On the optical nonlinearity in the GeSbSe chalcogenide glasses

Chalcogenide glasses GexSb40−xSe60 with composition 12, 25 and 30 at.%, synthesized from elements with 5N purity (Ge, Sb, Se) by the conventional melt-quenching method were studied. The spectrophotometer’s measurements were recorded to determine the optical properties. Models based on the absorbance and absorption coefficient are used to determine the optical band-gap energy. The Urbach energy is deduced in the GexSb40−xSe60 thin film alloys with composition x = 12, 25 and 30 at.%. The electronic and structural properties are studied, and the influence of the Urbach energy in estimating of the nonlinearity in the optical properties of these glasses is discussed. The analysis is performed with respect to the Urbach parameter that quantifies the degree of crystallinity of the structure which can be used to understand the behavior of different diffractive, wave-transmission and fiber structures.


Introduction
More recently, ternary chalcogenide GeSbSe glasses were intensively studied and proposed for the development of optoelectronic devices due to their thermal, mechanical and chemical properties [1]. The melting and evaporation properties of these materials depend to a very large extent on the completeness of the chemical reaction. By varying the chemical composition of GeSbSe thin films, the network undergoes structural changes reflected in the structural phase transformations [2][3][4], in the effect of doping Sb on the electronic structure [5] and in the threshold transition in the physical parameters [6]. The presence of Sb and Se have strengthened in the material generated stable SbSe bonds and cross-linkages in GeSe-SbSe structural chains [7][8][9] with a material very versatile informing.
This paper aims to evaluate the optical constants of Spectrophotometer. Using the UV/Vis spectra the Urbach energy was detected. The influence of the Urbach energy in estimating of nonlinear optical properties of these glasses is discussed in this paper. The Urbach edge arises from fluctuations of short-distance forces in chalcogenides. The weak tail that appears in the absorption diagram can be described by antibonding states of wrong connections Ge-Ge or Se-Se that produce unoccupied states in the conduction band. Electronic excitations generate holes at the edge of the valence band and electrons in the conduction band, or holes in the valence band and electrons in the tail of the conduction band.
In amorphous materials, due to the absence of long-range forces, the valence and conduction bands do not have sharp cut off but have tails of localized states. Due to these band tails, the optical absorption edge is not sharp and has a tail at lower energies. When we make the Tauc plot we do not get a straight line in the whole energy range. Urbach energy has an inverse relation with enhancement in crystalline structure or with texture factor. The Urbach energy indicates the degree of crystallinity of the structure and induces nonlinearity in the optical properties of GeSbSe. These glasses have highly optically nonlinearities which are mainly reflected in devices such as optical switching. Chalcogenide layers can be obtained by different deposition methods. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.

Experimental details and results
Layers thin films -Ge Sb Se x x 40 60 with composition x=12, 25 and 30 at.%, were synthesized from elements with 5N purity (Ge, Sb, Se) by conventional melt-quenching method. The mixture of the elements with proper weight percent was placed in a quartz ampoule and evacuated down to a pressure of 10 -3 Pa. The ampoules were loaded in a rotary furnace and heated up to 950°C.
For a homogeneous melting, the glassy mixture was kept at this temperature for continuously two hours by rotating the furnace. Then, the ampoules were pulled out, and the melts were rapidly cooled down in the ice water. The parts of synthesized glasses were served as parent material for deposition on the quartz substrate using a resistive crucible of 0.1mm molybdenum sheet from having the shape and size of the 0482070 from the UMICORE catalog. The degassing took place at a pressure of 10 −1 Pa, for 12 min in the N 2 , and during that time, the dome with the quartz substrates are rotated with 10 rot min −1 . This process was removing the impurities on the walls from the vacuum deposition installation and on the bulk. At the´-4 10 3 Pa pressure, the heating resistance is coupled, by ensuring the temperature of 300°C in the evaporation chamber while the dome rotation was kept.
The powder material was evaporated at an electric current at least 400 mA. The optical monitoring control was done by TFCalc 3.5 software for approximately 6 min with a deposition rate of 3 nm s −1 and showed 1300 nm thickness. After evaporation, the samples were measured by Lambda 950 Spectrophotometer. Using the transmission spectra, the optical properties also the band gap and Urbach energy are computed.
The spectrophotometer's measurements were recorded on Lambda 950 UV/VIS/NIR with double beam and double monochromator at the room temperature, in the spectral range UV-vis-NIR, with 266 nm min −1 a scanning speed for normal incidences. Absorptance is light that is not transmitted or reflected by material but is absorbed. Having the transmission spectra and absorptance, the equation describes the theory [11][12][13] can be used to calculate the reflectance where T is transmittance, R the reflectance, and A the absorptance.
The results obtained by chalcogenide layers 60 alloys with composition x=12, 25 and 30 at.% was determinate from the envelope function transmission spectra using the Swanepoel method [11].
The optical properties of materials depend on parameters as the preparation technique and the cleaner surface and also the preparative conditions for surface morphology. The study of the spectral absorption coefficient gives information about the electronic states in the high energy part of the optical absorption spectrum, while the other lower energy part of the spectrum corresponds to the atomic vibrations [11]. There are several applications based on optical absorption such as optoelectronics devices, sensors, display devices, solar cells.
The optical absorption spectra and the optical absorption coefficient a ( ) should be studied here. The absorption coefficient α can be determined from the transmittance, T % ( )and reflectance, R % ( )by using the following formula [12] a l = - where d is the thickness, T, the transmittance and R, the reflectance. The dependence of the absorption coefficient, a l ( ) on the photon energy n h is represented in figure 3. Figure 3 indicates the value of the absorption coefficient, the increase/decrease of the Ge/Sb content upon photon energy incident for all the samples of Refractive index can be obtained using the normal incidence reflectance according to Fresnel's equations [12,13] computed by relation (4): Figure 5 shows the results obtained by the refractive index according to (4).  The value of the refractive index and extinction coefficient decrease/ increase with Ge / Sb content [14][15][16][17].
The optical band gap E g was derived assuming indirect transitions between the edge of the valence and conduction band. In this work, we have used six models to determine the optical band-gap energy in the 60 thin films alloys with composition x=12, 25 and 30 at.%, as a function of Germanium content, is presented in figure 7. The figure shows that E g grows with increasing Germanium content.
Along the absorption coefficient curve and near the optical band edge there is an exponential part called Urbach tail. This exponential tail appears in the low crystalline, poor crystalline, disordered and amorphous materials because these materials have localized states which extended in the band gap. In the low photon energy range, the spectral dependence of the absorption coefficient a ( ) and photon energy n  is known as Urbach empirical rule, which is given by the following equation [18]   n a a where A is the absorptance, α, the absorption coefficient, A, ã are constants and E u is the Urbach energy. The Wemple-DiDomenico (WD) model is using to calculate various dispersion parameters such as band-gap energy (E g ) oscillator energy (E 0 ) and dispersion energy (E d ) [16,19,20]. Accordingly, a graph (figure 5) is constructed with ( ) According to the single oscillator model, the data other dispersion of the refractive index can be evaluated using the equation: where n is the refractive index, E 0 is oscillator energy and E d the dispersion energy.
Oscillator energy E 0 is calculated from the slope E E 1 d 0 / and dispersion energy E d is calculated from the intercept E 0 /E d on y axis figure 11. The various dispersion parameters are also given in table 1, E g value is an average between the model based on the absorptance and absorption coefficient, as a function of the photon energy n  . While the band gap energies E g and E 0 increase, the E d , values show a tendency to decrease by increasing the Ge content, correspondingly decreasing the Sb ( figure 12). This indicates the strong influence of the character and amount of chemical bonds on the GeSbSe material parameters.

Estimation of the dielectric properties
The GeSbSe, like all chalcogenides in general, are characterized by important fluctuations of the atomic distances in material as suggested in figure 13(a). The peaks in interatomic distances for Ge-Sb, Ge-Ge, Sb-Sb, and Se-Se atoms appear to be 3.80±0.05 Å, 3.85±0.05 Å, 3.80±0.05 Å, and 3.80±0.05 Å, respectively [16]. The atomic structure of GeSbSe is presented in figure 13(b).  Forces with a short domain of action that characterize the structure of chalcogenides are identified by the distribution functions of the pairs of Ge-Se and Sb-Se atoms that can be performed using a 3D simulation in a configuration with a given number of atoms. A simulation expectation was realized in [24] for ternary films of Ge 15 Sb 25 Se 60 and Ge 35 Sb 5 Se 60 with a configuration of 200 atoms. The results are obtained from x-ray and neutron diffraction correlated with the Reverse Monte Carlo simulations in binary and ternary films indicate that Sb atoms incorporated in Ge 40 Se 60 are covalently bonded to Se and form trigonal Sb-Se units.
The results are shown in figure 14. The distribution functions of the pairs of atoms are evidence of the presence of short-distance bonds in the amorphous material. By increasing the Ge concentration, respectively decreasing the Sb concentration, the interatomic distances in the Ge-Se bonds increase from 2.37 Å to 2.40 Å.

Estimation of dielectric properties
Along the absorption coefficient curve and near the optical band edge there is an exponential part called Urbach tail. This exponential tail appears in amorphous materials because these materials have localized states which extended in the band gap. In the low photon energy range, the spectral dependence of the absorption coefficient (α) and photon energy n  is known as Urbach empirical rule, which is given by (5) a a n where α 0 is a constant,  the Planck's constant, n photon's frequency and E u is the energy of the band tail or the Urbach energy, which is weakly dependent upon temperature and is often interpreted as the width of the band tail due to localized states in the normal band gap that is associated with the disordered or low crystalline materials.
Urbach energy has an inverse relation with enhancement in crystalline structure or with texture factor. So, Urbach energy is a key factor in characterizing the internal structure of GeSbSe. Therefore, the properties of GeSbSe depend strongly on the Urbach energy.
The optical absorption edge in amorphous semiconductors is generally not as steep as that in crystalline semiconductors. In general, the absorption spectrum a w  can be divided into three parts [24] (see figure 6(c)). For α2×10 4 cm −1 , the spectrum shows a linear dependence a w w » -  E . where n is the refractive index. The nonlinear dielectric constant is the third-order optical susceptibility e c = d 3 3 defined by the third harmonic generation that cannot be experimentally predicted [25,26].
For estimating theoretically the dielectric constants, the theory of surface tension of Hilliard is applied [27,28]. The local energy calculated from the interaction of atoms is the predominant term in the atomic pseudopotentials of Ge, Sb and Se atoms.
The distribution functions allow the representation of the nearest neighbours of each atom in a given reference system, necesary to calculate the energy for an amorphous material as the GeSbSe glass.
Good identification of the distribution functions of the pairs of Ge-Se and Sb-Se atoms can be done by 3D simulations of a small configuration of 200 atoms in the glass [25].
The components = D i    where V is the pseudopotential energy, and Ω the cell volume. From (9) and (10)    The constants are determined from (11) as is the linear optical susceptibility, n is the refractive index and e c = d 3 3 is the third-order optical susceptibility measured by the third harmonic generation [28].
In order to estimate e = i j , , 1, 2, 3, The model of Jankowski and Tsakalakos for the energy V i of an atom i (the green atom) is adopted [27,28] å å where V ij is the potential between the atom i and its neighbour j, and r ij is the distance from atom i to the neighbour atom j, ã is the repulsive energy parameter, and δ is the repulsive range parameter which depends on 2 with respect to the green Se atom. In view of (14), V can be interpreted as a measure of the Born-Mayer repulsive energy. The parameter α is measured in Ryd (Rydberg) 1 Ryd=13.6 eV=2.092×10 −21 J, and the parameter β, in atomic units [ua]. Total atomic energy V is computed from with respect to atomic coordinates r r r , ,..., .

Conclusions
The thin films Ge x Sb 40-x Se 60 with composition x=12, 25 and 30 at.%, have been synthesized from elements with 5N purity (Ge, Sb, Se) by the conventional melt-quenching method. The mixture part of the elements served as parent material for deposition on the quartz substrate. Models based on the absorbance and absorption coefficient are used to determine the optical band-gap energy. Urbach energy is the primary means for study the nonlinear optical properties of the glasses. Novel optical switching, for example, is an application of chalcogenide glasses in which the optical nonlinearities is the key for the optimal functionality of the femtosecond switches. The paper proposes a theoretical formalism for evaluating the optical properties for GexSb40-xSe60 thin films with composition x=12, 25 and 30 at.%, with respect to a parameter which quantifies the Urbach energy. The algorithm addresses new results regarding the induced nonlinearities and the possibility to enhance them to be used in optical nonlinear devices.