The Use of Electron Probe MicroAnalysis to Determine the Thickness of Thin Films in Materials Science

Electron Probe MicroAnalysis (EPMA) was born around 1950 when Raymond Castaing, a French graduate student working under the supervision of André Guinier, built his first microanalyser (Castaing & Guinier, 1950; Castaing, 1951; Grillon & Philibert, 2002). The principle of EPMA is to bombard the sample surface with a focused electron beam and to collect the X-rays emitted from the sample. The X-rays are dispersed using Bragg diffraction on a mobile monochromator, which enables to get the whole X-ray spectrum from zero to more than 10 keV. The technique of dispersion is called WDS (Wavelength Dispersive X-ray Spectroscopy). The spectrum is made of continuous background (Bremstrahlung emission) and characteristic peaks, which allow elemental qualitative and quantitative analysis of the material. EPMA-WDS can be carried out in dedicated instruments called “microprobes” (usually fitted with 4 WDS spectometers) or in high current Scanning Electron Microscopes (SEM) equipped with one single WDS spectrometer. More recently, Energy Dispersive X-ray Spectroscopy has been developed and has nowadays become a cheap and widespread technique. Most SEM in materials science laboratories are equipped with an EDS spectrometer. EPMA-EDS performances are far below those of EPMA-WDS with regards to sensitivity and spectral resolution, although it can achieve very good qualitative and quantitative results in many cases. EPMA quantification of the sample composition is usually possible by using a standard material of known composition. Unfortunately there is in general no direct proportionality between the concentration of an element and the X-ray emission intensity (peak height) coming from this element. Since the early years of EPMA, many models have been proposed in the literature to correlate the concentration of an element and the associated X-ray emission intensity: ZAF (Philibert & Tixier, 1968), MSG (Packwood & Brown, 1981), PAP and XPP (Pouchou & Pichoir, 1987; Pouchou et al., 1990)... The XPP model (implemented in several microanalysis software packages) has now reached a good level of maturity and reliability, even in difficult situations involving light elements and strong bulk absorption. It is based on an accurate calculation of the (z) curve, which describes the depth-dependence of the X-ray emission intensity of a particular line in the sample. In EPMA analysis of

From Eq. (1), the correlation between elemental weight fraction and X-ray emission intensity can be determined. Let us consider for example the simple case of a nickel-palladium binary www.intechopen.com The Use of Electron Probe MicroAnalysis to Determine the Thickness of Thin Films in Materials Science 103 alloy (this system was considered here because nickel and palladium are totally miscible in the solid state and it is possible to get homogenous Ni-Pd alloys of any composition from pure nickel to pure palladium). Fig. 2 shows the composition dependence of the Pd L kratio (I / I Std ) at 20 kV. The standard material was assumed to be pure palladium here. It can be observed from Fig. 2 that there is no simple proportionality between the Pd L k-ratio and the Pd weight fraction. The reason for this is that the  function in Eq. (1) depends on the composition. In general, the composition of a sample analysed by EPMA is not known a priori. It is then not possible to accurately calculate the  function, which is needed to correlate the elemental weight fraction and the k-ratio using Eq. (1). An iterative calculation is then needed: in a first step, the elemental weight fraction is assumed equal to the measured k-ratio (1 st iteration), which enables to do a first estimation of the  function. Then, the elemental weight fraction can be re-estimated using Eq. (1) (2 nd iteration). This iterative process is carried out again until it converges to the correct value of the weight fraction (in most cases, a few iterations are sufficient). EPMA is usually presented as a "bulk" analysis technique, as the typical depth of analysis is about 1 µm. It should be mentioned that this 1 µm depth of analysis is only "typical" as it actually strongly depends on both the beam voltage and on the material density (see Fig. 1). Furthermore, EPMA is also very sensitive to "surface" composition and can be used to derive quantitative data such as the thickness and composition of very thin films, down to the monolayer range. The "difficulty" of EPMA applied to thin films is that the probed volume is larger than the film thickness. Since the late eighties, dedicated models have been proposed to overcome that difficulty and to derive thin film thicknesses and compositions from simple and non destructive EPMA measurements (Bastin et al., 1990;Pouchou & Pichoir, 1991;Pouchou, 1993;Pouchou & Pichoir, 1993;Staub et al., 1998;Llovet & Merlet, 2010). It can be observed nevertheless that EPMA has remained rather underused for the study of thin films with regards to its good sensitivity and quantitative capabilities, real "surface" techniques such as Auger spectroscopy or XPS being often preferred to EPMA. The aim of this paper is to demonstrate the quantitative capabilities of EPMA (associated with either EDS or WDS) for the thickness determination of thin films in materials science.
2. EPMA-EDS: A fast, cheap and simple tool for the characterization of surface thin films from 10 to 1000 nm 2.1 Principle Let us consider a simple example: a substrate of pure nickel coated with a pure copper layer whose thickness is smaller than the depth of analysis (Fig. 3). In that situation, both nickel and copper X-rays are detected on the EDS spectrum. Assuming that the standard material is pure copper, the Cu k-ratio is given by: where µ is the copper film mass thickness (g cm -2 ). (z) and  Std (z) describe the Cu K emission respectively in the Cu/Ni stratified sample and in the standard material (pure copper). Fig. 4 shows the beam voltage dependence of the Cu K line k-ratio for several copper mass thicknesses µ. The calculation was carried out using the Stratagem software (http://www.samx.com) based on the XPP model (Pouchou, 1993). In such a simple situation (film of known composition on a substrate of known composition), a single voltage approach is sufficient, i.e. µ can be determined from the k-ratio measured at one voltage only. The voltage must be high enough so that the depth of analysis should be higher than the film thickness, otherwise the k-ratio is always equal (or close) to 1 no matter how thick the film is, and the determination of µ is not possible. Once µ is determined, the copper thickness can be worked out from Eq. (3), assuming that the density  (g cm -3 ) of the film is known: Examples of thin film thickness determination by EPMA-EDS are given in the following sections. Unless otherwise stated, the experimental data were acquired on a Leo S440 SEM equipped with an INCA EDS system from Oxford Instruments.

EPMA-EDS determination of alumina thickness on aluminium samples
Aluminium is a highly oxidizable metal: any aluminium sample is always covered by an alumina (Al 2 O 3 ) layer. EPMA-EDS was used here to determine the alumina thickness on two aluminium samples. The first one was annealed at 500°C under air and a quite thick oxide layer is expected. The second one was stripped using nitric acid. EPMA-EDS analyses were carried out at 20 kV on 2020 µm areas (rastering beam) throughout the aluminium sample. Fig. 5a shows the typical EDS spectra measured on both samples. The effect of stripping on the oxide layer and hence the oxygen K intensity is clearly demonstrated. The case depicted here is simple (film of known composition on a substrate of known composition) and a single voltage approach was used to determine the oxide layer. The quantification equation is the same as Eq.
(2). Ten EDS spectra were acquired on each sample and an average oxygen k-ratio was determined using an Al 2 O 3 standard material. Fig. 5b shows the oxygen K k-ratio measured at 20 kV for the two samples, as well as the corresponding oxide mass thickness µ determined from Eq. (2) using the Stratagem software, and the oxide thickness e calculated from Eq. (3) assuming an alumina density  = 3.96 g cm -3 (Bauccio, 1994). The oxide mass thicknesses found on the annealed sample and on the stripped one are 18.2 µg cm -2 and 4.0 µg cm -2 respectively, which corresponds to thicknesses of 46 nm and 10 nm. It is clear from the spectra shown in Fig. 5a that even for an oxide layer as thin as 10 nm, the peak-to-background ratio of oxygen K line is still about one, which is undoubtedly above the limit of detection of EDS.
To ensure the reliability of the EPMA-EDS thickness measurements, XPS depth profiling was undertaken on the annealed aluminium using a ThermoVG Thetaprobe spectrometer equipped with a hemispherical analyser and a monochromatic AlK primary beam (spot diameter of 400 µm). The sputtering sequences were carried out using 3 keV argon ions with an incidence angle of 45° onto a 4 mm 2 rastered area with a 9 A cm -2 current density. Both oxide and metal components of the Al2p peak were acquired over sputtering time.
Sputtering time was converted to depth using a sputtering rate previously measured on another aluminium sample. The depth profiles are shown in Fig. 6. No metal aluminium peak is detected within the first ~40 nm, which corresponds to the oxide thickness (the very smooth transition from pure oxide to pure metal, i.e. from ~40 to >~500 nm depth, observed in Fig. 6 is due to the sample roughness). It can be concluded that the oxide layer thickness determined on the annealed aluminium by the two techniques are in very good agreement: ~40 nm and 46 nm by XPS and EPMA-EDS respectively.

EPMA determination of gallium thickness on rough gallium-coated aluminium samples
The second example deals with gallium "thick" films deposited on aluminium substrates for brazing applications (Ferchaud, 2010). Solid gallium films were obtained by vapour deposition under vacuum. The typical film surface morphology is shown in Fig. 7a. It can be observed that the film thickness is not homogeneous at the micrometer scale. Thirteen aluminium samples (4x10x40 mm 3 ) were coated with gallium using different deposition times. For each sample, the Ga film thickness was determined from the film mass measured using a high precision balance (0.01 mg) and from EPMA-EDS analysis. The EPMA-EDS analysis conditions were the same as those depicted in the previous section. Fig. 7b is a comparison of the gallium thicknesses determined by the two techniques. It can be observed that the EPMA-EDS measurements are slightly underestimated (within ~20%) with respect to the thicknesses determined from the film mass. That discrepancy could be due to the gallium film being partly oxidized, in which case the difference between the two techniques would correspond to the oxygen mass in the film. Anyway, it can be observed that the agreement between the two techniques is good although the conditions of EPMA-EDS analyses are far from ideal because of the high surface roughness.

EDS versus WDS
EPMA-WDS is known to achieve better quantitative results than EPMA-EDS. It is interesting to compare the two techniques with regards to the analysis of thin films. Four copper layers of various thicknesses were electro-deposited on nickel substrates. The copper thickness was determined using both EPMA-EDS and EPMA-WDS at 20 kV. The WDS data were acquired using a SX50 microprobe from Cameca. The results are shown in Fig. 8. EDS and WDS results are found to be consistent with one another within 5%, except for the smallest copper thickness. Fig. 9 shows the EDS spectra acquired on the four copper thin films. It should be emphasized that EDS analysis of small amounts of copper in nickel is not an easy case because of the partial interference between Cu K and Ni K (this interference is of course easily overcome using WDS whose spectral resolution is far better). Nevertheless, it can be observed from Fig. 8 that the copper thickness determination by EDS is very reliable with respect to the WDS one. The discrepancy between the two techniques is actually within 5% apart from the thinnest film, for which the Cu K peak height is very small and undoubtedly affected by a high uncertainty (see red spectrum in Fig. 9). Anyway the generally good agreement between the two techniques demonstrates the good reliability of the routine peak deconvolution procedures implemented in most up-to-date EDS software packages.

More complicated samples -Multiple voltage approach
The quantification of thin film thickness in the examples shown in the previous sections is quite easy as both the thin film and substrate compositions are known, and a single voltage approach is sufficient. EPMA-EDS can also be used for the analysis of thin films in more complicated situations including thin films and/or substrates of unknown composition, as well as multilayer structures. In those cases, a multiple voltage approach is usually required. This is out of the scope of this paper but nice examples of such complex samples can be found in (Pouchou & Pichoir, 1993).

Principle
The principle of thin film analysis by EPMA-WDS is exactly the same as the one detailed for EPMA-EDS in the previous section. The difference is that WDS has a much better sensitivity than EDS and hence enables the quantification of much thinner films, down to the submonolayer range. The use of EPMA-WDS for the quantification of such thin layers has been described in details in (Christien & Le Gall, 2008;Nowakowski et al., 2011). For very thin surface layers, the quantification equation (Eq. (2)) can be simplified. As the layer mass thickness µ is very small, Eq.
(2) reduces to: or, if the standard material is not a pure element: where X Std is the weight fraction of the analysed element in the standard material. So in the case of a very thin surface layer, the layer mass thickness µ is simply proportional to the measured k-ratio: with: K can be easily determined for any system at a given beam voltage using the XPP model. Let us consider for example a substrate of nickel covered by a fractional monolayer of sulphur www.intechopen.com

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(the Ni-S system is chosen here as an example as the next sections are devoted to it). Fig. 10 shows the  functions for the S K line at 20 kV in nickel and in the FeS 2 compound which was used here as a standard material. The sulphur weight fraction in FeS 2 is X Std = 0.534. We finally obtain: K = 256.1 µg cm -2 at 20 kV. It should be emphasized that the K constant is voltage-dependant: the higher the beam voltage, the higher the K constant. The use of EPMA-WDS to quantify surface monolayers and sub-monolayers is quite recent. It can be of great interest for the investigation of surface and grain boundary segregation phenomena in materials science (Christien & Le Gall, 2008;Nowakowski et al., 2011). The well-known case of sulphur segregation in nickel will be considered in the next sections. Nickel and nickel alloys always contain traces of sulphur at the level of some ppm or tens of ppm. When the material is annealed at an "intermediate" temperature (typically 400°C to 800°C), sulphur atoms tend to gather on the surfaces and at the grain boundaries as a monolayer or fraction of a monolayer. This is what we call "interface segregation" which is a very important metallurgical phenomenon as it can dramatically affect the metal properties (Saindrenan et al., 2002;Lejcek, 2010). EPMA-WDS data presented in this section were acquired either on a Cameca SX50 microprobe equipped with four WDS spectrometers or on a Carl Zeiss Merlin high current SEM equipped with an Oxford Instrument INCA Wave spectrometer.

Surface segregation
A nickel sample containing 7.2 wt ppm of sulphur was annealed for 112 h at 800°C under high vacuum and then introduced in the microprobe. After annealing, the surface is expected to be covered by a sulphur fractionnal monolayer because of surface segregation. An example of sulphur K peak acquired by EPMA-WDS on that sample at 10 kV is shown in Fig. 11. As demonstrated later, this peak is entirely due to the sulphur fractional monolayer covering the nickel substrate, and not to the sulphur located in the sample bulk. A good peak-to-background ratio is demonstrated, which illustrates the very good sensitivity of WDS.
www.intechopen.com  Fig. 11. WDS spectrum of the S K line acquired at 10 kV on a nickel sample covered with a fractional monolayer of sulphur. Fig. 12 shows the voltage-dependence of the S K k-ratio measured at the sample surface. The strong decrease of the k-ratio over the beam voltage indicates that the detected sulphur signal is coming from the surface (and not from the bulk). The k-ratio corresponding to the sulphur bulk content (7.2 wt ppm) can be calculated and it is expected to be as low as ~10 -5 (no matter what the beam voltage is) which is far below the experimental k-ratio values. So the bulk contribution to the sulphur WDS signal measured here can be considered negligible.

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The surface sulphur mass thickness µ can be quantified here from the experimental k-ratio measured at any voltage (again, a single-voltage approach would be sufficient here). The µ values determined at the ten different beam voltages investigated here were found to be consistent with each other within 5%. On average, we found: This mass thickness can be converted to a number of sulphur atoms. It corresponds to 7.910 14 atoms cm -2 , which is about half the density of a (100) nickel plane (1.610 15 atoms cm -2 ).

Grain boundary segregation
The conventional route for the analysis of grain boundaries using surface techniques such as Auger spectroscopy is to fracture the sample and to analyse the fractured surface. When elements such as sulphur or phosphorus are segregated, the material usually breaks along the grain boundaries which makes it possible to analyse them using surface analysis techniques. The same procedure was undertaken in this work for EPMA-WDS analysis. Nickel samples containing 5.4 wt ppm of sulphur in bulk were annealed at 550°C, 750°C and 900°C. Each of them was then fractured using tensile test in liquid nitrogen and one half of the broken specimen was introduced into the Merlin SEM chamber for WDS analysis. The WDS analyses were carried out using a beam voltage of 20 kV and a beam current of 400 nA. It should be emphasized that in this work the samples were fractured ex-situ with a conventional tensile machine, in contrast to the Auger spectroscopy procedure where the sample must be fractured in-situ (i.e. in the ultra-high vacuum of the spectrometer chamber) to avoid any surface contamination. Fig. 13a shows the principle of grain boundary segregation analysis by EPMA-WDS and Fig. 13b is one of the fracture surfaces observed in the Merlin SEM. For each of the three samples, about 15 to 20 grain boundary facets were analysed with a counting time of 6 minutes each. One difficulty of this kind of analysis is that the analysed facet is in general not perpendicular to the primary electron beam. In that case, Eq. (6) becomes: www.intechopen.com where  is the tilt angle (i.e. the angle between the facet normal and the primary beam). The tilt angle can be determined for each analysed facet from the measurement of the absorbed specimen current using Eq. (10) (a detailed description of that technique is given in (Nowakowski et al., 2011)): where C B is the primary beam current and C ABS is the absorbed specimen current. It should be noticed that the 0.36 constant in Eq. (10) is correct only for a nickel sample and at a beam voltage of 20 kV. As the sample is fractured before analysis, the initial sulphur grain boundary concentration is randomly split on both fracture surfaces so that the sulphur concentration detected by WDS is only one half of the initial grain boundary concentration. This has to be taken into account in the quantification equation which becomes: Fig. 14 shows the distributions of the sulphur mass thickness µ over the analysed grain boundary facets for the three nickel samples with different annealing temperatures. It is demonstrated that the average sulphur grain boundary concentration µ significantly decreases with the annealing temperature, which is consistent with the Langmuir-McLean formalism of segregation (Saindrenan et al., 2002;Lejcek, 2010). The limit of detection of EPMA-WDS for the analysis of very thin surface layers has been determined in (Christien & Le Gall, 2008). For a primary beam current of 400 nA and a counting time of a few minutes, it is of the order of 1 ng cm -2 , which corresponds to about 1% of a monolayer. The main advantage of EPMA-WDS with respect to Auger spectroscopy (which has been the most common technique for the analysis of interface segregation for decades) is that it is insensitive to surface contamination from the atmosphere. This is due to the "high" energy of K X-rays with respect to Auger electrons. For example, in the case of sulphur, the K line energy is 2.3 keV. This enables the X-rays to get through the thin contamination layer that forms when the sample is in contact with air (Nowakowski et al., 2011). On the contrary, the sulphur Auger electrons have an energy of 0.15 keV only and are totally absorbed in the atmospheric contamination layer. The consequence is that the sample preparation for Auger analysis has to be done in-situ (including cryogenic fracturing of the sample needed for grain boundary segregation analysis), whereas it can be done ex-situ for EPMA-WDS analysis, which is a very substantial advantage.

Principle
It has been demonstrated in the previous sections that EPMA is a powerful technique for the quantification of surface thin films. That technique can be extended to the case of "sandwich" films, which is a very common configuration in materials science (grain boundary segregation, multilayered structures in microelectronics…) as well as in geology or biology. Let us consider for example a gold sandwich film in a nickel matrix (Fig. 15). The technique consists in preparing a cross-section of material and acquiring an EPMA concentration profile across the film as shown in Fig. 15. The film is assumed thin enough (<~50 nm) to have no significant effect on the electron probe size and shape. In other words, the probe is supposed to be the same as it would be in pure nickel (or in nickel containing a very small concentration of gold). As demonstrated in the following, the gold peak that is detected on the concentration profile can be used to quantify the gold mass thickness. The analysed volume V is schematically represented on Fig. 16a. l is the length of the concentration profile and S is the surface of gold film in the analysed volume. A Peak is the peak area measured on the concentration profile (g cm -2 ) (Fig. 16b). A general characteristic of microbeam techniques is that an object of real size A analysed with a probe of size B has an "observed" size ~ A+B. In our case, the size of the object (the www.intechopen.com

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Au film) is negligible in comparison to the probe size (~ 1000 nm at 20 kV). The "observed" object size is then equal to the probe size. In other words, the peak width observed in the Au concentration profile is not the Au film width, but the electron probe size. Fig. 16. a) Schematic shape of the volume analysed by EPMA during a profile along the x direction. V is the analysed volume, l is the length of the concentration profile and S is the surface of gold film in the analysed volume. b) Measured gold concentration profile across the film. A Peak is the profile peak area (g cm -2 ).
The mean gold concentration C (g cm -3 ) over the analysed volume is defined by (Fig. 16b): By definition, the peak area A Peak is: So that: Assuming that this mean concentration C is originating entirely from the gold film, we can determine the gold mass thickness µ expressed in g cm -2 : From Eqs (14) and (15): www.intechopen.com

X-Ray Spectroscopy 116
The Au mass thickness µ (g cm -2 ) can be converted into an Au thickness (cm), as long as the layer density  Au is known: AuA u µA e   (17)

Example
A 23 nm thick Au sandwich film in a nickel matrix was analysed by EPMA-EDS. Fig. 17 shows the experimental EPMA-EDS gold concentration profiles obtained at 15, 20 and 25 kV. Data processing using Eq. (17) gives e Au = 25.6 nm at 15 kV, 26.2 nm at 20 kV and 24.8 nm at 25 kV. The results are in good agreement with the expected value of 23.0 nm. It is interesting to notice also that as expected the result does not depend on the beam voltage. This technique has been for example used recently to measure gallium sandwich thin films in aluminium obtained by grain boundary penetration of liquid gallium. That work is to be published elsewhere.
The results presented in Fig. 17 are quite exploratory, but very promising. The development of the EPMA technique applied to very thin sandwich films is still in progress. In the near future, it should be possible (especially using WDS rather than EDS) to quantify much thinner sandwich films (down to the monolayer range), which is of great interest for many applications in materials science.

Conclusion
It has been demonstrated in this paper that EPMA can be used to accurately determine the thickness of thin films. Examples have been given demonstrating that EDS is a very simple tool for the quantification of thin films in the range 10 nm to 1000 nm, including in complicated situation involving "light" elements (oxygen) and rough surfaces.

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The Use of Electron Probe MicroAnalysis to Determine the Thickness of Thin Films in Materials Science 117 WDS offers much higher sensitivity than EDS and enables the determination of ultra-thin surface layers down to the sub-monolayer range, which makes it a competitive technique for surface analysis with respect to more usual techniques such as Auger spectroscopy. EPMA-WDS has even been very successfully used for the quantification of grain boundary segregation on fractured samples. "Sandwich" thin films can also be quantified using EPMA. Some preliminary results on a 23 nm thick gold film in a nickel matrix were presented in this work. These promising results show that it should be possible in the near future to quantify sub-monolayer sandwich thin films using EPMA (especially with WDS rather than EDS), which is of great interest for various applications in materials science.