Microelectronics fabrication requires reliable metrology techniques to characterize chip microstructures. Areas of concern include chip critical dimension (CD), reproducibility, and uniformity. Methods such as atomic force microscopy (AFM) and scanning electron microscopy (SEM) partially address these concerns, but SEM requires a vacuum environment and AFM is a contact metrology.^{1-3} Scatterometry provides a non-contact, nondestructive alternative that does not require special environmental conditions such as vacuum. Scatterometry in itself is not a new metrology, but its simplicity, versatility, and good sensitivity make it highly competitive. Our group has increased the sensitivity of the method by extending the range of measurable physical quantities and the sensitivity optimization algorithms.

Scatterometry is an optical metrology technique designed for the characterization of test samples from lithography. The diffraction-based method involves ellipsometric measurements of the light diffracted from the samples in various experimental configurations. A data fit to theoretical predictions provides the most probable values for the sample parameters; sensitivity analysis allows us to achieve maximum information and sensitivity from existing equipment.

**Figure 1.** A scatterometry test structure consists of a unidimensional grating placed on top of a stack of thin films, ending with a silicon substrate. The grating parameters in the figure are the linewidth *lw*, the grating height *h*_{g}, the pitch Λ, and the antireflection coating (ARC) height.

A sample consists of a reflective diffraction grating with a linewidth *lw* equivalent to the CD of the device under study (see figure 1). The linewidth is the most important parameter of the sample to be determined, but others include grating height and pitch, as well as the height of the antireflection coating beneath. The light back-diffracted by the grating falls into multiple orders. Because the zeroth order is generally the strongest, it is usually the only one that is measured. Also, in the conditions of the continuous miniaturization trend in the microelectronics industry, this order is oftentimes the only one available.

**how it works** **Figure 2.** Ellipsometric scatterometer performs two functions: incident angle (θ) and azimuth (Φ) scanning. The addition of a phase modulator (red) converts the experimental arrangement into the phase-modulated scatterometer.

A typical scatterometer consists of a laser source, a photodiode detector, and a sample holder that turns about its vertical axis and horizontal axis (see figure 2). During the measurement process, the sample holder rotates about the vertical axis to effectively scan the beam through a range of incident angles, and about its horizontal axis to effectively scan the beam through a range of azimuthal angles. Other experimental arrangements exist, most notably the spectroscopic scatterometer, in which a tunable source provides wavelength scanning.

After acquisition, the data undergoes a fit to predictions calculated using theoretical tools such as rigorous coupled-wave analysis and modal analysis. These diffraction theories make the connection between the quantities that are measured experimentally and the parameters of the sample that we want to determine. Quantities we can measure with this technique include grating linewidth (the CD), height, and antireflection coating height.

The power outputthe measurable quantity of the scatterometeris a function of the sample reflection coefficients *r*_{uv}, where *u* is the polarization (either *s* or *p*) of the output and *v* is the polarization (either *s* or *p*) of the input. The reflection coefficients in their turn are functions of the sample parameters.^{2}

Without the phase modulator inserted in the system, figure 2 represents a typical ellipsometric scatterometer. The introduction of the phase modulator in the system changes the scatterometer quite radically, allowing it to capture a multiple-harmonic signal.^{3} These harmonics are the measurable quantities of the phase-modulated scatterometer. The advantages of the phase-modulated scatterometer include higher accuracy and a larger volume of data acquired in the measurement process.

**analyzing performance** The sample parameters are not directly measured but estimated through fitting; thus, the most important aspect of the technique is the sensitivitywe want to have good estimation precision for the sample parameters. The estimation precision depends on two factors: the measurement precision and the sensitivity dependence of the measurable quantities with respect to changes in sample parameters.^{4} The estimation precision has a complex dependence on measurement precision and the sensitivity, but monotonic, namely it increases and decreases synchronously with them. In the simplest case, the estimation precision is simply the product of measurement precision and sensitivity. For scatterometry, the estimation precision is especially critical because of the miniaturization trend in the microelectronics industrytoday's sub-100-nm CDs require subnanometric precision estimation, rather than the tens of nanometers acceptable in the past.

To check the measurement precision of our scatterometer, we conducted tests. For 633-nm output from a helium-neon laser, the ellipsometric scatterometer showed a measurement precision of

σ^{2} = 1.0 x 10^{-8} + 1.3 x 10^{-5 }*R *^{2 }[1]

where *R* is the power output of the scatterometer calibrated to the power input. The measurement precision of the phase-modulated scatterometer is

σ^{2} = 1.0 x 10^{-6} + 5.0 x 10^{-4 }*I *^{2 }[2]

where *I* is one of the harmonics of the calibrated output signal. Clearly, the precision for the ellipsometric scatterometer is better than for the phase-modulated scatterometer. However, the phase-modulated scatterometer may be preferred because it has better accuracy.

**getting small** The miniaturization trend just mentioned forced us to use light sources of shorter wavelength, such as the 442- and 325-nm lines of the helium-cadmium laser. The use of shorter wavelengths increases the sensitivity of scatterometry because the wavelength becomes closer to the dimensions of the microscopic features of the sample. The wavelength change presented several challenges, however. The lower stability of the laser sources and the reduced quality of commercially available optics for these wavelengths degraded the measurement precision. Also, we had to change the photodetection system from silicon photodiodes to photomultiplier tubes in order to accommodate the UV wavelength (325 nm). This change also impacted the performance and the cost of the system. The sensitivity increase afforded by the wavelength shift more than compensated for the loss in measurement precision, however.

An algorithm called sensitivity analysis for fitting (SAF) provides another method for optimizing sensitivity.^{5} This algorithm searches over the domain of possible sample parameters and the domain of experimentally available measurement configurations. A measurement configuration is defined by the parameters of the experimental arrangement that remain constant during the measurement process; for instance, during an incidence-angle scan, the azimuth remains unchanged, and vice versa. SAF optimizes the sensitivity with respect to the measurement configuration over which we have control. With respect to sample parameters, which we do not control, it makes worst case assumptions for combinations of sample parameters and sensitivity. The process yields the optimum measurement configuration, which is the configuration that yields the most sensitive measurements for the least advantageous sample parameters. It combines optimum sensitivity with respect to the measurement configuration and maximum stability with respect to the sample parameters. The existence of resonances and anomalies in the desired measurement range is a matter of luck, however. In their absence, one must rely exclusively on SAF.

SAF is a brute-force approach that requires large computational times. There are more direct and quicker methods that yield similar results; for example, looking for Fabry-Pérot resonances or Wood anomalies of the sample. With this method, the measurement configuration that has maximum overlap with a resonance or an anomaly provides the optimum sensitivity.^{2,3}

The application of the optimization methods described yields estimation precision for the sample parameters that are well within the requirements of the microelectronics industry. Indeed, our group has measured linewidth to subnanometric precision. Scatterometry has great potential for improvement due to the large domain of the available measurement configurations to choose from. With such adjustments, scatterometry will satisfy lithography needs for today and tomorrow. **oe**

*References*

*1. J. McNeil, S. Naqvi, et al., in Encyclopedia of Materials Characterization, Richard Brundle, Shaun Wilson, Eds., Butterworth-Heinemann, Woburn, MA (1992).*

*2. P. Logofatu, Appl. Opt. 41(34), 7179-7186 (2002).*

*3. P. Logofatu, Appl. Opt. 41(34), 7187-7192 (2002).*

*4. P. Logofatu, J. McNeil, Proc. SPIE 4344, 447-453 (2001).*

*5. P. Logofatu, J. McNeil, Proc. SPIE 3677, 177-183 (1999).*

**Petre Catalin Logofatu**

*Petre Catalin Logofatu is a post-doctoral fellow at the Center for High Technology Materials University of New Mexico, Albuquerque, NM.*