### Analyzing luminescence spectra

Researchers use many luminescence techniques as a qualitative, exploratory tool and to frequently analyze data variations from different laboratories. However, it is essential to distinguish between differences that arise from sample variations or treatments versus signal collection and processing artifacts. Below are steps we recommend following when analyzing and reporting spectral data.

1. Perform measurements under known scanning electron microscope conditions, e.g., electron dose and power density.

2. Collect the raw data (in wavelength, I(λ)dλ versus λ) and verify the data is repeatable.

3. Process the data.

1. Removal of dark current (if any).

2. Correct for any non-linearities in the efficiency of the detection system.

3. Convert spectra from dispersive units of wavelength (nm) to energy (eV).

4. Use linear least-squares fitting to deconvolve spectral features.

4. Publish the data and ensure to include the factors above.

Unfortunately, not all researchers follow these steps and a range of systematic errors make their way into the published literature. The following section aims to explain why each step is important and the potential issues you may encounter.

#### Power density

It is important to characterize the power density in many specimens since most luminescence processes exhibit a strong variation in the intensity of cathodoluminescence (CL) emission with electron beam current, size of interaction volume, and scanning area. Failure to investigate or account for this effect can lead to drawing incorrect conclusions. However, this effect is useful to investigate the nature of a luminescence signal and reveal details of the recombination mechanism by plotting the CL intensity versus power density.

The power density versus emission intensity can be written as follows:$$Intensity_{CL} ∝Dose^m$$

Plotting the intensity versus dose relationship using $$log[Intensity_{CL}]∝m.log[Dose]$$ allows m to be determined.

When m ≤ 1, the mechanism is via deep levels (impurities) or free-bound and donor-acceptor pairs; when m ≥ 1, corresponds to near band edge emission and for excitonic processes, 1 ≥ m ≤ 2 with m = 1 for free exciton and m = 1.5 for bound excitons.

Increasing electron dose (power density) can also lead to a peak shift in materials that exhibit a piezoelectric field, e.g., nitride semiconductors with the wurtzite crystal structure.

#### Verify the data is repeatable

It is often assumed that capturing luminescence signal(s) is a passive process, and indeed in some cases, this is correct. However, the act of sample stimulation by an electron beam can modify the intensity and emission spectra. For example, radiation damage may occur to the sample and track with changes to the electron microscope's beam exposure. Several noticeable examples include:

• Quenching of emission from covalently bonded molecules
• Creation of new point defects when using electrons with energies greater than the knock-on damage threshold—particularly important in the analysis of semiconductors in the TEM
• Rearrangements into new defect complexes and/or charges that are transferred between sites

These effects can modify the intensity, spectrum, and associated excited-state lifetimes of the processes. Therefore, it is prudent to minimize the electron dose and acquire the spectra with minimal beam-induced effects. When studying new materials, it is often a valuable exercise to investigate these effects before drawing any conclusions.

Luminescence spectroscopy also offers insight into these dynamic processes and techniques may include simultaneous excitation methods to follow transient events.

#### Process the data

Typically, a raw spectrum is captured and plotted as a 1D plot displaying intensity versus wavelength. However, accurate analysis and processing of the data require several steps and careful consideration of any system contributions to the data.

Removal of the dark current

Most luminescence detectors (e.g., CCDs and photomultiplier tubes (PMTs)) exhibit a dark current that needs to be removed to prevent errors in subsequent processing. The dark current is a relatively small electric current that flows through photosensitive devices even when no photons are entering the device. Dark (frame) subtraction can remove an estimate of the mean fixed pattern, but sometimes this must be performed as a post-processing step.

Correct for change(s) in the detection system

A wide range of detection systems are available to measure luminescence spectra, including commercially supplied detectors and home-built setups. In both cases, these detectors may incorporate a wide range of elements, including the optical components (mirrors, lenses, spectrometers) and detectors (PMTs and cameras). The performance (reflectivity, transmission, or sensitivity) of individual components will vary by wavelength (and polarization). These components may be combined within a system to deliver a unique response by wavelength (and polarization) that can vary by several orders of magnitude across the wavelength range. This correction may be essential when trying to compare a measured spectrum to the literature or compare the intensity ratio of peaks in a spectrum. Be mindful that the literature does not always make it clear whether raw or corrected data is being presented.

With modern equipment, it is often possible to correct for the system response. Within Gatan Microscopy Suite® software, right-click the mouse on a CL spectrum to access this correction.

Below are key components of a standard luminescence system and where you typically observe significant changes in performance:

Focusing optics

Many detection systems utilize focusing optics to couple the collected light into the spectrograph. However, the transmission lenses or mirror reflection efficiencies can vary significantly with wavelength. For example, many mirror components use protected aluminum that has a reflectivity of ~96% at visible wavelengths but falls to <70% at 200 nm. In transmission lenses, one must also consider the effect of chromatic aberration—the change in focal length of an optical component by wavelength—which can reduce the light coupling efficiency by a factor of >1000 compared to visible wavelengths.

Diffraction gratings

Diffraction gratings form the dispersive element of a spectrometer or spectrograph, producing a signal on a linear wavelength axis. The ruling density (also known as groove- or line-density) determines the dispersion (different levels of spectral resolution) and the blaze wavelength (λBlaze); the wavelength at which it operates most efficiently. The response efficiency usually falls to less than 10 – 20% of the peak value by ∼½λBlaze and ∼2λBlaze; this defines the useful spectral range of the grating. Careful selection of the appropriate diffraction grating blaze for a given experiment is needed and, when covering a significant wavelength range, the change in response must be considered.

Diffraction gratings also exhibit higher-order diffraction (dsinq = where q is the diffraction angle and n an integer). When a spectrum covers a wide spectral range, you may observe second-order peaks unless order sorting blocking filters are used. For example, you may use a grating blazed at 300 nm to capture a spectrum spanning 200 – 700 nm, and, at a wavelength setting of the spectrometer of 600 nm one will also detect the second-order light of 300 nm, and the third-order light of 200 nm.

Detectors

A CL system may employ several types of detectors, including PMTs, photodiodes, cameras (CCD or CMOS), and linear diode array. You can record a change in sensitivity across the wavelength range that each detector type exhibits during a CL experiment. For instance, when you use a scientific-grade camera with a nominal operating range from 200 – 1100 nm, the efficiency fluctuates by almost two orders of magnitude over that range. There also exists a significant variation within each type of detector and it may change with age. These limitations must be recognized.

We recommend that published data clearly states whether the correction for the total system response is applied. However, please note that publications do not always include this information.

In contrast, it is not necessary to apply this correction during some experiments, e.g., when performing initial analyses or when analyzing a very limited wavelength range. However, for peaks with a broad full width at half maximum, this becomes almost essential as the system response often leads to an apparent change between the peak position in raw and corrected data.

Convert spectra from dispersive units of wavelength (nm) to energy (eV)

The intrinsic shapes of luminescence emission bands are symmetrical peaks (often Lorentzian- or Gaussian-shaped) when displayed in energy (E, eV) as the unit of dispersion. This shape is due to the broadening of the electronic energy levels which drive the electron transitions that generate photon emissions. Most hardware for luminescence spectrum acquisition, record the data dispersed by wavelength (λ, nm) using a fixed wavelength bandwidth (dλ), e.g., a spectrum is plotted as (I(λ)dλ versus λ). However, due to the inverse relationship of energy and wavelength, dλ versus dE is not a constant and therefore, spectral features displayed in wavelength as the dispersive units are not symmetrical. This leads to several possible issues:

• Deconvolution using the non-linear least squares (NLLS) fitting has no physical meaning in spectra with wavelength as the units of dispersion
• An apparent difference in peak positions of wavelength and energy data
• When a spectrum consists of more than one spectral feature, the relative intensity of the peaks will alter

The reason for these difficulties is that in the transformation from wavelength(λ) signals (I(λ)dλ versus λ) into the energy plot (I(E)dE versus E) the transformation of the wavelength axis into terms of energy is obvious (i.e. using $$E ∝ hc/λ$$). However, for the intensity axis, the transformation requires an intensity correction from wavelength to the energy of (I(E) dE) and a change from the fixed wavelength bandwidth to a fixed energy bandwidth, related by dE = -hc/λ2dλ. Particularly for broader luminescence features, the (1/λ2) term has a major distortion effect on the curve shapes.

Deconvolve spectral features

Please refer to NLLS Models section.

Spectral calibration

The central wavelength of a peak in a spectrum is often reported with high precision (two decimal places or more), but the error in this measurement is rarely stated. In many systems with a manual grating selection, the accuracy of spectral calibration may be as much as ±0.2 nm and the precision ±2 nm unless a spectral calibration is performed immediately before measurement.

Thus, take care when comparing measured to data to that in the literature. Fortunately, in many CL experiments that occur at room temperature, it is often the wavelength shift that is important rather than the accuracy of a single measurement.

#### Summary

The section highlights the need to process luminescence spectra in a meaningful way, make accurate calibrations, and to recognize that this is done to varying degrees in the literature. This is true for all luminescence methods regardless of the excitation source. The intention here is to provide sufficient information that a researcher may understand which methods are important when drawing conclusions from an experimental result.