Potassium titanyl phosphate Z- and Y-cut surfaces from density-functional theory

While potassium titanyl phosphate (KTP) is widely used for various optics applications, essentially nothing is known about its surfaces and electronic properties. Here the ground-state atomic structures of KTP [001] and [010] surfaces, frequently termed Z and Y cuts, respectively, have been determined using ground-state density-functional theory total-energy calculations. The calculated surface phase diagrams in dependence on the chemical potentials of the materials constituents show several stable nonstoichiometric terminations. A tendency to form oxygen-rich surfaces is observed. The ${\mathrm{Z}}^{+}$ and ${\mathrm{Z}}^{-}$ surfaces, discriminated by oppositely orientated internal electric fields, are found to differ with respect to their stoichiometry and structure. Occupied O-derived and in some cases unoccupied Ti-derived surface states appear in the lower and upper part of the bulk band gap, respectively.

Figure 1

Left: Stacking sequence of ${\mathrm{K}}_2{\mathrm{Ti}}_2{\mathrm{P}}_2{\mathrm{O}}_4$ and ${\mathrm{O}}_6$ layers in Z-cut KTP. Bulk layers are kept fixed during relaxation, while all four surface layers as well as the termination atoms are free to relax. K, Ti, P, and O atoms are depicted in purple, blue, green, and red, respectively. The direction of the internal polarization $\vec{P}$ is indicated. Right: Atomic arrangement of bulk cut (a) ${\mathrm{O}}_6({\mathrm{y}}_{\text{O}}$), (b) ${\mathrm{O}}_6({\mathrm{x}}_{\text{O}}$), (c) ${\mathrm{K}}_2{\mathrm{Ti}}_2{\mathrm{P}}_2{\mathrm{O}}_4$(y), and (d) ${\mathrm{K}}_2{\mathrm{Ti}}_2{\mathrm{P}}_2{\mathrm{O}}_4$(x) terminations. Surface atoms are highlighted in yellow.

Figure 2

Left: Stacking sequence of ${\mathrm{Ti}}_2{\mathrm{P}}_2{\mathrm{O}}_{12}$ and ${\mathrm{K}}_4{\mathrm{Ti}}_2{\mathrm{P}}_2{\mathrm{O}}_6$ layers in Y-cut KTP. Bulk layers are kept fixed during relaxation, while all four surface layers as well as the termination atoms are free to relax. The color coding follows Fig. 1. Right: Atomic arrangement of bulk cut (a) ${\mathrm{Ti}}_2{\mathrm{P}}_2{\mathrm{O}}_{12}$(z) and (b) ${\mathrm{K}}_4{\mathrm{Ti}}_2{\mathrm{P}}_2{\mathrm{O}}_8$(x) terminations. Surface atoms are highlighted in yellow.

Figure 3

Binodal curves within the KTP phase diagram, directly enclosing the stability region for bulk KTP formation, indicated in red (see text).

Figure 4

Phase diagrams of KTP Y-cut (up), ${\mathrm{Z}}^{+}$ (left), and ${\mathrm{Z}}^{-}$ (right) surfaces. Bulk stability region is sketched in white. UHV conditions have been assumed in order to determine the chemical potential of oxygen.

Figure 5

Left: Localized surface states of ${\mathrm{K}}_2{\mathrm{P}}_2{\mathrm{O}}_3$(y) termination on the ${\mathrm{Z}}^{+}$ surface. Right: Localized surface states of ${\mathrm{O}}_3({\mathrm{y}}_{\text{O}}$) on the ${\mathrm{Z}}^{-}$ surface. Blue Ti $3d$ states are empty, while red O $2p$ states are occupied. Shaded area indicates KTP bulk band structure. Size of the circles correspond to the degree of localization within the first surface layers. Charge densities of Ti $3d$ and O $2p$ derived surface states are depicted in (a)–(d).

Figure 6

Work functions $W$ and relative change of the surface dipole $\mathrm{\Delta }{\mathrm{\Phi }}_{\text{Dip}}$ (see text) of all investigated terminations for (a) ${\mathrm{Z}}^{+}$, (b) ${\mathrm{Z}}^{-},$ and (c) Y-cut surfaces. Stable surfaces are highlighted in red.

Figure 7

Surface band structure of ${\mathrm{PO}}_4$(z) termination on KTP y-cut. Shaded area indicates KTP bulk band structure. Size of the circles correspond to the degree of localization within the first surface layers. Charge densities of the occupied O $2p$ surface states are depicted in (a) and (b), respectively.