3.2. Optical results

Both of optical transmittance (T) and reflectance (R) for these crystals are shown in Figs. 4 (a, b). From Fig. 4a it is clear that, these samples have the same behavior of transmittance, but (Y-Ca12A7) single crystals has a higher transmittance values than Ca12Al14O33 single crystals, on the other hand, Fig. 4 b shows that, the behavior of reflectance for these crystals are completely different from each other and the (Y-Ca12A7) single crystals had a lower reflectance value than Ca12A7, this could be attributed, that the Yttrium (Y) is an element which had a dark-gray color which gives the probability of decrease a reflection and increase a possibility of absorption.

The optical energy gap (Eg) is determined from the absorption curves using the equation [45]:

(5)

Where ? is the absorption coefficient, A is a constant, ? is the frequency of the incident radiation and h is Planks constant. The constant p takes he value 0.5 for direct energy gap due to direct allowed transition, while the constant p has the value 2 for indirect energy gap due to indirect allowed transition.

the (?) of these studied thin crystals were determined as follow [46]

(6)

where d is the film thickness. (?) dependence on the photon energy (h?) for these studied crystals is shown in Fig. 4d. The optical direct energy gap Egdirc were determined from this Fig.4d by the extrapolation of the linear part of the curves as in Fig. 4d.

For these crystals, it is found that, Egdirc had a values of 3.00 and 3.80 eV for (C12A7) and (Y-Ca12A7) respectively, this could be attributed to, that the electron mobility for Ca12Al14O33 (C12A7) crystals is higher than the electron mobility of (Y-Ca12A7) single crystals, these electrons mobility affected on the conductivity of these studied samples, which finally decrease the direct optical energy gap.

The extinction coefficient for all films were calculated from the relation: –

(7)

The dependence of k of these crystals on photon energy (h?) is shown in Fig. 5a. As we can see, the Yttrium element increased of k due to the leakage current that resulted from the rare earth element.

The refractive index (n) for these crystals were calculated as follow [47]

(8)

Fig. 5b shows the dependence of (n) on wave length for these investigated samples, from this Fig. it is clear that, the (C12A7) single crystals had a higher value of (n) than (Y-Ca12A7) single crystals. The concept of the single oscillator phenomena of these crystals were studied from the dispersion of refractive index for (C12A7) and (Y-Ca12A7) single crystals, which can be expressed by the WempleDiDomenico relationship [48]

(9)

where E is the photon energy, The values of Eo and Ed are determined as the intercept and the slope resulting from the extrapolation of the line of Fig. 5(c). The values of E0 and Ed for all samples are shown in Table. 2. From this table it was seen that the value of Eo~ 2Eg[49]. On the basis of the above-mentioned model, the M-1 and M-3 moments of ?/ (h?) optical spectrum [50] can be derived from the relations:

(10)

(11)

Table 2. shows the values of the first order moment (M-1) and third order moment ( M-3) for (C12A7) single crystals and (Y-Ca12A7) single crystals.

Another important parameter called the oscillator strength (f) which was calculated as follow [51]

(12)

The value of (f) is shown in Table 1, from this table it was seen that the value of oscillator strength increases with doping. The relation between (n)2 and (wavelength)2 for the studied samples is shown in Fig. 6c. The ratio of the free carrier concentration / effective mass (N/m*) for these studied samples were determined optically from this Figure as follow [52]

(13)

Where ?L is the lattice dielectric constant, ?o is the permittivity of free space, e is the charge of electron, N is the free carrier concentration and c is the speed of light. From this figure the slope of the gotten line equal to the value of (e.N/4?c2?0m*), so the ratio of free carrier concentration / effective mass (N/m*) for these crystals were calculated as shown in Table. 2. From Fig. 5c the value of ?L for these thin films was determined by the extend line will intercept with the y-axis at value of (n2) [53].

Another important parameters such as dielectric loss (?) and dielectric tangent loss(?\) were determined optically [54]

(14)

(15)

Figs. 6 (a, b) shows the dependence of both (?) and (?\) on photon energy for the investigated samples. From Fig. 6a, it is clear that, the behavior of (?) and (?\) is completely inverse each other.

(VELF) and (SELF) for these films were determined optically as follow [55]:-

(16)

(17)

The relation between VELF/SELF for these crystals is shown in Fig. 6c. From this figure the values of VELF/SELF for Ca12Al14O33 single crystals decrease with photon energy, while the values of VELF/SELF for Y-Ca12Al14O33 single crystals increase with photon energy.

As a result of its optical application in electronic devices, Another important parameter had been determined optically for these crystal, it is the degree of nonlinearities is the third-order nonlinear optical susceptibility ?(3). Which is depends mainly on thy photon energy (h?) and both of oscillator energy (Eo) and dispersion energy (Ed) [56]:

(18)

The relation between third-order nonlinear optical susceptibility ?(3) and photon energy is shown in Fig. 6d. From this Fig. it was noticed that, the both crystals had the same third-order nonlinear optical susceptibility ?(3) behavior with photon energy, but the values of third-order nonlinear optical susceptibility ?(3) for (Y-Ca12A7) single crystals is higher than Ca12A7 single crystals.

4. Conclusion

A high quality Ca12Al14O33 (C12A7) single crystal was prepared using Traveling-Solvent Floating Zone (TSFZ) method. The doping was achieved for this crystal using Y-element. The doing affected on the structure parameters such as number of defects, lattice strain and number of crystallites, and the doping plays an important rule for changing the measured optical parameters such as transmittance and reflectance. The direct optical energy gap increases with doping, because of changing the electron mobility and conductivity. Another optical result such as oscillating and depression energy, oscillating strength had affected by doping. The ratio free carrier concentration / effective mass (N/m*) decreased by on order of magnitude by doing because of increase the electrons number, on the other hand the doping process had affected strongly on the dielectric results, where the behavior for the dielectric loss and dielectric tangent loss had completely inversed for these crystals. While the third-order nonlinear optical susceptibility ?(3) valued had increased by doping. Finally, our results confirmed the doping of Y-ion in C12A7 can be good candidate for optical applications.

Acknowledgements. We thank Dr. Park at Korean standard and measurements institute for XRD and Laue Experiments., This Project supported from BK21 (Korean Government) through Yonsei University.