18th World Conference on Nondestructive Testing, 16- April 1, Durban, South Africa Use of Back Scattered Ionizing Radiation for Measurement of Thickness of the Catalytic Agent Active Material Boris V. Artemiev, Andrey E. Shubochkin, Alexander A. Bukley 1 Joint-Stock Company Research Institute of Introscopy of MSIA Spectrum, Bld. 1, Usacheva St. 35, Moscow 11948, Russia; Phone: +7 499 455656, Fax: +7 499 468888; niiin@spektr-group.ru Abstract Catalytic agents in the form of thin metal films applied on a massive and internally non-homogeneous base (substrate) of ceramics (Si, C, Al, etc.) mainly are used widely in chemical industry. As a rule, in the process of sputtering of various coatings, it is very difficult to provide control of substance quantities from the part of sputtering source. Therefore, in order to ensure the proper source control, it is required to carry out measurements of the actual coating thickness. Similar problems occur in microcircuitry and production of crystal oscillators. Paper presents simulation results of a process for the coating thickness gage control in the range from.1 to.3 µm and substantiates selection of optimal parameters for the source of radiation. Keywords: Back scattered radiation, thickness gage control, metal coating, sputtering source 1. Introduction Analyzing data obtained under Monte-Carlo method, some issues of measuring the thickness of thin metal films on the surface of large articles of materials with considerably lower atomic number that is performed by recording of scattered photons of the scanning radiation beam are discussed. Methods and techniques for theoretical analysis of these problems are proposed. In industry, for example, during production of microcircuit chips, catalytic agents, crystal oscillators, etc., technological processes for sputtering various coatings like thin metal (Au, Pt, etc.) films on a massive and internally non-homogeneous base (substrate) of ceramics (Si, C, Al, etc.) mainly are used widely. In the process of sputtering, it is very difficult to provide control of substance quantities from the part of sputtering source. Therefore, in order to ensure the proper source control, it is required to monitor the thickness of sputtering. Process of measurement of the sputtered film thickness is simulated taking into account the following approximations. In X-ray testing, measurements under the radiation recording method are referred to radiometric methods. Therefore, condition of the signal-to-noise ratio (SNR) maximum is a common approach to selection of the radiation source power. During these measurements, noise is defined by both instrumentation error and statistical one fluctuations of photons recorded by detector.
1. Source;. Detector; 3. Lead screen; 4. Substrate; 5. Sputtered film Figure 1. Geometry of experiment. Among the whole range of currently existed thickness gauging tasks, the most crucial situation that occurs in industry is discussed, i.e. measurement of thickness of the thin golden film on a massive silicon substrate. The power of probing X-ray photons E is the main parameter of a system defining its property. Ua E = E de (1) Unlike to to mono-lines of isotopic sources, application of X-ray apparatus as a source of radiation provides continuous spectrum, and, following common approach E ef =/3U a () where: U a is the X-ray tube anode voltage, E ef is an effective quanta energy. Exposure dose D is the next system parameter. Its value depends on the tube anode current I a, anode voltage U a, and exposure time. k d P NS Д N ; (3) N where: N - is the number of quanta falling on the unit area surface in one measurement; - quanta recording efficiency of a detector; d - radiological contrast; N taking into account approaching of (Е ) to 1 SF scattering function equal to
its value for collimated beam approaches to 1. F S Д P 1 exp( ) (4) f Table 1. Values of probabilities of the measured thickness variation detection depending on SNR. k h SNR Probability of thickness variation detection f(k ) (k ).5.69.383 1..84.683 1.5.93.866..977.954.5.9935.9987 3..99987.99973 Under condition of the Gaussian distribution of fluctuations, probability of detection of the test object thickness variation with one-sided tolerance limit, when either thickening or thinning is assumed as variation, is determined as follows: assumed as variation, is determined as follows: f ( k ) 1 1 1 k k 1 exp( k ) dk (5) In the case of symmetric tolerance, when both thickening and thinning is assumed as variation of thickness, probability of variation detection decreases. f ( k) 1 k k 1 exp( k At the same time, for specific engineering developments, geometric parameters of a system and technological constraints like primary filtering of radiation by the tube anode and instrument protective structures are of great importance. Overall relative measurement error sum can be presented as the sum of errors with largest contribution: sum = system + random = ( move + incl + stand + approx + drift + adc_nonlinear ) + ( number_fl + energy_fl + tem_noise + rad_instab ) (7) where: move is movement of the article front edge in relation to the test plane (Fig.1); incl is inclination of the plane normal of tested article in relation to the axis of radiation beam; ) dk (6)
stand is an error of manufacturing of standard specimens; approx is errors conditioned by non-conformity of approximating functions with real function of tested thickness variation; drift is thermal and temporal drift of the measuring system parameters; adc_nonlinear is nonlinearity of analog-to-digital converters; number_fl is fluctuations of the number of quanta entering detector per time unit (for the time of one measurement); energy_fl is fluctuations of energy given up by a quantum to the detector working volume for single interaction; tem_noise is a noise of input cascades of analog devices (is eliminated completely during operation in counting mode; rad_instab is instability of radiation sourcesнестабильность источников излучения. вр.из is an error occurring due to distortion of the signal spatial frequency by measuring system. Random component of the relative error has normal distribution, while systematic errors shift the centered position in one or another side from true one. Therefore, in order to obtain closer approximation, their effect on the measurement accuracy will be discussed separately. Quantum nature of noise both as fluctuations of the number of quanta getting the detector per time unit and fluctuations of the energy amount given by each quantum in the detector is the main unavoidable random error. Systematic errors move and incl are simplest ones for understanding and description of their effect. When rolling plane normal is inclined with regard to axis of the probing radiation beam, thickness gauge readings vary by an amount being proportional to cosine of the angle formed by rolling plane normal and beam axis. Inclination of the rolling plane normal by three degrees results in increase of the relative systematic error by.11%. Effect of the test object movement along the beam axis is somewhat more complex one, because it depends on the object thickness and its material (Fig.1). Manufacturing error of standard specimens is unavoidable in principle and contributes always the overall measurement error. In this connection, for calibration of instruments, it is necessary to use the certified standard specimens only, and it is possible to discard such an error during calculations. Errors conditioned by non-conformity of approximating functions with real function of tested thickness variation have zero values in reference points and grow up during shift from these points to the center of interval. The simplest way to minimize values of this error during performance of computational experiment is to increase the number of reference points for calibration and to use valid approximating functions. Error of standard specimens is the most hardly compensable one among systematic errors. Some errors related with conversion of analog signals into digital ones ( tem_noise, adc_nonlinear ) are considered and compensated easily by modification of instrument circuitry. For example, in order to obtain.1% conversion accuracy at SNR equal to 3, convertor with 15-bit capacity and conversion non-linearity lower than.5 of least significant digit, if measurements are performed in one point. In order to overlap the dynamic range of signal variation in 1 times, it is sufficient to increase the convertor s bit capacity or to use the input signal scaling, while maintaining the conversion non-linearity value. It is important to understand difference between the dynamic range of measured thicknesses and dynamic range of signals obtained from primary transducer (detector, in this case), because, varying anodic voltage of the X-ray tube and radiation spectrum, it is possible to vary the dynamic range of
measured thicknesses at constant parameters of secondary (converted) signal, i.e. it is possible to bring it to a form convenient for conversion. All above listed parameters and their effects on measurement results were taken into account during performance of computational experiment. In thickness gauging, system performance is defined by the time taken by one measurement of thickness. In order to consider thickness gauge as operating in conditions of quazi-zero spatial frequency, it is necessary for the thickness gauge speed of response to be in -5 times higher than one of executive system (metal sputtering system). For operation in such conditions, it is sufficient to have system response time within.5 1 s, which is implemented currently for the required dynamic range quite easy. Geometrical dimensions of the beam aperture cross-section at the level of article surface are determined on the basis of state standards (GOST s) on surface roughness of machined material. In other words, the beam cross-section must in 1, times larger than the admissible surface roughness, but its size must as minimal as possible. In this case, a circle of mm diameter is obtained. Thermal and temporal drift of the measuring system is decreased for the account of thermal stabilization of analog circuits and is eliminated completely during system calibration. Therefore, it was not taken into account. Noise of input cascades and primary transducers is the random component of measurement error and cannot be eliminated during calibration. Admissible threshold for the noise of such kind must not exceed 1/3 1/5 of the signal level D. No X-ray radiation, 1 scintillator, 3 - photoconverter Fig.. Diagram of the detector sensitivity D = N Sд e -µd N (7) D = N Sд e -µd N - N Sд e -µd+d N = N Sд N (1-e -µd ) (8) Let s consider simulated range from.1 to.3 µm.
Fig.3. Dependence of the signal-to-noise ratio k (U) on the anodic voltage of X-ray tube Traditional measuring technique under shadow method (Fig.4) cannot be applied for solution of this problem. It is due to the fact that error introduced into measurement by the substrate non-homogeneity exceeds considerably signal of the sputtered film thickness increment. Therefore, measurement technology being different in principle was applied thickness gauging by back scattering (Fig.1). Radiation source Under condition Detector Fig.4. Geometry of experiment - option. Fig.3 shows dependence of the signal-to-noise ratio k (U) on the anodic voltage of X-ray tube (Ua) for various thicknesses of coating. It is seen clearly that 5-4 kv range of anodic voltages is an optimal one for all thicknesses within the range from.1 to.3 µm. In order to define anodic voltage more accurately and to optimize resources of X-ray source, it is desirable to minimize energy of single measurement (Q).
Fig.5. Dependence of the single measurement energy Q on the anodic voltage of radiation source. Fig.5 shows dependence of the single measurement energy Q on the anodic voltage of radiation source. Basing on analysis of both dependences, it is possible to state the following: for the given thicknesses, Ua 5-35 kv value of anodic voltage is an optimal one growing from 5 kv for minimal thicknesses to 35 kv for maximal thicknesses of the range. Fig.6. Dependence of the signal-to-noise ratio k (U) on the anodic voltage of X-ray tube On Figs. 6 and 7, similar dependences are presented for coatings within the thickness range from.1 to.1 µm. Estimation of the X-ray tube current required to perform measurements at.1 µm thickness for the gold has demonstrated that tube current of up to ma is required at 1 s exposure time and 35 kv voltage, because Q=65 J.
Ia = Q/Ua*t meas =65/1*35=18.57*1-3 ma (9) Fig.7. Dependence of the single measurement energy Q on the anodic voltage. When film thickness increases to.1 µm, the value of anodic current falls to ma fractions. It is acceptable for construction of systems, since existed sources of X-ray radiation provide it. Accordingly, it is not rational to measure thicknesses lesser than. µm by means of X-ray radiation. For solution of such problems, application of radiation of other type like one is more efficient. References 1. B.V. Artemiev, X-ray thickness gauging of metals., Mashinostroenie-1, Moscow,.