E18 · Electron excitations

Cathodoluminescence: Where Light Is Born

Scan a synthetic semiconductor. Follow carrier diffusion, radiative emission and nonradiative capture, then select a region in the recorded wavelength cube. Compare spectral windows with total brightness.

Recorded region photons $\text{—}$

Recorded defect-window photons $\text{—}$

Defect-window share of counts $\text{—}$

Model mean residence time $\text{—}$

Assumed generation footprint FWHM $\text{—}$

Specified band emission wavelength $\text{—}$

Raster acquisition time $\text{—}$

Selected stored pixels $\text{—}$

Experiment target $\text{—}$

Predict · acquire · explain

Does a dark spot mean the beam generated fewer carriers?

Landing energy

E_0

5\,\mathrm{keV}

Incident beam current

I

10\,\mathrm{pA}

Dwell per scan pixel

t_d

0.005\,\mathrm{s}

Specified temperature

T

100\,\mathrm{K}

Nominal bulk diffusion length

L_0

0.15\,\mathrm{\mu m}

Extra nonradiative rate in domain

\Gamma_q

1\,\mathrm{\frac{1}{ns}}

Optical collection solid angle

\Omega

0.8\,\mathrm{sr}

Region center: horizontal

x

0.8\,\mathrm{\mu m}

Region center: vertical

y

0\,\mathrm{\mu m}

Region radius

r

0.3\,\mathrm{\mu m}

Target: collect at least 500 defect-window photons from a region contained inside the specified domain. Keep temperature at or below 150 K, nominal diffusion length at or below 0.2 micrometers, landing energy at or below 8 keV and additional nonradiative rate at or below 2 per ns.

Projected, linear, steady-state teaching model on a 4 micrometer square, 20 by 20 reflecting grid. A specified circular defect domain adds radiative and nonradiative rates. All material energies, lifetimes, yields and their temperature dependence are assumed; no real semiconductor is identified. A normalized Gaussian generation footprint broadens with landing energy; this is not an electron transport calculation. A finite-volume diffusion equation conserves generated carriers across both recombination channels. Emitted energy-domain Gaussian lines are integrated through wavelength-bin boundaries; photon collection assumes isotropic escape, 40 percent efficiency and no reabsorption. Each pixel stores a seeded count spectrum, with a normal counting approximation above 40 expected counts. Fixed windows may lose a shifting peak; independent log colors are not absolute concentrations. ROI and profiles reuse acquired counts. Lifetime is a forward-model diagnostic, not a measured time-resolved lifetime. No saturation, charging, damage, optical interference, depth transport or calibrated diffusion-length inversion. Specimen and carrier paths in 3D are enlarged and schematic.

Physics tutorial

Cathodoluminescence: Where Light Is Born

BackgroundScan a synthetic semiconductor. Follow carrier diffusion, radiative emission and nonradiative capture, then select a region in the recorded wavelength cube. Compare spectral windows with total brightness.

Why it mattersTarget: collect at least 500 defect-window photons from a region contained inside the specified domain. Keep temperature at or below 150 K, nominal diffusion length at or below 0.2 micrometers, landing energy at or below 8 keV and additional nonradiative rate at or below 2 per ns.

Start with the essentials

Focus question: Does a dark spot mean the beam generated fewer carriers?
One-sentence intuition: Brightness combines generation, carrier migration, competing recombination and collection. A photon map locates where the beam excited the sample; it does not directly locate every emitting carrier.

Core mathematical model

Carrier continuity

-D\nabla^2n+(\Gamma_b+\Gamma_d+\Gamma_{nr})n=G

The steady transport solution partitions every generated carrier among competing recombination channels.

Photon spectrum

\mu_j=\frac{\eta\Omega}{4\pi}\int_{\lambda_j^-}^{\lambda_j^+}S_E\!\left(\frac{hc}{\lambda}\right)\frac{hc}{\lambda^2}\,d\lambda

The wavelength Jacobian and bin integrals connect the energy-domain lines to recorded photons.

Migration scale

L=\sqrt{D/\Gamma_{bulk}}

The nominal control sets diffusivity with a one-nanosecond reference lifetime. Actual competing rates vary in the domain.

Common difficulties

Read the measurement boundary

Typical misconceptionA brighter or cleaner plot guarantees a more local measurement.

Better mental modelBrightness combines generation, carrier migration, competing recombination and collection. A photon map locates where the beam excited the sample; it does not directly locate every emitting carrier.

Run the experiment

01
Predict the dark domain
Compare the local-domain and nonradiative-capture presets at the same beam current.
What to observe: Generation is unchanged, but fewer carriers leave through radiative channels.
02
Track carrier migration
Increase the nominal diffusion length. Compare the known domain with the recorded central profile.
What to observe: Counts are indexed by excitation position; carriers can travel before emitting.
03
Use the stored cube
Move the selected region to the matrix and back, then reach the target. Try heating before interpreting a fixed window.
What to observe: Region extraction does not reacquire photons. A shifting peak changes a fixed-window map.