as potential sources of strain relief, which is in agreement with both the confocal Raman as well as the confocal PL results.

Transition metal dichalcogenides (TMDCs) are a family of materials with an MX

 composition, consisting of metallic (M = W, Mo, Nb, and Ta) and chalcogen (X = S, Se, and Te) atoms. They are arranged in layered structures in the form X-M-X and are considered as a single monolayer, with the chalcogen atoms in two hexagonal planes separated by one plane of transition metal atoms (1–5). Similar to graphene, they can be exfoliated to one or few layered materials or grown using different growth methods such as chemical vapor deposition (CVD). These single- or few-layer materials exhibit unique electronic and optical properties, which are significantly different from the bulk precursor. Bandgaps of semiconducting TMDCs can be tuned by changing the number of layers, the chemical composition, or the strain of the materials (1–8). Their possible applications include the production of transistors, photodetectors, light emitting diodes (LEDs), and photovoltaic cells (9,10).

To produce high-quality devices, the synthesis processes must be evaluated efficiently. Nondestructive imaging techniques are required for monitoring crystal properties and features such as grain boundaries, layer numbers, defect densities, and doping and strain fields. In many cases, a combination of measurement techniques, such as the ones outlined below, leads to a more thorough understanding of the properties of these materials.

Atomic force microscopy (AFM) is widely used to characterize the topographic composition of 2D materials. It determines the number of monoatomic steps and ripples in the 

-direction, and resolves lattice orientations and surface defects in the 

-plane. It can also reveal nanomechanical, nanoelectromechanical, or nanoelectrochemical properties of 2D materials (11–15).

Raman and photoluminescence (PL) spectroscopy and imaging are nondestructive techniques that reveal the lattice dynamics of single-layer and multilayer TMDCs and enable the determination of their electronic structures (1,5,15–22).

Second harmonic generation (SHG) imaging is a technique sensitive to changes in crystal orientation and symmetry. It can visualize grain boundaries, and polarization-dependent SHG measurements are often used to reveal strain fields by rotating the polarization direction of the excitation light while recording the intensity of the correspondingly polarized SHG signal component (1,4,6–8,23–26).

In this study, the combination of the abovementioned techniques made possible the correlation of strong, localized changes in PL signals on the outer edge of the observed WSe

 crystals with strain in the lattice as well as topographic inhomogeneities. It was also possible to correlate the absence of strain and the absence of the changes in PL in locations where it could have been expected, with the location of grain boundaries as observable through SHG.

 were grown at atmospheric pressure and 900 °C directly on SiO

/Si substrates by solid-source CVD using selenium and WO

 precursors, as previously reported (27). The WSe

 crystals were predominantly monolayered with small overgrown bilayer regions commonly found with this growth method. All experiments were performed using an alpha300 RA confocal Raman AFM microscope at room temperature (WITec). AFM measurements were performed in AC mode with a force modulation cantilever (Nanosensors) with a nominal spring constant of 2.8 N/m and a nominal resonance frequency of 80 kHz.

For confocal Raman and confocal PL measurements, the alpha300 microscope was equipped with a 100x (NA = 0.9) Epiplan Neofluar Zeiss objective, a 532-nm excitation laser with a power before the objective of 2 mW, and a UHTS300 VIS spectrometer (28). The spectrometer was equipped with various gratings mounted on a motorized turret. The 1800 g/mm grating allowed for a resolution of better than 1 cm

 and was used for high resolution Raman imaging, whereas a 300 g/mm grating with a resolution better than 3 cm

 (0.33 meV) was used for PL measurements.

For confocal SHG measurements a fiber-coupled linear-polarized 7.8 ps pulsed laser (λ = 1064 nm) was used as the excitation source. The same objective for the Raman measurements was used to focus the pulsed laser with a spot size of approximately 700 nm onto the sample. The reflected optical signal was collected with the same objective, transmitted via photonic fiber and then directed into the UHTS300 VIS spectrometer. A 950 nm short-pass filter was used before the pinhole to block the excitation laser beam. The SHG signal for this setup is detected at 532 nm, corresponding to half of the fundamental excitation wavelength of 1064 nm.

Polarization-dependent SHG measurements were performed by adding a super-achromatic λ/2 retarder plate on a motorized rotation mount in the beam path before the objective as well as a retractable linear polarization filter in the detection beam path in front of the pinhole.

Figure 1 shows the (a) AFM topography map, (b) line scans, and (c) phase image of the studied WSe

 crystal. The marked cross sections (cs1 and cs2) are shown in Figure 1b. The topography image reveals a 0.7 ± 0.1 nm step height of the WSe

 crystal, corresponding to a monolayer deposited on the Si/SiO

 substrate, in good agreement with previously reported studies (12,13,15). The topographically elevated triangular structures are about 2 nm higher than the monolayer, corresponding to a fourfold-layered crystal. Besides the large fourfold-layered crystal in the center, smaller crystals of the same height are also visible and are marked with arrows in Figure 1a. The side length of such a small triangle is in the range of 350–400 nm. The simultaneously recorded phase image reveals a down-shift for the monolayer whereas the fourfold-layered region shows the same contrast as the substrate. The smaller triangles also show a similar phase shift indicating that the same material is likely to be present there. Such phase shifts in AC mode for AFM images are associated with a change in the viscoelastic properties of the material, indicating that the fourfold layers are similar in those properties to the substrate, whereas clear differences are visible for the single layer.

FIGURE 1: (a) Atomic force microscopy (AFM) topography image, including (b) cross sections marked in the topography image, and (c) phase image of the studied WSe

 substrate. The arrows in the topography image indicate the positions of small triangular structures.

The rounded edges of the monolayer crystal are also of interest, which developed because of the temperature and precursor fluxes during growth conditions (12). These two factors have been shown to have a significant impact on monolayer morphology in MoS

 (29). The monolayer crystal is surrounded by a 2 nm high edge. The width of the edge is in the range of 150 nm. It is only in the convex-rounded corners that a substantially increased width to approximately 300 nm is detected. The phase image is for the entire edge similar to the monolayer value, which indicates that the viscoelastic properties of the edge are similar to those of the monolayer. Thus, the 2 nm height of the edge is unlikely to be a result of multilayer growth in this area.

In Figure 1a, it can be seen that the area directly inside the elevated edge is the flattest area on the flake. To illustrate this further, a zoom-in scan was performed and the variance of the topography signal was evaluated (Figure 2). It can clearly be seen that just inside the flake, an area of about 1 μm in width shows a much smaller variance in topography than the rest of the flake. Because only the inner part of the flake shows higher topographical variance, sample contamination can be excluded as the cause.

FIGURE 2: AFM topography variance of a zoomed-in area of the flake. The uniform area on the inside of the elevated edge (faint gray line) can be seen clearly.

 crystals obtained by exfoliation or various growth methods is widely represented in literature (5,16–21,30), whereas few references can be found for confocal Raman imaging of WSe

 (12,14,22). The same crystal as shown in Figure 1 was measured in confocal Raman imaging mode using the parameters listed in Figure 3. The presented Raman spectra were evaluated from a 2D array of Raman spectra using multivariate spectral analysis methods (31). As expected, the Raman spectra (Figure 3b) associated with the monolayer (green) and fourfold layer (red) show different characteristics, as described previously using Raman spectroscopy and theoretical calculations (20,21,30). The Raman image (Figure 3a) reveals the presence of the monolayer displayed in green and the fourfold-layered crystals in red. Although the small crystals (marked with arrows) have a baseline of only 350–400 nm as shown in the AFM image, they provide enough signal to be detected in the Raman image with a confocal Raman microscope. The edge shows the same Raman spectrum as the inner monolayer. Therefore, it confirms the assumption made based on the AFM results, that the small triangles are fourfold crystals, whereas the edge with its elevated height cannot be explained by a multilayer effect.

FIGURE 3: (a) Color-coded Raman image and the (b) corresponding Raman spectra evaluated from the two-dimensional (2D) array of spectra. Raman imaging parameters: 30 x 30 μm

, 120 x 120 pixels, Raman excitation laser 532 nm, laser power 2 mW, integration time per spectrum 0.1 s, 1800 g/mm grating.

Furthermore, by fitting Lorentzian curves to the Raman band at about 248 cm

 for all 14,400 acquired Raman spectra, the precise peak position for every location on the flake was obtained (Figure 4a). It reveals a relatively uniform peak position over the monolayer at ~247.8 cm

, whereas at the edges a small red shift of ~0.34 cm

 can be determined. Figure 4b shows the histograms evaluated from the monolayer without the edge and four- fold layer (blue), and also from the edge only (green). This clearly shows the shift in peak position of the 

 Raman band, characteristic for in-plane molecular vibrations in WSe

, and associated in literature with strain of the monolayer (32). The fourfold-layer crystal is associated with a larger red shift compared to the monolayer, in good agreement with the literature (20). The width of the Raman band (Figure 4c) does not show specific, detectable changes between the monolayer and the edge, confirming the presence of one crystal with strained edges (15).

FIGURE 4: Raman analysis. (a) Map of fitted Raman band around 248 cm

 showing peak shifts at the rounded edges of the crystal. (b) Histograms of the Raman band positions acquired from the monolayer without the edges and from only the edges. (c) The width of the analyzed Raman band does not show significant changes between the monolayer and the edges.

Figure 5 shows the color-coded PL image of the studied WSe

 crystal, measured with the parameters listed in the figure caption. The presented PL spectra were evaluated from the 2D array of spectra using multivariate spectral analysis methods (31). The colors in the image of Figure 5 match the colors of the spectra next to it. The monolayer shows a uniform PL distribution (shown in blue). The PL intensity of the fourfold crystal is shown in green and is, as expected, much weaker. According to bandgap calculations reported in the literature (16), the monolayer of WSe

 is a direct bandgap semiconductor. Multilayer WSe

 crystals however are indirect band gap semiconductors that display decreased photoluminescence intensity compared to monolayers. This could be detected in the central triangle, as well as for the small triangles indicated again with arrows in Figure 5. At the entire edge of the crystal, an increase of the PL intensity could be observed. The highest PL intensity was found at the convex edge, where Raman imaging revealed the highest strain in the monolayer (see Figure 4).

FIGURE 5: (a) Color-coded confocal photoluminescence (PL) image and the (b) corresponding PL spectra evaluated from the 2D array of spectra. PL imaging parameters: 30 x 30 μm

, 120 x 120 pixels, excitation laser 532 nm, laser power 2 mW, integration time per spectrum 0.05 s, 300 g/mm grating.

All measured PL spectra have an asymmetric curve form, indicating that more than one process is contributing to the PL emission (15). With defect density distribution having an impact on the level of degeneration observed in the involved layers, varying numbers of fit curves were used (15,16). For the present case, fitting three Lorentzian curves to the PL spectra provided a good description of the experimental data. The fits are presented as dashed lines in Figure 5 and follow the experimentally obtained data (colored curves) well. The characteristic features, such as peak position, width, and area, of these Lorentzian fits are presented in Figure 6. According to Fang and others (15), the three Lorentzian functions fitted to the PL spectra correspond to three different emission processes: The neutral exciton at about 1.62 eV, a trion at 1.6 eV, and a defect emission caused by lattice defects at about 1.53 eV. Figure 6 shows (a) the positions, (b) area and (c) width of the three individual peaks into which each measured curve is deconvoluted. The errors based on the fitting algorithm are indicated and where they are smaller than the displayed markers in the figure.

FIGURE 6: PL spectra evaluation: (a) the peak positions, (b) the area, and (c) the full width at half maximum of individual Lorentzian fits used to deconvolute each measured curve (triangles = neutral exciton peak; squares = trion peak and diamonds = defect peak).

For the monolayer, we can observe a consistent shift to lower energies of approximately 25 meV for the neutral exciton and the trion peak compared to the literature (15), whereas the defect peak appears at approximately 10 meV higher energy.

For the edge, no significant changes in the position of the trion peak were observed, whereas the position of the neutral exciton is upshifted relative to the monolayer. The defect band is downshifted for the edge and even further downshifted for the convex edge. The area plot (Figure 6b) shows a clear increase in the intensities for the convex edge for all three peaks, whereas for the remaining edge, only the peak associated with the neutral exciton seems substantially increased. The width of the peaks (Figure 6c) seems to increase similarly for all three peaks with the monolayer being the narrowest and the convex edge being the broadest.

The enhancement of the defect peak intensity for only the convex edge fits well with the increased strain as observed from the Raman measurements because a higher strain may be associated with a higher defect density. The change in the width of the fitted peaks may reflect the level of uniformity in the respective areas.

Figure 7 shows the results of confocal SHG microscopy measurements of the analyzed WSe

 crystal. The monolayer reveals a strong SHG signal, whereas the fourfold layer shows a small signal (integrated intensity of the SHG peak near 532 nm) as highlighted in the image (Figure 7a). As with most TMDCs, WSe

, in the 3R phase with two Se-W-Se unit cells of trigonal prismatic coordination (5). For odd layers (such as the monolayer) the lack of inversion symmetry gives rise to finite second-order nonlinearity. An even numbers of layers (such as the fourfold layers) show little or no second-order nonlinearity (4,23).

FIGURE 7: SHG analysis of the studied crystal. (a) Integrated intensity image of the SHG signal; (b) SHG signal from the Si-substrate (pink), monolayer (blue) and fourfold layer (green). (c) Polar plots of the SHG signal intensity as a function of the excitation polarization angle at the color-coded marked positions. SHG imaging parameters: 30 x 30 μm

, 120 x 120 pixels, pulsed 1064 nm laser, laser power: 28 mW, 0.1 s integration time per pixel.

The SHG intensities acquired from the monolayer (blue), the fourfold-layered crystal (green) and silicon-substrate (purple) are shown in Figure 7b. These data reveal an enhancement of the nonlinear SHG signal of the WSe

 monolayer by three orders of magnitude compared to the fourfold-layered crystal, which is in good agreement with previously reported second-order susceptibility measurements on exfoliated WSe

 (1). Although the analyzed crystal shows uniform Raman (Figure 3) and PL (Figure 5) signals over the entire monolayer, the SHG image reveals the polycrystalline nature of the monolayer because the SHG signal is substantially lower at the grain boundaries. The incident polarization of the pump laser is approximately along the 

-axis of the SHG-image (Figure 7a) and the total second harmonic radiation is collected. For these measurements the linear polarization filter in the detection beam path was removed. The uniform SHG intensity within each grain indicates that the individual grains are single crystals. At the grain boundaries, the SHG is suppressed as a result of the destructive interference and annihilation of the waves generated from the neighboring grains with different orientations (24,25). Although the grain boundaries are only a few atoms in width, the crystal boundaries can be clearly visualized. Similar results are reported from monolayers of molybdenum disulfide (MoS

) as a result of different chirality of the stitching areas of the domains of neighboring crystals (24,25).

Polarization measurements were carried out at the individual grains and their positions are marked with blue crosses (Figure 7a). They all show the same six- fold symmetry with the same orientation, depicted as the blue curve in the polar plot (Figure 7c). The polarization series shown in green (Figure 7c) was acquired from the fourfold-layered crystal. The intensity of this second-harmonic signal is three orders of magnitude smaller than that of the monolayer. It was plotted at a magnified intensity to reveal the differences in the relative intensities of the lobes.

 crystal was analyzed with AFM, confocal Raman, PL, and SHG microscopy. The overlay of the images acquired by the different techniques is presented in Figure 8 and visualizes the complementary findings from the techniques used. Figure 8a shows the overlay of the AFM and PL images. From this view, it can be seen that the area with high topographic variance (compared with Figure 2) correlates extremely well with the area of the enhanced PL in the edge area. Figure 8b shows the overlay of the SHG and PL images. This view indicates that the concave corners of the flake correlate with grain boundaries and that at these positions, no change of the PL signal relative to the remaining edge can be seen. From this, it may be concluded that the stress level at the grain boundaries is significantly lower than at the rounded edges. This finding is in agreement with the Raman findings as well (Figure 4). Although the slightly elevated topography at the edges may play a role in the edges’ PL signal, it seems more likely that the flat topography as well as the stress on the convex corners plays the more significant role. In Figure 8c, the SHG image is overlaid onto the AFM topography, showing the polycrystalline nature of the analyzed WSe

 monolayer. The AFM image does not reveal detectable topographic changes at the grain boundaries and the SHG–AFM combination additionally shows that the SHG intensity decreases in a similar manner at the outer edges as it does at the internal grain boundaries.

FIGURE 8: Overlay of images obtained with various techniques: (a) AFM and PL, (b) SHG and PL and (c) AFM and SHG.

By combining the various techniques, it was possible to obtain a better understanding of the sample than would have been possible by only employing the individual techniques in isolation. It was especially interesting that a topographically flat edge of about 1 μm in width shows an enhanced PL signal, where only the neutral exciton emission seems to be enhanced. The rounded edges show additional PL enhancement of all postulated processes and exhibit a clear shift of the Raman peaks, indicative of increased stress in these areas. By adding SHG as a fourth measurement technique, the multicrystalline nature of the flake became apparent and the concave edges could be identified as grain boundaries, which explains why the PL signal was not increased here and the Raman did not show an enhanced strain.

(1) J. Ribeiro-Soares, C. Janish, Z. Liu, A.L. Elias, M. S. Dresselhaus, M. Terrones, L. G. Cancado, and A. Jorio, 

(2) R. Zhang, H. Li, G. Hao, W. Liu, Y. Ye, Z. Li, X. Yuan, and C. Liu, 

(3) M. Ye, D. Winslow, D. Zhang, R. Pandey, and Y.K. Yap, 

(4) Y. Wang, J. Xiao, S. Yang, Y. Wang and X. Zhang, 

(5) R. Saito, Y. Tatsumi, S. Huang, X. Ling, and M. S. Dresselhaus. 

(6) C. Janish, Y. Wang, D. Ma, N. Mehta, A.L. Elias, N. Perea-Lopez, M. Terrones, V. Crespi and Z. Liu, 

(7) X. Li, W. Liu, Y. Song, C. Zhang, H. Long, K. Wang, B. Wang, and P. Lu, 

(8) H. Chen, V. Corboliou, A. S. Solntsev, D.Y. Choi, M. A. Vincenti, D. de Ceglia, C. de Angelis, Y. Lu, D. N. Neshev, 

(9) W. Choi, N. Choudhary, G. H. Han, J. Park, D. Akinwade, and Y. H. Lee, 

(10) H. Chen, Y. Tang, T. Jiang, and G. Li, 

(11) H. Zhang, J. Huang, Y. Wang, R. Liu, X. Huai, J. Jiang, and C. Anfuso, 

(12) B. Liu, M. Fathi, Liang Chen, A. Abbas, Y. Ma and C. Zhou, 

(13) S. Tongay, J. Suh, C. Ataca, W. Fan, A. Luce, J.S. Kang, J. Liu, C. Ko, R. Raghunathanan, J. Zhou, F. Ogletree, J. Li, J. C. Grossmann, and J. Wu, 

(14) H.S. Jang, J.Y. Lim, S.G. Kang, S.H. Hyun, S. Sanhu, S.K. Son, J.H. Lee, and D. Whang, 

(15) L. Fang, H. Chen, X. Yuan, H. Huang, G. Chen, L. Li, J. Ding, J. He, and S. Tao, 

(16) H. Sahin, S. Tongay, S. Horzum, W. Fan, J. Zhou, J. Li, J. Wu, and F.M. Peeters, 

(17) W. Shi, M.L. Lin, Q.H. Tan, X.F. Qiao, J. Zhang, and P.H. Tan, 

(18) P. Tonndorf, R. Schmidt, P. Böttger, X. Zhang, J. Börner, A. Liebeig, M. Albrecht, C. Kloc, O. Gordan, D. R. T. Zahn, S.M. de Vascocellos, and R. Bratschitsch, 

(19) W. Zhao, Z. Ghorannevis, A. K. Kumar, J. R. Pang, M. Toh, X. Zhang, C. Kloc, P.H. Tan, and G. Eda, 

(20) E. Del Corro, H. Terrones, A. Elias, C. Fantini, S. Feng, M.A. Nguyen, T.E. Mallouk, M. Terrones, and M. Pimenta, 

(21) H. Terrones, E. Del Corro, S. Feng, J. M. Poumirol, D. Rhodes, D. Smirnov, N.R. Pradhan, Z. Lin, M.A.T. Nguyen, A. L. Elias, T. E. Mallouk, L. Balicas, M. A. Pimenta, and M. Terrones, 

(22) M. O ́Brian, N. McEvoy, D. Hanlon, T. Hallam, J.N. Coleman, and G. Duesberg, 

(23) L. Malard, T.V. Alencar, A.P.M. Barboza, K.F. Mak, A.M. dePaula, 

(24) X. Yin, Z. Ye, D.A. Chennet, Y. Ye, K. O`Brien, J.C. Hone, and X. Zhang, 

(25) H. Hu, Z. Yang, L. Du, J. Zhang, J. Shi, W. Chen, P. Vhen, M. Liao, J. Zhao, J. Meng, G. Wang, J. Zhu, R. Yang, D. Shi, L. Gu, and G. Zhang, 

(26) Y. Li, Y. Rao, K.F. Mak, Y. You, S. Wang, C.R. Dean, T.F. Heinz, 

(27) J. Chen, C.S. Bailey, Y. Hong, L. Wang, Z. Cai, L. Shen, B. Hou, Y. Wang, H. Shi, J. Sambur, W. Ren, E. Pop, S. Cronin, 

(29) S.Y. Yang, G.W. Shim, S. Seo, and S. Choi, 

(30) X. Luo, Y. Zhao, J. Zhang, M. Toh, C. Kloc, Q. Xiong, and S. Y. Quek, 

, T. Dieng, and O. Hollricher J. Toporski, Eds. (Springer, Heidelberg, Germany, 2019), pp. 89–121.

(32) Y. Wang, C. Cong, C. Qiu, and T. Yu, 

 are with the Department of Electrical Engineering at Technion in Haifa, Israel. 

 are with the Department of Electrical Engineering at Stanford University in Stanford, California. Direct correspondence to: 

Articles

Using confocal Raman imaging and other advanced measurement techniques, we study the localized strain characteristics of tungsten diselenide (WSe2),
an important nanomaterial used for optoelectronic device applications.

A Comprehensive Study of WSe2 Crystals Using Correlated Raman, Photoluminescence (PL), Second Harmonic Generation (SHG), and Atomic Force Microscopy (AFM) Imaging

	The sensitivity of a high-resolution Raman imaging system is crucial to the quality of the acquired information. The spectral and spatial resolutions are among the primary factors that influence the obtainable results. The limits of resolution are defined theoretically by the laws of physics, but are experimentally determined by the instrument parameters. In this article, the theoretical background and the possibilities in practical applications are discussed.
	 

Key Elements of Confocal Raman Microscopy for High-Resolution Imaging

The sensitivity of a high-resolution Raman imaging system is crucial to the quality of the acquired information. The spectral and spatial resolutions are among the primary factors that influence the obtainable results. The limits of resolution are defined theoretically by the laws of physics, but are experimentally determined by the instrument parameters. In this article, the theoretical background and the possibilities in practical applications are discussed.

Confocal Raman microscopes are the instruments of choice for many Raman measurements in a wide variety of applications ranging from geosciences (1–3), biology (4–6), nanocarbon materials (7–9) to pharmaceutical compounds (10,11), just to name a few. This article sheds light on the possibilities and, in part, the origins in terms of spectral and spatial resolution for confocal Raman systems in general. 

Any confocal Raman system will have a spectral resolution which is mainly determined by the following parameters:  					

the focal length of the spectrometer (the longer the focal length, the higher the spectral resolution)

the grating (the higher the groove density, the higher the spectral resolution)

the pixel size on the charge-coupled device (CCD) camera (the smaller the pixels, the higher the spectral resolution)

the entrance slit or pinhole (the smaller the slit or pinhole the higher the spectral resolution)

the line shape preservation (equals imaging quality) of the spectrometer.

In some cases, one of the parameters can put limitations on the spectral resolution. If, for example, the projection of the pinhole onto the CCD is already large compared to the pixel size on the CCD camera, then a further reduction of pixel size will not increase the spectral resolution. 

Please note that the microscope components such as the objective used for collection of the signal should not influence the spectral resolution if the entrance slit or pinhole is the limiting element. This is preferential with confocal Raman microscopes. 

The determination of the spectral resolution is often a point of debate. First, one should clearly differentiate the spectral resolution from the sensitivity of the system to detect shifts of individual peaks. Relative peak shifts can be detected with a much higher accuracy using fitting algorithms as has been demonstrated with a sensitivity down to 0.02 rel. 1/cm standard deviation of the peak shift of a Si peak (12). The maximum achievable fit accuracy depends heavily on the number of detected photons and the width of the peak that is fitted. This shift analysis is especially relevant for examining stress within a sample, but may not be taken as a measurement for the spectral resolution. 

The spectral resolution, which determines how the system can measure (that is, full width at half maximum [FWHM] of a narrow peak or how well overlapping peaks can be differentiated), needs to be addressed separately from the peak shift sensitivity. There are various ways to state the spectral resolution, and some of the most common ones are outlined below. 

 is the difference in wavenumbers when moving from one pixel on the CCD camera to the next and is independent of factors such as slit width or peak width of the detected peak. This can only be seen as the true resolution limit if the pixel size and not the size of the entrance slit or pinhole is the limiting factor. For example, if the image of the slit or pinhole on the CCD camera is 100 µm in diameter and the pixel size on the CCD camera is 26 µm, then the resolution would be significantly worse than the distance (in wavenumbers) between two pixels. Since wavenumbers are measured in reciprocal space, it also needs to be noted that the pixel resolution will differ depending on the spectral position where it is determined. The resolution close to the Rayleigh line can, in this way, differ by almost a factor of two from the pixel resolution near 3500 rel. 1/cm in the case of 532-nm excitation. 

For this criterion two times the pixel resolution is taken. The logic behind this is that to discriminate two neighboring peaks one needs to have one pixel on one peak, one in the minimum between the peaks, and a third one on the next peak. This criterion is analogous to the Nyquist theorem in signal processing. The same limitations as outlined for the pixel resolution criterion apply in this case.  

Full Width at Half Maximum of Atomic Emission Lines

Atomic emission lines are typically much narrower than any Raman line. Their narrow width makes them a good probe to check the resolution. Figure 1 shows an atomic emission line of mercury near 579.07 nm. The 

-axis is given in units of rel. 1/cm assuming a 532.00-nm excitation laser. The spectrum was recorded using a mercury and argon calibration lamp coupled via a 10-µm core diameter multimode fiber to a UHTS300 spectrograph (WITec GmbH) equipped with both 1800- and 2400 grooves/mm gratings (BLZ at 500 nm) and a Newton electron multiplying charge coupled device (EMCCD) camera with a pixel size of 16 µm. The integration time was 0.1 and 0.24 s, respectively, for the spectra. The FWHM derived through this approach is a good measure of the resolution, but care must be taken to ensure that enough points are available within the curve to ensure a good fit to the curve. 

Figure 1: Spectra of the mercury atomic emission line at 579.066 nm plotted as a function of wavenumber assuming a 532.00-nm excitation. The red line is the fitted curve (pseudo voight function) and the blue diamonds are the measured data points for the 1800-grooves/mm grating. The green triangles and the purple curve show the results obtained using the 2400-grooves/mm grating.			

Measurement of Peak Resolution on Known Reference Samples

There are a few samples that are established standards to demonstrate spectral resolution. The most prominent is probably CCl

. Figure 2 shows two spectra of this substance recorded with different spectral resolutions. It can clearly be seen, that the peaks are nicely separated in the red spectrum whereas the separation is not as clear for the purple spectrum. 

Figure 2: Raman spectrum of CCl4 with 532-nm excitation at different spectral resolutions.			

Therefore, spectral resolution can be defined in many different ways and, thus, it is advisable to specify exactly how a spectral resolution was or should be determined. Comparing actual measurement results under identical measurement conditions is certainly one of the best ways to illustrate this. It should also be noted that with few exceptions the natural linewidths of Raman lines are typically larger than 3 rel. 1/cm. Taking the Nyquist criterion into consideration, a resolution in the range of 1 rel. 1/cm should be sufficient for the majority of samples. 

When considering the spatial resolution of a confocal Raman microscope one may distinguish between the lateral (

) resolution and the depth resolution. However, in either case, it is possible that the limitations arise because of one of the five following points: 					

basic physics (that is, diffraction limit)

limited positioning accuracy of the mechanical components used

limitations because of the optical components used in the beam path (that is, beam distortion)

nondiffraction limited sample illumination

In terms of the positioning system, it is important to differentiate the single step accuracy of a stepper motor, the positioning reproducibility, and linearity. The reproducibility and linearity are the key factors for an imaging system since this allows a line by line imaging. If, for example, a straight line is imaged, then this line will only be imaged with the accuracy of the positioning reproducibility even though the step size might be much smaller. Figure 3 illustrates this effect with Figure 3a showing insufficient positioning reproducibility and Figure 3b showing sufficiently high positioning reproducibility. 

Figure 3: A straight line imaged with (a) insufficient positioning reproducibility and (b) sufficient positioning reproducibility.			

The necessary positioning reproducibility should therefore be several factors better than the smallest imaged object, or if the system should allow the best physically possible resolution, several factors (that is, 10×) better than the diffraction limit. 

Using high-quality components and positioning systems should allow imaging approaching the limits of physics. 

Based on the diffraction theory of Ernst Karl Abbe, Lord Rayleigh defined the diffraction limit in 1896. Rayleigh thereby quantified the minimal distance at which two point light sources can be identified. In this case, one of the sources is located at exactly the distance of the first minimum of the Airy function (point spread function) of the other one. This distance (

) can be expressed as a function of the wavelength emitted (λ) and the numerical aperture (NA) of the objective used as: 

The equation 1.22 λ/NA is often also found in this context, but this describes the distance between the two first minima of the Airy function and not the diffraction limit as described by Lord Rayleigh. Using the definitions of the Airy function the resolution can be easily derived by how much the intensity between the two emitting points has to decrease according to the Rayleigh criterion. Please note that the distance is different for other criteria of diffraction such as the Abbe criterion or the Sparrow criterion. 

To derive the resolution of a microscope using either of those criteria it would be necessary to have a variety of very small, well scattering objects (small compared to the size of the Airy disk; for example individual TiO

 particles) at varying distances. Following high-resolution Raman imaging, one would then have to analyze the signal intensities and based on the detectable distances between the spots one would have to derive the resolution. 

An easier way to determine the lateral resolution power of a system uses the FWHM of small objects. Based on the Airy function the relation between the FWHM of the light emitted from an object and the diffraction limited distance (

Because the measured signal is always a convolution between the object size, the emission characteristics, and the system function, the objects measured in such experiments also have to be small compared to the Airy disk. Mathematically speaking, the object's size should approach a delta function for the convolution. Such small objects naturally have only limited material which scatters and thus one may expect small Raman signals emitted by them. Carbon nanotubes (CNTs) on the contrary show a large Raman signal while being very small in diameter (typically ranging from subnanometer to a few nanometer range) and comparatively long (up to a few micrometers typically). These samples are thus the ideal probes to check the lateral resolution of a confocal Raman microscope. For a 532 nm excitation laser and an objective with an numerical aperture (NA) of 0.9 one should therefore be able to obtain a FWHM across CNTs of about 301 nm. 

Figure 4a shows the integrated intensity of the G-band on a sample of CNTs on a Si substrate. The scan range was 1.5 µm × 1.5 µm with 50 × 50 points and an integration time of 23 ms per point was used. An alpha300R system (WITec GmbH) was used for the measurement in combination with a fiber-coupled, frequency-doubled Nd:YAG laser (532 nm emission), a Zeiss 100× NA 0.9 objective, and a 50-µm multimode fiber acting as the pinhole for confocal microscopy. For this microscope and objective this corresponds to a projected pinhole size of 500 nm in the focal plane. The spectrometer used was a UHTS300 (WITec GmbH) with a 600-grooves/mm grating (BLZ at 500 nm) combined with a back-illuminated CCD camera.  

Figure 4: Integrated intensity of the G-band of a carbon nanotube with (a) the cross section position marked in red and (b) the cross-sectional intensity along this line. The lateral resolution of the microscope system can be characterized by the FWHM and is about 272 nm.			

The red line in Figure 4a indicates where the cross section shown in Figure 4b was extracted from. It can clearly be seen that the FWHM is even narrower than the predicted minimum. 

The theory of confocal microscopy (for example, see reference 13) shows that the achievable resolution can further be decreased by a maximum of 1/√2. In confocal Raman microscopy this fact is rarely used to its limit, because it requires a strong reduction of the pinhole diameter, which in turn reduces the throughput. 

Depth resolution is the best proof of the confocality of a system. The instrument design has a key influence on the achievable resolution, but the pinhole or slit as well as the way the sample is illuminated also play a crucial role for the depth resolution. Therefore, these points are outlined below before the physical limit of the depth resolution is discussed. 

The sensitivity of a high-resolution Raman imaging system is crucial to the quality of the acquired information.

The development of nanostructured materials requires detailed knowledge of their chemical and structural properties, leading to a growing demand for characterization methods for heterogeneous materials on the nanometer scale. However, certain properties are difficult to study with conventional characterization techniques due to either limited resolution or the inability to differentiate materials chemically without inflicting damage or using invasive techniques such as staining. By combining various analytical techniques such as Raman spectroscopy, confocal microscopy, and atomic force microscopy (AFM) in one instrument, the same sample area can be analyzed nondestructively with these methods, providing a more complete understanding of the materials. Raman spectroscopy, a chemical analysis technique, combined with confocal microscopy, enables confocal Raman imaging (1–8). The power of Raman imaging stems from the extensive chemical information contained within molecular vibrational spectra. In the Raman spectral imaging mode, a complete Raman spectrum is recorded at every image pixel, producing a two-dimensional array consisting of tens of thousands of complete Raman spectra. From this array, images are extracted by analyzing various spectral features (such as sum, peak position, and peak width). Differences in chemical composition, although completely invisible in optical images, will be apparent in the Raman image and can be analyzed with a resolution down to 200 nm (3,6,9). The recently implemented high-speed electron multiplying charge coupled device (EMCCD) detector, in conjunction with an ultrahigh throughput spectrometer, allows a reduction in Raman data acquisition time by another factor of 20, down to 760 μs for a spectrum (ultrafast confocal Raman imaging) (10,11). 

If higher resolution is required, the confocal Raman microscope can be transformed into an atomic force microscope by simply rotating the microscope turret. This technique is employed to trace the topography of samples with extremely high resolution by recording the interaction forces between the surface and a sharp tip mounted on a cantilever. The sample is scanned under the tip using a piezo-driven scan-stage, and the topography is reproduced with specialized software that translates this information into images. Structures below the diffraction limit can be visualized using this imaging technique (9). This article describes further improvements that allow the automated analysis of large samples with confocal Raman imaging and AFM. In addition to the acquisition of large area scans (12), it is possible to predefine measurement sequences at any user-defined selection of measurement points on the sample, guaranteeing the most comprehensive surface analysis tool for systematic and routine research tasks. 

For the studies described here, a new microscopy system (WITec alpha500, Ulm, Germany) was used. It combines a high-throughput confocal Raman microscope for 3D chemical imaging and an atomic force microscope for high-resolution morphological imaging in an automated system for large samples. A piezo scanner, with a scan range of 200 μm × 200 μm, is mounted on top of a motorized 

 stage. This stage is driven by stepper motors and allows an extension of the scanning range along the 

 axes to 150 mm × 100 mm with a step size of 100 nm. As well as expanding the scanning range, this stage can be used to perform multiarea–multipoint measurements on any user-defined number of measurement points. An example of such a multipoint scan is shown in the software screenshot in Figure 1. The table on the right side lists the coordinates of the points of interest, whereas the graph on the left displays the points of interest and the travel path for automated point measurements. Through scripting functions, several consecutive tasks can be executed automatically without any online process control by an operator.  

A series of AFM and Raman measurements were performed on a dynamic random access memory (DRAM) chip (Infineon Technologies, Neubiberg, Germany) to show the automation capabilities of the alpha500. In the first step, white light video images were recorded at three positions on the sample (Figure 2). The following scripts were used for this procedure: autoillumination for optimum white light illumination of the sample; autofocus to bring the sample into focus based upon the video images; and the snapshot acquires a video image at each preselected point.  

The video images from Figure 2 were recorded with an Olympus 100× (NA = 0.95) objective and reveal the different patterns selected from the DRAM chip. 

Parts of the three selected areas shown in Figure 2 were then imaged with Raman spectral imaging. In this imaging mode, a complete Raman spectrum is recorded at every image pixel, producing a 2D array of 150 × 150 Raman spectra. The integration time for each individual Raman spectrum was 10 ms; thus, the array of 22,500 Raman spectra was acquired in less than 4 min. By evaluating the position of the first order Si Raman band at 520/cm, stress images of the selected areas can be obtained (13). Figure 3 shows the stress images taken from the three preselected areas.  

By simply rotating the microscope turret, the confocal Raman microscope was converted into an atomic force microscope. By using the same positions as used before for the acquisition of the Raman images, and the additional auto-tip-approach scripting function, AFM images were recorded from the same sample areas. Figure 4 shows the AFM images recorded from the three selected sample areas. The line structure in the area shown in the top image consists of parallel grooves that are 80 nm deep. The pits from areas shown in the other two images have a diameter of 300 nm and a depth of 300 nm.  

By combining two nondestructive sample analysis methods in an automated system, precisely the same sample position can be investigated with either technique. Multipoint–multiarea measurements can be performed routinely at various areas on the sample. The motorized sample stage can be used to perform large overview scans, whereas the additional piezo-scan-stage allows the acquisition of high-resolution images from selected areas of the overview image. The implemented scripting routines, such as auto-focus and auto-AFM-tip-approach, guarantee standardized routine measurement procedures without any online process control by an operator during the measurement. 

Ute Schmidt, Olaf Hollricher, Thomas Dieing

(2)  U. Schmidt, A. Jauss, W. Ibach, and O. Hollricher, 

(3)  U. Schmidt, S. Hild, W. Ibach, and O. Hollricher, 

(6)  A. Jauss, H. Fischer, and O. Hollricher, 

(7)  O. Hollricher, W. Ibach, A. Jauss, and U. Schmidt, 

(8)  U. Schmidt, W. Ibach, J. Mueller, and O. Hollricher, 

(9)  U. Schmidt, F. Vargas, T. Dieng, K. Weishaupt, and O. Hollricher, 

(11) Ultra-fast Confocal Raman Imaging, Application Note, 

(12) alpha500 – Large area Scans of Tablets, WITec Application Note, 

(13) U. Schmidt, W. Ibach, J. Mueller, K. Weishaupt, and O. Hollricher, 

The combination of confocal Raman and atomic force microscopes allows chemical and surface topography imaging of large samples without any ongoing process control by an operator. This article describes the relevant measurement principles and presents examples of automated measurements on nanostructured materials.

Thomas Dieing

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