DD251611A1 - METHOD FOR DETERMINING STATISTICAL MOMENT OF SURFACE SMOKING - Google Patents

Abstract

The invention relates to a method for determining statistical moments of the surface roughness of very finely worked surfaces. It is used to control the quality of smooth (polished) surfaces under production conditions of the Feingeraetetechnik and for the simultaneous evaluation of more than two independent sample properties, eg. As layers, applicable. The extraction of additional information about the roughness parameters RMS roughness and correlation length from scattered light measurements is achieved by measuring an indicatrix with angular resolution according to the invention and determining the moments by integrating the measured values and the determined calibration factors by successive determination. figure

Description

Explanation of the essence of the invention

The object of the invention is to realize a method which makes it possible to determine more than two statistical moments from a measured scattering matrix, without assuming any special assumptions on the course of the indicatrix or on the autocorrelation function.

The solution to this problem is achieved by a method for bandwidth-limited determination of several statistical moments of the surface roughness from angle-resolved scattered light measurements according to the invention by measuring angular resolution and determining the bandwidth-limited moments by means of integrations of the measured values and determined calibration factors by successive determination. The measurement and evaluation procedure is based on the following mathematical principles. According to (Optical Engineering 18 No.2 [1979], 1824), the moments m _{n of} the order η are calculated

m _n = 2 et seq * JW (r) * r ^{n + 1} dr, (1)

fmin

where W (r) is the spectral power density, r = r (9j, 9 _{S /} phi, λ) is the spatial frequency with θ ₅ as the scattering angle and λ the measuring light wavelength. The power spectrum is calculated by means of the physical optical and the Rayleigh factor Q and the relative normalized angle-resolved scattering intensities I _S (9 _S ) according to (Applied Optics 21 [1982], 1824)

W (r) = I _s (r) / Q (2)

In the following it will be demonstrated how the moments of arbitrary order can be determined by successive determination. Equation (1) can be defined by a calibration factor X _{0 which} , for example, is established via a TIS relationship which establishes a relationship with the O. order moment m ₀ in a known manner:

''Max

m ₀ = X ₀ J l _s (r) rdr =

r _mi p (3)

= Xo (WLS-HS).

In this case, r _min = 0 is approximately assumed and IS or IIS results from the indicator matrix

Tmax

IS = / l _s (r) dr 0

r _ma * (4)

HS = JIS (r) dr

 0

The term in brackets in the definition equation (3) represents a measurement function O. order MF ₀ , which is determined by indicatrix measurement and by IS and IIS determination by integration. The determination of the moment 0 order is limited to the determination of the measuring function O.Ordnung. The transition to the moment I.order rri | takes place according to the scheme of equation (3) by definition

m ₁ = 2 _I rjTjr) r ² dr = (5)

l "max

= m, = X ₀ (m _o / X _o - J m _o / X _o dr). (6)

The determination of the moment n-th order is made by successively determining m _n from knowledge of m. The integration can be carried out both numerically or by measurement, and by developing the integrand into a power series, the coefficients need only be determined once for all moments of the following orders. Simplified integration by performing power series development requires good convergence properties of the measurement function, which are fulfilled only from a characteristic order, depending on specimen specific and measurement conditions. It is advantageous to use both methods of integration in order to be able to determine the moments with a minimum of required convergence properties and computing time. The invention has several advantages. As a result of indicatrix measurement and TIS determination, it is possible to calculate any number of moments without costly calculation of the power spectrum and to obtain additional information about the roughness of the surface, for example. As tilt variance, curvature and grain size of dust are obtained. The presence of empirical values and target indices with corresponding integrated scattering values allows target-actual comparisons by means of simple TIS measurement, which so far allowed the determination of a maximum of 2 parameters.

embodiment

The essence of the invention will be explained in more detail in an illustrated in the drawing embodiment. The figure shows the scheme of an arrangement according to the invention.

The surface 7 to be tested is illuminated by means of a light source 1, preferably a LASER, wherein the illumination beam can be chopped by a special device 2 and 3. The indicatrix is measured by means of a detector arrangement 5 which detects a specific scattering angle range and which is preceded by filters for attenuating the intensity and selection of the measuring light wavelength in the case of multispectral illumination of the sample, which can preferably be controlled by computer control. At the same time, if the individual detector elements are interrogated by the electronics 4, scattering-dependent integrations of the measuring signal can be carried out, which deliver the simply integrated scattering values (indicative or measuring function) and the doubly integrated scattering values are determined by downstream integration. Presence of desired values permits a desired-actual comparison in an in-process regime, preferably in that interfaces exist at the location of the evaluation unit 6 which make it possible to use the arrangement shown, for to operate in a control loop.

Claims (2)

1. A method for the bandwidth-limited determination of several random moments of any order of surface roughness by measuring the indicatrix, TIS determination via integration of the indicatrix and determination of the moment O.Ordnung from the TIS, characterized in that a calibration factor for determining moments from the 0th determined moment is used, with the aid of which a measurement function of interest order from the moment of previous order is determined and the moment of interest order is successively calculated by summation of the measurement function and a proportion to be determined by integration of the indicatrix or the moment of previous order. 2. Method according to item 1, characterized in that TIS or indicatrix measurements which permit a desired-actual comparison and satisfy the T-values and indicator matrices for torque determination by knowledge of desired TIS values and characteristic integrated scattering values are sufficient In-process Regrime can be used or are suitable as a member of a control loop. For this 1 page drawing Field of application of the invention The invention relates to a method for determining statistical moments of finely machined surfaces. These represent surfaces whose mean square roughness is less than one fifth of the used measuring light wavelength. The invention is suitable for quality controls of smooth surfaces under production conditions of the Feingerätetechnik, as well as for the simultaneous evaluation of more than two independent sample properties, for example of layers. Characteristic of the known technical solutions The evaluation of the surface properties by evaluation of scattered light data includes the determination of the average roughness value (corresponds to RMS roughness), as well as the correlation length (Journal Opt. Soc. Am. 53 [1963], 1389). These are used in angle-resolved measurements with the aid of the calculation of the power spectrum from the determined scattering matrix (Journal Opt Soc Am 73 VoI 11 [1983], 1596) by curve fitting methods (Applied Optics 21 [1982], 1824) or by determining the autocorrelation function (Journal of Opt. Soc., Am. 73 Vol. 10 [1983], 1235). These parameters are the measurement wavelength and the scattering angle range used by the measurement conditions, ie they depend on the band width limits (A. Duparre 'Dissertationsschrift, Jena [1985]). This property is of a physical-technical nature and is increasingly effective for the statistical moments of increasing order. Therefore, the roughness parameters measured with scattered light methods are always indicative quantities (Optik 72 No.4 [1986], 153), which, however, are quite suitable for surface evaluation (Thin Solid Films, 123 [1985], 27). Accurate measurement of the two parameters RMS roughness and correlation length, which meet production requirements, requires high precision in hardware and the use of computational technology. Integral scattered light measurements also provide a maximum of two parameters and are strongly subject to the near-angle problem (Optik72 No.4 [1986], 153), since a significant part of the scattered light is lost through the inlet opening of the integrating measuring device (Appl. Optics Vol.22 No. 20 [1983 ], 3207). Direct scattered light methods for AKF measurement (DD-WP 222959) require, per measuring point, the measuring time for scanning the sheared scattered patch in reproducible steps smaller than one tenth of the measuring light wavelength. The measurement results also depend on the bandwidth limitation of the measurement due to refraction properties of the sample, through the aperture of the imaging objective and the measurement light wavelength. Object of the invention The invention pursues the goal of obtaining additional information about the usual roughness parameters RMS roughness and correlation length from scattered light measurements and the technical realization for testing, for example, under in-process conditions of samples for a plurality of properties.