Surface recombination and out-of-plane diffusivity of free excitons in hexagonal boron nitride

We present an experimental protocol using cathodoluminescence measurements as a function of the electron incident energy to study both exciton diffusion in a directional way and surface exciton recombination. Our approach overcomes the challenges of anisotropic diffusion and the limited applicability of existing methods to the bulk counterparts of two-dimensional (2D) materials. The protocol is then applied at room and at cryogenic temperatures to four bulk hexagonal boron nitride crystals grown by different synthesis routes. The exciton diffusivity depends on the sample quality but not on the temperature, indicating it is limited by defect scattering even in the best quality crystals. The lower limit for the diffusivity by phonon scattering is 0.2 ${\mathrm{cm}}^2{\mathrm{s}}^{-1}$. Diffusion lengths were as much as 570 nm. Finally, the surface recombination velocity exceeds ${10}^5{\mathrm{cm}}^2{\mathrm{s}}^{-1}$, at a level similar to silicon or diamond. This result reveals that surface recombination could strongly limit light-emitting devices based on 2D materials.

Figure 1

Scheme of the CL experiment in a 1D geometry to analyze the out-of-plane exciton diffusion in the bulk crystal and the recombination properties of the surface.

Figure 2

(a) Generation profile for a 5-kV incident electron beam in hBN calculated by MC simulations (in black) and its square approximation (in red). Both profiles share the same mean excitation depth $\langle z_e\rangle$ calculated by MC simulation. (b) $I/I_0$ as a function of $\langle z_e\rangle$ for a steady excitation inside the crystal. The results are obtained either numerically with discrete generation profiles from MC simulations (cross) or analytically with Eq. (8) considering the square profile.

Figure 3

(a) CL intensity $I/I_0$ as a function of the acceleration voltage and the corresponding mean excitation depth $\langle z_e\rangle$ (see Appendix pp1). The analytical equation, Eq. (8), is depicted for a diffusion length $L$ of 92 nm and various values of the parameter $a$. (b) Temporal decay of the free-exciton luminescence filtered at 215 $\pm$ 7.5 nm measured in the same area after the interruption of a 15-kV electron beam. The bulk lifetime of the free exciton $\tau$ is determined by fitting the data with an asymptote.

Figure 4

(a) $I/I_0$ as function of the mean excitation depth $\langle z_e\rangle$, and (b) temporal decays of the free-exciton luminescence after interruption of a 15-kV steady excitation at $t=0$, recorded on HPHT1, HPHT2, APHT, and PDC samples. The out-of-plane diffusion length $L$ is deduced by fitting Eq. (8) in (a), while the bulk exciton lifetime $\tau$ is measured by time-resolved CL in (b). (c) Diffusivity as function of the exciton lifetime $\tau$ for the four samples. Note that $\tau$ is used to quantitatively compare the global quality of the samples.

Figure 5

(a) $I/I_0$ as function of the mean excitation depth $\langle z_e\rangle$ during continuous excitation and (b) temporal decays of the free-exciton luminescence after interruption of the 15-kV electron beam, recorded on the HPHT1 sample at 6 and 300 K. The best fit plots in (a) are obtained with $a=-1$ and the $L$ values indicated on the graph.

Figure 6

Generation rate $g\left(z\right)$ as a function of depth $z$, in hBN (a) and wGaN (b). They were calculated by Monte Carlo simulations for different acceleration voltages $V$ of the incident electron beam. (c) Mean excitation depth $\langle z_e\rangle$ as a function of acceleration voltage $V$ extracted from the $g$(z) profiles shown in (a). The results are fitted by power laws

Figure 7

$I/I_0$ as a function of $\langle z_e\rangle /L$. The results are obtained numerically using the generation profiles from the Monte Carlo simulations (cross) on hBN and GaN, and analytically with the square generation profile approximation [see Fig. 2].

Figure 8

Spectra acquired on HPHT2 sample at 300 K for different acceleration voltages and with a constant excitation power of $1\mu \mathrm{W}$.