Measuring linewidth (the size of the features etched on a wafer) is a key element of quality control in the semiconductor fabrication process and is mainly carried out using a critical dimension scanning electron microscope (CD-SEM). The appeal of CD-SEM is that it can measure linewidth with subnanometer repeatability. Unfortunately, the technique has an indeterminately large bias, which means, for example, that it cannot measure the line profile (edge shape) or establish the traceability of the measurement (reference metrology) with absolute accuracy. Consequently, although CD-SEM is useful in fabrication process control, it cannot be properly compared with other methods of measurement. Yet doing so is increasingly essential for physical simulations such as scatterometry (to measure optical critical dimensions) and evaluating the performance of transistors.

Establishing a reference measuring method for CD-SEM, CD-AFM (atomic force microscopy), scatterometry, and physical simulations requires absolute measurement that takes into account subnanometer uncertainty of linewidth and line-profile measurement. CD-SEM poses several challenges to this objective.^{1–4} For example, no good standard exists for magnification, how to determine an edge is not well defined, and the literature related to absolute measurement is scant. Here, we propose a novel means of achieving subnanometer accuracy for linewidth and line-profile measurement using scanning transmission electron microscopy (STEM).^{5} We establish the traceability and reference metrology for the desired parameters using silicon (Si) lattice structures and by evaluating uncertainty.

**Figure 1. **Examples of scanning transmission electron microscopy (STEM) images taken at 200kV for image magnification (a) ×150,000 and (b) ×1,000,000. Si: Silicon.

We began by cutting a standard-width line 100nm deep into a Si 110 surface using a focused ion-beam microsampler.^{6} Next, we obtained bright-field STEM (HD-2700)^{7} images of the specimen at an accelerating voltage (i.e., electron energy) of 200kV (see Figure 1). The high-magnification STEM images clearly show the silicon lattice structures.^{8, 9}

We detected the line profile from the images according to the following procedure. First, we transformed the STEM image to a frequency domain image using 2D fast-Fourier transform.^{10} The peaks of the frequency domain indicate the magnification and inclination angle of the STEM image deduced by the relationship between the silicon lattice structure and the pixels (see Figure 2). Second, we estimated the size of the pixels and magnification by comparing them with the size of the silicon lattice. Third, we devised a novel noise-reduction method that reveals the edge of the silicon lattice area by increasing the image contrast (see Figure 3).

Noise in STEM images is influenced by magnification, the scanning speed of the microscope, and the condition of the specimen. Assuming that the noise is random, a simple averaging method is normally applied. However, this method also degrades the silicon lattice pattern. To avoid this problem, we used a stenciled pattern in place of the silicon lattice. The horizontal and vertical intervals of the stencil agree with the positions of five lattices, which reduces random noise and emphasizes the lattice structures.

**Figure 2. **Frequency domain image by 2D fast-Fourier transform showing silicon lattice peaks.

**Figure 3.** Sample images of the silicon lattice structure (a) before and (b) after averaging.

**Figure 4. **Local standard deviation map (b) derived by calculating the standard deviation inside a specified frame (a).

Finally, we calculated the standard deviation in a specified frame (see Figure 4) and defined the edge position on each silicon lattice line as 50% of the intensity of the standard deviation map. We applied this procedure to the conventional 45nm silicon linewidth (see Figure 5) and found the standard deviation of the edge positions to be <0.1nm. We evaluated the expanded uncertainty (i.e., a confidence level of 99.73%) of the line-edge positions considering a number of factors, including repeatability, image magnification, silicon lattice counting by edge detection, and environmental conditions. We determined that, in this case, silicon lattice counting and image magnification weighed most significantly. Based on our calculations, we estimated the expanded uncertainty (*k*=3) (3 sigma, or the confidence level for 99.73%) to be <0.5nm.

**Figure 5.** Example of edge detection: (a) STEM image; (b) averaging; (c) local standard deviation map; and (d) detection of left and right edges.

In summary, we have described a method that has the potential to replace CD-SEM and CD-AFM as the standard approach to measuring CD linewidth and profile. As next steps, we plan to evaluate the thickness of the oxide film of the silicon line and compare the line-profile results by STEM with results by CD-SEM and CD-AFM. We will then perform detailed calculations of the uncertainty of our proposed method to establish the traceability and reference metrology for testing linewidth.

Kiyoshi Takamasu

University of Tokyo

Tokyo, Japan

Kiyoshi Takamasu is a professor in the Department of Precision Engineering. He received his DEng in precision engineering from the University of Tokyo (1982). His current research focuses on uncertainty analysis for coordinate metrology and nanometrology.

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