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Color of TiN and ZrN from first-principles calculations
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Image of FIG. 1.
FIG. 1.

(Color online) CIE RGB color matching functions used in this study; red (solid line), green (dashed line), and blue (dotted line) fractions in monochromatic light as announced by CIE in 1931.18,19

Image of FIG. 2.
FIG. 2.

(Color online) Calculated band structures of TiN (black solid line) and ZrN (red dashed line). The Fermi level is set at 0 eV.

Image of FIG. 3.
FIG. 3.

(Color online) Calculated dielectric functions of (a) TiN and (b) ZrN. Upper panel, imaginary part; lower panel, real part. Contribution of intraband (red dashed line) and interband (blue dotted line) transitions to the total dielectric function (solid line) was also plotted separately. The bare plasma frequency, (7.62 eV for TiN; 8.82 eV for ZrN) is shifted to the screened plasma frequency, (2.41 eV for TiN; 3.06 eV for ZrN) when the effect of interband transition () is added. Calculated reflectivity (R, solid line) and absorption (L, dotted line) spectra are shown in (c) for TiN and (d) for ZrN. Again, the contribution from the intraband transition is separately plotted (Rintra, red dashed line; Lintra, red dotted-dashed line). Computer-generated colors from our calculations and experiment (Ref. 2 for TiN and Ref. 3 for ZrN) are drawn for comparison as inset.

Image of FIG. 4.
FIG. 4.

(Color online) (a) Calculated plasma frequencies (upper panel) and the Fermi level shift (lower panel) of TiN (black solid line) and ZrN (red dashed line) upon substitutional doping within the rigid band approximation. Experimental data for TiCxNy with are also plotted with empty5 and filled28 circles. The doping level is given in unit of electron per unit formula. (b) Imaginary (upper panel) and real part (lower panel) of dielectric function due to interband transition of TiN for three different carrier densities (solid line, neutral; dashed line, +0.5 electron/formula unit; dotted line, −0.7 electron/formula unit) as controlled by substitutional doping of non-metal atoms.

Image of FIG. 5.
FIG. 5.

(Color online) Calculated reflectivity of TiN upon electron doping. The doping level is from −0.7 to +0.5 electron per formula unit (TiN) with an increment of 0.1 electron per formula unit. The plasma frequency and the Fermi level were obtained by using the rigid band model. Color variation for corresponding reflectivity is shown in the boxes at the top. We observe that electron-poor TiN becomes darker whereas electron-rich TiN becomes brighter and more yellowish. The reflectivity and color of ZrN is also shown.

Image of FIG. 6.
FIG. 6.

(Color online) Reflectivity of TiN (also ZrN in the inset) with respect to inverse relaxation time (eV). Corresponding color change is shown in the boxes in the bottom. When is changed, the color looks almost the same but the chroma does change significantly.


Generic image for table
Table I.

Calculated bare () and screened () plasma frequencies for TiN and ZrN. The screened plasma frequency determined at absorption maxima is given in the parenthesis with *. The inverse of relaxation time () in our calculations, which is adopted from Ref. 1, is also given. Experimental values are given for comparison. Calculated and measured CIE color space coordinates (L*a*b*) for the two compounds are shown.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Color of TiN and ZrN from first-principles calculations