Kramers-Kronig-consistent optical functions of anisotropic crystals: generalized spectroscopic ellipsometry on pentacene

Abstract

The Kramers-Kronig relations between the real and imaginary parts of a response function are widely used in solid-state physics to evaluate the corresponding quantity if only one component is measured. They are among the most fundamental statements since only based on the analytical behavior and causal nature of the material response [Phys. Rev. 104, 1760-1770 (1956)]. Optical losses, for instance, can be obtained from the dispersion of the dielectric constant at all wavelengths, and vice versa [Handbook of optical constants of solids, Vol. 1, p. 35]. Although the general validity was never casted into doubt, it is a longstanding problem that Kramers-Kronig relations cannot simply be applied to anisotropic crystalline materials because contributions from different directions mix in a frequency-dependent way. Here we present a general method to identify frequency-independent principal polarizability directions for which the Kramers-Kronig relations are obeyed even in materials with lowest symmetry. Using generalized spectroscopic ellipsometry on a single crystal surface of triclinic pentacene, as an example, enables us to evaluate the complex dielectric constant and to compare it with band-structure calculations along the crystallographic directions. A general recipe is provided how to proceed from a macroscopic measurement on a low symmetry crystal plane to the microscopic dielectric properties of the unit cell, along whose axes the Kramers-Kronig relations hold.

Optical, structural, and magnetic properties of cobalt nanostructure thin films

“…22 Nevertheless, nondestructive optical techniques such as ellipsometry have proven to be extremely suitable for determining structural ͑major polarization axes' orientation͒ and physical ͑dielectric tensor͒ properties of highly anisotropic thin films. It has been recently reported for orthorhombic 23 and triclinic 24 thin films as well as for monoclinic slanted columnar thin films from Ti and Cr. 25,26 In this paper we study the structural, optical, and magnetic properties of GLAD grown highly orientationally coherent Co nanostructures by generalized ellipsometry ͑GE͒ and superconducting quantum interference device ͑SQUID͒ magnetometer investigations.…”

“…Due to the complexity of this subject, thorough discussion of this issue is beyond the scope of this paper, and referral is made to literature. 23,24,[28][29][30][31][32][33] The linear polarizability response of structured thin films due to an electric field E is a superposition of contributions along certain directions a = a x x + a y y + a z z, b = b x x + b y y + b z z, and c = c x x + c y y + c z z: P = a a + b b + c c that are phenomenologically equivalent to ͑but physically different from͒ the crystallographic unit-cell vectors in bulk materials. In the laboratory Cartesian coordinate system the structured thin film is described by the second rank polarizability tensor as follows: …”

“…Kramers-Kronig consistency tests can then be done individually for dielectric functions along each axis. 24 …”

Triplet diffusion in singlet exciton fission sensitized pentacene solar cells

“…Ellipsometry measurements on pentacene single crystals described in Ref. 26 reveal that the peak at 1.86 eV is mostly excited by a photon polarization parallel to a crystallographic axis a that lies almost in plane with the substrate. The higher-energy peaks are predominantly excited by photon polarizations parallel to a crystallographic axis b almost perpendicular (95 ) to a.…”

Monoclinic optical constants, birefringence, and dichroism of slanted titanium nanocolumns determined by generalized ellipsometry

“…[4][5][6] Due to the complexity of this subject, thorough discussion of this issue is beyond the scope of this paper, and referral is made to the literature. [4][5][6][7][9][10][11][12] The linear polarizability response of CTFs due to an electric field E is a superposition of contributions along certain ͑major͒ intrinsic directions ͑"unit-cell vectors"͒ a = a x x + a y y + a z z , b = b x x + b y y + b z z , c = c x x + c y y + c z z: P = a a + b b + c c. In the laboratory Cartesian coordinates, the CTF is described by the second rank polarizability tensor and P = E.…”