1887
banner image
No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
Infrared dielectric anisotropy and phonon modes of rutile TiO2
Rent:
Rent this article for
USD
10.1063/1.4802715
/content/aip/journal/jap/113/16/10.1063/1.4802715
http://aip.metastore.ingenta.com/content/aip/journal/jap/113/16/10.1063/1.4802715

Figures

Image of FIG. 1.
FIG. 1.

Experimental (symbols) and best-match model calculated data (solid lines) of the ellipsometric parameters and for c-plane rutile TiO2. Very good agreement between experimental and best-match model calculated data was achieved by applying the factorized MDF in Eq. (12) . The energetic position of transverse and longitudinal phonon modes of Eu - and -symmetry is indicated by brackets (solid brackets: TO phonons; dashed brackets: LO phonons). Two additional modes needed to be included for each component of the dielectric function tensor in order to achieve the excellent match between experimental and model data in the spectral range between 500 cm−1 and 800 cm−1. Their energetic position is indicated by arrows (solid arrows: additional modes in ; dotted arrows: additional modes in ). and approach unity at different energies above the reststrahlen bands. The loss in p- and s-reflectivity causes the derivative-like structure in near 900 cm−1. Note the nearly indistinguishable overlap of the experimental data points determined on the custom-built far-IR ellipsometer and the commercial mid-IR ellipsometer in the spectral range between 300 cm−1 and 650 cm−1.

Image of FIG. 2.
FIG. 2.

Calculated bands of total reflection for p- (a) and s-polarized light (b) for c-plane rutile TiO2 as a function of (hatched areas). The data in (b) are also representing the bands of total reflection of s-polarized light for an a-plane sample with and of p-polarized light for an a-plane sample with .

Image of FIG. 3.
FIG. 3.

Same as Fig. 2 for a-plane rutile TiO2 as a function of (hatched areas). (rp at and rs at ). The bands of total reflection for rs at and rp at are identical to those of rs in Fig. 2(b) .

Image of FIG. 4.
FIG. 4.

Calculated p- (solid) and s-polarized light reflection coefficients (dotted lines) at an angle of incidence of 72° for high-symmetry orientations of rutile TiO2: (a) c-plane, (b) a-plane, , (c) a-plane, . The data were calculated by using the dielectric functions and obtained in this work and neglecting broadening for clarity.

Image of FIG. 5.
FIG. 5.

Same as Fig. 1 for an a-plane sample of rutile TiO2 for which the c-axis is oriented in the plane of incidence ( ).

Image of FIG. 6.
FIG. 6.

Same as Fig. 1 for an a-plane sample of rutile TiO2 for which the c-axis is oriented perpendicular to the plane of incidence ( ).

Image of FIG. 7.
FIG. 7.

Experimental (symbols) and best-matching model calculated (solid lines) real and imaginary part of the second derivative of the pseudo-dielectric function for c-plane rutile TiO2. Critical point structures related to phonon modes are marked by arrows. The inset magnifies the spectral range between 520 cm−1 and 1000 cm−1. The position and type of additional modes are also indicated in the inset. The derivative-like structure near 900 cm−1 is caused by the subsequent loss in p- and s-reflectivity above the reststrahlen range.

Image of FIG. 8.
FIG. 8.

Experimental (symbols) and best-matching model calculated (solid lines) imaginary part of the second derivative of the pseudo-dielectric function for a-plane rutile TiO2 with c-axis oriented perpendicular ( ) and parallel to the plane of incidence ( ). Critical point structures related to phonon modes are marked by arrows. The inset magnifies the spectral range between 520 cm−1 and 1000 cm−1. The position and type of additional modes are also indicated in the inset. The derivative-like structure near 900 cm−1 is caused by the subsequent loss in s- and p-reflectivity above the reststrahlen range.

Image of FIG. 9.
FIG. 9.

Comparison of the real and imaginary part of the dielectric function tensor components and of rutile TiO2 as determined by applying the parameterized MDF in Eq. (12) (solid lines) and a point-by-point fit (symbols) determined in a simultaneous analysis of a c-plane oriented sample and an a-plane oriented sample measured at highly symmetric sample orientations ( and ). The energetic position of TO phonons, the high-frequency edge zero-crossing of the real part of and (highest-frequency LO phonons), and the positions for which and equal ( ) are indicated by markers. Features caused by additional modes are highlighted by arrows. Note the excellent agreement between model dielectric function and point-by-point fit even in the range of additional modes.

Image of FIG. 10.
FIG. 10.

Imaginary part of the dielectric loss functions and as determined form the parameterized model dielectric function analysis. The position of LO phonons coincides with the maximum positions and is indicated by brackets. Signatures related to additional modes are marked by arrows.

Image of FIG. 11.
FIG. 11.

Phonon dispersion and phonon density of states of rutile TiO2 as determined by DFT calculations. The spectral positions of the phonon modes at the Γ-point determined by IR spectroscopic ellipsometry are marked by squares (TO modes) and triangles (LO modes). The spectral positions of additional modes are marked by horizontal lines.

Image of FIG. 12.
FIG. 12.

Experimental (symbols) and best-matching model calculated data (solid lines) of the ellipsometric parameters and in the Jones-matrix representation for rutile TiO2 sample of (111) orientation measured at four different in-plane orientations at an angle of incidence . The model data were calculated by applying the determined phonon mode parameters without further regression analysis. Only the Euler angles for in-plane orientation φ and tilt of the c-axis with respect to the z-axis of the laboratory coordinate system θ were varied during the model analysis. Excellent agreement even for the off-diagonal Jones-matrix elements was achieved.

Image of FIG. 13.
FIG. 13.

Ordinary ([ ) and extraordinary ([ ) room-temperature optical functions of rutile TiO2. Symbols refer to room temperature data taken from literature. 43

Tables

Generic image for table
Table I.

Bands of total reflection in rp and rs for high-symmetry orientations of rutile TiO2. The frequencies are defined by . Total reflection occurs for frequencies ω exclusively in one set of frequencies.

Generic image for table
Table II.

Room temperature transverse and longitudinal optical phonon mode frequency parameters for rutile TiO2 in units of cm−1. Frequency parameters for additional modes included in the analysis are also given.

Generic image for table
Table III.

Room temperature transverse and longitudinal optical phonon mode broadening parameters for rutile TiO2 in units of cm−1. Broadening parameters for additional modes included in the best-matching model are also given.

Generic image for table
Table IV.

Low-frequency (“static”) and high-frequency dielectric constants of rutile TiO2 at room-temperature.

Loading

Article metrics loading...

/content/aip/journal/jap/113/16/10.1063/1.4802715
2013-04-25
2014-04-19
Loading

Full text loading...

This is a required field
Please enter a valid email address
752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Infrared dielectric anisotropy and phonon modes of rutile TiO2
http://aip.metastore.ingenta.com/content/aip/journal/jap/113/16/10.1063/1.4802715
10.1063/1.4802715
SEARCH_EXPAND_ITEM