Enhancement of the dielectric and nonlinear optical properties of PbSe nanomaterial thin films with different contents of Polyethylene Glycol AbstractPbSe nanocrystals were prepared using hydrothermal method with different contents of poly ethylene glycol (PEG) (20, 60, 80 and 100 mg). The reflectance spectra were measured for these samples, and also refractive index (n) values were calculated, and increase with PEG ratio. The values of both dispersion energy (Ed) and oscillating energy (Eo) were determined optically, which increase with PEG content.
The free carrier concentration/effective mass (N/m*) ratio decreased with PEG content. On the other hand, the first order of moment (M-1), the third order of moment (M-3) and static refractive index (no), were determined. Both of dielectric loss (µ) and dielectric tangent loss (µ\) peak position decrease with photon energy (hЅ). Also the same behavior was detected for both of the real part of optical conductivity (1) and imaginary part of optical conductivity (2) with (hЅ). The Linear optical susceptibility ((1)) increases with (hЅ) for all samples. The nonlinear optical parameters such as, nonlinear refractive index (n2), and the third-order nonlinear optical susceptibility ((3)) decrease with PEG, as a result of increasing the sample density with PEG.
The non-linear absorption coefficient (Іc) , were determined theoritically. Both of the electrical susceptibility (e) and relative permittivity (µr) has blue shift with photon energy for all samples. The ratio of the density of conduction band/electron effective mass ( Nc/ m*e (cm-3)), density of valence band/ hole effective mass (Nv/m*h (cm-3)) were calculated theoretically.Key words:- PbSe nanocrystals with different PEG contents, optical conductivity, dielectric properties, nonlinear optical properties and semiconducting properties.1. Introduction In the recent time the most common precision and advanced industries depend mainly on nanomaterials as a result of their wide electronic and optoelectronics applications, as a result of their sorption[2-5], catalytic[6-8], optical , electrical, and other special properties [10-11]. Lead chalcogenides are promising materials due to their narrow band gap . PbSe has narrow energy band gap (0.27 eV) , which increases to (~1.5 eV) by decreasing crystallite size .PbSe nanocrystals have a large electronic applications such as, field effect transistors , infrared detectors , thermoelectric material . PbSe thin films had been prepared with different methods such as, electrodeposition , Inert gas condensation , electron beam evaporation , Chemical bath deposition . PbSe thin films had a polycrystalline structure [22-23] with cubic structure and lattice constant (a = 6.124 A) . The optical properties of PbSe thin films were studied by many authors[25-30], PbSe thin films had band gap of 1.18 eV, with range (1.5-1.8 eV), (1.5 and 1.9 eV) energy gap decreased with increasing film thicknesses [28-30]. It decreased from (1.89-1.60 eV) for films with thickness . The electrical properties of PbSe thin films were studied [22, 31-34]. The electrical resistivity decreased with film thickness , and applied pressure , Ac conductivity is thickness independent . The dopant effect on physical properties for PbSe thin films were investigated [35-38]. It was found that, the Te dopant make the PbSe thin films have stable photoresponse to infrared light, electrical resistivity decreases with increasing Te ratio . PbSe thin films prepared by different contents of PEG were studied . It was found that, both of energy gap and electrical resistivity increase with PEG content..3. Results and Discussions 3.1. Optical results The measured optical transmittance (R) for PbSe thin films with different dopant ratios is shown in Fig. 1, from this Fig, it is clear that, the dopant ratios affect strongly on the behavior of R . The refractive index (n) for these films were calculated using the following equation  (1)Fig. 2 shows (n) dependence on the (“) for for PbSe films prepared with content of PEG (20, 60, 80 and 100). From this figure it was seen that, the behavior of n with ” is the same for all samples, but the n values increase with PEG content, this could be due to increasing the sample density since n depends on density . 3.2. Dielectric, optical conductivity and linear optical susceptibility results The single oscillator for these sample can be as follow : (2)Where E is the photon energy (hЅ), Eo is the oscillator energy and Ed is the dispersion energy. The values of Eo and Ed for all samples are shown in table 1. From this table it was noticed that, values of both Eo and Ed increase with PEG content, as a result of increasing n values of these samples. Fig.3 represents the relation between (n2-1)-1 vs. (hЅ) for these thin films. It is shown that (n2-1)-1 increases as the PEG. While, Fig. 4 shows, the relation of n2 and “2 to determine (n/m*) and the lattice dielectric constant (µL) using the following equation : (3)Where µo is the permittivity of free space, e is the charge of electron, k is absorption index of these films respectively, which was determined in a previous work , and c is the speed of light, so the values of both of (N/m*) and µL are shown in table 1. From this table it was noticed that, the value of (N/m*) decreases with PEG, due to increasing the sample density, which causes an increase of m* of these sample. The first order of moment (M-1) and the third order of moment (M-3) are that, central and standardized motion of electrons respectively and were derived from the relations : (4) (5)Table 1 shows, the values of the M-1 and M-3 for these thin films. The oscillator strength (f ) was calculated as follows : (6)The values of the f are shown in table 1. Another important parameter depending on both of Eo and Ed is that, static refractive index no, which is the medium ability to refract the light depending on the electron oscillations, and was determined as : (7)The values of no increase with PEG content as shown in table 1, because of all values of Eo, Ed and samples density increase with PEG. Both of (µ) and (µ\) for these films were calculated as follows : (8) (9) Figs. 5(a,b) show both of (µ) and (µ\) versus (hЅ) for PbSe films. From this figure, it was seen that, both of (µ) and (µ\) decreased with (hЅ) for all studied samples, and the peak maximum values position increases with PEG content, due to the decreased of electron motilities. The optical conductivity was calculated from the following equations : (9) (10)Figs 6(a,b) show, the both of (1) and (2) dependence on (hЅ) for these films. The behavior of both (1) and (2) for all these studied films is the same with (hЅ). ((1)) describes the response of the material to an optical wave length, ((1)) was determined using the following relation : (13)The relation between ((1)) and (hЅ) for these samples is shown in Fig.7, it was seen that, ((1)) increases with hЅ, this means that, there is a possibility of changing in optical response by changing in PEG content for these samples.3.3. Nonlinear optical propertiesThe non-linear refractive index (n2), which can be explained as: when light with high intensity propagates through a medium, it causes nonlinear effects, n2 was determined from the following simple equation [50-51]: (14)The dependence of n2 on (“) for PbSe these samples shown in Fig.8. The values of n2 decrease with ” for all these studied samples, and also n2 decrease with PEG, which means that the light propagation decrease with PEG as a result of increasing the sample density with PEG. An important parameter to assess the degree of nonlinearities is ((3)), which was determined using the following equation : (15)Where A =1.7 x 10-10 e.s.u . The dependance of (3) on and (hЅ)for these samples is shown in Fig.9. It was noticed that, the behavior of ((3)) is the same for all the samples, the values of ((3)) increses with (hЅ), this is due to the fact that, when (hЅ) increses the deflection of the incident ligth beam increases . On the other hand, the nonlinear absorption coefficient (Іc) is determined as follows : (16) Fig. 10 shows the influence of hЅ on (Іc). It is observed that, (Іc) increses with increasing hЅ for all samples as shown in Fig. 10. Because of the higher values of (hЅ), the large number of excited electron overcome the band gap.3.3. Electrical results Electrical susceptibility ((e)) was determined using the following relation : (17) Fig. 11 shows the relation between ((e)) and (hЅ) of these investigated samples. From this figure it is clear that, the values of ((e)) increase with (hЅ). This is due to, the electron mobility increases with (hЅ). The relative permittivity (µr) was calculated using the following relation  (18) The relation between (µr) and (“) for these thin films is shown in Fig. 12. It is clear that, the values of (µr) increase with (hЅ) for all these samples; this could be attributed to, the electron mobility increases with (hЅ).3.4. Electronic resultsThe density of states (DOS) of a system describes the number of states per interval of energy at each energy level available to be occupied. The Nv and Nc play very important rule of examination the linear optical transition and non-linear optical properties. The Nv and Nc were calculated as follows :- (19) (20)The determined values for both Nv, Nc were shown in table 1. 4. ConclusionBoth of R and n of PbSe thin films increase with different PEG contents (20, 60, 80 and 100 %), as a result of increase the sample density. The determined values of Ed and Eo (Eo from (3.60-5.30 eV), Ed (5.2 -7.8 eV) increase for PbSe thin films with PEG content , due to increase the electron variation, and the wave dispersion through a medium, and also (N/m*) decreases with PEG content, as a result of increasing m* with PEG of these sample. The values of M-1 and M-3 also increase with increasing PEG content of the studied films, due to increase both of Eo and Ed, the medium ability to refract the light increase with PEG ratio, causing increase of no. Both of (µ) and (µ\) increases with (hЅ), and the peak maximum had a blue shift with PEG content, this is due to the decrease of electron motilities. This result is also similar to both of (1) and (2). ((1)) increased with (hЅ), for these samples, and the peak position had blue shift with PEG, which is meaning that: these films had a high response for changing their properties with PEG ratios, while both of ((3)) and Іc increased with (hЅ), this is due to: when (hЅ) increased the deflected light increased and also the number of excited electrons which overcome the band gap. The increase of electron mobility leads to increase both of ((e)) and (µr) with photon energy for all these samples. The determined values for both of Nv and Nc increase the effective mass of these samples with PEG contents. Fig.1. Reflectance spectra dependence on wave length for PbSe films Prepared with different content of PEG.Fig.2. Refractive index dependence on wave length for PbSe films prepared with different contents of PEG.Fig. 3.The relation of (n2-1)-1 and (hЅ)2 for PbSe thin films with different contents of PEG.Fig. 4. The relation of (n2) and (“2) for PbSe thin films with different contents of PEG.Fig. 5. Dependence of (µ) (a) and (µ\) on (hЅ) for PbSe thin films with different contents of PEG. Fig. 6: Influence of (hЅ) on (1) and (a) and (2) for PbSe thin films with different contents of PEG. Fig 7: Relation between ((1)) and (hЅ) for PbSe thin films with different contents of PEG. Fig. 8: Relation between n2 and wavelength for PbSe thin films with different contents of PEG. Fig. 9: Dependence of ((3)) on (hЅ) for PbSe thin films with different contents of PEG.Fig. 10. The influence of hЅ on (Іc) for PbSe thin films with different contents of PEG.Fig. 11. The influence of hЅ on (c) for PbSe thin films with different contents of PEG.Fig. 12. The influence of hЅ on (µr) for PbSe thin films with different contents of PEG. Table 1: the determined values of PbSe thin films with different contents of (PEG), such as, µL, Eo, Ed, M-1, (f), (no), (N/m*), (NC/m*h) and (Nv/m*e).Nv/m*e NC/m*h N/m* no Field strength (f) (eV)2 M-3 (eV) M-1 (eV) Dispersion energy Ed (eV) Oscillation energy Eo (eV) lattice dielectric constant µL PbSe nanomaterial thin with PEG content (mg)4.10E+21 9.3E+20 1.1E+51 1.56 18.72 2.28 4.33 5.20 3.60 2.00 20 3.50E+21 7.3E+20 8.2E+50 1.56 21.84 2.37 4.67 5.60 3.90 15.00 60 3.30E+21 8.6E+20 7.2E+50 1.60 31.95 2.66 5.65 7.10 4.50 25.00 80 3.18E+21 8.2E+20 6.9E+50 1.57 41.34 2.79 6.43 7.80 5.30 15.00 100