Isotope composition dependence of the band-gap energy in diamond

We present experimental results on the band-gap energies of homoepitaxial diamond films with isotopic compositions ranging from nearly pure carbon-12 (${}^{12}$C) to nearly pure carbon-13 (${}^{13}$C). Diamond crystals were grown by microwave plasma-assisted chemical vapor deposition, which controls the isotope composition and minimizes the density of impurities and defects. We find that the isotope substitution of ${}^{12}$C by ${}^{13}$C increases the band-gap energy in diamond by up to 15.4 meV at 79 K. The increase at room temperature is estimated from the temperature dependence of the band-gap renormalization due to electron-phonon interaction and is found to be even larger than that at low temperatures. These results unambiguously demonstrate the possibility of band-gap engineering of diamond via control of the isotopic composition.

Figure 1

Luminescence spectra of free excitons in homoepitaxial diamond films grown from mixture of methane in hydrogen by means of a microwave plasma-assisted CVD. The spectra illustrate the effects of isotope composition ${}^{12}$C${}_{1-x}$${}^{13}$C${}_x$ ($x$ $=$ 0.001, 0.247, 0.494, 0.740, and 0.987) mixed in the CVD gas phase. All spectra are normalized to the same height.

Figure 2

First-order Raman spectra obtained from the samples used in the CL measurement (Fig. 1). The inset displays the first-order Raman peak shift as a function of ${}^{13}$C concentration ($x$) in gas. The solid line represents a prediction of the harmonic approximations. The dashed line corresponds to the polynomial of Eq. (2).

Figure 3

Excitonic band-gap energy $E_{\mathrm{ex}}$ obtained for the CL peak energies in Fig. 1 as a function of the ${}^{13}$C concentration of the films ($x_f$). The actual ${}^{13}$C content of the films was calculated from the peak position of the first-order Raman spectrum. The solid line is a linear regression fit of the data.

Figure 4

TO phonon energy obtained from density functional perturbation theory, including the isotope disorder effect. The dashed line is a harmonic approximation calculation.