Dr. Shangshang Mu, Applications Engineer, EDAX
A couple of weeks ago, a question regarding the minimum detection limits (MDL) of our Energy Dispersive Spectroscopy (EDS) quantitative analysis was forwarded to me from a potential customer. This is a frequently asked question I get from customers during EDS training. We understand researchers are looking for a simple answer; however, they don’t get a straightforward answer from us most of the time. This is not because we don’t want to tell the customer the configurations of our systems, but detection limits depend on various factors, including detector window, geometry, detector resolution, collection time, count rate, and sample composition. The detection limit for a given amount of an element in different sample matrixes is not the same. For example, calcium in indium has a much higher detection limit than it has in carbon because calcium energy lines are heavily absorbed by indium, but not by carbon. The limit also changes if you have a bit more of a given compound in the sample. The limits are lower if the data collection time is doubled. So, it is impossible to provide a general MDL for an EDS system or even a given element, but we can calculate the MDL for a given spectrum.
This function is available in APEX™ Software for EDS version 2.0 or later. For each element identified in the spectrum, the MDL is given in the quantification table and flagged if it is below the detection limit (Figure 1). To determine the MDL for a given spectrum, one must look at the statistical significance of the signal above the background. We generally use the single-channel definition for peak and background counts.
Figure 1. Quantification table with MDL.
Figure 2. Illustration of background and peak counts.
For a given element to be above the significance level, it requires that the total number of counts on the peak NP be above background counts NB by a predetermined confidence, see Figure 2. For significance, we use 1.7 standard deviations (SD) in a one-tail test since we are only concerned about having counts above the threshold (Figure 3). A SD of 1.7 corresponds to about 95% confidence for a single-tail.
Figure 3. Single-tail normal distribution. NB is the background mean level.
The significance level can be calculated as:
NS=NB+1.7σB= NB+1.7√(NB)
This means that the requirement for an element to be considered significant is:
NP≥ NB+1.7√(NB)
For the MDL calculation, we are considering the net counts on the peak (NP-NB). Analog to the significance level, it is required that the counts are above the background plus a significance level, but we are now considering net counts instead of gross counts.
NDL=NB+∆(NP-NB)
To calculate the error, we consider the error of the peak and the background. If an element is close to the detection limit, the number of counts are comparable to the background counts, and we can approximate the total error:
∆(NP-NB)=√(NP+NB)≈√(2NB)
Using a 2s/95% confidence level, we can write the count detection limit as:
NDL=NB+2√(2NB)~2.8√(NB)
With the count-based detection limit and assuming the counts are linear with concentration, the concentration MDL can be calculated from the concentration C of a given element in a spectrum:
MDL=2.8√(NB)*C/NP
As I mentioned earlier, the detector window is one of the most important factors determining the MDL. With the introduction of Silicon Drift Detectors (SDD) and the development of fast and low-noise pulse processors, EDS analysis has seen remarkable increases in throughput and reliability in the last decade. But one often overlooked aspect of the detection technology is the detector window. A variety of window technologies are available, including beryllium, polymer films, and the most recent addition by EDAX, silicon nitride. Due to the polymer window’s composition and thickness, a significant part of the low-energy X-rays is absorbed before reaching the X-ray detector. This absorption effect is vastly reduced in the range below 2 keV for the silicon nitride windows, as shown in Figure 4.
Figure 4. Transmission curves for silicon nitride and polymer windows measured using synchrotron radiation.
The MDL for spectra acquired from the same samples with different window configurations can be calculated by employing the derived equation above. This study was led by Dr. Jens Rafaelsen at EDAX using five different standards. To eliminate the detector resolution and response as a variable in the experiment, the window was removed from a standard detector, and exchangeable caps with silicon nitride and polymer windows were mounted in front of the electron trap. Figures 5 and 6 show the relative improvement in MDL for the window-less and silicon nitride window configurations compared to the polymer window. Figure 6 documents the silicon nitride’s superiority over the polymer window in the low energy range with improvements of over 10% for the MDL of oxygen. While Figure 5 shows that further improvements can be gained in the window-less configurations, the silicon nitride window still allows for the use of variable pressure mode and spectrum collection from samples exhibiting cathodoluminescence (CL).
On a side note, our friends at Gatan recently captured fantastic EDS and CL data simultaneously from a meteorite thin-section using an EDAX Octane Elite EDS Detector and a Gatan Monarc CL Detector mounted on the same SEM. Check out the blog post written by Dr. Jonathan Lee to see how combined EDS and CL analysis can provide a glimpse into the history of our solar system’s evolution.
Figure 5. Relative gain in MDL for window-less configuration compared to polymer window.
Figure 6. Relative gain in MDL for silicon nitride configuration compared to polymer window.
Hello! I am interested in knowing how to reduce the error in the EDS analysis done by EDAX TEAM. I assume if more scans are completed on a specific point, the program generated error in the report will be lower. Is that true? How could you achieve the goal of minimizing error to less than 5%? Thank you.
Hello, the quality of quantification results is highly dependent on the number of counts in the spectrum. More statistics increase accuracy and precision and reduce errors by using higher count rate, longer collection time or faster amp time. Sample prep is also very important. In principle, if you prepare your sample very well, you can do the same level of analysis as using EPMA. The error can be further reduced by carefully preparing your sample (e.g., flat, homogeneous, well polished, clean, conductive).