Photon Bunching in Cathodoluminescence

We have measured the second order correlation function [$g^{(2)}(\tau )$] of the cathodoluminescence intensity resulting from the excitation by fast electrons of defect centers in wide band-gap semiconductor nanocrystals of diamond and hexagonal boron nitride. We show that the cathodoluminescence second order correlation function $g^{(2)}(\tau )$ of multiple defect centers is dominated by a large, nanosecond zero-delay bunching ($g^{(2)}(0)>30$), in stark contrast to their flat photoluminescence $g^{(2)}(\tau )$ function. We have developed a model showing that this bunching can be attributed to the synchronized emission from several defect centers excited by the same electron through the deexcitation of a bulk plasmon into few electron-hole pairs.

Figure 1

CL-STEM setup. (a) A parabolic mirror ($M$) with a high numerical aperture has been incorporated inside the STEM to collect the CL signal efficiently, forming a collimated beam which is then coupled to a multimode optical fiber (OF). The fiber output beam is sent either to an imaging spectrograph to record the emission spectrum for each pixel, or to a Hanbury Brown–Twiss interferometer for $g_{\mathrm{CL}}^{(2)}(\tau )$ measurement shown in (b). Annular dark field (ADF) detector, sample (S), scanning coils (SC), electron gun (EG). (c) Simultaneously recorded ADF image (left) and filtered CL maps (right) of the nanodiamond studied in Fig. 2 (scale bar 50 nm).

Figure 2

$g_{\mathrm{CL}}^{(2)}(\tau )$ measurement (continuous lines) for intensities $I$ ranging from 1.2 to 11 pA for an invidividual ND, 60 nm thick. Each measurement lasted 5–20 min. The data were fitted with the Monte Carlo simulations explained in the text (dashed line). The lifetime ${\tau }_{\mathrm{NV}}$ was retrieved using an exponential fit of the bunching curves, leading to ${\tau }_{\mathrm{NV}}\approx 26\pm 1\mathrm{ns}$. All the parameters of the Monte Carlo simulation were kept fixed except the current, which was changed until a good agreement between the experiment and the simulation was found. The resulting fitted currents are written in parenthesis next to the measured experimental values. Inset, left: PL $g_{PL}^{(2)}(\tau )$ measurements performed at two different laser excitation powers on another ND from the same batch. Inset, right: $g_{\mathrm{CL}}^{(2)}(\tau )$ measurement and Monte Carlo simulation for defect centers in $h\text{−}\mathrm{BN}$.

Figure 3

$g_{\mathrm{CL}}^{(2)}(0)$ calculated from Monte Carlo simulations within the two different models for the decay mechanism (see text) compared to experimental data points extracted from Fig. 2. For all the simulations, all parameters are fixed except the current. Error bars in the simulations are generated by introducing a $\pm 1\mathrm{ns}$ error in the estimate of ${\tau }_e$ and a very conservative $\pm 10\%$ error on $L/{\lambda }_e$. The bunching effect is qualitatively reproduced by both models.

Figure 4

Simulation for a ND with $L=30\mathrm{nm}$ and ${\tau }_e=20\mathrm{ns}$. For $N=1$ the $g_{\mathrm{CL}}^{(2)}(\tau )$ is independent of the probe current. For $N>1$ (here $N=2$) the expected antibunching behavior is retrieved at high current but not at low current.