# Thickness Measurement of V2O5 Nanometric Thin Films Using a Portable XRF

Authors: Fabio Lopes; Luís Henrique Cardozo Amorin; Larissa da Silva Martins; Alexandre Urbano; Carlos Roberto Appoloni; Roberto Cesareo
Journal: Journal of Spectroscopy
 (2016)

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## Abstract

Nanometric thin films have always been chiefly used for decoration; however they are now being widely used as the basis of high technology. Among the various physical qualities that characterize them, the thickness strongly influences their properties. Thus, a new procedure is hereby proposed and developed for determining the thickness of V2O5 nanometric thin films deposited on the glass surface using Portable X-Ray Fluorescence (PXRF) equipment and the attenuation of the radiation intensity Kα of calcium present in the glass. It is shown through the present paper that the radiation intensity of calcium Kα rays is proportional to film thickness in nanometric films of vanadium deposited on the glass surface.


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## Body

## 1. Introduction

Thin films have always been intended to be utilized primarily for decorative purposes; however they are currently being used for multiple purposes. It has contributed to the technological revolution of integrated circuits and telecommunications [1–4].Moreover, when physical and chemical techniques are combined, thin films can be produced from any material including organic or inorganic, metals, metal oxides, and polymers [5, 6].Thin films are layers whose thickness is naturally decisive for their electromagnetic and quantum characteristics [7–9]. Nowadays, several techniques are used to measure thin films thickness, even in an indirect way. In this paper, the techniques of Rutherford which are back scattering [10, 11], Scanning Electron Microscopy, profilometry [12, 13], interferometry, and the low explored X-ray fluorescence [14–19] are highlighted.The thickness measurement of materials, especially thin films, is currently being made by sophisticated and very expensive devices which often need a proper sample treatment to perform the desired measurement.Among those techniques, the Portable X-Ray Fluorescence (PXRF) presents a low cost that dispenses sample preparations. Furthermore, it can be installed forin situ measures, which has a notably good experimental error when compared with the other existing methodologies or measurement techniques [20–24]. An application of the PXRF technique to measure the thickness of the vanadium pentoxide (V2O5) has not been found in the literature, which is widely used in the production of electrooptical devices. The objective was to investigate the analytical potential of a Portable X-Ray Fluorescence (PXRF) system for vanadium oxide thin films (or layers) thickness measurement. Along these lines we propose a fast and precise empirical method based on the attenuation law of radiation in order to determine the thin films thickness vanadium pentoxide (V2O5) deposited on the glass surface.


## 2. Methods and Materials

### 2.1. Preparing the Samples

Vanadium oxide thin films were deposited by resistive thermal evaporation in high vacuum. Glass plates as substrates were used for both microscope and X-rays fluorescence measurements. The substrates were cleaned in ultrasonic acetone baths solutions followed by isopropanol, which were subsequently dried in hot plate to complete the evaporation of solvents and water. Vanadium oxide films of different thicknesses were deposited with an amount variation of V2O5 powder mass, Figure 1.Figure 1
V2O5 thin films were used in the calibration techniques with 160, 110, and 48 nm of thickness, respectively, from left to right, measured by SEM.The evaporation bath containing the oxide to be evaporated in tablet form is made of metallic tungsten. The material in tablet form was obtained from uniaxial quantities of 130 mg, 100 mg, 55 mg, 45 mg, and 35 mg from V2O5 powder (Sigma-Aldrich, 99.9%) weighted on an analytical scale. The film depositions were done in a brand system called HHV (Auto 306). The substrates were held in a rotated substrate holder to ensure a better uniformity in the film thickness during the deposition.The substrate holder and the substrates were kept in room temperature. A glow-discharge process was performed to ensure the cleanliness of the substrates before the deposition. The back pressure was 7.89 × 10−6 mbar and 1.15 × 10−5 mbar during the deposition.


### 2.2. Scanning Electron Microscopy

In the Scanning Electron Microscopy (SEM) an electron beam is accelerated with a potential difference of thousands of volts; when it reaches the sample, it is reflected and directed to the detector. In case of nonconductive samples as the studied films, a thin film conductor ought to be deposited on its surface so that an electric charge of the surface does not occur; this could lead to an electrostatic deviation of the incident electrons.A SEM was employed to determine the thin films thickness from 100 mg, 70 mg, and 35 mg of V2O5 powder; this thickness is subsequently confronted with the Portable X-Ray Fluorescence technique average thickness. A FEI Quanta 200 microscope (Oregon, USA) which belongs to the University of Londrina Electron Microscopy Laboratory and Microanalysis was used. The images were performed employing an acceleration voltage of 30 kV.


### 2.3. Instrumentation

Ahome-made Portable X-Ray Fluorescence (PXRF) spectrometer was employed for the analysis with the following items.


#### 2.3.1. X-Ray Tube

A MAGNUM MUHV Mini X-ray tube manufactured by Moxtec (Moxtec Inc.) with both silver target (Ag) electric current and electric voltage is controlled by a high-voltage source. This tube can be operated in up to 40 kV and 100μA with a maximum power of 4 W, although it was employed at 28 kV maximum voltage and maximum current 15 μA in our analysis.For a better system performance Ag filter with 100μm thick was used in the outlet of it. This filter was selected because it allows a strong filtering of the Ag K line excitation increasing the sensitivity and decreasing the background that is highly produced from the major constituent of substrate (glass) SiO2.Therefore, the use of the Ag filter provides a better value for the peak/background ratio, allowing an accurate analysis of the elements in the energy range of 3–15 keV [25] which is especially suitable for the energies Kα 4.95 and Kβ 5.43 keV of vanadium and calcium (Kα = 3.69 and Kβ = 4.01 keV) [26].


#### 2.3.2. Detector

An XR-100CR Si-PIN detector with a preamplifier, a thermoelectric cooling system, a conjugated high-tension source module, and an amplifier was also employed. This detector has 6 mm2 crystal by 500 μm thick with 12.5 μm Beryllium window thick and 145 eV energy resolution for Mn-Kα of 5.9 keV. It was connected to a multichannel analyzer model MCA8000A (Amptek Inc.).


#### 2.3.3. Geometry

X-rays from the samples were collimated using a 1 cm long by 0.5 mm diameter Ag cylinder. This collimator was used to minimize the dead time in the measurement and the Compton scattering. Both the detector and the tube were positioned at 45° on the samples surface.The measurements were performed with the samples 2 cm away from the tube and 2.5 cm from the detector; as a result the analyzed area was approximately 0.8 cm2. The excitation and detection time for each measurement was 300 seconds. Each sample was analyzed in triplicate.The spectral analyses were performed using WinQXAS software. The whole system is shown in Figure2.Figure 2
Portable X-Ray Fluorescence system: (1) sample support, (2) X-ray minitube, (3) X-ray detector, (4) standard electronic (5) laptop computer.


#### 2.3.4. Theoretical Background

When the X-ray photons go through the matter, the emerging beam intensity (I) is smaller than the incident beam intensity (I0) due to the interaction (absorption and scattering) with the constituent atoms of the material. It is experimentally verified that the decreased number of photons of the incident beam is directly proportional to the absorbing material thickness, which is related to it through the law of radiation attenuation in the matter given by(1)I=I0e-μ′x,where μ′ is the Linear Attenuation Coefficient (cm−1) of the material and its value depends on the energy of the incident radiation, the attenuating material density, and its chemical composition; x represents the material thickness in centimeters; I0 is the incident beam intensity in the sample; I is the emerging beam intensity in the sample.If we consider a simple case of a thin film of vanadium deposited on a glass flat surface (substrate), the film thickness could be determined by the measurement of a constituent element attenuation intensity of the substrate [27–29].Critical analyses of five substrates were previously performed to identify the main constituent elements of the substrate (glass) and then determine which element had the best peak/background (P/B) ratio and also the best resolution (FWHM). An illustrative spectrum is presented in Figure3.Figure 3
PXRF spectra obtained for the substrate. Measurement time 300 s.


## 2.1. Preparing the Samples

Vanadium oxide thin films were deposited by resistive thermal evaporation in high vacuum. Glass plates as substrates were used for both microscope and X-rays fluorescence measurements. The substrates were cleaned in ultrasonic acetone baths solutions followed by isopropanol, which were subsequently dried in hot plate to complete the evaporation of solvents and water. Vanadium oxide films of different thicknesses were deposited with an amount variation of V2O5 powder mass, Figure 1.Figure 1
V2O5 thin films were used in the calibration techniques with 160, 110, and 48 nm of thickness, respectively, from left to right, measured by SEM.The evaporation bath containing the oxide to be evaporated in tablet form is made of metallic tungsten. The material in tablet form was obtained from uniaxial quantities of 130 mg, 100 mg, 55 mg, 45 mg, and 35 mg from V2O5 powder (Sigma-Aldrich, 99.9%) weighted on an analytical scale. The film depositions were done in a brand system called HHV (Auto 306). The substrates were held in a rotated substrate holder to ensure a better uniformity in the film thickness during the deposition.The substrate holder and the substrates were kept in room temperature. A glow-discharge process was performed to ensure the cleanliness of the substrates before the deposition. The back pressure was 7.89 × 10−6 mbar and 1.15 × 10−5 mbar during the deposition.


## 2.2. Scanning Electron Microscopy

In the Scanning Electron Microscopy (SEM) an electron beam is accelerated with a potential difference of thousands of volts; when it reaches the sample, it is reflected and directed to the detector. In case of nonconductive samples as the studied films, a thin film conductor ought to be deposited on its surface so that an electric charge of the surface does not occur; this could lead to an electrostatic deviation of the incident electrons.A SEM was employed to determine the thin films thickness from 100 mg, 70 mg, and 35 mg of V2O5 powder; this thickness is subsequently confronted with the Portable X-Ray Fluorescence technique average thickness. A FEI Quanta 200 microscope (Oregon, USA) which belongs to the University of Londrina Electron Microscopy Laboratory and Microanalysis was used. The images were performed employing an acceleration voltage of 30 kV.


## 2.3. Instrumentation

Ahome-made Portable X-Ray Fluorescence (PXRF) spectrometer was employed for the analysis with the following items.


### 2.3.1. X-Ray Tube

A MAGNUM MUHV Mini X-ray tube manufactured by Moxtec (Moxtec Inc.) with both silver target (Ag) electric current and electric voltage is controlled by a high-voltage source. This tube can be operated in up to 40 kV and 100μA with a maximum power of 4 W, although it was employed at 28 kV maximum voltage and maximum current 15 μA in our analysis.For a better system performance Ag filter with 100μm thick was used in the outlet of it. This filter was selected because it allows a strong filtering of the Ag K line excitation increasing the sensitivity and decreasing the background that is highly produced from the major constituent of substrate (glass) SiO2.Therefore, the use of the Ag filter provides a better value for the peak/background ratio, allowing an accurate analysis of the elements in the energy range of 3–15 keV [25] which is especially suitable for the energies Kα 4.95 and Kβ 5.43 keV of vanadium and calcium (Kα = 3.69 and Kβ = 4.01 keV) [26].


### 2.3.2. Detector

An XR-100CR Si-PIN detector with a preamplifier, a thermoelectric cooling system, a conjugated high-tension source module, and an amplifier was also employed. This detector has 6 mm2 crystal by 500 μm thick with 12.5 μm Beryllium window thick and 145 eV energy resolution for Mn-Kα of 5.9 keV. It was connected to a multichannel analyzer model MCA8000A (Amptek Inc.).


### 2.3.3. Geometry

X-rays from the samples were collimated using a 1 cm long by 0.5 mm diameter Ag cylinder. This collimator was used to minimize the dead time in the measurement and the Compton scattering. Both the detector and the tube were positioned at 45° on the samples surface.The measurements were performed with the samples 2 cm away from the tube and 2.5 cm from the detector; as a result the analyzed area was approximately 0.8 cm2. The excitation and detection time for each measurement was 300 seconds. Each sample was analyzed in triplicate.The spectral analyses were performed using WinQXAS software. The whole system is shown in Figure2.Figure 2
Portable X-Ray Fluorescence system: (1) sample support, (2) X-ray minitube, (3) X-ray detector, (4) standard electronic (5) laptop computer.


### 2.3.4. Theoretical Background

When the X-ray photons go through the matter, the emerging beam intensity (I) is smaller than the incident beam intensity (I0) due to the interaction (absorption and scattering) with the constituent atoms of the material. It is experimentally verified that the decreased number of photons of the incident beam is directly proportional to the absorbing material thickness, which is related to it through the law of radiation attenuation in the matter given by(1)I=I0e-μ′x,where μ′ is the Linear Attenuation Coefficient (cm−1) of the material and its value depends on the energy of the incident radiation, the attenuating material density, and its chemical composition; x represents the material thickness in centimeters; I0 is the incident beam intensity in the sample; I is the emerging beam intensity in the sample.If we consider a simple case of a thin film of vanadium deposited on a glass flat surface (substrate), the film thickness could be determined by the measurement of a constituent element attenuation intensity of the substrate [27–29].Critical analyses of five substrates were previously performed to identify the main constituent elements of the substrate (glass) and then determine which element had the best peak/background (P/B) ratio and also the best resolution (FWHM). An illustrative spectrum is presented in Figure3.Figure 3
PXRF spectra obtained for the substrate. Measurement time 300 s.


## 2.3.1. X-Ray Tube

A MAGNUM MUHV Mini X-ray tube manufactured by Moxtec (Moxtec Inc.) with both silver target (Ag) electric current and electric voltage is controlled by a high-voltage source. This tube can be operated in up to 40 kV and 100μA with a maximum power of 4 W, although it was employed at 28 kV maximum voltage and maximum current 15 μA in our analysis.For a better system performance Ag filter with 100μm thick was used in the outlet of it. This filter was selected because it allows a strong filtering of the Ag K line excitation increasing the sensitivity and decreasing the background that is highly produced from the major constituent of substrate (glass) SiO2.Therefore, the use of the Ag filter provides a better value for the peak/background ratio, allowing an accurate analysis of the elements in the energy range of 3–15 keV [25] which is especially suitable for the energies Kα 4.95 and Kβ 5.43 keV of vanadium and calcium (Kα = 3.69 and Kβ = 4.01 keV) [26].


## 2.3.2. Detector

An XR-100CR Si-PIN detector with a preamplifier, a thermoelectric cooling system, a conjugated high-tension source module, and an amplifier was also employed. This detector has 6 mm2 crystal by 500 μm thick with 12.5 μm Beryllium window thick and 145 eV energy resolution for Mn-Kα of 5.9 keV. It was connected to a multichannel analyzer model MCA8000A (Amptek Inc.).


## 2.3.3. Geometry

X-rays from the samples were collimated using a 1 cm long by 0.5 mm diameter Ag cylinder. This collimator was used to minimize the dead time in the measurement and the Compton scattering. Both the detector and the tube were positioned at 45° on the samples surface.The measurements were performed with the samples 2 cm away from the tube and 2.5 cm from the detector; as a result the analyzed area was approximately 0.8 cm2. The excitation and detection time for each measurement was 300 seconds. Each sample was analyzed in triplicate.The spectral analyses were performed using WinQXAS software. The whole system is shown in Figure2.Figure 2
Portable X-Ray Fluorescence system: (1) sample support, (2) X-ray minitube, (3) X-ray detector, (4) standard electronic (5) laptop computer.


## 2.3.4. Theoretical Background

When the X-ray photons go through the matter, the emerging beam intensity (I) is smaller than the incident beam intensity (I0) due to the interaction (absorption and scattering) with the constituent atoms of the material. It is experimentally verified that the decreased number of photons of the incident beam is directly proportional to the absorbing material thickness, which is related to it through the law of radiation attenuation in the matter given by(1)I=I0e-μ′x,where μ′ is the Linear Attenuation Coefficient (cm−1) of the material and its value depends on the energy of the incident radiation, the attenuating material density, and its chemical composition; x represents the material thickness in centimeters; I0 is the incident beam intensity in the sample; I is the emerging beam intensity in the sample.If we consider a simple case of a thin film of vanadium deposited on a glass flat surface (substrate), the film thickness could be determined by the measurement of a constituent element attenuation intensity of the substrate [27–29].Critical analyses of five substrates were previously performed to identify the main constituent elements of the substrate (glass) and then determine which element had the best peak/background (P/B) ratio and also the best resolution (FWHM). An illustrative spectrum is presented in Figure3.Figure 3
PXRF spectra obtained for the substrate. Measurement time 300 s.


## 3. Results and Discussions

As it can be seen in Figure2, three elements have been found in the glass container: K, Ca, and Fe. Among all of elements found only two of them (Ca and Fe) were selected to be analyzed, P/B and FWHM, due to the fact that both presented a high intensity; there is a considerable distinction between the others and in almost all of them a noninterference with the peaks of vanadium Kα = 4.95 and vanadium Kβ = 5.43 keV. The results are shown in Table 1.Table 1
Average values for the ratio peak/background and FWHM for the glass substrate number 5.
Element
Energy (keV)
Peak/background
FWHM
(Channel)
(keV)
Fe
6.40
1.15
4.99
0.14
Ca
3.69
1.07
4.12
0.11Based on the results shown in Table1, it has been determined that the calcium element was the one that presented the best resolution and the best peak/background ratio among the twelve existing elements in the glass substrate. Thereby, we used the attenuation of the Ca-Kα line at 3.69 keV to estimate the thickness of the vanadium films, according to (1).Thus, assuming that a thin film with a nanometric vanadium thickness is deposited on a substrate of another element (Ca), the measured intensity for the X-rays in which characteristic of the Ca-Kα is exponentially attenuated as an example is simulated in Figures 4 and 5 of the theoretical attenuation according to (1) for Ca-Kα (3.69 keV) through the vanadium film.Figure 4
Theoretical attenuation according to (1) for the Ca-Kα (3.69 keV) through the vanadium film.Figure 5
Theoretical attenuation according to (1) for the Ca-Kα (3.69 keV) through the vanadium film.Despite the fact that the attenuation of the radiation by the matter is exponential, for sub-micrometers thicknesses (μm) and nanometers (nm) as can be seen in the theoretical simulated graphs of Figures 4 and 5, it is possible to use a linear approximation to determine the thickness of the film [30–33]. Moreover, an appropriate calibration curve for PXRF system must be carried out, especially to decrease the uncertainties arising from the geometry used and minimize the background and scattered radiation.


### 3.1. Calibration Curve

To determine the thickness of the vanadium film in unknown samples using PXRF with the proposed theoretical model a calibration method for the portable spectrometer is required. The calibration method proposed was made with a series of standard samples with known thicknesses where a net area curve (counts) under the peak calcium (Kα-3.69 keV) was plotted against thicknesses of vanadium film, V2O5.Three samples of vanadium film, V2O5, with known masses were deposited on a glass substrate as described in Section 2.1 and their respective thicknesses were determined by Scanning Electron Microscopy (SEM) to determine the calibration curve. For all the samples, a calibration curve was made by calculating the mean of three measurements of the net area of Ca-Kα. The films thicknesses utilized to determine the calibration curve are shown in function of their mass deposition in Table 2.Table 2
Thicknesses of deposited films in terms of material mass that has been used for each evaporation.
Mass (mg)
Thickness measured by SEM (nm)
Surface density (μg/cm2)
100 ± 2.5
160 ± 5.41
53.7 ± 3.8
70 ± 2.5
110 ± 3.45
36.9 ± 3.0
35 ± 2.5
48 ± 7.4
16.1 ± 3.3Figure6 demonstrates a micrograph of a vanadium oxide + glass film. The measured thickness of V2O5 film is 160 nm, for the evaporated mass of 100 mg.Figure 6
Scanning Electron Microscopy of the deposited film with 100 mg evaporated over the glass substrate.Figure7 presents a graph of calibration curve determinate where the net area of the Ca-Kα line is Y-axis and vanadium thickness is X-axis.Figure 7
Calibration curve for net area of Kα line of calcium (Ca) versus thickness of vanadium determined by SEM.As can be seen in Figure7, the reasonable fit of the data points is shown. It is an indication of the absence of significant matrix effects in our samples. An excellent agreement with the theoretical model used is also evidenced in the calibration curve, especially for thickness of nanometer order, where the absorption of X-rays of Kα line of calcium by vanadium is small but not negligible.Analysis of variance or ANOVA has been carried out to verify the quality of the adjustment of the model used in the calibration curve. The result is presented in Table3, where the equation is determined (Y=10611.42-13.34X), where Y is the net area (counts) of Kα line of calcium and X is thickness of vanadium.Table 3
Analysis of adjustment variance of the model presented in Figure7.
Model
Source of variation
Quadratic sum
Degrees of liberty
Quadratic average
R
2
Y
=
10611.42
-
13.34
X
Regression
0.70939
1
0.70939
0.98
Residues
0.00102
6
0.00204
Total
0.71041
7AlthoughR2 found for the model is 0.98 the sum of the quadratic regression corresponds to 98.85% of the total variance, indicating that the linearity of the model is very good. This fact is also evidences with very low waste values and indeed for thicknesses analyzed in this scientific paper, there is a good linear relationship between the net area of Kα line of calcium (counts) and the thickness of vanadium.


### 3.2. Unknown Samples Analyses

Three samples with different mass were produced with the same methodology used in the preparation of the calibration samples. Each sample had the size of 7.5 cm by 2.5 cm and the analyses were done in three different points. The net area of Ca-Kα line for the spectra obtained by PXRF was determined, and the correspondent thickness was calculated using the equation obtained with the calibration curve. The results found for the thickness and superficial densities of vanadium with their respective deviations for three samples are presented in Table 4. Results show that the three measures have relatively small uncertainties, all of them below 5%.Table 4
Thickness of unknown samples of the vanadium films calculated.
Mass
Net area
Thickness
Superficial density
(mg)
Ca-Kα
(nm)
(μg/cm2)
45 ± 2.5
9783 ± 108
62 ± 3.3
20.8 ± 0.2
55 ± 2.5
9512 ± 167
75.6 ± 4.1
25.4 ± 0.4
130 ± 2.5
8132 ± 93
185.7± 6.0
62.4 ± 0.9Figure8 shows a plot of the Ca-Kα line net area experimentally obtained for the three unknown samples as a function of the vanadium thickness determined by the calibration equation. The correlation coefficient found for three samples was 0.997.Figure 8
Vanadium thickness on the glass substrate calculated using a calibration equation.A typical spectrum obtained with the Portable X-Rays Fluorescence system for the sample of thickness185.7±1.2 nm is shown in Figure 9.Figure 9
PXRF spectrum of vanadium layer on a glass substrate for the thickness of 185.7 nm. Measurement time 300 s.In this spectrum we can clearly see the presence of other elements as Si, Ar, Ag, W, and Au. The presence of W may be attributed to a contamination that occurred in the sample preparation process at issue [34]. The other elements are from the equipment used and of course there is air between the films of vanadium and the detector, since the samples were not analyzed in a vacuum system. In Figure 10 there is a graph that shows the calculated thickness of the model versus the vanadium oxide superficial density deposited on the glass substrate determined by the Portable X-Ray Fluorescence to all the samples, three of them with their thickness previously determined by the SEM and another three determined by the proposed methodology.Figure 10
Thickness determined by PXRF for all the samples of V2O5 versus that determined by the deposited mass.A variance analysis or ANOVA has been used to verify the adjustment quality for all the samples. The result is presented in Table5.Table 5
Adjustment of variance analysis of the points presented in Figure10.
Source of variation
Quadratic sum
Degrees of liberty
Quadratic average
R
2
Regression
7202.264
4
7202.264
1
Residues
0.01599
6
0.004
Total
7202.27999
11Figure10 demonstrates a linear relationship vanadium thickness (nm) determined by PXRF and the mass (μg/cm2) for all the samples. The variance analysis presented in Table 5 also shows the linearity of the model, which is strongly evidenced by very low residues amounts and R2 equals 1.Even though there is a relationship between the intensity attenuated by the film thickness and a theoretical exponential relationship, one can perform a linear approximation for the region to be examined as it has an extremely thin thickness range.


## 3.1. Calibration Curve

To determine the thickness of the vanadium film in unknown samples using PXRF with the proposed theoretical model a calibration method for the portable spectrometer is required. The calibration method proposed was made with a series of standard samples with known thicknesses where a net area curve (counts) under the peak calcium (Kα-3.69 keV) was plotted against thicknesses of vanadium film, V2O5.Three samples of vanadium film, V2O5, with known masses were deposited on a glass substrate as described in Section 2.1 and their respective thicknesses were determined by Scanning Electron Microscopy (SEM) to determine the calibration curve. For all the samples, a calibration curve was made by calculating the mean of three measurements of the net area of Ca-Kα. The films thicknesses utilized to determine the calibration curve are shown in function of their mass deposition in Table 2.Table 2
Thicknesses of deposited films in terms of material mass that has been used for each evaporation.
Mass (mg)
Thickness measured by SEM (nm)
Surface density (μg/cm2)
100 ± 2.5
160 ± 5.41
53.7 ± 3.8
70 ± 2.5
110 ± 3.45
36.9 ± 3.0
35 ± 2.5
48 ± 7.4
16.1 ± 3.3Figure6 demonstrates a micrograph of a vanadium oxide + glass film. The measured thickness of V2O5 film is 160 nm, for the evaporated mass of 100 mg.Figure 6
Scanning Electron Microscopy of the deposited film with 100 mg evaporated over the glass substrate.Figure7 presents a graph of calibration curve determinate where the net area of the Ca-Kα line is Y-axis and vanadium thickness is X-axis.Figure 7
Calibration curve for net area of Kα line of calcium (Ca) versus thickness of vanadium determined by SEM.As can be seen in Figure7, the reasonable fit of the data points is shown. It is an indication of the absence of significant matrix effects in our samples. An excellent agreement with the theoretical model used is also evidenced in the calibration curve, especially for thickness of nanometer order, where the absorption of X-rays of Kα line of calcium by vanadium is small but not negligible.Analysis of variance or ANOVA has been carried out to verify the quality of the adjustment of the model used in the calibration curve. The result is presented in Table3, where the equation is determined (Y=10611.42-13.34X), where Y is the net area (counts) of Kα line of calcium and X is thickness of vanadium.Table 3
Analysis of adjustment variance of the model presented in Figure7.
Model
Source of variation
Quadratic sum
Degrees of liberty
Quadratic average
R
2
Y
=
10611.42
-
13.34
X
Regression
0.70939
1
0.70939
0.98
Residues
0.00102
6
0.00204
Total
0.71041
7AlthoughR2 found for the model is 0.98 the sum of the quadratic regression corresponds to 98.85% of the total variance, indicating that the linearity of the model is very good. This fact is also evidences with very low waste values and indeed for thicknesses analyzed in this scientific paper, there is a good linear relationship between the net area of Kα line of calcium (counts) and the thickness of vanadium.


## 3.2. Unknown Samples Analyses

Three samples with different mass were produced with the same methodology used in the preparation of the calibration samples. Each sample had the size of 7.5 cm by 2.5 cm and the analyses were done in three different points. The net area of Ca-Kα line for the spectra obtained by PXRF was determined, and the correspondent thickness was calculated using the equation obtained with the calibration curve. The results found for the thickness and superficial densities of vanadium with their respective deviations for three samples are presented in Table 4. Results show that the three measures have relatively small uncertainties, all of them below 5%.Table 4
Thickness of unknown samples of the vanadium films calculated.
Mass
Net area
Thickness
Superficial density
(mg)
Ca-Kα
(nm)
(μg/cm2)
45 ± 2.5
9783 ± 108
62 ± 3.3
20.8 ± 0.2
55 ± 2.5
9512 ± 167
75.6 ± 4.1
25.4 ± 0.4
130 ± 2.5
8132 ± 93
185.7± 6.0
62.4 ± 0.9Figure8 shows a plot of the Ca-Kα line net area experimentally obtained for the three unknown samples as a function of the vanadium thickness determined by the calibration equation. The correlation coefficient found for three samples was 0.997.Figure 8
Vanadium thickness on the glass substrate calculated using a calibration equation.A typical spectrum obtained with the Portable X-Rays Fluorescence system for the sample of thickness185.7±1.2 nm is shown in Figure 9.Figure 9
PXRF spectrum of vanadium layer on a glass substrate for the thickness of 185.7 nm. Measurement time 300 s.In this spectrum we can clearly see the presence of other elements as Si, Ar, Ag, W, and Au. The presence of W may be attributed to a contamination that occurred in the sample preparation process at issue [34]. The other elements are from the equipment used and of course there is air between the films of vanadium and the detector, since the samples were not analyzed in a vacuum system. In Figure 10 there is a graph that shows the calculated thickness of the model versus the vanadium oxide superficial density deposited on the glass substrate determined by the Portable X-Ray Fluorescence to all the samples, three of them with their thickness previously determined by the SEM and another three determined by the proposed methodology.Figure 10
Thickness determined by PXRF for all the samples of V2O5 versus that determined by the deposited mass.A variance analysis or ANOVA has been used to verify the adjustment quality for all the samples. The result is presented in Table5.Table 5
Adjustment of variance analysis of the points presented in Figure10.
Source of variation
Quadratic sum
Degrees of liberty
Quadratic average
R
2
Regression
7202.264
4
7202.264
1
Residues
0.01599
6
0.004
Total
7202.27999
11Figure10 demonstrates a linear relationship vanadium thickness (nm) determined by PXRF and the mass (μg/cm2) for all the samples. The variance analysis presented in Table 5 also shows the linearity of the model, which is strongly evidenced by very low residues amounts and R2 equals 1.Even though there is a relationship between the intensity attenuated by the film thickness and a theoretical exponential relationship, one can perform a linear approximation for the region to be examined as it has an extremely thin thickness range.


## 4. Conclusions

In this scientific work, thickness measurement of nanometric thin films made by a Portable X-Ray Fluorescence technique based on the attenuation of the radiation field is proposed. Although the methodology is simple, the use of calibration curves for unknown samples led to consistent results within the expected range for the thickness. In fact, the main issue which can eventually make interpretation of data difficult is the correct determination of the calibration curve using reliable standards. Therefore, this empirical method is fast and accurate for measuring thicknesses of nanometric films. In addition, it provides a simple and convenient method for thickness monitoring.



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*Source: 9509043-2016-01-24.xml*