Patent Number: 056195486
Section: description

BEST MODE FOR CARRYING OUT THE INVENTION Referring to FIG. 2, an X-ray scattering system for measuring thin-film structures in accord with the present invention includes an X-ray source 31 producing an X-ray bundle 33 that comprises of a plurality of X-rays shown as 35a, 35b and 35c. An X-ray reflector/reflecting surface 37 is placed in the path of the X-ray bundle 33. The reflector 37 directs the X-ray bundle 33 onto a test sample 39, typically including a thin-film layer 41 disposed on a substrate 43, held in a fixed position by a stage 45. A detector 47 is positioned to sense X-rays reflected/scattered from the test sample 39 and produce signals corresponding to the intensity and an angle of reflection of the X-rays sensed. Referring also to FIG. 3, information corresponding to the intensity and the angle of reflection of the X-rays is received from the detector 47 by a processing unit 49 along line 51. X-ray source 31 may be an electron-impact X-ray tube, a high temperature plasma or a synchrotron accelerator. It is preferred, however, that the X-ray source 31 be a X-ray tube with a chromium anode such as the Rigaku 1.2 kW, 60 kV rotating x-ray tube. This type of x-ray tube typically produces an x-ray having a wavelength of 2.3 angstroms. To facilitate small-angle intensity measurements, some degree of monochromatization of the X-rays incident on the sample is necessary, particularly if the X-ray source 31 is a synchrotron accelerator. To that end, the X-ray reflector/reflecting surface 37 is typically a monochromator, defining two focal areas. The monochromator may be shaped as a toroid or an ellipsoid, each defining two focal points, or a cylindrical shape, defining a point focus and a line focus. It is preferred, however, that a Huber quartz J-G cylindrically curved single-crystal monochromator be employed and configured to satisfy the Guinier conditions. The diffraction of the incident bundle 33 of X-rays within the single-crystal monochromator isolates a narrow band of the spectrum when the Bragg condition for a particular wavelength is satisfied. The diffraction produces a monochromatic bundle 55 of X-rays, shown as 57a, 57b and 57c, which are directed onto the test sample 39. The monochromator is considered curved because the monochromator is cylindrically shaped. As the monochromator satisfies the Guinier conditions, the focal areas need not be equally spaced from the monochromator. It is preferred, however, that X-ray source 31 be positioned proximate to the point focus twelve centimeters from the monochromator 37, so that a maximum flux of X-rays produced by the source 31 impinge on the monochromator. Typically, all the X-rays produced by the source impinge on the monochromator. This greatly improves the X-ray flux directed toward the sample surface 39. The test sample 39 is positioned proximate to the line focus twenty-one centimeters from the monochromator 37. Referring to FIG. 4, the X-rays 35a, 35b and 35c, forming the incident bundle 33, diverge from the X-ray source 11 to simultaneously impinge upon the curved monochromator 37 at different spatial positions 59, 61 and 63, along the y axis. The monochromatic X-rays 57a, 57b and 57c produced by the curved monochromator 37 corresponding to incident X-rays 35a, 35b and 35c, respectively. The monochromatic X-rays 57a, 57b and 57c are directed to focus on a line in the x-z plane. Due to the X-rays 35a, 35b and 35c impinging on the monochromator at different spatial positions, the monochromator directs X-rays 57a, 57b and 57c to simultaneously impinge upon the thin-film layer 41 of the test sample 39 at differing angles of incidence, shown as .psi..sub.1, .psi..sub.2 and .psi..sub.3, respectively. Typically all the incident angles, shown as .psi..sub.1, .psi..sub.2 and .psi..sub.3, of X-rays are greater than a critical angle, .psi..sub.c. The critical angle .psi..sub.c is approximated as follows: EQU .psi..sub.c =0.203 .rho..sup.1/2 /h.orgate. where .psi..sub.c is defined in terms of radians, .rho. is the mass density of substrate 43 in units grams/cubic centimeter and hu is the X-ray energy in units of keV. It is critical that the X-rays are incident on the test sample 39 at angles greater than .psi..sub.c to produce interference fringes upon reflection, discussed more fully below with respect to FIG. 5. Referring also to FIG. 5, X-rays 65a, 65b and 65c reflected from the test sample 39 are shown corresponding to monochromatic X-rays 57a, 57b and 57c, respectively. The reflected rays 65a, 65b and 65c result from constructive and destructive interference of X-rays reflecting from thin-film surface 75 and thin-film/substrate interface 77. It can be seen that the angle of reflection .psi..sub.11, .psi..sub.22 and .psi..sub.33, correspond to X-rays 65a, 65b and 65c, respectively. The function between the angles of incidence and the angles of reflection is linear and can be described as follows: EQU .psi..sub.11 =.psi..sub.1 EQU .psi..sub.22 =.psi..sub.2 EQU .psi..sub.33 =.psi..sub.3 Given that the reflected X-rays 65a, 65b and 65c reflect from the test sample 39 at differing angles of reflection, the beams diverge with respect to one another and may be spatially resolved along the y axis, in a detector plane located transverse to the plane of the test sample 39. In this manner, X-rays, shown as 65a, 65b and 65c, will impinge upon the detector plane 67 at points 69, 71 and 73, respectively. Thus, it can be seen that X-rays impinging in the detector plane 67 can be identified as being uniquely associated with a particular angle of incidence. To take advantage of these properties, typically detector 47 is a position sensitive detector capable of resolving the X-rays reflecting from the test sample 39 along the one axis. Although FIG. 5 shows spatially resolving the X-rays along the y axis, both the detector 47 and monochromator may be rotated so that resolution is obtained along the x or z axis, as well. Any position sensitive detector may be employed, for example, photographic film. The preferred detector, however, is a solid-state device such as a Reticon R12048S self-scanning photo-diode array (SSPA) positioned at the detecting plane 67. L. N. Koppel, in "Direct X-Ray Response of Self-Scanning Photodiode Arrays", Advances in X-Ray Analysis, vol. 19 (1975), describes the implementation of SSPAs to measure the spatial distribution of X-rays. Also, a linear or area-sensitive charged-coupled device, a multiple-anode microchannel plate detector, or a photostimulated storage phosphor image detector may be employed in place of an SSPA. The detector 47 is positioned to receive a maximum flux of X-rays, as shown by 65a, 65b and 65c, reflected from the test sample 39. Typically, the detector 47 is positioned to receive all of the X-rays reflected from the test sample 34. The X-rays impinging at points 69, 71 and 73 are resolved as interference fringes resulting from constructive and destructive interference of X-rays reflected from the top surface 75 of the thin-film 34 and from the thin-film substrate interface 77. The detector 47 produces signals which are subsequently digitized and analyzed by circuitry associated with the detector 47. Referring again to FIG. 3, the electronic circuitry associated with the detector 47 is shown generally as pre-amplifier 81 and signal conditioning circuit 83. The electronic circuitry amplifies the signals from the detector 47, shapes the signal into energy proportional voltage pulses and selects the pulses corresponding to the desired photon energy, thereby suppressing noise and polychromatic radiation. The pulses are digitized and fed into the processor 49 which determines a reflectivity curve that may be depicted logarithmically as reflectivity (R) versus reflection angle (.psi.). The information determined by the processor may be stored on a magnetic media or it may be visualized on an analyzer, as shown by curve 85 in FIG. 6. The reflectivity curve 85 may be analyzed employing the least-squares refinement described by T. C. Huang and W. Parrish in "Characterization of Single- and Multiple-Layer", Advances in X-Ray Analysis, vol. 35, pp. 137-142 (1992) to determine a plurality of properties concerning the thin-film layer. As discussed by Huang and Parrish, the maxima 87 and/or minima 89 of the interference fringes are related to the thickness of the thin-film by the modified Bragg equation as follows: EQU sin.psi..sub.i.sup.2 =.psi..sub.c.sup.2 =(n.sub.i +.DELTA.n.sup.2).lambda..sup.2 4t.sup.2 where .psi..sub.i is the angle for the maximum or the minimum of the ith interference fringe, .psi..sub.c is the critical angle for total reflection, n.sub.i is an integer, and .DELTA.n equals 1/2 or 0 for a maximum and minimum, respectively. t is the thickness of the thin-film layer and .lambda. is the wavelength of the X-rays. From the data concerning the thickness, Huang and Parrish continue to describe how the density of the thin-film layer can be determined, as well as the smoothness of the thin-film surface and the thin-film substrate interface, mentioned above. With the above-described features of the claimed invention, a plurality of properties of a thin-film layer on a substrate may be simultaneously determined, including the thickness, density and smoothness of both the thin-film surface and the thin-film/substrate interface.