Plasmonic properties of refractory titanium nitride

The development of plasmonic and metamaterial devices requires the research of high-performance materials alternative to standard noble metals. Renewed as a refractory stable compound for durable coatings, titanium nitride has recently been proposed as an efficient plasmonic material. Here, by using a first-principles approach, we investigate the plasmon dispersion relations of TiN bulk and we predict the effect of pressure on its optoelectronic properties. Our results explain the main features of TiN in the visible range and prove a universal scaling law which relates its mechanical and plasmonic properties as a function of pressure. Finally, we address the formation and stability of surface-plasmon polaritons at different TiN-dielectric interfaces proposed by recent experiments. The unusual combination of plasmonics and refractory features paves the way for the realization of plasmonic devices able to work at conditions not sustainable by the usual noble metals.

Figure 1

Electronic and optical properties of TiN bulk at equilibrium (NaCl structure, $P=0$ Mbar). (a) Band structure. (b) Total (black area), Ti- (orange dashed line) and N-projected (blue straight line) DOS. (c) Real (${\epsilon }_1$, black straight line) and imaginary (${\epsilon }_2$, red dashed line) components of the dielectric function. Inset shows the simulated color; the corresponding RGB code is also indicated. (d) Reflectivity (R, black straight line) and transmissivity (T, red dashed line) spectra. The zero-energy reference in panels (a) and (b) is set to the Fermi level (${\mathrm{E}}_F$, dashed line). Horizontal straight (dashed) line in panel (c) identifies the values for which ${\epsilon }_1$ is zero (minus one), respectively. Vertical lines in panel (d) indicate the visible range.

Figure 2

Simulated loss function for TiN bulk at increased transferred momentum $\left|\mathbf{q}\right|$ in units of $2\pi /a_0$. Dot-dashed line follows the low-energy single-particle (el-h) contribution at increasing $\left|\mathbf{q}\right|$. Two sets of experimental EELS spectra (gray curves) are superimposed for comparison. Experimental set 1 is adapted from Ref. [59], and set 2 is from Ref. [58].

Figure 3

Plasmon energy $E_p\left(q\right)$ dispersion relations. Red circles are the calculated lowest-energy plasmon resonances $E_p$ of Fig. 2, and black dashed line is the corresponding fit from Eq. (3). ${\epsilon }_F$ and ${\mathrm{k}}_F$ are the Fermi energy and the Fermi momentum in the free-electron model. $q_c^{\prime }$ (black) and $q_c$ (red) are the theoretical and simulated critical momenta, respectively. Gray shaded area covers the range of allowed single-particle excitations.

Figure 4

(a) Loss function spectra for $q=0$ and (b) plasmon energy $E_p\left(q\right)$ dispersion for TiN bulk under pressure ($B_1$ phase). Color-pressure code is reported in panel (b). (c) Bulk modulus $B_0$ plotted against plasmon energy $E_p$ at increasing pressure and zero momentum transfer.

Figure 5

TiN bulk in $B_2$ phase. (a) Total (black area), Ti- (shaded orange area), and N-projected (straight line) DOS. Inset shows the simulated color, the corresponding RGB code is also indicated. The zero energy reference is set to the Fermi level ($E_F$, dashed line). (b) Loss function as a function at increased transferred momentum $\left|\mathbf{q}\right|$ in units of $2\pi /a_0$.

Figure 6

TiN surfaces. (a) Total (black area), Ti- (shaded orange area) and N-projected (straight line) DOS. The zero-energy reference is set to the Fermi level ($E_F$, black line).

Figure 7

SPP dispersion relation at TiN-dielectric interfaces. Dashed lines are the dispersion relations for light in the corresponding dielectrics.