Handbook of Optics(Third Edition)MEASUREMENTS.pdf
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1、 PART 1 MEASUREMENTS This page intentionally left blank SCATTEROMETERS John C. Stover The Scatter Works, Inc. Tucson, Arizona 1.1 GLOSSARY BRDF bidirectional refl ectance distribution function BTDF bidirectional transmittance distribution function BSDF bidirectional scatter distribution function f f
2、ocal length L distance P power R length r radius TIS total integrated scatter q angle qN vignetting angle qspec specular angle l wavelength s rms roughness solid angle 1.2 INTRODUCTION In addition to being a serious source of noise, scatter reduces throughput, limits resolution, and has been the une
3、xpected source of practical difficulties in many optical systems. On the other hand, its measurement has proved to be an extremely sensitive method of providing metrology information for components used in many diverse applications. Measured scatter is a good indica- tor of surface quality and can b
4、e used to characterize surface roughness as well as locate and size 1.3 1 1.4 MEASUREMENTS discrete defects. It is also used to measure the quality of optical coatings and bulk optical materials. This chapter reviews basic issues associated with scatter metrology and touches on various indus- trial
5、applications. The pioneering scattering instrumentation132 work started in the 1960s and extended into the 1990s. This early work (reviewed in 1995)11 resulted in commercially available lab scatterometers and written standards in SEMI and ASTM detailing measurement, calibration and reporting.3336 Un
6、derstanding the measurements and the ability to repeat results and communicate them led to an expansion of industrial applications, scatterometry has become an increasingly valuable source of noncontact metrology in industries where surface inspection is important. For example, each month millions o
7、f silicon wafers (destined to be processed into computer chips) are inspected for point defects (pits and particles) with “particle scanners,” which are essentially just scatterometers. These rather amazing instruments (now costing more than $1 million each) map wafer defects smaller than 50 nm and
8、can distinguish between pits and particles. In recent years their manufacture has matured to the point where system specifications and calibration are now also standardized in SEMI.3740 Scatter metrology is also found in industries as diverse as medicine, sheet metal production and even the measurem
9、ent of appearancewhere it has been noted that while beauty is in the eye of the beholder, what we see is scattered light. The polarization state of scatter signals has also been exploited2528, 4144 and is providing additional product information. Many more transitions from lab scatterometer to indus
10、try application are expected. They depend on understanding the basic measurement concepts outlined in this chapter. Although it sounds simple, the instrumentation required for these scatter measurements is fairly sophisticated. Scatter signals are generally small compared to the specular beam and ca
11、n vary by sev- eral orders of magnitude in just a few degrees. Complete characterization may require measurement over a large fraction of the sphere surrounding the scatter source. For many applications, a huge array of measurement decisions (incident angle, wavelength, source and receiver polarizat
12、ion, scan angles, etc.) faces the experimenter. The instrument may faithfully record a signal, but is it from the sample alone? Or, does it also include light from the instrument, the wall behind the instrument, and even the experimenters shirt? These are not easy questions to answer at nanowatt lev
13、els in the visible and get even harder in the infrared and ultraviolet. It is easy to generate scatter datalots of it. Obtaining accurate values of appropriate measurements and communicating them requires knowledge of the instrumentation as well as insight into the problem being addressed. In 1961,
14、Bennett and Porteus1 reported measurement of signals obtained by integrating scatter over the reflective hemisphere. They defined a parameter called the total integrated scatter (TIS) as the integrated reflected scatter normalized by the total reflected light. Using a scalar diffraction theory resul
15、t drawn from the radar literature,2 they related the TIS to the reflector root mean square (rms) roughness. By the mid-1970s, several scatterometers had been built at various university, government, and industry labs that were capable of measuring scatter as a function of angle; however, instrument
16、operation and data manipulation were not always well automated.36 Scattered power per unit solid angle (sometimes normalized by the incident power) was usually measured. Analysis of scatter data to characterize sample surface roughness was the subject of many publications.711 Measurement com- pariso
17、n between laboratories was hampered by instrument differences, sample contamination, and confusion over what parameters should be compared. A derivation of what is commonly called BRDF (for bidirectional reflectance distribution function) was published by Nicodemus and coworkers in 1970, but did not
18、 gain common acceptance as a way to quantify scatter measurements until after pub- lication of their 1977 NBS monograph.12 With the advent of small powerful computers in the 1980s, instrumentation became more automated. Increased awareness of scatter problems and the sensitivity of many end-item ins
19、truments increased government funding for better instrumentation.1314 As a result, instrumentation became available that could measure and analyze as many as 50 to 100 samples a day instead of just a handful. Scatterometers became commercially available and the number (and sophistication) of measure
20、ment facilities increased.1517 Further instrumentation improvements will include more out-of-plane capability, extended wavelength control, and polarization control at both source and receiver. As of 2008 there are written standards for BRDF and TIS in ASTM and SEMI.3336 This review gives basic defi
21、nitions, instrument configurations, components, scatter specifications, measurement techniques, and briefly discusses calibration and error analysis. SCATTEROMETERS 1.5 1.3 DEFINITIONS AND SPECIFICATIONS One of the difficulties encountered in comparing measurements made on early instruments was get-
22、 ting participants to calculate the same quantities. There were problems of this nature as late as 1988 in a measurement round-robin run at 633 nm.20 But, there are other reasons for reviewing these basic definitions before discussing instrumentation. The ability to write useful scatter specificatio
23、ns (i.e., the ability to make use of quantified scatter information) depends just as much on understand- ing the defined quantity as it does on understanding the instrumentation and the specific scatter problem. In addition, definitions are often given in terms of mathematical abstractions that can
24、only be approximated in the lab. This is the case for BRDF. BRDF differentialradiance differentialirradi = a ance dP d P P P s is s is / cos / cos (1) BRDF has been strictly defined as the ratio of the sample differential radiance to the differential irradiance under the assumptions of a collimated
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