Characterization of deep-hole structure of semiconductor devices using transmission small-angle X-ray scattering

In order to realize non-destructive cross-sectional profile measurement for deep hole advanced devices, we have applied a transmission small angle X-ray scattering instrument that employs a Mo-target X-ray source and a high-sensitivity two-dimensional detector. It enables us to measure the average cross-sectional profile of periodic hole patterns that are several tens of nanometers in diameter and several micrometers in depth. The structure, characterized by hole diameter, tilt angle, and ellipticity as functions of depth, was successfully evaluated. The obtained average depth profile of the holes was compared with that from a cross-sectional SEM and a milling SEM, and it was confirmed that they agreed very well.


Introduction
As semiconductor devices have become three-dimensional (3D), holes with a depth of 1 μm or more have been formed on the surface of a wafer. For example, the hole depth of 3D-NAND memory [1][2][3] will be expected to reach several tens of micrometers in the near future, and the aspect ratio of depth to diameter will be well over 100. In order to ensure the device performance formed in the deep holes, the following characteristic is required for the deep-hole structure. First, the holes must be perpendicular to the wafer surface. Second, the hole shape and its size must be uniform in the depth direction. Third, roughness such as depth, diameter, and hole position must be as small as possible. The control of these parameters is crucial for the device performance. Of course, etching systems have been extensively studied so that the above ideal hole structure can be obtained. [4][5][6] For inspecting such deep structures during fabrication processes, existing metrologies (CD-SEM, 7,8) OCD, 9,10) etc.) are facing serious difficulties as the probes (electrons or lights) cannot penetrate into the deep structures and/or do not have enough sensitivity. Therefore, there is a strong demand for a proper in-line metrology tool to investigate the characteristics of deep-holes without destroying the device structure.
The small-angle X-ray scattering (SAXS) method is one of the candidates for measuring such cross-sectional profiles and their uniformity non-destructively. The history of applying SAXS to semiconductor devices is short, but various application examples have been reported. [11][12][13][14][15][16][17][18] The X-ray can analyze nanometer size structures with high accuracy due to its short wavelength nature (typically, λ < 0.1 nm). We have already developed a grazing incidence SAXS (GI-SAXS) metrology, which has high-sensitivity to analyze very thin surface nanostructures even with fewtens of nanometers in depth. 19) It has been used and has played an important role in the measurement of various surface patterns, such as planar NAND memories, quartz templates for nanoimprint lithography, and many kinds of resist patterns. [20][21][22][23][24] However, GI-SAXS can apply a pattern, which is below fewhundreds of nanometers in depth, as the X-ray does not reach the bottom of a deep hole in the grazing incidence geometry. On the other hand, employing the SAXS (T-SAXS) transmission geometry with a short wavelength X-ray, which can penetrate through the device pattern and its silicon substrate at the same time, enables us to measure SAXS for deep-hole structure without destroying the wafer. In order to realize a highperformance T-SAXS instrument, we have employed a highbrilliance X-ray source with a Mo Kα line, high-precision X-ray optics, 25) and a high-sensitivity two-dimensional (2D) pixel detector. 26,27) In this paper, we report the results of the cross-sectional profile of deep hole patterns formed on a 300 mm wafer by applying the T-SAXS using our instrument and a comparison with that measured by a cross-sectional SEM and a milling SEM.
2. Principle of the X-ray metrology 2.1. Relationship between the X-ray scattering and the patterned structure When X-rays are irradiated to the patterned area, incident X-rays are scattered. Then, as shown in Eq. (1), the scattering amplitude A(Q) is given by the Fourier transform of the electron number density distribution ρ(r) of the pattern, [28][29][30] where Q is the scattering vector in the reciprocal space, given as Q = k − k 0 , and where k 0 and k are the wave vectors of the incident and scattered X-rays, respectively. r is the real space coordinates. From the X-ray scattering measurement, one can collect scattering intensity I(Q), which is the square of the absolute value of A(Q) as shown in Eq. (2).
Scattering amplitude from the periodic structure When scatters (holes) are arranged in a periodic lattice as shown in Fig. 1(a), the integral terms of Eq. (1) can be factorized into the form factor F(Q) and the structure factor S(Q X , Q Y ; a, b, θ) as follows: 19) The form factor F(Q) is the integral term in a unit cell, and depends on only the shape of the scatter. The structure factor S(Q X , Q Y ; a, b, θ) depends on only the lattice structure. Diffraction X-rays are observed when the denominator of Eq. (5) becomes zero, and the diffraction condition can be expressed by two integers, h and k as follows, Each diffraction point is identified by a set of the diffraction indices (h k).

Structure factor in consideration of the pitch variation
As shown in Fig. 1(b), when the positions of the scatters are fluctuated from the ideal lattice points, the structure factor S(Q X , Q Y ; a, b, θ) can be calculated by the convolution integrals of their distribution functions, and rewritten by the multiplication of the Laue function L(Q X , Q Y , a, b, θ) and Debye-Waller type decay factor B(Q X , Q Y , σ P,X , σ P,Y ) as follows: 28) q s s q s s where σ P,X and σ P,Y are the pitch variations in the X and Y directions, respectively, and these values are 1σ of the Gaussian distribution.

Modeling of the shape of the scatter
The electron number density distribution ρ(r) can be calculated by the inverse Fourier transform of the form factor F(Q) as shown in Eq. (4). However, T-SAXS data includes only the X-ray intensity I(Q) and lacks phase information. In other words, the electron number density distribution cannot be directly determined by the inverse Fourier transform. In order to overcome this phase problem, we decided to analyze the electron number density distribution based on a model fitting algorithm. We assume the electron density profile ρ(r) can be expressed using a shape function z(ρ, X, Y) including many structural parameters as shown in Fig. 2. For example, when  The Japan Society of Applied Physics by IOP Publishing Ltd a hole is sliced into N layers in the depth direction, each layer has six parameters: the electron number density ρ, thickness t, hole diameters of D X and D Y and hole positions of Δ X and Δ Y . The tilt angles of the hole in the X and Y directions can be calculated from the depth profiles of Δ X and Δ Y , respectively. The ellipticity depth profile can be evaluated from the ratio of the depth profiles of D X and D Y . These model parameters are optimized by a least-square method until the difference of the scattering intensities between the experimental and the calculation becomes minimum. It should be noted that such an analysis method without phase information cannot distinguish upside-down hole shapes. Therefore, a somewhat characteristic shape should be used as the initial shape. We have also taken into account the variation of the diameter and depth of the holes by performing convolution integrals to assume the distribution functions of the variation.

Cross-sectional profile measurement of deep holes
A 300 mm wafer with hole patterns on the surface was prepared as a sample. The holes are arranged in a tetragonal lattice in the lateral plane with a 48 nm pitch (a = 48 nm, b = 48 nm, θ = 90°). The design values of the hole diameter and the hole depth are about 30 nm and 1.2 μm, respectively. In this section, we report the results of the cross-sectional profile measurements of the deep holes at typical points on the 300 mm wafer. Figure 3(a) shows the measurement geometry of the T-SAXS. X-rays are irradiated from the back of the wafer and diffraction spots corresponding to the tetragonal lattice are observed on a 2D detector as shown in Fig. 3(b). Figure 3(c) shows the integrated intensity of each diffraction spot at the vertical incidence condition (ω = 0° ). In order to determine the 3D hole shape, it is necessary to measure the scattering vector Q Z dependence of the integrated intensity of each diffraction spot. To change Q Z is the almost same as to change the projection direction of the hole to the detector, and it realizes this by rotating the hole to the incident x-ray. When the wafer is rotated around the Y axis as shown in Fig. 3(a), the Q Z changes as w » -Q Q tan . Z X Figure 3(d) shows the Q Z dependence of the diffraction intensity of each diffraction spot when the rotation angle ω is from −12°t o +12°, and profiles in the graph are shifted for better visibility.

Measurement method
Each diffraction spot has a characteristic interference fringe. From the typical period ΔQ Z of about 0.005 nm −1 of the interference fringes, the hole depth is estimated to be about The period and the phase of the interference fringes, which strongly depend on the diffraction spot, reflect the hole shape, and the cross-sectional profile can be obtained by analyzing these fringe patterns based on the model fitting algorithm described in Sect. 2.4.
The maximum values of Q R and Q Z in this experiment are 1.2 nm −1 and 0.2 nm −1 , respectively. The real space resolutions in the X-Y plane and Z direction are estimated to be ΔR ∼ 5.2 nm and ΔZ ∼32.3 nm, respectively. These resolutions are sufficient to characterize the precise hole shape with an average hole diameter of 30 nm and hole depth of 1.2 μm.

3.2.
Cross-sectional profile measurements at the wafer center and the wafer edge T-SAXS data measured at the wafer center (0 mm, 0 mm) are shown in Figs. 3(c) and 3(d). T-SAXS data measured at the wafer edge (−147 mm, 0 mm) are shown in Figs. 4(a) and 4(b). A notable difference in the T-SAXS data between the two measurement points is the phase of the interference fringes. The interference fringes shown in Fig. 3(d) are symmetrical about the Q Z origin, whereas those shown in Fig. 4(b) are asymmetrical. This qualitatively indicates that deep holes are etched vertically and straight at the wafer center, whereas the deep holes are tilted and/or undulated at the wafer edge.
Cross-sectional profile analyses based on the model fitting algorithm for both measurement points were performed, and the calculated data, using the optimized parameters with a The tilt angles in the X and Y directions are 0.013°and 0.038°, respectively. On the other hand, the holes at the wafer edge are elliptical, and the ellipticity is changing as a function of the depth Z. The hole diameter in the X direction is about 10% larger on average than the hole diameter in the Y direction. The tilt angles in the X and Y directions are −0.475°and −0.004°, respectively, indicating that the holes are inclined toward the wafer center.
To evaluate the accuracy of the T-SAXS results, a crosssectional SEM and a milling SEM were used as reference tools for the X-Z and X-Y cross sections, respectively. Figure 7 shows cross-sectional SEM images overlapped with the results of the T-SAXS analysis (red line). It can be seen that the T-SAXS results agree very well with the images of cross-sectional SEM, not only for diameters and depths but also detailed sidewall shapes and tilt structures. Figure 8 shows the milling SEM images observed at the depth of 250 nm overlapped by the X-Y cross section graphs of the X-ray and milling SEM results. The X-Y cross section of the milling SEM is calculated from the average of 50 holes. The difference of hole diameter is only about 1.8 nm between the T-SAXS and the milling SEM at the both measured positions. The ellipticities of the holes at the wafer edge measured by the T-SAXS is 0.918 and it is very close to that measured by the milling SEM as 0.928.
As a result of comparison with SEM observations, it can be concluded that the T-SAXS has sufficient sensitivity and accuracy to measure the cross-sectional profile of deep holes.

Tilt angle distribution
As described in Sect. 3.2, the hole-patterned wafer shows a characteristic tilt angle distribution, holes at the wafer center are almost vertical, whereas holes at the wafer edge have a large tilt angle of about 0.5°. Generally, evaluating a tilt angle distribution in a wafer is very important, not only for quality control of the device manufacturing process, but also for determining etching conditions. Therefore, the tilt angle