Calibration principles

Calibration principles
Title .. Kayvon Savadkouei GD application lab New Jersey

Introduction GD-OES is a comparative technique, it therefore needs calibration for quantitative bulk and depth profiling General principles of calibration as they apply to GD-OES Bulk Calibration Specificity of CDP calibration: Sputtering rate model Use of coating as a standard Layer model

Reference books The methodology presented there follows what this book suggests. We strongly recommend to purchase this book. When you finish to read this book, you have all information you need to use the instrument and interpret your results. Reference book: available to purchase on the above web site

Vocabulary Concentration: mass content (mass %)
Calibration curve: relationship between Intensity and concentration Standard: reference sample CRM: certified reference material Sputtering rate: sputtered mass per unit of time and area Precision: closeness of results for several replicate using the same method Accuracy: measure of how well a measured value agrees with the accepted value Precision can be separated into internal and external precision. Internal precision is the repeatability of several measurements in the same impact; external precision is the repeatability of several different impacts on the same sample. Typically internal precision is 0.3-2% for major (>~10%) and minor elements (>~0.5%), due mainly to statistical variations in the signal from small fluctuations in the plasma. External precision is affected by these fluctuation plus several additional factors: inhomogeneity in the sample from area to area, small variations in sample flatness which can affect the sample-to-anode distance, lack of care in placing the sample, and variations in cleaning the anode. External precision is therefore generally worse than internal precision but with care and good sample selection and preparation can approach the values for internal precision. Accuracy is the ultimate aim of precision and calibration. If the instrument and operator technique is precise and the calibration is done well then the accuracy achieved should approach the precision, i.e %.

Quantification in GD-OES

Comparative technique
200000 Pure Cu spectrum Pure Si spectrum The GD sputtering efficiency is sample dependant. Large difference of sputtering rate between matrices. Relative intensities must take into account the sputtering rate factor.

Quantification: Simple equation
where ci concentration qM sputtering rate Ii intensity ki constant

Sputter Rate Correction
Multimatrices Calibration for Cr Aluminum Base Which Concentration of Cr should give the same light in a material having a SR = 1? Which Concentration of Cr should give the same light in a material having a SR = 1? Iron / Steel Bases SR 0.1 SR 0.4 Virtual Base Concentration % SR 1 Apply Sputter Rate Correction to this point Apply Sputter Rate Correction to this point Zinc Base SR 1.2 Conc. X SR Conc. X SR Lead Base SR 2.0 10% Cr IAl IFe IZn IPb Light Intensity

Multimatrices Calibration for Cr X SR Only ONE Cr Calibration Curve Valid for Multimatrices Analysis of Unknown Sample Virtual Base Concentration % SR 1 Virtual Cr Concentration I X Light Intensity

Analysis of Unknown Sample Fe Cr Ni Mn Virtual Cr % Virtual Fe % Virtual Ni % Virtual Mn % I Fe I Cr I Ni I Mn Virtual Concentration Fe . SR + Cr . SR + Ni . SR + Mn . SR = 75 % Fe . SR % Cr . SR % Ni . SR % Mn . SR % All the elements within the unknown sample have the SAME SR Total (Conc. X SR) = 75 % (Fe + Cr + Ni + Mn) . SR = 75 % Real Concentration SR = 75 % / (Fe + Cr + Ni + Mn) Fe = 50 % / 0.75 = % Cr = 10 % / 0.75 = % Ni = 10 % / 0.75 = % Mn = 5 % / 0.75 = % Sum of Concentration = 100 % Sum Normalization SR = 75 / 100 = 0.75 Total (True Conc.) = 100 %

CDP : the quantification chain
Measure of intensities Calibration curves Get ccq Sum of ccq gives q Calculation of cc Estimation of density Depth Rf-GD-OES permits to obtain quantitative analysis. However as this is an optical spectrometer, calibration is required in order to obtain quantitative data. The purpose today is not to describe in details the quantification process in GD (called CDP by the ISO : compositional depth profile). It is enough to mention that there is a chain of calculations each one bringing some uncertainties. Among these uncertainties is the calculation of the erosion (or sputtering) rate and the estimation of the density of a layer by the knowledge of its elemental composition. Rf-GD-OES permits to obtain quantitative analysis. However as this is an optical spectrometer, calibration is required in order to obtain quantitative data. The goal here is to show the chain of calculations each one bringings some uncertainties. Among these uncertainties are the calculation of the erosion (or sputtering) rate and the estimation of the density of a layer by the knowledge of its elemental composition. CDP stands for compositional Depth Profile

Typical result by RF GD OES
Qualitative result: Int vs time Quantitative result: At% vs depth (µm) Another example from a different field. Here the sample is a multilayer coating deposited by PVD. We show both the qualitative profile (intensities in arbitrary units vs time) to illustrate the speed of analysis and the quantitative result after calibration in Atomic % vs depth. Sample: Complex multi layer coating: TiN/Ti2N Aeronautic industry Result: Comparative technique All elements detected Observations Contamination Extreme surface Interface

Methodology procedure
Optimization of operating conditions Choice of calibration samples Density measurement Sputtering rate measurement Preparation of calibration samples Method parameters optimization for calibration Calibration measurements Calibration modes selection Calibration function Calibration parameters Optimizing calibration curves Accuracy validation

Procedure

2. Choice of Calibration Samples
CRM vs RM vs in-house samples Bulk vs coated samples Number of samples Concentration range Families coverage CRMs are essential for tracability, i.e. when it is important to trace results back to official certifying laboratories. In many cases this is not necessary and internal reference samples can be used. If necessary these could be traced back to CRMs using other analytical techniques but this is making the trace a bit long. The two major advantages of traceability are when there are legal issues, e.g. forensic evidence, and in comparisons between laboratories. CRMs also use the average values of a range of analytical techniques, whereas in-house samples are usually only analyzed by one technique. Otherwise, in-house reference samples offer many advantages: lower cost (maybe), wider choose, properties more related to the analyte samples. Calibrating with in-house samples using values obtained with another technique, e.g. ICP-OES, means the GD-OES results should be similar to the other technique, but remember if the other technique is wrong then the GD-OES results will also be wrong. Currently there are no suitable certified coated samples. When analyzing coated samples it makes good sense to use similar coated samples for calibration, provided the reference coatings are well characterized. Experience, particularly in Japan, shows such calibration can be superior to using bulk CRMs. It is also possible to combine CRMs and coated samples in the same calibration. The quality of calibration and analysis improves roughly as the square-root of the number of samples in the calibration. Increasing the number of samples therefore generally improves a calibration but increases the amount of work and cost. Any useful calibration is therefore a compromise. For semi-quantitative analysis, it is recommended to have about five samples in the calibration curve for each element. For high accuracy analysis, a minimum of 15 samples for each element is recommended. The best accuracy in analysis is near the centre of the calibration curve. This is a statistical effect common to all types of calibration on all relative techniques. It is therefore essential, for accurate analysis, that the range of the calibration curve extends well above and well below the range of possible analyte concentrations. This is not always possible given the limited availability of reference samples and the often unexpected nature of unknown analyte samples. The analyst and their customer need to be aware of this fundamental property of analysis. Different matrices can be divided into different families. In GD-OES the nature of different families is determined largely by their sputtering rates and electrical characteristics, e.g. zinc in brass and zinc in aluminium form two different families for zinc calibration because both the sputtering rates and electrical characteristics of the two sample type differ markedly. The most accurate analysis always occurs when the family of the analyte sample matches the family of the calibration samples. In high accuracy analysis different calibration curves should be made for each family. For semi-quantitative analysis it is possible to mix families, and in quantitative depth profiling it is essential to include a number of different families each matching different parts of the analyte coated samples.

3. Density Measurement Accuracy required:  3% Methods:
Archimedes method Regular shapes Calculated from composition Density equals mass divided by volume, so the first step is to measure the mass on an accurate balance. The volume is more difficult. The most common method used to measure the volume of CRMs and other reference samples is Archimedes’ method, which involves measuring the difference in the mass of a beaker of liquid with and without the sample suspended in it. There are commercial attachments available for balances to facilitate this. The apparent mass change in the beaker of liquid equals the equivalent mass of liquid displaced by the sample. If we know the density of the liquid then we can calculate the volume of the sample. The most common liquid used is water though some laboratories use ethanol. Some assume the density of water is 1 g cm-3 which means the mass change simply equals the volume of the sample in cm3, however, for more accurate results it is possible to correct for the temperature of the water since the density of pure water significantly varies with temperature. Care should be taken to exclude bubbles and porous materials. Often CRMs have a regular shape, e.g. cylinder, it is then possible to calculate the volume using the dimensions of the sample. The volume of a cylinder = Height x ( Diameter)2 / 4 Note that the achieve the desired accuracy each dimension must be measured with an accuracy of  1%. For many materials especially metal alloys, e.g. zinc-aluminium alloys, the density of the material can be calculated from the formula given. This formula is based on a constant atomic volume and is problematic for materials such as oxides where the atomic size is very different from the pure material. where  is density, ci concentration of element i, i density of pure i

4. Sputtering Rate Measurement
Accuracy required:  10% Methods: Profilometry Mass loss Measurement of reference sample and CRM in same conditions Various analysis time Measure corresponding depths Calculate erosion rate Input in standards DB in Quantum Absolute sputtering rate is the mass removed per unit time. In GD-OES, because the analysis area is constant it is more useful and simpler to calculate the sputtering rate as the mass removed per unit area per unit time. We are not aware of anyone using direct mass loss measurement (i.e. measuring the sample mass before and after sputtering). The reason is obvious if we consider the mass change during a typical measurement. Assume we have a steel CRM of total mass 100 g and density of 8 g cm-3. We use a 4 mm diameter anode and sputter a crater of 20 um depth. The volume removed is 5 e-4 cm3 and the mass removed is 4 mg. A 10% accuracy means 0.4 mg. It’s possible on a microbalance but difficult, given that you have to put the sample on and off the GD source without changing the total mass. A second problem in measuring mass loss this way is that you also need to measure the area of the crater accurately so that you can convert the mass loss into mass loss per unit area. The method generally adopted is to measure the average depth of the crater after sputtering and convert the depth per unit time into mass per area per unit time by multiplying by density. The most common means to measure crater depth is by a contact stylus profilometer (also called a surface roughness instrument). Some lucky operators can use lasers or interferometry. Special care is needed with these optical devices when studying dielectric materials, e.g. glass, since the optical focussing could become confused. In using any linear scanning device it is recommended to use the average of several scans at different places on the sample. ISO currently recommends four scans. Also it should be remembered that a linear scan is weighted equally along the scan whereas the crater being measured is a circle (usually) and so the area of each segment, in going out from the centre, increases as the square of the distance from the centre. This means a region near the outside of a crater may be more important than a region near the centre of the crater because the area is greater near the outside. This is not a problem if the crater is flat. Relative sputtering rate (RSR) is a further powerful simplifying step. A reference sample is chosen, it is given an RSR of 1 and all other samples are ratioed to this by dividing their sputtering rates by the sputtering rate of the reference. These RSRs are used in depth profiling to calculate a ‘relative’ depth. The final step in calculating the true depth is to multiply the relative depth by the sputtering rate of the reference.

5. Preparation of Calibration Samples
When possible use same preparation for calibration and analysis samples Grinding works but final wet polishing with a fine paper (e.g. 600 or 1200) is better Some materials are better cut on a lathe Critical factor is to keep analyzed face flat Best to keep front and back faces parallel Avoid centre of bulk CRMs, prefer outside

6. Calibration Modes “analysis mode)
Bulk analysis: Normal (single major element) Virtual (relative): same family but several major elements ex: stainless steel 100% (2 major elements) Surface analysis: Virtual (when Major element common to substrate and coating) Sputtering rate (multi matrix calibration) Layer mode: no CRM available, use of one single sample as reference

7. Method Parameters RF Source: already set Sequence: Power Pressure
Preburn (preintegration) time Averaging time (named integration time) Quali opt. Quanti opt.

Method parameters: Pre-integration time optimization
Used only in bulk measurement and calibration Run sample in surface analysis Define the pre-integration time as the signal in bulk material is stable for major elements (here ≈115s) Report this value in the method (meas. Part) Check with another sample Pre-integration time is the time required to sputter the depth affected by contamination and sample preparation (polishing)

8. Calibration measurements
Bulk CRM Several craters (min 2.) 3-4 replicates (same crater) Check RSD (on major elements only): One crater: RSD< 1% Two or more craters: RSD <2% Coated home made sample Special config in Quantum (Options) or Quantum XP

Measurement in calibration: layered sample
Click « Options » button Quantum or XP

Measurement in calibration: layered sample
Select indirect calc. Modify the fields: - Pre-integration time (5s ~or less) - Measurement time (like a surface analysis) - average time 3. Click “OK” button 4. Measure

Measurement of the layered material in calibration:
Click for the lower limit Click for the upper limit At the end of measurement, a graphic window is displayed (similar to the window in surface analysis). A message indicates you must select the zone corresponding to the average calculation over the coating by clicking with the mouse with left button. Quantum or XP

Click on « Curves » button
Measurement of the layered material in calibration: Optimize selection zone by line Press « 1 » Click on « Curves » button Then as a normal standard, you get an intensity corrsponding to the selected zone. But as the average zone is maybe not the same for all elements, you could select the average zone line by line. Here we will take the example on C.

This could be done for each line independently
Calibration Measurement of a layer: Get better intensity: C line as example Zoom use on the graphic window Click on Select the C line Enter the low and upper limit by dialog box or use graphic selection by mouse Click “update” This could be done for each line independently 852 You click on « curves » button. Then you make a zoom on the C profile to see the horizontal zone to select. Once the period defined (here is 20s and 240s), you select the button sigma at the top of graphic window. You sellect in the dialog box C only (click on the line). Then enter in dialog box the limits you define and click OK. You can do as described on every element contained into the coating.

10. Calibration Parameters (A)
Chi-squared, the minimising function,  2 Estimated values for the fit parameters ai-di. SD of the estimated values. BEC, background equivalent concentration: BEC = -ai and its SD is the same as for ai. where is estimated concentration using calibration function. Lower as possible The minimising function is the one used to determine the fit parameters in the calibration function. Here weighting wi is included; later equations are shown with equal weighting of data for simplicity. Correct weighting is an essential part of good calibration. This is best illustrated with the minimising function, if we change the values of wi then we will change the resulting fit parameter values. Weighting means that some data points are given more or less importance than others. The weight should be inversely related to the uncertainty in each data point. The weight is calculated using an in-built algorithm and then the operator can overwrite individual weights. The algorithm should include uncertainty in Ii and Ci.

12. Optimizing Calibration Curves
Choose first or second order. Choose second order only when there is a big improvement (perhaps 2) in parameters. as low as possible and R as close to 1 BEC should be small and negative. If necessary adjust weights to ensure this. The standard error of estimate and relative standard error of estimate indicate the accuracy of analysis at the centre of the calibration. If the accuracy is inadequate: - increase number of calibration samples, - reduce the weight of outliers - repeat the calibration with more measures on each sample - reduce the range of calibration - change the calibration function.

Summary We have covered the key principles to good calibration/analysis in GD-OES. Next step is to learn how to apply these using Quantum, to see some extra features (Vdc correction, H correction, layer mode etc)

Extra feature : H correction
An other important aspect to consider is the presence of H (and N) in the plasma. H is often present on the surfaces and can have a dramatic influence as it changes the plasma conditions. This was studied by Hodoraba and other workers and published in JAAS. In this example, the presence of H is responsible of an apparent decrease of Ti on the surface and a corresponding increase of N. Either a correction can be applied in the software or the gas (pure Ar) can be replace by an ArH mixture (typically Ar + 1 or 2% of H : this leads to a less efficient plasma but minimizes and makes neglectable the effect of H coming from the sample). H correction No H correction Another important aspect to consider studied by Hodoraba is the presence of H (and N) in the plasma. H is often present on the surfaces and can have a dramatic influence as it changes the plasma conditions. In this example, the presence of H is responsible of an apparent decrease of Ti on the surface and a corresponding increase of N. Either a correction can be applied in the software or the gas (pure Ar) can be replace by an ArH mixture (typically Ar + 1 or 2% of H : this leads to a less efficient plasma but minimizes and makes negligible the effect of H coming from the sample).

Where to Get More Information
JY manuals Practical guide to GD-OES Nelis,Payling (RSC 2003) Principles and Practice of Spectroscopic Calibration, H Mark, John Wiley, NY (1991)

Bulk Calibration

Typical bulk calibration curve

Bulk calibration One matrix only, one family
Homogeneous samples (apart from top surface that needs to be cleaned) Good sensitivity for trace elements Reproducibility Accuracy Analysis time, ease of use

Sequence for bulk calibration
Sample selection Select calibration, recalibration, minicalibration samples Check composition ranges Creation of the method Select elements Select appropriate spectral lines Select source conditions Sample preparation Preparation techniques Sample preparation and sample handling Validation of the instrument operation Calibration Measurements of selected samples Analysis mode selection (normal, no/with Internal standard, virtual, 100%) Optimize regression Check drift correction standards (recalibration) Validation of the calibration Analysis methodology

Bulk analysis First analysis: use a CRM to control the accuracy of the curve (control measurement) => if not enough accurate, check the curves again or use “mini calibration” sample Routine analysis: run a CRM as a control If OK: run unknown samples If not: run recalibration samples, check coefficients, run control sample, then unknown samples

Bulk analysis 2 Minicalibration:
After re-calibration: if not good enough, check your instrument (see good operation practices) Recalibration coefficients: Alpha: typical variation between 0.75 and 1.25 Beta: typical variation up to 10% of the High standard intensity

Sequence for bulk analysis
Prepare samples Check if drift correction is required If required, do recalibration Do analysis Check values are sensible Check uncertainties Check grade if required Report results

Specificity of depth profile calibration

Calibration for depth profiling. Multimatrix calibration
Samples here are various steels, Ti, Ni and carbides. Coatings can also be used within multimatrices calibrations.

CDP calibration Multimatrix
Simultaneous quantification of concentrations and depth Extended ranges Additional elements Selection of samples Precision

Sequence for CDP calibration
Sample selection Select calibration, recalibration samples Check composition ranges Check RSR exist for all calibration sample in Standards DB Creation of the method Select elements Select appropriate spectral lines Select source conditions Sample preparation Preparation techniques Sample preparation and sample handling Validation of the instrument operation Calibration Measurements of selected samples Analysis mode selection (virtual, Sputtering rate) Optimize regression Check drift correction standards (recalibration) Validation of the calibration Analysis methodology

Layer mode: semi quantitative model
WHY: No reference material to build calibration curves Based on one single known sample (coated) composition of all major elements of each coating and substrate Thickness of all coatings and final depth of the chosen measurement as reference Density (optionally but real one is better)

Layer mode: sequence Method parameters selection
Measurement of reference sample Selection of « Layer mode » in current Method Select the “Multilayer calibration setup” in Quantum from results then Surface analysis Development of the quantification model from the reference result Automatic determination by Quantum of the layers Input information about composition of each layer Input the depths corresponding to the change of layers Calculation of the calibration curves Validation of the model (Save the reference model) Apply it on Results => surface analysis

CDP analysis First analysis after calibration: use a Known sample to control the accuracy of the curves (Surface analysis measurement=> check good qualitative) Quantify and check the accuracy => if not enough accurate, check the curves again and add more standards to cover the intensity range Routine analysis: run a Known sample as a control Check qualitative performance Then if Quantified OK also: run unknown samples If not: run recalibration samples, check coefficients, run control sample, then unknown samples

CDP analysis 2 After re-calibration: if not good enough, check your instrument (see good operation practices) Recalibration coefficients: Alpha: typical variation between 0.75 and 1.25 Beta: typical variation up to 10% of the High standard intensity

Calibration principles

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