SCANNING Vol. 19, 31 315 (1997) Received July 18, 1996 FAMS, Inc. Accepted with revision August 8, 1996 Applications The Method of Increasing COMPO Contrast by Linearization of Backscattering Characteristic =f(z) DANUTA KACZMAREK Institute of Electronic Technology, Technical University, Wroclaw, Poland Summary: The backscattered electron signal (BSE) in the scanning electron microscope (SEM) has been used for investigation of a specimen surface composition (COMPO mode). Creation of a material composition map is difficult because the dependence of backscattering coefficient on the atomic number Z for Z > 4 is nonlinear. The method of increase in SEM resolution for the BSE signal by use of digital image processing has been proposed. This method is called the linearization of the =f(z) characteristic. The function approximating the experimental =f(z) dependence was determined by numerical methods. After characteristics linearization, the digital image in COMPO mode allows to distinguish between two elements with high atomic numbers if their atomic numbers differ by Z = 1. Key words: atomic number, scanning electron microscope, backscattered electron signal, COMPO mode Introduction Address for reprints: Danuta Kaczmarek Institute of Electronic Technology Technical University of Wroclaw Janiszewskiego 11/17 5-372 Wroclaw, Poland The backscattered electron signal (BSE) is a very useful tool for investigation of a specimen surface in the scanning electron microscope (SEM). Since this signal increases approximately monotonically with the element atomic number Z (Niedrig 1982, Robinson 19), it can be used for estimation of the specimen material composition (Ball and McCartney 1981, Kaczmarek 1991, Reimer et al. 1987, Robinson 19, Robinson et al. 1984, Takahashi et al. 1989, Wassing et al. 1981). However, the BSE signal reaches its saturation value for the higher atomic numbers. This paper presents results of the investigation performed to establish a method for enhancing material contrast in SEM. The sum of signals from several semiconductor detectors is often used for obtaining the material contrast (COMPO mode) in SEM (Kaczmarek 1991, Wassing et al. 1981). The proposed method enables a creation of precise material composition maps with the use of the BSE signal. The estimation of maximum material resolution of the BSE signal in SEM was made using specially prepared specimens. In this paper, the material resolution Z is defined as the smallest difference in atomic numbers between adjacent elements possible to distinguish in the SEM image. This parameter is especially important in the analysis of specimen composition and mapping of the material phase. In this work, the COMPO mode was obtained as the sum of the BSE signal from two semiconductor detectors. Experiment For an investigation of the COMPO mode in SEM, two p-i-n diodes of 1.6 1 5 m 2 surface area were placed opposite to each other and parallel to a scan line. The detectors were placed at high angles ( 67 o ) with respect to the specimen surface. The beam energy was 2 kev. The special test samples were made for estimation of material resolution Z of the BSE signal in the SEM. Two test samples consisting of electron beam-welded materials with similar atomic number Ni-Cu and Ta-W were chosen for the method presentation. Although the atomic number difference Z between Ni(28) and Cu(29) is 1, the areas of particular elements are distinguishable in the photograph (Fig. 1a). However, in the case of materials with high Z atomic numbers W(74) and Ta(73), where also Z=1, the resolution is rather poor (Fig. 1b). Among other things, this effect is caused by the change of backscattering characteristics with element atomic number Z (Niedrig 1982). The experimental results (Heinrich 1968; Niedrig 1982, 1984; Reimer and Tollkamp 19; Reuter 1972) have shown that the electron backscattering is characterized by the almost linear characteristic = f(z), but only within the range of about 3 < Z < 4. This curve is not only a function of Z but also of the electron beam energy E (Hunger and Küchler 1979, Reimer and Tollkamp 19). However, Reimer and Tollkamp confirm that it is only a weak dependence on electron energy for E 1 kev. The tabulated results by Hunger and Küchler (1979) have shown that the difference between (Ni) and (Cu) values is.8 when E=1 kev and 3 kev. It is similar to for Ta and W ( =.6 when E = 3 kev). However, the percentage value of the / ratio equals 2.7% for Ni and Cu, whereas for Ta and W it is only ~1.2%.
D. Kaczmarek: The method of increasing COMPO contrast 311 Furthermore, the fluctuation effect should be taken into consideration. Thus, a small value of connected with fluctuations corresponds to a small deviation of Z 1 in the linear range of the characteristic (Fig. 2). However, in the range where reaches its saturation value, the same value corresponds to a higher value of Z 2 (Fig. 2). In practice, the averaging of Z a would appear on the microphotograph of the specimen surface. It is caused by different Z noise value existing at the different neighboring surface points. These problems make the specimen surface analysis in the wide range of atomic numbers relatively difficult. The method of SEM resolution improvement of the BSE signal using digital image processing has been proposed. This method has been labeled the linearization of the backscattering characteristic versus element atomic number. The appropriate = f(z) characteristic has been chosen from the literature data (Ball and McCartney 1981, Neidrig 1982, Reuter 1972). However, in the case of investigations based on the system consisting of small detectors, it was necessary to check whether the detector system caused no essential changes in the run of the = f(z) characteristic. The test of the detectors was carried out with the use of a specially prepared specimen. This specimen consisted of several mechanically compressed materials with different atomic numbers. The surface image after digital data processing is shown in Figure 3. The image was prepared as a file with bitmap format BMP with dimensions of 12 1. Next, the analysis of the chosen line of the digital image, running along the whole specimen, was performed and the brightness level J of the image as a function of the kind of material was determined (Fig. 4). The brightness level depends on the atomic number Z of the element. The dependence J=f(Z) obtained with semiconductor diodes has been compared with literature data (Niedrig 1982) in Figure 5. Such comparison was possible since the brightness level J as well as the backscattering coefficient are proportional to the BSE current intensity. As seen in Figure 5, the shapes of both plots are similar; therefore, the use of dependence = f(z) from the literature was reasonable. For this purpose, a short analysis of both experimental and theoretical diagrams = f(z) produced by many workers has been reviewed..5.3 1 2 3 4 5 6 7 Z a Fig. 2 Z 1 Z 2 Backscattering coefficient dependence on the atomic number. (a) (b) FIG. 1 Scanning electron microscopy images of ground cross section of (a) Cu(29)-Ni(28) weld, (b) Ta(73)-W(74) weld. Fig. 3 Digital image of specimen consists of Ta(73)-Mo(42)-Cu(29)- Ti(22)-brass. Bar=5 µm.
312 Scanning Vol. 19, 4 (1997) = f(z) Dependence The backscattering ratio in the SEM is defined as (Niedrig 1982): = I BSE I o where I o is the intensity of the primary electron beam and I BSE is the intensity of the backscattered electrons. The dependence of the ratio on the atomic number was determined using numerous theoretical and experimental 1 9 Ta (1) results obtained by various researches (Heinrich 1968; Niedrig 1982, 1984; Reimer and Tollkamp 19; Reuter 1972). The experimental results (obtained among others by Bishop, Reimer, Drescher, Heinrich, Sieber) were described using the formulae resulting from the BSE theory. On the basis of Thomson-Whiddington s law, Everhart (Niedrig 1982) obtained the formula properly describing the experimental results only for Z < 4. However, for Z > 4, the characteristics differ from the experimental data by about 3% (Fig. 6). Based on a diffusion model, Archard (Niedrig 1982) obtained a relation which is close to the experimental results for Z > 5, but gives negative values for Z < 8. The formula proposed by Arnal, Verdier, and Vincensini (Niedrig 1982) describes the characteristic of = f(z) considerably better. From this formula for Z > 4, we get a characteristic which differs from the experimental data by about 5%. The results mentioned above are shown in Figure 6. Brightness J (%) 7 6 5 4 3 Fig. 4 Brightness J (%) 1 9 7 6 5 4 3 Mo 1, 2, 3, 4, 5, 6, 7, Sample width (µm) A plot of the brightness level J along the specimen..55.5 5.35.3.25.2 5 2.5 1. 1 2 3 4 5 6 7 Fig. 5 Comparison of J=f(Z) (dots) and = f(z) (crosses) curves (Niedrig 1982). Cu Ti Brightness J Brass The Numerical Description of = f(z) Characteristic Application of numerical methods (Fortuna 1982, Kaczmarek 1994, Reuter 1972) allows a more accurate determination of the function approximating the experimental dependence = f(z). A fitting polynomial was assigned with the use of the program calculating polynomial coefficients with the least squares method (Kaczmarek 1994). This program enables the user to assign the optional degree of the polynomial. The third-degree polynomial was used for = f(z) characteristic approximation (Kaczmarek 1994). This polynomial was also readjusted for experimental data (Niedrig 1982). The values of the obtained polynomial coefficients (a o a 3 ) are shown in the Table I. The curves obtained using the proposed polynomials agree well with the experimental points, as shown in Figure 7. There are a lot of experimental results of BSE coefficient measurements (Joy 1984, Reimer and Tollkamp 19), but for presentation of the linearization method the choice of data was not essential. The proposed method has been tested using polynomials fitted (Table I) to Heinrich experimental data (Heinrich 1968). These polynomials for Z > 4 are very close to the experimental results; however, for Z < 4 they differ by TABLE I Polynomial coefficients fitted to experimental data Beam energy Research (kev) a 3 a 2 a 1 a Sieber 2 9.71 1 7.193.15.256 Sieber 53 37 1 7.768.118.852 Heinrich 1 12.4 1 7.294.192.745 Heinrich 49 14.8 1 7.271.193.522
D. Kaczmarek: The method of increasing COMPO contrast 313 about 2% (Fig. 7). The new polynomial matched to Heinrich data for an energy of 3 kev may be expressed by: (Z) = 7.91 1 7 Z 3.179Z 2 +.158Z.215 (2) This polynomial was applied for the testing of the proposed method. The Method of = f(z) Characteristic Linearization The method of = f(z) characteristic linearization for high atomic numbers is shown in Figure 8. As can be seen, the.5.3.2 1 2 3 4 5 6 7 Arnal Everhart Archard Sieber 2 kev Heinrich 1 kev Heinrich 49 kev Fig. 6 The experimental and theoretical values of ratio dependence on the atomic number Z (Heinrich 1968, Niedrig 1982) (beam energies are given next to the authors names). polynomial taken for = f(z) characteristic description is linear for the atomic number Z < 2. It is possible to define a slope of a straight line running through this part of the characteristic. The linear function may be written as: Lin2(Z) =.123Z.17 (3) In practice it is more convenient to use the coefficient, which corresponds to both the BSE current from the examined specimen and the atomic number Z of the material. Therefore, it is useful to apply a linearizing polynomial enabling transformation of Eq. (2) into the linear characteristic. The linearizing polynomial has the following form: Lin2() = 13.74 3 6.38 2 + 1.83 1.192 (4) Then, the variation in BSE coefficient can be directly incorporated into the linearization equation. To use Eq. (4) in practice, a special computer program was written for = f(z) characteristic linearization. At the first stage of the analysis of material composition, the normalization of the = f(z) characteristic defined by Eq. (2) is necessary. For this purpose, a standard sample consisting of two known elements should be tested. A designed computer program enables recounting of brightness at all points of the digital image from the bit value into the ratio. The limit values of atomic numbers Z A and Z B, which are of interest, can be defined optionally. Then the bit value is assigned to elements with atomic numbers from Z=1 to Z A (the first palette s color-black), while the 255 bit value (white color) is assigned to elements with atomic numbers over Z B. The elaborated computer program allows for linearization of any fragment with arbitrary small dimensions of the = f(z) characteristic for atomic number Z>2 (not only for elements with high atomic numbers). The method facilitates distinguishing of intermediate values of atomic numbers (alloys, material phases). It can be very useful for examination of penetration depth of impurities in semiconductors with.5 1.8.3.2 Sieber 2 kev Sieber 53 kev Heinrich 1 kev Heinrich 49 kev Polynomial Sieber 2 kev Polynomial Sieber 2 kev Polynomial Heinrich 1 kev Polynomial Heinrich 49 kev 1 2 3 4 5 6 7 Fig. 7 Diagrams obtained by using the numerical method compared with experimental results (Niedrig 1982, Reimer and Riepenhausen 1985). Own polynomial (Eq. 2).2 Linear function (Eq. 3) Linearizing polynomial (Eq. 4) 1 11 21 31 41 51 61 71 Fig. 8 Diagrams showing the method of the = f(z) linearization characteristic.
314 Scanning Vol. 19, 4 (1997) Microscopic image of the specimen Digital image of the specimen = f(z) characteristic Approximation of the characteristic with a polynomial Taking into account the influence of detection system (a) Fitting the linearizing polynomial Linearization procedure by a computer program Digital image of the linearization Fig. 1 Block diagram. (b) Fig. 9 Surface digital image consisting of Ta(73) and W(74): (a) without linearizing, (b) after = f(z) characteristic linearization. Bar=36 µm. BSE signal. Specimens consisting of pure metals were applied in this work only for explicit presentation of linearization results. The proposed method has been applied in the case of a sample consisting of two elements Ta(73) and W(74) (Fig. 1b). The digital image of this sample surface obtained after linearization is shown in Figure 9(b). The surfaces of both elements, Ta and W, are well distinguishable. Figure 1 shows a block diagram, which illustrates the procedure applied in the proposed method of the = f(z) characteristic linearization. Conclusion The method of enhancement of SEM resolution in the case of BSE signal application for material analysis has been presented. It aims at using the BSE signal for material composition mapping and is one of the methods improving the COMPO mode in the SEM. Correction of the COMPO mode resulting from the theoretical description of the system electron beam-specimen-detector is the other contrastenhancing method (Kaczmarek 1991). This theory predicts the possibility of better separation of TOPO and COMPO modes by the compensation of the signals disturbance (Mulak and Kaczmarek 199). It is also possible to enhance the composition contrast by appropriate color assignment for different atomic numbers. The linearization method presented in this paper can be used simultaneously with the other methods of digital visualization of specimen composition. Acknowledgment The author thanks Dr. Z. Radzimski of North Carolina State University for valuable discussions.
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