Band gap exciton in ferroelectric TlInS₂: Dimensionality and screening

Abstract

This work reports two-dimensionality of band-gap exciton in layered ferroelectric TlInS 2 , accessed by spectroscopic phase modulated ellipsometry in a wide range of temperatures embracing normal, incommensurate, and commensurate phases of this material. A significant decrease in exciton binding energy is observed upon approaching the temperature region of the incommensurate phase on cooling or heating. The effective static rather than optic dielectric screening is shown to be responsible for the observed behavior of exciton binding energy that remains larger than the energy of the longitudinaloptical phonon at all accessed temperatures. The temperature dependence of this screening is remarkable in that it obeys Currie-Weiss law. The values of the exciton's reduced mass and three-dimensional effective Bohr radius are obtained. The former keeps constant to be 0.928 the mass of the free electron while the latter irregularly changes with temperature, remaining within 14-19 Ålimits. The last values correspond to the doubled thickness of a single layer.

Spectroscopic Ellipsometry Studies and Temperature Behaviour of the Dielectric Function of TlInS2 Layered Crystal

“…As can be seen from the figure, with decreasing temperature the spectra shift towards higher energies in agreement with the data of Ref. [26]. Note that a detailed analysis of the real and imaginary parts of the TlInS2 dielectric function in the energy range of 2-2.7 eV, i.e.…”

“…A phenomenological approach applied for the description of the phase transitions in TlInS2 enabled qualitative agreement with the experimental dependence of thermodynamical functions on temperature to be obtained [3][4][5]. For these materials extensive temperature studies of acoustic [6], electrical [7][8][9][10][11][12], and optical [13][14][15][16] properties were carried out while ellipsometric studies of A III B III C VI (A  Tl, B  (In, Ga), C  (S, Se)) chalcogenides were subject of several publications [17][18][19][20][21][22][23][24][25][26].…”

“…in the range of direct and indirect transitions was carried out in Ref. [26], therefore we will concentrate our discussion mostly beyond this spectral interval.…”

“…Interband transitions for TlGaSe2 [22,23], TlGaS2 [23,24], TlInSe2 [25], and TlInS2 [24,27] were determined. Ellipsometric measurements in the photon energy range 1.5-4.2 eV were performed for TlInS2 in the temperature interval of 100-400 K [26]; however, the behaviour of the real and imaginary parts of the TlInS2 dielectric function was analysed in detail only within the energy range of 2-2.7 eV, i.e. in the range of direct and indirect transitions.…”

“…in the range of direct and indirect transitions. Moreover, the temperature dependence of the exciton transition energy was analysed [26]. To our knowledge, in the literature available no analysis of the TlInS2 dielectric function second derivative spectra, neither its amplitude A, critical point energy Ecp, broadening parameter Γ, and phase angle  were reported for various temperatures, including the phase transition range.…”