Critical Dimension Error Research Articles

Simulation of critical dimension error using Monte Carlo method and its experimental verification

In order to assess the effects of process parameter variations, we developed an optical lithography simulation program that handles the parameter variations statistically by the Monte Carlo (MC) method and predicts the mean and standard deviation of critical dimensions (CDs). As an application of the simulation program, we analyzed the error sources that contribute to the in-shot wafer CD uniformity. For experiments, we employed an attenuated phase-shift mask that is actually used for manufacturing a memory device. The CD uniformity of the mask was 4 nm on wafer scale. We performed a MC simulation using mask uniformity of 4 nm, illumination uniformity of 3%±1% (where the error stands for three times the standard deviation), defocus of 0.0±0.2 μm, mask transmittance error of ±0.3%, and mask phase error of ±5°. Simulation gave wafer CD uniformities of 19.2 and 13.3 nm for 0.7 and 0.8 NA, respectively. These predictions agree reasonably well with experimental values 21.7 and 11.4 nm. The error sources were analyzed for both values of NA. In either case, the contribution of mask uniformity is very significant, being about 85%.

Critical dimension error analysis for 0.13 μm photolithography and beyond

This article reports on a comprehensive study of critical dimension (CD) error analysis for the 0.13 μm generation and beyond. Systematic CD distribution is extracted by averaging nine wafers. The remaining noise signals are treated as random CD errors. Systematic CD error is further broken down into intra- and interfield CD errors by Fourier analysis. Interfield CD error is brought in comparison with the temperature distribution of postexposure bake hot plate, and they are found in good match. A polynomial expansion method further decomposes the interfield distribution into tilt and spiral parts, which are supposedly contributed by hot-plate and spin modules. The random CD error is also analyzed in this article.

Defect Printability for 100 nm Patterns in X-Ray Lithography

In order to estimate the sensitivity required for the next-generation inspection system for X-ray masks, we studied defect printability using the lithographic simulator, Toolset. In a previous work, based on 10nm critical dimension (CD) error, we reported the sensitivity of defect inspection for 100 nm line-and-space (L&S) patterns. In this study, we focused on have investigated the CD errors due to various defects such as adhesion of organic materials, and clear and opaque defects at the edge or the center of the space in 100 nm L&S, isolated space, and hole patterns, particularly for a low-contrast mask. From the present study, it has been confirmed that organic defects are rarely printed in X-ray lithography. Moreover, the maximum critical defect size resulting in 10 nm CD errors is estimated to be 30 nm for clear defects and 24 nm for opaque defects in 100 nm patterns. Therefore, the required detection sensitivity is somewhat more relaxed than the critical defect size (20 nm) required by the International Technology Roadmap for Semiconductors (ITRS).

Printing characteristics of proximity x-ray lithography and comparison with optical lithography at 100 and 70 nm technology nodes

The printing characteristics of proximity x-ray lithography (PXL) were compared with those of ArF and F2 optical lithography using model patterns of memory and logic devices at 100 and 70 nm technology nodes. Aerial-image simulations of both optical lithography and PXL were carried out, and exposure experiments were performed to confirm the simulation results for PXL. Both the aerial images and the exposure results show that PXL has sufficient resolution for patterns with a 100 nm minimum feature size without the need for any additional resolution enhancement techniques (RETs). It exhibits better pattern printing fidelity than either ArF or F2 lithography with strong RETs, such as an alternate-type phase shift mask and off-axis illumination techniques. PXL provides a wide latitude (on the order of microns) in the proximity gap, and is robust with regard to critical dimension errors in mask patterns. For the optical lithography, the fidelity for complex patterns and the narrow depth of focus (DOF) are still issues to be resolved. At the 70 nm node, PXL provides acceptable resolution even at a gap of 10 μm, while F2 lithography requires further advanced RETs to achieve sufficient resolution and an acceptable DOF.

Critical dimension control optimization methodology on shallow trench isolation substrate for sub-0.25 μm technology gate patterning

The impact of shallow trench isolation (STI) chemical mechanical polishing on gate critical dimension (CD) control for submicron technology was studied. The CD depends on the STI process scheme, whether it is recessed or elevated STI. We investigated the surface topography for both STI schemes at different stages of patterning and how it affected the CD control. Surface topography affected organic bottom antireflective coating (BARC) and resist thickness uniformity, led to variation in the effective exposure dose and caused CD nonuniformity across the wafer [C. A. Mack, Appl. Opt. 25, 1958 (1986)]. We used an atomic force microscope surface scan to study substrate topographical variations. The solution is to optimize BARC and resist thickness by using simulations of topographical swing curves and CD error contour plot. Excellent agreement was found between simulation and experimental results.

Inspection of Critical Dimension and Transmission Uniformity of Contact Patterns by Deep UV Imaging and Regression Algorithm

We have developed an inspection method for critical dimension (CD) and transmission uniformity using deep UV imaging (257 nm) and regression algorithm. Evaluation of this inspection system was performed using specimens with programmed CD errors or ionized beam radiation. The magnitude of transmission sensitivity at 257 nm is 93% of that at the stepper's exposure wavelength (248 nm). The minimum sensitivity is 10.0% in transmission for 600 nm contact patterns and 5.8% for 800 nm contact patterns with a range of 6–25% pattern density. This method will improve current inspection capabilities, thereby meeting the requirements of 180 nm node.

Determination of proximity effect parameters and the shape bias parameter in electron beam lithography

For CD (critical dimension) control with high accuracy, it is important to correct the proximity effect as well as to compensate the shape bias in electron beam lithography (EBL). In this work, we propose a method for determining the proximity effect parameters and the shape bias parameter concurrently. Due to the beam current instability of the E-beam writer, it is difficult to determine the parameters of the forward scattering range by delineating sub-0.1 μm patterns. Accordingly, it is important to determine the proximity effect parameters without the errors that can occur in delineating sub-0.1 μm patterns. Though the pattern bias has a small value such as tens-nm, it affects the CD control at sub-micron regime. For demonstrating the accuracy of the parameters, proximity effect correction (PEC) is carried out using the conventional dose modulation method after shape bias compensation. The variation of CD errors for Lines and Spaces (L&S) patterns with PEC is less than 4% using the obtained parameters.

The mask error factor in optical lithography

The primary cause of greater than unity mask error factor (MEF) is degradation of image integrity. Mathematical description of image formation reveals the gradual loss of image shape control by photomask features as the critical dimension decreases below 0.8(/spl lambda//NA). The growing contribution of mask critical dimension error to line-width variation prompts generalization of the conventional two-dimensional (2-D) exposure-defocus window (ED window) to a three-dimensional (3-D) mask-exposure-defocus volume (ED volume), adding mask tolerance to exposure latitude and depth-of-focus as the important parameters of a process. The increase in MEF with feature nesting means that the relative importance of sources of line-width variation changes with pattern pitch. Mask improvement is the most effective means to reduce line-width variation for dense features, but lens quality is the most significant factor affecting line-width control for sparse patterns. The approximately 20% higher MEF of dark-field masks, low MEF of alternating phase-shifting masks, and relatively high MEF of assist features all have ramifications on lithography strategies for printing sparse lines. The MEF does not simply indicate a need for high-quality masks, it also sheds light on the critical areas in which improvements are needed for successful lithography, and the disciplines that need to cooperate for successful device fabrication.

Studies on Defect Inspectability and Printability Using Programmed-Defect X-Ray Mask

The defect inspectability and printability of X-ray masks have been studied. To clarify the issues concerning the present inspection system, we made an X-ray mask programmed with various defects, such as clear and opaque defects, dimension error and positional shift, for typical patterns such as line-and-space (L&S), hole and 2-dimensional patterns. Both the mask pattern and printed pattern on the wafer were specially inspected using the electron-beam inspection system SEM-Spec701 for the case of L&S patterns. In order to estimate the sensitivity required of the next-generation inspection system, we investigated the critical dimension (CD) errors due to mask defects, by comparing the printed patterns of the programmed-defect mask and the dose image profile calculated with the lithographic simulator Toolset, developed at Wisconsin University. Based on these results, we discussed the critical mask defect sizes that result in 10 nm CD error, and found that defects larger than 40 nm would significantly affect 100 nm L&S patterns.

Critical Dimension Controllability Evaluation Based on Process Error Distribution for 150 nm Devices

In this study, the critical dimension (CD) controllability of 150 nm patterns was evaluated by aerial image simulation. We considered three types of process errors (dose errors, focus errors, and mask CD errors) and evaluated the CD error distribution by calculating both the CD and the probability for each of the various combinations of process errors. The effects of high numerical-aperture (NA) KrF exposure on CD controllability were investigated in detail. In contact hole patterns and line patterns with various pitches, the CD controllability was significantly improved by increasing the NA, up to about 0.72. However, NA of more than 0.72 does not seem to have further significant effects on the CD controllability. We also investigated the CD controllability in ArF exposure. ArF exposure is expected to exhibit better CD controllability for contact hole patterns and line patterns with various pitches, even under lower NA conditions than KrF exposure.

High-Precision Binary Optical Element Fabricated by Novel Self-Aligned Process

In the conventional procedure for fabricating binary optical elements (BOEs), we ascertained, by optical simulation, that the alignment error is a principal factor in diffraction efficiency. To deal with this problem we have developed a novel self-aligned procedure, and we have fabricated BOEs with high diffraction efficiency. The key point of the novel procedure is that every step of the element is determined by the first Cr hard mask. To achieve this, we used a negative photoresist with back exposure. We fabricated four-level BOEs, and the diffraction efficiency of the BOEs is only 3% below the theoretical value. Furthermore, we investigated the influence of the remaining fabrication error in the novel method. The remaining error consists of the etching depth error and critical dimension (CD) error. According to the optical simulation, the CD error negligibly affects the diffraction efficiency. The only factor we should consider is the etching depth error.

High-throughput, high-spatial-frequency measurement of critical dimension variations using memory circuits as electrical test structures

Critical dimension (CD) errors are traditionally specified and characterized without reference to their spatial frequency spectra. However, a given amplitude of CD variation can have very different consequences depending on its spectrum. CD errors whose variation is over a few micrometers can be much more serious than those of the same magnitude that extend over several chips. Existing CD metrology tools, such as scanning electron microscopy or electrical resistance measurements, are seldom used to characterize these short-range CD variations, particularly those with spatial wavelengths below 100 μm, because of the large amount of data required and the difficulty of collecting data in such a dense grid. We report a new method of measuring CD variations using static random-access memory (SRAM) circuits in which direct measurements of bit-line currents reveal the individual transistor gate length variations within each memory cell. With the compactness and regularity of the SRAM layout we can measure CD variations with spatial periodicities down to 6 μm. By repeatedly measuring each cell in a memory chip and recording the corresponding currents we can achieve sufficient data to minimize noise, and through two-dimensional bandpass filtering 0.2 nm CD variations can be detected. Two designs of 4 Mbit SRAMs fabricated using 250 nm design rules were studied. The resulting CD variations yielded spectra that were dominated by peaks whose origins included uncorrected electron beam and optical proximity effects. Pattern-independent variations ascribable to the reticle generator itself appeared to contribute only a small fraction of the total error observed.

Economical sampling algorithm using Fourier analysis for mapping wafer critical dimension variations

Characterizations of critical dimension (CD) errors on wafers are usually based on the assumption that the errors are random and normally distributed, and that they therefore can be fully described by a mean and 3σ value. However many sources of CD errors are known to be primarily systematic and are often spatially correlated. In order to establish an efficient measurement sampling scheme and data analysis algorithm that accounts for such nonrandom errors, we collected 900 CD data points using electrical test structures on each of nine wafers that were fabricated in two different fabrication facilities. Wafers using both phase-shifting mask and conventional mask lithography were measured. Fourier analysis was then used to study the errors in the spatial frequency domain. It was found that in all cases systematic and spatially correlated errors, in particular a set of errors that were largely repetitive with stepper field periodicity, dominated over random CD errors. By taking advantage of the correlated nature of these errors, an economical two-step sampling algorithm is defined that significantly reduces the amount of sampling needed (by approximately fourfold). By combining the results of the two-step sampling in the spatial frequency domain, an accurate map of actual error spatial distribution can be extracted. The accuracy of the scheme is verified by using subsets of the 900 data point measurements, and comparing the results to those from the full set of data.

Optically induced mask critical dimension error magnification in 248 nm lithography

One form of optical proximity effect that further complicates lithography is the unexpected response of the printed image to small perturbations [critical dimension (CD) errors] in the reticle. In this way mask CD errors are actually magnified (they are reduced by less than the reduction factor of the optics) during the optical transfer to the wafer. This effect will require even tighter specifications for mask CD control when the error magnification factor is significantly above unity. The effect is particularly pronounced for tight pitches of small features, but can also impact the printing of small isolated lines. Both resist and optical nonideal responses are involved in this mask error factor (MEF). This article discussed the optical effects that produce the MEF. This article will show where the MEF due to optical effects can be ignored and where they cannot when using 248 nm lithography with a high numerical aperture (NA) tool. We will demonstrate how the NA, partial coherence, and variations in focus can effect the mask error magnification factor. We will also show that resolution enhancement techniques can be used to reduce the mask error magnification factor. In particular, Levenson phase shift masks show particularly low mask error magnification factors for small lines. For some applications it should be possible to design the mask so that the mask error magnification factor of the smallest features is significantly below unity. This would allow loosened reticle CD specifications and/or better CD control of the lithography process.

Critical dimension control at stitched subfield boundaries in a high-throughput SCALPEL® system

Scattering with angular limitation projection electron-beam lithography (SCALPEL®) is a stitching lithography system, using a segmented mask pattern which is assembled on the wafer by dynamic imaging. Critical objects may lie on the original pattern segment boundaries (seams), but their stitched images must adhere to conservatively interpreted +/−10% critical dimension (CD) control requirements. Stitching with butted (touching) spatial image parts requires an aggressive placement-error allocation of approximately +/−CD/20, along with allowed values for dose control, mask, resist, and process in the CD control budget. Further analysis has shown that a seam-blending scheme increases the stitching-error tolerance by as much as five times, and allows redistribution of all values in the CD error budget. The seam-blending approach provides overlapped image portions in a small area common to neighboring segments which receive complementary illumination dose portions.

Reduction of CD variance by using optical proximity correction for patterning with DUV phase shift mask

Critical dimension (CD) variation with the use of attenuated phase shift mask (PSM) at 248nm wavelength has been simulated and analyzed. Optical proximity effect was found to be severe and can take up the whole CD error budget for 0.25μm process. PSM/OPC conversion rules were developed for a test pattern. Two rules-based automated PSM/OPC conversion programs, one of them with hierarchy management, were used. Bias between isolated and nested features was significantly reduced with the correction. Issues concerning computation time and data multiplication are also discussed.

Printability of substrate and absorber defects on extreme ultraviolet lithographic masks

Extreme ultraviolet lithography (EUVL) is a candidate for high-volume production of integrated circuits with 0.1 μm design rules. As a reduction imaging technique with robust mask substrates, EUVL reduces the mask contribution to the critical dimension (CD) error budget. However, the ability to manufacture EUVL mask blanks that are free of printable defects remains an important challenge. Electromagnetic simulations and imaging experiments have suggested that defects in the substrates and reflective coatings, in particular, may be highly printable and difficult to detect. A defect printability study using programmed defects was performed in order to determine the printing behavior of mask defects of different sizes and locations with respect to absorber features. Imaging was performed using a 10× Schwarzschild camera operating at 13.4 nm with a numerical aperture of 0.08, corresponding to a Rayleigh resolution of 0.1 μm. This system has an effective exposure field of 0.4 mm diam. Measurements of the defect-induced linewidth variations on the printed resist lines were performed with scanning electron microscopy and atomic force microscopy. Results show that defects located on the substrate and overcoated by the reflective coating are more printable compared to defects of the same sizes located above the reflective coating. In addition, defects centered in the clear region of lines-and-space (L/S) pattern are more printable compared to those located at the line edge programmed defects located in L/S patterns that are larger than 1/3 of the linewidth caused ≥10% CD variations, while defects that are ≤1/6 of the linewidth did not cause measurable CD variations.

Spatial correlation of electron-beam mask errors and the implications for integrated circuit yield

Specifications for masks are usually based on the assumptions that pattern errors can be adequately described by a stationary Gaussian distribution of independent point processes. Critical dimension and feature position errors across chrome-on-glass photomask plates were measured, and the results show that a description of these errors in terms of a 3-sigma variation about a mean value based on the above description is inadequate and often misleading. Mask dimensional errors exhibit considerable spatial correlation across a plate, and have a spatial power spectrum that has implications for integrated circuit yield because of the different ways that photolithography systems can transfer reticle errors to the wafer. Depending on the spatial correlations of the errors and the specific lithography system the implications could be either positive or negative. As a result any quantitative consideration of the effect of mask errors on device performance and yield must consider mask error spatial correlations specifically.