Precise 3D profile determination of high aspect ratio hole patterns by transmission small-angle X-ray scattering

The etching process of high aspect ratio (HAR) hole patterns on a wafer surface is a key step for fabricating new-generation semiconductor memory devices with vertically stacked structures. As the stacking number of these memory devices increases, it is getting more challenging to maintain the ideal etching profile of HAR holes. Therefore, detailed profile evaluation of these HAR holes is increasingly important. In this study, we have measured 4.2 μm deep holes by transmission small-angle X-ray scattering (T-SAXS) to determine the precise three-dimensional (3D) hole profile. By applying an improved 3D shape model for a hole, we successfully determined a hole profile whose cross-section parallel to the sample surface changes from elliptical to rectangular along its depth. This 3D profile measurement demonstrated that T-SAXS has sufficient sensitivity to evaluate a cross-sectional shape change along the depth of HAR holes.


Introduction
Increasing the density of semiconductor memory devices became even more challenging after shrinking the critical dimension (CD) reached technical or physical limitations for planar devices. In order to overcome these limitations, vertically stacked device structures were designed for memory devices. For example, NAND flash memory adopted vertically stacked transistor cells (3D NAND), [1][2][3] and the stack number of cells has reached 176 in volume production. 4) In the same way, DRAM adopted cylindrical capacitors to reduce the device footprint on the wafer surface while maintaining capacitance. 5) Furthermore, 3D-DRAM, the concept of vertical stacking of the memory cells composed of the capacitors and the transistors, is being studied. 6) These vertical-type memory devices have device structures around or inside deep holes fabricated on the wafer surface. The aspect ratio of the depth to the diameter of these deep holes has gradually increased along with the device stack number, and it will be over 100 in the 3D-NAND case. 6) Controlling the etching process of such high aspect ratio (HAR) holes is challenging, and several profile distortions (e.g. tapering, centerline tilting, and bowing) occur. 7) Note that process control techniques are constantly being developed to maintain the ideal hole etching profile. [8][9][10] Therefore, for quality control of HAR holes and the development of etching techniques, metrologies to evaluate the detailed profile of HAR holes are in high demand.
The primary conventional metrologies to evaluate semiconductor devices are optical scatterometry (or optical CD, OCD) and scanning electron microscopy (SEM)/transmission electron microscopy (TEM). 11) OCD can non-destructively provide the average CD profile of holes in the measurement area with high throughput. 11,12) However, it is not easy for OCD to achieve both resolution and penetrating power for HAR structures due to its probe properties. The wavelength of the OCD probe is usually from UV to NIR (190 nm-1.7 μm), 12) which is insufficient to determine the precise shape profile of sub-100 nm features. On the other hand, a longer wavelength (mid-IR region, 5 μm ∼) is needed to penetrate deep holes. 13) SEM measurement can deliver the rough three-dimensional (3D) shape profiles of holes without sample destruction by tilting the incident electron beam. 11) However, for precise shape profile determination, milling SEM or TEM investigations (both requiring sample destruction) are usually used. Because of throughput and measurement area limitations, evaluating a wide area on the wafer using milling SEM or TEM is not a small burden.
Small-angle X-ray scattering (SAXS) is another candidate for determining precise shape profiles of semiconductor device structures. Due to their high penetration power and short wavelength (typically, ∼0.1 nm) nature, X-rays can analyze nanoscale structures precisely and non-destructively. In the past, applying SAXS to semiconductor metrology has been studied as a synchrotron-based technique in its early stage. 14) However, thanks to the development of high-brightness compact X-ray sources and highly sensitive two-dimensional (2D) pixel detectors, 15,16) inline SAXS metrology has been implemented for practical use at present.
Many reports have demonstrated that grazing incident SAXS (GI-SAXS) is effective for shallow patterns evaluation. [17][18][19][20][21][22][23] For HAR holes evaluation, our group already reported the measurement of 1.2 μm deep holes using transmission SAXS (T-SAXS). [24][25][26] In these reports, we demonstrated that T-SAXS can provide the detailed CD and centerline profiles of HAR holes whose cross-section parallel to the surface can be approximated as an ellipse. Other groups also have reported the CD profile and centerline tilt measurement of HAR holes or pillars with simple crosssectional shapes by X-ray scattering. 27,28) In some practical cases, the hole cross-sectional shapes are too complicated to be approximated as an ellipse. In this study, we performed T-SAXS measurement on a 4.2 μm deep HAR hole whose cross-sectional shape changes along the depth direction. By adopting an improved hole-shape modeling method for T-SAXS analysis, we have successfully determined the precise 3D profile of this HAR hole.

Principle of the metrology
The intensity of the scattered X-rays I(Q) of a periodic structure (like hole patterns of memory devices) is represented by the form factor of the unit of scatterer F(Q), which is the Fourier transform of its electron density ρ(r), and the structure factor of the periodicity S(Q) as follows, [29][30][31] where k 0 and k are the wave vectors of the incident and scattered X-rays. In general, the individual scatterer units are not identical and have pitch variation and local CD variation. We represent these variations as Gaussian distribution and convolute them into the structure factor S(Q). 26) When the periodicity is expressed as shown in Fig. 1, the scattered X-rays are observed as periodical diffraction spots, and the diffraction condition can be expressed by the lattice constants a, b, and γ, and a set of indices h k, 26) The task of the current study is to reconstruct ρ(r) consistent with the intensities of all measured diffraction spots characterized by h k. For this purpose, we have made a HAR deep hole structural model having shape parameters (such as CD, hole depth, and tilting angle) and optimized those parameters by least-squares fitting.

Experimental setup
The experimental geometry of the T-SAXS measurement is shown in Fig. 2(a). The X axis is parallel to the lattice vector a, and the Y axis is perpendicular to the X axis. The Z axis is normal to the sample surface. The sample is irradiated by X-rays from the backside. Then, the diffraction spots are collected by the 2D detector.
As shown in Eqs. (1) and (2), the 3D hole shape profile is determined from the 3D Q dependence of the scattering intensities. In the T-SAXS geometry, the obtainable range of Q Z is quite limited compared to that of Q X and Q Y . To measure the Q Z dependence of the scattering intensity over a wide range, the sample is rotated around the axis parallel to the surface, as illustrated in Fig. 2(b). When the sample is rotated around the Y axis with the rotation angle ω, Q Z is approximately represented as Q Z ≈ −Q X tan ω. 26) In this manner, one can collect various Q dependencies of the scattering intensities.
We prepared a 300 mm Si wafer with a hole pattern on the wafer surface for a T-SAXS experiment. The lattice structure of the hole pattern was hexagonal with a = 160 nm, b = 160 nm, and γ = 60°. The designed value of the hole depth was 4.2 μm and the diameter was 80 nm. The T-SAXS experiment was performed using the XTRAIA CD-3000T from Rigaku under the conditions summarized in Table I. 4. 3D profile analysis of HAR hole 4.1. Hole shape modeling based on the X-ray diffraction pattern The X-ray diffraction image from the sample at the rotation angle ω = 0°is shown in Fig. 3(a). In this image, it is observed that the cross-shape marked area shows higher intensity than the other areas. This pattern is reflected by the form factor F(Q). Figure 3(b) shows the simulated X-ray scattering images from an elliptical [ Fig. 3(b) left] and a rectangular [ Fig. 3(b) right] shape of the scatterer. X-ray scattering from an elliptical shape shows an elliptical intensity distribution. On the other hand, the scattering from a rectangular shape shows higher intensity in the cross-shaped area and a rectangular intensity distribution. By comparing the observed and simulated scattering images, it was inferred that the hole has a mixture of ellipse and rectangle characteristics.
Based on this consideration, we assumed the hole XY cross-sectional shape of the hole can be represented by the hole diameter in the X(Y) direction L X(Y) and the corner radius R X(Y) as shown in Fig. 3(c). When the ratio of the corner radius R X(Y) to the diameter L X(Y) is close to 0.5, which means the corner radius is equal to half of the hole diameter, the hole XY cross-sectional shape is close to an ellipse. On the other hand, when the ratio R X(Y) to L X(Y) is close to 0.0, which means the corner radius is 0.0, the hole XY cross-sectional shape is close to a rectangle. We assume the ratio R X to L X and the ratio R Y to L Y have the same value at each depth in this analysis. The 3D hole shape model is constructed by stacking 100 layers of 42 nm thick, as shown in Fig. 3(c). Each layer has the independent XY cross-sectional shape parameters described above. Therefore, this 3D hole shape model can represent not only the changes in the CD but it can also represent the XY cross-sectional shape in the depth direction as it changes from an ellipse to a rectangle.

T-SAXS data analysis
The T-SAXS measurement patterns of the sample are shown in Figs. 4(a) and 4(b). Figure 4(a) shows the integrated   Fig. 4(a) upper], which indicates the present hole shape model is considered to represent the characteristics of the hole XY cross-sectional shape. Figure 4(b) shows the Q Z dependence of the experimental (dotted lines) and calculated (solid lines) integrated intensities of each diffraction spot obtained by rotating ω from −10°to 10°. We used 122 diffraction spots for the analysis, with each spot corresponding to the specific (Q X , Q Y ) value as indicated in Eq. 3. A representative 20 of them are shown in this graph. The profiles in this graph are offset for better visibility. Each diffraction shows characteristic interference fringes, which contain information about the 3D hole shape. The experimental patterns are well reproduced by the calculation, and the obtained 3D hole shape model is considered to reproduce the real HAR hole structure of the measured sample.

T-SAXS sensitivity evaluation
The following simulation demonstrates that the interference fringes of the diffractions have sufficient sensitivity to the hole XY cross-sectional shape change along the depth direction. We have compared the scattering patterns with the following three simplified models without changing the XY cross-sectional shape of the hole along the depth direction. The first is an ellipse, the second is an intermediate shape between an ellipse and a rectangle, and the third is a rectangle with the same CD profiles and centerline shifts. Note that this "intermediate of ellipse and rectangle" is the shape where the ratio of the corner radius R X to the diameter L X is 0.31. The calculated diffraction intensities from these three simulation models are compared to that from the optimized hole shape model.
The resultant four simulated scattering patterns are shown as solid lines in Fig. 5(a), with the colors red, blue, green, and black corresponding to optimized, intermediate, ellipse, and rectangle, respectively. This figure shows that the models with different XY cross-sectional shapes show different interference fringe patterns, even when the CD profiles are the same. The enlarged figure of the (3 0) diffraction and the (2-2) diffraction are shown in Figs. 5(b) and 5(c), respectively. In these figures, the calculated diffraction intensities from the optimized hole shape and the simulated intensities from the three simplified models are overlaid on the experimental intensities shown as dotted lines. These figures show that the calculated intensities from the three simplified models with constant XY cross-sectional shapes do not fit the experimental patterns. Therefore, it can be noted that the present SAXS data have enough information to analyze the precise hole XY cross-sectional shape and how it changes along the depth direction.

3D hole profile determination
The obtained hole cross-sectional profiles are shown in Fig. 6(a), and its 3D display is in Fig. 6(b). The overall hole shape looks like a golf tee, with a bow shape near the surface and tapering toward the bottom. The XY cross-section of the hole shows an intermediate shape between an ellipse and a rectangle.
To confirm the reliability of the T-SAXS measurement results, we compared the obtained hole CD profiles with that measured by STEM (Hitachi HD-2700, 200 keV). The result is shown in Fig. 7(a). The STEM result is calculated as the average of 15 measurement points at each depth, and the error bar corresponds to the standard deviation. It should be noted that the T-SAXS results have reasonably good agreement with the STEM, especially on the bowing shape near the surface. The CD linearity between the T-SAXS and STEM results is shown in Fig. 7(b). There are strong correlations in the X and Y directions with R 2 of 0.996 and 0.988, respectively, even though small offsets remain in the bottom region, especially in the X direction.

Detailed investigation of XY cross-sectional shape change
For a more detailed evaluation of the 3D hole shape, we investigated the XY cross-sectional profile of the hole at each depth from near the sample surface (depth: 0.1 μm) to the hole bottom (depth: 4.0 μm) in about 1 μm increments. As a reference, we sliced the sample horizontally to the wafer surface by FIB and obtained the top-view STEM image at each depth. Figure 8(a) shows the comparison results. The XY cross-sectional profile of the hole obtained by T-SAXS is overlaid on the top-view STEM image at each depth. This figure shows that the XY cross-section of the hole is relatively elliptical near the surface, and it changes to more rectangular with sharp corners at 1.2 μm depth. The corner radius increases again at 1.8 μm depth and beyond. It is remarkable that this hole XY cross-section obtained by T-SAXS almost matched the STEM image at each depth.
To evaluate this hole XY cross-sectional shape change in the depth direction more quantitatively, we calculated the ratio of the corner radius to the diameter R X /L X and The Japan Society of Applied Physics by IOP Publishing Ltd investigated its change in the depth direction. The result is shown in Fig. 8(b). The R X /L X values of the STEM result were obtained by fitting the hole shape parameters (the hole diameter L X and the corner radius R X ) to the extracted outline from the STEM images. The R X /L X value of the STEM result is calculated as the average of 7 holes at each depth, and the error bar corresponds to the standard deviation. At the sample surface, the R X /L X value of the T-SAXS result shows 0.4, which is closest to 0.5 (the hole shape is an ellipse). It gradually decreases to 0.18, closest to 0.0 (a rectangle), at 1.4 μm depth. The R X /L X value steeply increases to approximately 0.3 in only 500 nm from 1.5 to 2.0 μm depth, and it remains almost flat to the hole bottom. This R X /L X change in the depth direction of the T-SAXS result shows a good agreement with that of the STEM result, which quantitatively supports that the hole XY cross-sectional shape change in the depth direction analyzed by T-SAXS has high reliability.

Conclusions
In this study, we successfully determined the precise 3D hole profile of 4.2 μm deep holes from T-SAXS measurement by adopting a new hole shape model that can represent changes in the XY cross-sectional shape of the hole along the depth direction. The determined hole profile shows large CD changes, such as bowing or tapering, and the hole XY crosssectional shape changes from elliptical to rectangular along the depth. The high reliability of these results is supported by the STEM measurement results. The experimental SAXS pattern could not be explained by the scattering intensities calculated from the three simplified models, and it was only reproduced by that from the obtained hole profile with the XY crosssectional shape changing in the depth direction. This simulation demonstrates that T-SAXS has sufficient sensitivity to determine the precise hole 3D profile.
Of particular note, non-destructive measurement of the hole XY cross-sectional shape change is a breakthrough achievement. In this study, the hole XY cross-section was represented by an intermediate shape between an ellipse and a rectangle. As described in Sect. 4.1, X-ray diffraction images directly reflect the scatterer shape. This means that T-SAXS, in theory, can analyze the hole shape profile with arbitrary XY cross-sectional shape. Therefore, it can be expected that T-SAXS can play a large part in evaluating the shape of complex HAR structures and contribute to