Intervalence plasmons in boron-doped diamond

Abstract

Doped semiconductors can exhibit metallic-like properties ranging from superconductivity to tunable localized surface plasmon resonances. Diamond is a wide-bandgap semiconductor that is rendered electronically active by incorporating a hole dopant, boron. While the effects of boron doping on the electronic band structure of diamond are well-studied, any link between charge carriers and plasmons has never been shown. Here, we report intervalence plasmons in boron-doped diamond, defined as collective electronic excitations between the valence subbands, opened up by the presence of holes. Evidence for these low-energy excitations is provided by valence electron energy loss spectroscopy and near-field infrared spectroscopy. The measured spectra are subsequently reproduced by first-principles calculations based on the contribution of intervalence band transitions to the dielectric function. Our calculations also reveal that the real part of the dielectric function exhibits a crossover characteristic of metallicity. These results suggest a new mechanism for inducing plasmon-like behavior in doped semiconductors, and the possibility of attaining such properties in diamond, a key emerging material for quantum information technologies.

Fig. 1. IVB transitions in diamond enabled by boron-doping.

Calculated band structures of intrinsic diamond (a) and BDD (b), showing the valence band (green), the conduction band (light blue), and the acceptor energy state (E_a) introduced by boron doping of diamond at ca. 0.37 eV (dark blue). Electrons in the top of the valence band move to the boron acceptor state, resulting in empty states that open up IVB transitions (inset, b). c Schematic of STEM-VEELS (left) and near-field IR spectroscopy (right) showing two different experimental approaches to probing the contribution of IVB transitions to the dielectric function of BDD using either an electron beam or a tip-enhanced mid-infrared (MIR) laser.

Fig. 2. Effects of boron doping on the vibrational properties of diamond.

a Micro Raman spectra obtained from BDD and undoped diamond (left) showing the ZCP at ca. 1332 cm⁻¹. The spectrum for BDD has an asymmetric Fano lineshape (right) caused by the interference of the ZCP with electronic states created by hole doping which can be modeled as an electronic continuum (EC) that, along with phononic contributions, gives rise to this characteristic lineshape (Supplementary Note 2). b First-principles calculation of the phonon density-of-states (PDoS) of BDD for an equivalent boron concentration of ~2300 ppm, and intrinsic diamond.

Fig. 3. VEELS characterization of BDD.

a Analysis of representative VEEL spectra measured from a 1 × 1 nm region of BDD (top) and undoped diamond (bottom) by fitting the ZLP to a vacuum spectrum and thereby isolating an inelastic signal at roughly 0.15 eV that only appears for BDD. The total fit, i.e., the sum of the vacuum and the inelastic contributions, agrees well with the raw spectrum. All spectra are normalized to the maximum intensity of the ZLP. b Annular dark field (ADF)-STEM image of a section of a BDD particle (top left) and undoped diamond particle (top right), and false color maps showing the spatial variation of the normalized inelastic VEEL signal across BDD (bottom left) and undoped diamond (bottom right) at an energy slice of 0.15 eV. All scale bars equal 10 nm.

Fig. 4. Near-field infrared spectroscopic characterization of BDD.

a Representative photo-induced force microscopy (PiFM) spectra collected from BDD and undoped diamond. b–g Representative s-SNOM images collected from BDD and undoped diamond: atomic force microscopy (AFM) topography images (b) and (c), respectively, amplitude, $s\left(\omega \right)$, (d) and (e), respectively, and phase, $\phi \left(\omega \right),$ (f) and (g), respectively. Laser energy was 1048 cm⁻¹ (~0.13 eV), corresponding to the resonance observed in (a). The amplitude and phase signals correspond to the second harmonic of the tip oscillation frequency and were normalized with reference to the Si substrate. All lateral scale bars correspond to 1 µm.

Fig. 5. First-principles model of dielectric function for BDD based on IVB transitions.

Illustration of the Fermi level shift which is modeled as an effective Fermi level that starts at the top of the valence band for intrinsic diamond, and is lowered as a result of boron doping which introduces carriers in the form of holes (a), and calculated results for the Fermi energy shift as a function of hole density, n_H which follows a $\mathrm{\Delta }{\epsilon }_F\propto n_H^{2/3}$ trend, as expected from a parabolic energy dispersion in three dimensions (b). c Simulated valence electron energy-loss (VEEL) spectra (left) and simulated infrared absorption coefficients (right) as a function of hole density. The dashed lines indicate the shift in the peak energies. d Intervalence plasmon frequency calculated from the loss function as a function of hole density, and e full-width at half-maximum (FWHM) of the loss-function peak (c, left) as a function of hole density.