Study of non-linear optical properties, electrical susceptibility and semiconducting dependence on substrate temperature for ZnO thin films prepared by Radio Frequency techniqueAbstractZnO thin films which were prepared by radio frequency technique with different substrates temperature were investigated optically. The both of first linear optical susceptibility ((1)) and third order non-linear optical susceptibility ((3)) were determined. More ever another important non-liner optical parameters such as non linear refractive index and non linear absorption coefficient Іc were determined for these studied samples. The electric susceptibility c and relative premitivity µr for these samples were calculated optically.

Finally an important semiconducting parameters such as density of valence band Nv, density of conduction band Nc, free carrier concentration (Nd-Na), position of Fermi level Ef and surface electric field Es were determined for these studied samples.Keywords : ZnO thin films, RF sputtering, different substrate temperature, structure, first linear optical susceptibility, non-linear optical susceptibility, electrical susceptibility and semiconducting results.1. Introduction Recently Metal oxides have been attracted attentions as a result of their applications such as, gas sensors [1], surface acoustic devices [2], transparent electrodes [3], solar cells [4, 5], light emitting diodes [6], spintronic devices [7], nanolasers [8] and Surface Acoustic Wave (SAW) device [9,10].

ZnO is an oxide semiconductor which has an electronic applications such as as photo-catalysts [11], thin film gas sensors [12], varistors [13] and another applications such as solar cell windows [14-16] and gas sensors [17″19]. Structural of ZnO Thin Films had been studied by many authors [20-22], it was found that, ZnO samples have hexagonal structure[23]. ZnO thin films have a good nonlinear second-order susceptibility [24-26]. The study of third-harmonic generation in thin nanocrystalline ZnO near-IR radiation has studied [27]. The second-harmonic generation theory of ZnO samples had investigated [28-32]. The nonlinearity on at different conditions [33] and two-photon resonance [34], doping effect on nonlinear susceptibility were studied [35-36]. The nondegenerate nonlinear absorption coefficient for ZnO using pairs of extremely nondegenerate photons was investigated [37]. On the other hand the influence of substrate temperature physical of nano- ZnO thin films were studied [38] , it was found that, the energy gap decreased with substrate temperature.3. Results and Discussion:3.1. StructureThe surface structure for the ZnO thin films with different temperature is shown in Fig. 1.From this Fig. it was seen that, the grain size of these samples increase with substrate temperature. While surface topography using Atomic Force Microscope (AFM). The X-ray results of these studied samples was carried out in our pervious work[38] . The third-order nonlinear optical susceptibility (3) was determined using the following formula [39]: (1)where A is =1.7 x 10-10 e.s.u [39], Eo is the oscillator energy and Ed is the dispersion energy for these studied samples and had been determined in our pervious work [38].The dependence of (3) on wave length (“) for these samples is shown in Fig. 2. From this Fig. it is seen that, (3) increase with photon energy (hЅ) for all these studied samples. This could be due to, when (hЅ) increses, the defliction of the incident ligth beam increases. While (3) increased with substrate temperture, when substrate temperature increases, the conductivity of these samples increase as a result of increasing the mobility of electron .On the other hand the both of real and imaginary part (3) was determined using the following equs [40] (2) (3)Where µo is Vacuum permittivity µo = 8.854187817—10€’12 F‹…m€’1 [41], Іc is the nonlinear absorption coefficient, c is the speed of light, no is the static refractive index and n2 is the nonlinear refractive index.The relation between photon energy (hЅ) and both of the Re (3) and Im (3), for these samples are shown in Figs. 3,4. Respectively. From this Fig it was noticed that, Re (3) and Im (3) increase with photon energy for all these studied samples, this could be attributed to, when the (hЅ) increases this leads to increase of excited electrons which increase of (3). An important parameter of the non-linear optical parameters is that the nonlinear refractive index (n2), which was determined from the following simple equation [42-43]. (4)Where (no) is static refractive index, Which was determined for these studied samples using the following Equ. [44] (5)The values of (no) for all studied samples is shown in Table 1. no increased with, this could be attributed to, the increase of both value of Eo, Ed with substrate temperature, as shown in table 1. The dependence of the determined nonlinear refractive index (n2) on wave length is shown in Fig. 5,as it is clear from this Fig. (n2) increases with substrate temperature, this could be attributed to, when substrate temperature increase the grain size of these films increased as shown in SEM pictures Fig 1.The nonlinear absorption coefficient (Іc) which is the different frequencies in order to excite a molecule from one to a higher energy electronic state, and was determined using the following equation[45]:- (6)Where n is the refractive index which had been calculated for these samples in our pervious work [38].The dependence of (Іc) on (hЅ) for ZnO thin films is illustrated in Fig.6, from this Fig. it shown that, the behavior of the (Іc) increased for all these samples with (hЅ), this could be attributed to, when (hЅ) increases the number of excited electrons increases, which cause an increase of the nonlinear absorption coefficient (Іc). 3.2. linear optical susceptibilitylinear optical susceptibility (1) describes the response of the material to an optical wave length, the linear optical susceptibility (1) was determined using the following relation [46]:- (7)The relation between (1) and (hЅ) for ZnO thin films with different substrate temperature is shown in Fig. 7.from this Fig. it was seen that , (1) increased for all these samples with (hЅ), this due to, the increase when (hЅ) increases, the incident light intensity, increases which cause an increase (1) .3.3. electrical susceptibility.Electrical susceptibility (e) which describe the electrical behavior of the samples under the influence of the electric field and was determined using the following relation[47] (8) Where k is the extinction coefficient which was calculated for these samples in our pervious work [38].The dependence of (e) on (hЅ) of these investigated samples is shown in Fig. 8. from this Fig. it is clear that, the values of (e) increase with (hЅ), for all these samples, this could be attributed to, the electron mobility increases with (hЅ), which leads to the increase of the electric susceptibility (e).The relative permittivity µr was calculated using the following relation [48] (9)The relation between µr and (“) for these films is shown in Fig. 9. From this Fig. it was seen that, the values of relative permittivity µr increases with (hЅ) for all these samples, this could be attributed to the increase of relative permittivity µr is due to the increase of the electrical susceptibility. 3.4. semiconducting results The semiconducting results plays an important role for changing both of electrical and optical properties, so it is important for explanation of the physical properties is that, determination of these semiconducting parameters.The density of state for both the valence and conduction band were calculated using the following equations [49]:- (8) (9)Where Nv, Nc were the density of states for both valence and conduction bands respectively, m*e is the effective mass of electrons and had a value of 0.24 mo [50], m*h is the effective mass of holes and had a value of 0.45 mo [51], K is the Boltzmann constant and T is the temperature on Kelvin. The determine values of both Nv, Nc is shown in table 1. The most important factor had determined as a function of Nv, Nc , this is the position of Fermi level, which was determined using the following relation [49] (10)The determined values of the Fermi level Position (FLP) from conduction band is shown in table 1, which showed that the values of (FLP) decreases with substrate temperature.The determined free carrier concentration give an indication of an important semiconducting parameter which is, surface electric field (Es), which was determined using the following relation (10)Where e is the electron charge, (Nd-Na) is the calculated free carrier concentration, µ dielectric permittivity of ZnO and had a value of 2.08 [52] And Vs is the pinning of Fermi level and equal 0.66 eV[53].The determined values of the surface electric field is shown in table .1, which showed that, the surface electric field decreases with substrate temperature, this is due, the electron mobility increases when the substrate temperature increase, which increase the electron hole recombination at the surface of the sample, which leads finally to decreased the surface electric field. 4. ConclusionThe high quality thin films of ZnO were prepared with different substrate temperature deposition (100″500 C) using RF method. The SEM pictures showed that, he grain size increased with substrate temperature. The values of (3) increase with (hЅ) for all samples as a result of increased the mobility of electron incresed, both of the real and imaginary part of (3) increased with (hЅ) for these samples for all substrate temperatures. The values of the n2 for all these studied samples decreased with (“), this id duo to the increasing of grain size with substrate temperature. (Іc) increased for all these samples with (hЅ), which is duo to, (hЅ) increase the number of excited electrons. The same behavior was noticed for (1) Which increased with (hЅ) as a result of increase of incident light intensity, also both of electrical susceptibility (e) and relative permittivity µr increase with (hЅ) as a result of the electron mobility increases with (hЅ). The values of both Nv, Nc increase with substrate temperature, this is due to the increase the electron and hole motilities. On the other hand the determined values of both of (FLP) and Es decreases with substrate temperature as a result of increasing the electron hole recombination at the surface of the sample with substrate temperature. These results give a great chance for control and change the important results such as structure, nonlinear optical results and semiconducting results By changing the substrate temperature of deposition only, this leads to important industrial applications suchas, electronic and optoelectronic devices with low coast. Table 1: the determined values of ZnO thin films such as, tatic refractive index (no), Free carrier concentration Nd-Na (cm-3), density of conduction band Nc (cm-3), density of valence band Nv (cm-3) and Fermi level position (eV) and Surface electric Es (kV).Surface electric Es field (kV) Nd-Na (cm-3) Fermi level position (eV) Nv (cm-3) Nc (cm-3) Static refractive index (no) N/m* [38] dispersion energy Ed (eV) [38] oscillator energy Eo (eV) [38] Temperature oC46.20 2.64E+20 1.16 3.30E+20 7.42E+20 1.56 1.1E+48 9.80 6. 80 10050.30 2.88E+20 1.00 9.32E+20 2.10E+21 1.59 1.2E+48 10.80 7.10 20040.70 2.33E+20 0.84 1.71E+21 3.85E+21 1.63 9.7E+47 12.20 7.30 30034.80 1.99E+20 0.80 2.64E+21 5.93E+21 1.65 8.3E+47 13.20 7.70 40034.80 1.99E+20 0.78 3.68E+21 8.29E+21 1.69 8.3E+47 14.40 7.80 500Fig. 1. Scanning electron Microscope (SEM) picture for ZnO thin films with different substrate temperature (a) 100, (b) 200, (c)300, (d) 400 and (e) 500 oC. Fig. 2 : The third-order nonlinear optical susceptibility (3)dependence on photon energy for ZnO thin films with different substrate temperature (a) 100, (b) 200, (c)300, (d) 400 and (e) 500 oC. Fig. 3 : Relation between the real part of third-order nonlinear optical susceptibility and photon energy for ZnO thin films with different substrate temperature (a) 100, (b) 200, (c)300, (d) 400 and (e) 500 oC. Fig. 4 : Relation between the imaginary part of third-order nonlinear optical susceptibility and photon energy for ZnO thin films with different substrate temperature (a) 100, (b) 200, (c)300, (d) 400 and (e) 500 oC Fig. 5 : The nonlinear refractive index dependence on wave length for ZnO thin films with different substrate temperature (a) 100, (b) 200, (c)300, (d) 400 and (e) 500 oC. Fig. 6 : The nonlinear absorption coefficient (Іc) dependence on photon energy for ZnO thin films with different substrate temperature (a) 100, (b) 200, (c)300, (d) 400 and (e) 500 oC. Fig. 7 : The linear optical susceptibility (1) dependence on photon energy for ZnO thin films with different substrate temperature (a) 100, (b) 200, (c)300, (d) 400 and (e) 500 oC. Fig. 8 : Relation between the electrical susceptibility (e) and photon energy for ZnO thin films with different substrate temperature (a) 100, (b) 200, (c)300, (d) 400 and (e) 500 oC. Fig. 9 : Relation between relative permittivity µr and photon energy for ZnO thin films with different substrate temperature (a) 100, (b) 200, (c)300, (d) 400 and (e) 500 oC.