Ultrahigh exciton diffusion in intrinsic diamond

We observe exceptionally high diffusion of excitons in diamond using time-resolved photoluminescence imaging. The diffusivity is found to increase with decreasing temperature more rapidly than well-established predictions. The highest diffusion constant, $9.2\times {10}^3{\mathrm{cm}}^2/\text{s}$, measured for thermalized excitons is 150 times that recorded previously in diamond. We elucidate the momentum relaxation mechanisms determining transport: intraband and interband scattering by acoustic phonons in the exciton fine-structure levels. The enhanced diffusivity above 100 K is explained by a free-carrier contribution.

Figure 1

Schematic of (a) exciton energy dispersion and relaxation by phonon emission, and (b) PL line shapes for different exciton effective temperatures $T_{\text{ex}}$. $T^{*}$ indicates the characteristic temperature for longitudinal acoustic phonons. Exciton masses $m_2=0.65m_0, m_3=1.05m_0$, and $m_4=0.76m_0$ [27], where $m_0$ is the free-electron mass, are used. (c) Occupancy of the fine-structure levels. The dots were derived from the spectral weights, and solid lines represent $f_i=exp(-\mathrm{\Delta }{E}_i/k_{B}T)$ normalized to the sum ${\sum }_{i=2,3,4}{f}_i$, where $\mathrm{\Delta }{E}_2=3.6$ meV, $\mathrm{\Delta }{E}_3=6.7$ meV, and $\mathrm{\Delta }{E}_4=13.6$ meV [26].

Figure 2

(a) Time-resolved PL image obtained at 7 K for different delay times: 0, 8, and 15 ns. The gate width was 1 ns. The area of each image is $1.0\times 1.0{\mathrm{mm}}^2$. (b) Spectrally resolved PL image at 20 K for 0, 30, 60, and 100 ns. The gate width was 10 ns. (c) Vertical profiles of the images at 20 K. (d) Time-resolved PL spectra at 20 K, normalized at Ex2.

Figure 3

Plots of ${\mathrm{\Delta }}^2$ as a function of delay time for temperatures (a) above 100 K and (b) below 60 K. The initial width at $t=0$ has been subtracted. A detection window corresponding to (a) $60\mu \mathrm{m}$ or (b) $1800\mu \mathrm{m}$ width on the sample was used.

Figure 4

Measured diffusion constants (squares) in comparison with the calculated ones. The dashed double-dotted line and thin solid lines represent intraband scattering of electrons [23] and excitons, respectively. The dashed and thick solid lines indicate weighted averages for the intraband and the intraband plus interband, respectively. The dashed-dotted line includes exciton ionization assuming a total carrier density $n_t=1.0\times {10}^{17}{\mathrm{cm}}^{-3}$. The inset shows a fraction of excitons to $n_t={10}^{15–17}{\mathrm{cm}}^{-3}$, calculated according to the mass-action law with an equilibrium constant of $1.2\times {10}^{16}{\mathrm{cm}}^{-3}$ at 300 K [41].