Cathodoluminescence (SEM-CL)

1. Theory

• Definition: Cathodoluminescence in an SEM collects the light emitted when the electron beam creates electron-hole pairs that recombine radiatively, mapping emission intensity and spectrum with the spatial resolution of the beam (Corfdir et al.).
• Defect contrast: Threading dislocations and other non-radiative centres appear as dark spots, allowing dislocation densities to be counted (Corfdir et al.; Attolight).
• Spectral maps: Peak energy maps reveal strain, composition and dislocation type (Attolight; Corfdir et al.).
• Time resolution: Pulsed beams give radiative and non-radiative lifetimes with picosecond resolution (Corfdir et al.).

2. Working Principle

• Collection: A parabolic mirror above the sample, or an optical objective integrated into the electron lens, collects the light (Corfdir et al.).
• Detection: Photomultipliers for panchromatic images and spectrometers with CCDs for hyperspectral maps (Corfdir et al.; Attolight).
• Beam conditions: About 3 to 10 $\mathrm{kV}$, set to place generation at the depth of interest (Corfdir et al.).
• Cooling: Cryogenic stages from about 10 to 300 $\mathrm{K}$ sharpen lines (Corfdir et al.; PDI).

3. Applications

• GaN epitaxy: Dislocation density and type in templates and LED layers (Attolight; Corfdir et al.).
• LEDs and lasers: LED and laser diode structures (Gatan).
• Nanostructures: Strain and lifetimes in nanowires and nanobelts (Corfdir et al.).
• Carrier transport: Diffusion lengths from energy profiles around dislocations (PDI).

Emission and Collection

Name	Formula	Related Formulae	Variables/Constants
Emission energy	$\lambda =\frac{1239.84}{E\left[\mathrm{eV}\right]}\mathrm{nm}$	$\Delta E=\frac{1239.84\Delta \lambda }{{\lambda }^2}$	$E:emittedphotonenergy$ $\begin{array}{r}\Delta \lambda :peakshift;conversion(computedfrom\\ hc/e;PLpage);Corfdiretal.:ZnO\\ nanobeltCLintegratedbetween3.34and\\ 3.40\mathrm{eV}at30\mathrm{K},apeakshiftofabout2\\ \mathrm{nm}alongthebeltfromlocalstrain,\\ intensitylossatabendfromashorter\\ non-radiativelifetime\end{array}$ $\begin{array}{r}(computed:3.37\mathrm{eV}is368\mathrm{nm},anda2\mathrm{nm}\\ shiftthereis18\mathrm{meV})\end{array}$
Generation volume and resolution	$d_{CL}\approx \sqrt{R_{gen}^2+L^2}$	$R_{gen}\approx 10\mathrm{nm}\text{to}1\mu \mathrm{m}(3\text{to}10\mathrm{kV})$	$d_{CL}:effectiveCLresolution$ $\begin{array}{r}{R}_{gen}:generation-volumesize(Kanaya-Okayama\\ range,SEMpage)\end{array}$ $\begin{array}{r}L:carrierdiffusionlength;Gatan:\\ resolutionaconvolutionofgeneration\\ volumeandcarriermovement;quadrature\\ combination(myreading);Corfdiretal.:\\ typical3to10\mathrm{kV},generationvolume\\ about10\mathrm{nm}to1\mu \mathrm{m}byvoltage,\\ dislocationsdetectedtoabout1\mu \mathrm{m}depth,\\ resolutiondowntothenanometrescale\end{array}$ $\begin{array}{r}(assumed:R_{gen}=50\mathrm{nm},L=100\mathrm{nm};\\ computed:d_{CL}=112\mathrm{nm},dominatedby\\ diffusion)\end{array}$
Collection efficiency	${\Omega }_{frac}=\frac{1-\cos {\theta }_{max}}{2},{\theta }_{max}=\arcsin NA$	${\eta }_{coll}\text{(objective, NA 0.72)}\approx 100\times {\eta }_{coll}\text{(mirror) over 300}\mu \mathrm{m}$	$\begin{array}{r}{\Omega }_{frac}:fractionofanisotropicemitte{r}^{\prime }s\\ lightwithinthecollectioncone;\\ geometricrelation(computed);Corfdiret\\ al.:Attolightdesignwithanoptical\\ microscopeinsidetheSEMobjective,NA\\ 0.72(f/0.5),achromaticUVtoIR,\\ photomultiplierdetection,conventional\\ parabolicorellipticmirrorswithfields\\ ofonlyseveralmicrometres,upto100\\ timestheefficiencyovera300\mu \mathrm{m}field\end{array}$ $\begin{array}{r}(computed:NA0.72accepts46.1degrees,\\ 15.3percentofanisotropicemitte{r}^{\prime }s\\ lightinair,beforerefractionlosses)\end{array}$

Dislocations

Name	Formula	Related Formulae	Variables/Constants
Threading-dislocation density	$N_{TD}=\frac{n_{spots}}{A}$	$\bar{s}=\frac{1}{\sqrt{N_{TD}}}$	$N_{TD}:dislocationdensity$ $n_{spots}:darkspotscountedinareaA$ $\begin{array}{r}\bar{s}:meanspacing;definitions(computed);\\ Corfdiretal.:GaNtemplatewithabout\\ 3\times 10^7\mathrm{c}{\mathrm{m}}^{-2},dislocationsdarkfrom\\ non-radiativerecombination;Attolight:CL\\ countingdescribedasaccuratefor\\ densitiesexceeding1\times 10^9\mathrm{c}{\mathrm{m}}^{-2}(seethe\\ Q/A),18\mu \mathrm{m}PMTimagesat1024by1024\\ pixels\end{array}$ $\begin{array}{r}(computed:3\times 10^7\mathrm{c}{\mathrm{m}}^{-2}isa1.83\mu \mathrm{m}mean\\ spacingand1\times 10^9\mathrm{c}{\mathrm{m}}^{-2}only316\mathrm{nm};an18\mu \mathrm{m}\\ fieldat1024pixelsis17.6\mathrm{nm}perpixel)\end{array}$
Dislocation types	$\mathbf{b}=n\mathbf{a}(\text{edge}),m\mathbf{c}(\text{screw}),n\mathbf{a}+m\mathbf{c}(\text{mixed})$	$\text{intensity map}+\text{peak-energy map}\Rightarrow \text{screw vs edge or mixed}$	$\mathbf{b}:Burgersvector$ $\begin{array}{r}\mathbf{a},\mathbf{c}:GaNlatticevectors;Attolight:\\ theseclasses,purescrewdislocations\\ suspectedasleakagepaths,darknessalone\\ insufficienttoseparatethem,combined\\ intensityandcentre-energymaps\\ identifyingscrewdislocations\\ non-destructively;PDI:piezoelectric\\ fieldsatedgedislocationsseparating\\ electronsandholesover100\mathrm{nm}fromthe\\ line(Kaganer,SabelfeldandBrandt2018)\end{array}$ $\begin{array}{r}(myreading:apurescrewdislocationhas\\ littlein-planestrain,consistentwith\\ itsweakerenergycontrast)\end{array}$
Diffusion length from dark-spot profiles	$I\left(r\right)=I_{\infty }\left[1-C{e}^{-r/L}\right](\text{phenomenological})$	$\text{energy profile }E\left(r\right)\text{sensitive to }L$	$\begin{array}{r}I(r):CLintensityatdistancerfroma\\ dislocation,I_{\infty }:far-fieldintensity\end{array}$ $\begin{array}{r}C:contrast;phenomenologicalform(my\\ reading);PDI:thisapproachgrossly\\ underestimatesthediffusionlength,\\ intensitycontrastdominatedbythe\\ piezoelectricfieldratherthandiffusion,\\ profilesnearlyindependentoftemperature\\ from10to200\mathrm{K}althoughdiffusionlength\\ changes,energycontrasthighlysensitive\\ todiffusionlengthandproposedasthe\\ newobservable,MonteCarloandrigorous\\ 3-Dmodels(Kaganeretal.2019)\end{array}$ $\begin{array}{r}(myreading:becausethedark-zonewidth\\ issetbyfieldsover100\mathrm{nm}ratherthan\\ byL,itswidthcannotbeconvertedtoL\\ directly)\end{array}$

Lifetimes and Temperature

Name	Formula	Related Formulae	Variables/Constants
Time-resolved CL	$\frac{1}{\tau }=\frac{1}{{\tau }_r}+\frac{1}{{\tau }_{nr}}$	${\eta }_{int}=\frac{\tau }{{\tau }_r},I_{CL}\left(t=0\right)\propto \frac{1}{{\tau }_r}$	$\tau :measureddecaytime$ ${\tau }_r,{\tau }_{nr}:radiativeandnon-radiativelifetimes$ $\begin{array}{r}{\eta }_{int}:internalquantumefficiency;Feixet\\ al.:theseraterelations,{\tau }_{r}fromthe\\ inversepeakintensity;Corfdiretal.:\\ picosecondelectronpulses,time\\ resolutionbelow10\mathrm{ps}withoutlossof\\ spatialresolution,CLintensityatt=0\\ inverselyproportionaltotheradiative\\ lifetime,nanobeltbendexplainedby\\ shorternon-radiativelifetimeatconstant\\ radiativelifetime\end{array}$ $\begin{array}{r}(assumed:{\tau }_r=1\mathrm{ns},{\tau }_{nr}=0.5\mathrm{ns};computed:\\ \tau =0.33\mathrm{ns}and{\eta }_{int}=33percent)\end{array}$
Temperature range	$T=15\text{to}300\mathrm{K}(\text{cryogenic stage})$	$E_g\left(T\right)=E_{g0}-\frac{\alpha T^2}{T+\beta }$	$\begin{array}{r}Corfdiretal.:optionalcryogenicstage\\ from15to300\mathrm{K},nanobeltmeasurementsat\\ 30\mathrm{K};PDI:hyperspectralCLmapsfrom10\\ to200\mathrm{K},exampleat120\mathrm{K};Varshni\\ relationfromthePhotoluminescence\\ Spectrometerpage\end{array}$ $\begin{array}{r}(computed:withNepa{l}^{\prime }sGaNparameters,\\ coolingfrom300to15\mathrm{K}blue-shiftsthe\\ gapby77\mathrm{meV})\end{array}$

Important Questions

Ques: How does SEM cathodoluminescence differ from photoluminescence?

It excites with a focused electron beam instead of a laser, so light is mapped with SEM resolution and depth can be tuned by voltage. Corfdir et al. describe typical voltages of 3 to 10 $\mathrm{kV}$ and generation volumes of about 10 $\mathrm{nm}$ to 1 $\mu \mathrm{m}$, so dislocations can be detected to about 1 $\mu \mathrm{m}$ deep, with resolution down to the nanometre scale. In practice, carriers diffuse before recombining, so resolution combines the generation size and the diffusion length; with an assumed 50 $\mathrm{nm}$ volume and 100 $\mathrm{nm}$ diffusion length it is about 112 $\mathrm{nm}$ if the two add in quadrature (Gatan describes a convolution; quadrature my reading; computed). Emission energies are read as in PL: ZnO near 3.37 $\mathrm{eV}$ emits at 368 $\mathrm{nm}$ (computed). The beam also excites wide-gap materials that are hard to excite optically. Reference: P. Corfdir, O. Gougeon, S. Sonderegger and J.-D. Ganiere, ‘Quantitative Cathodoluminescence Opens New Areas of Investigation in Semiconductor Research and Production’, Microscopy Today, January 2013 (fetch-tool summary); Gatan, ‘High spatial resolution cathodoluminescence’: spatial resolution a convolution of the generation volume and carrier movement before recombination, better than 50 nm in bulk-like nitrides, LED and laser diode structures (fetch-tool summary); Photoluminescence Spectrometer page of this vault.

Ques: How is CL light collected, and how efficient is it?

With a mirror or an integrated objective. Conventional systems place a parabolic or elliptic mirror above the sample, which Corfdir et al. note has a field of view of only several micrometres. The Attolight design embeds an achromatic optical microscope of NA 0.72 inside the SEM objective lens, collecting up to 100 times more light over a 300 $\mu \mathrm{m}$ field, with photomultiplier detection. An NA of 0.72 accepts a 46.1 degree cone, 15.3 per cent of light from an isotropic emitter in air (computed); refraction at the semiconductor surface traps most internally generated light, so absolute efficiencies are lower still. Hyperspectral modes record a full spectrum at each pixel. Reference: P. Corfdir, O. Gougeon, S. Sonderegger and J.-D. Ganiere, ‘Quantitative Cathodoluminescence Opens New Areas of Investigation in Semiconductor Research and Production’, Microscopy Today, January 2013 (fetch-tool summary).

Ques: Does CL dislocation counting work above or below $1\times 10^9$ per square centimetre?

Attolight’s page says conventional CL gives accurate densities for values exceeding $1\times 10^9$ $\mathrm{c}{\mathrm{m}}^{-2}$, while Corfdir et al. count a GaN template with about $3\times 10^7$ $\mathrm{c}{\mathrm{m}}^{-2}$. Counting requires dark spots to be resolved: at $3\times 10^7$ $\mathrm{c}{\mathrm{m}}^{-2}$ they are 1.83 $\mu \mathrm{m}$ apart on average, but at $1\times 10^9$ $\mathrm{c}{\mathrm{m}}^{-2}$ only 316 $\mathrm{nm}$ apart (computed), comparable to the dark-zone width of over 100 $\mathrm{nm}$ that piezoelectric fields create around edge dislocations (PDI). Spots begin to overlap above about $1\times 10^9$ $\mathrm{c}{\mathrm{m}}^{-2}$, so the more likely meaning is that CL is accurate up to about $1\times 10^9$ $\mathrm{c}{\mathrm{m}}^{-2}$, and the extracted wording ‘exceeding’ is a garbled ‘not exceeding’ or ‘up to’ (my reading). Reference: Attolight, ‘Dislocation type determination by cathodoluminescence’ application page (fetch-tool summary); P. Corfdir, O. Gougeon, S. Sonderegger and J.-D. Ganiere, ‘Quantitative Cathodoluminescence Opens New Areas of Investigation in Semiconductor Research and Production’, Microscopy Today, January 2013 (fetch-tool summary); Paul-Drude-Institut, ‘Can we determine the carrier diffusion length in GaN from cathodoluminescence maps around threading dislocations?’ scientific highlight, after Kaganer et al., Phys. Rev. Appl. 12, 054038 (2019) (fetch-tool summary).

Ques: Can the diffusion length be read from the dark zone around a dislocation?

Not reliably, according to the Paul-Drude-Institut. The common approach fits the intensity profile around a dislocation, often with a phenomenological exponential, and takes its width as the diffusion length; Kaganer et al. found this leads to a gross underestimation. Their simulations show that the dark zone is dominated by the piezoelectric field around the dislocation outcrop, which separates electrons and holes over more than 100 $\mathrm{nm}$, while diffusion has only a marginal effect. Experimentally, intensity profiles from 10 to 200 $\mathrm{K}$ barely changed although the diffusion length does change with temperature. Instead, the energy shift of the CL peak around the dislocation turns out to be highly sensitive to diffusion length, and they propose it as the observable to use. Reference: Paul-Drude-Institut, ‘Can we determine the carrier diffusion length in GaN from cathodoluminescence maps around threading dislocations?’ scientific highlight, after Kaganer et al., Phys. Rev. Appl. 12, 054038 (2019) (fetch-tool summary).

Ques: How does CL distinguish screw from edge dislocations?

By combining intensity and peak-energy maps. All threading dislocations in GaN appear dark because non-radiative recombination increases near their cores, so darkness alone cannot tell screw dislocations from edge or mixed ones (Attolight). Edge and mixed dislocations, with Burgers vectors containing an $\mathbf{a}$ component, distort the lattice in the plane and create strain and piezoelectric fields that shift the emission energy nearby, while pure screw dislocations, with $\mathbf{b}=m\mathbf{c}$, produce little such shift (Attolight; PDI; mechanism as my reading). Mapping both intensity and centre energy therefore identifies pure screw dislocations in one non-destructive step. This matters because pure screw dislocations are suspected leakage paths in GaN devices (Attolight). Reference: Attolight, ‘Dislocation type determination by cathodoluminescence’ application page (fetch-tool summary); Paul-Drude-Institut, ‘Can we determine the carrier diffusion length in GaN from cathodoluminescence maps around threading dislocations?’ scientific highlight, after Kaganer et al., Phys. Rev. Appl. 12, 054038 (2019) (fetch-tool summary).

Ques: What does time-resolved CL measure?

The radiative and non-radiative lifetimes at each point. Picosecond electron pulses excite the sample, and photon arrival times give decays with better than 10 $\mathrm{ps}$ resolution, without degrading spatial resolution (Corfdir et al.). The measured lifetime combines the two channels, $1/\tau =1/{\tau }_r+1/{\tau }_{nr}$, and the internal efficiency is $\tau /{\tau }_r$ (Feix et al.); with assumed 1 $\mathrm{ns}$ radiative and 0.5 $\mathrm{ns}$ non-radiative lifetimes, the decay is 0.33 $\mathrm{ns}$ and the efficiency 33 per cent (computed). Corfdir et al. note that the intensity immediately after the pulse is inversely proportional to the radiative lifetime, which separates the two. In a bent ZnO nanobelt, they found that dimming came from a shorter non-radiative lifetime while the radiative lifetime stayed constant. Reference: P. Corfdir, O. Gougeon, S. Sonderegger and J.-D. Ganiere, ‘Quantitative Cathodoluminescence Opens New Areas of Investigation in Semiconductor Research and Production’, Microscopy Today, January 2013 (fetch-tool summary); F. Feix et al., ‘Ga-polar (In,Ga)N/GaN quantum wells vs. N-polar (In,Ga)N quantum disks in GaN nanowires…’, arXiv:1703.06715: 1/tau_eff = 1/tau_r + 1/tau_nr, eta = tau_eff/tau_r, tau_r from the inverse peak intensity just after the pulse (fetch-tool summary).

Ques: How does CL reveal strain and why cool the sample?

Strain shifts the band gap, so emission peaks move, and cooling sharpens them. Corfdir et al. observed a peak shift of about 2 $\mathrm{nm}$ along a ZnO nanobelt at 30 $\mathrm{K}$, about 18 $\mathrm{meV}$ near 368 $\mathrm{nm}$ (computed), indicating local strain. Their cryogenic stage runs from 15 to 300 $\mathrm{K}$, and PDI recorded hyperspectral maps from 10 to 200 $\mathrm{K}$. Cooling narrows lines and shifts them to higher energy: with Nepal’s Varshni parameters for GaN, from the Photoluminescence Spectrometer page, the gap rises by 77 $\mathrm{meV}$ from 300 to 15 $\mathrm{K}$ (computed). Low temperatures also slow non-radiative recombination, raising signal. Peak-energy maps then show strain, composition and, around dislocations, piezoelectric fields. Reference: P. Corfdir, O. Gougeon, S. Sonderegger and J.-D. Ganiere, ‘Quantitative Cathodoluminescence Opens New Areas of Investigation in Semiconductor Research and Production’, Microscopy Today, January 2013 (fetch-tool summary); Paul-Drude-Institut, ‘Can we determine the carrier diffusion length in GaN from cathodoluminescence maps around threading dislocations?’ scientific highlight, after Kaganer et al., Phys. Rev. Appl. 12, 054038 (2019) (fetch-tool summary); Photoluminescence Spectrometer page of this vault.

References

1. P. Corfdir, O. Gougeon, S. Sonderegger and J.-D. Ganiere, “Quantitative Cathodoluminescence Opens New Areas of Investigation in Semiconductor Research and Production,” Microscopy Today, Jan. 2013, doi: 10.1017/S1551929512000983. Available: https://doc.rero.ch/record/289889/files/S1551929512000983.pdf
2. Gatan, “High spatial resolution cathodoluminescence.” Available: https://gatan.com/node/1643
3. F. Feix et al., “Ga-polar (In,Ga)N/GaN quantum wells vs. N-polar (In,Ga)N quantum disks in GaN nanowires: comparative analysis of carrier recombination, diffusion, and radiative efficiency,” arXiv:1703.06715. Available: https://arxiv.org/abs/1703.06715
4. Photoluminescence Spectrometer, page in this vault.
5. Attolight, “Dislocation type determination by cathodoluminescence,” application page. Available: https://attolight.com/applications/dislocation-type-determination-by-cathodoluminescence
6. Paul-Drude-Institut fur Festkorperelektronik, “Can we determine the carrier diffusion length in GaN from cathodoluminescence maps around threading dislocations?” scientific highlight (after V. M. Kaganer et al., Physical Review Applied, vol. 12, 054038, 2019). Available: https://www.pdi-berlin.de/science/scientific-highlights/can-we-determine-the-carrier-diffusion-length-in-gan-from-cathodoluminescence-maps-around-threading-dislocations

Related pages in this vault: Scanning Electron Microscope (SEM), Photoluminescence Spectrometer, EBIC and EBAC, Transmission Electron Microscope (TEM and STEM), X-Ray Topography, Electron Backscatter Diffraction (EBSD), CD-SEM, Light Emitting Diode (Homojunction and Heterojunction LED), Quantum Well LED (InGaN-GaN and AlGaInP), Electron-Matter Interaction.