Correlation between Thickness, Grain Size and Optical Band Gap of CdI 2 Film

Structural and optical property was studied as a function of film thickness for thermally evaporated CdI 2 films. Stoichiometric films (up to 250 nm thickness) showing hexagonal structure, and good c-axis alignment normal to glass substrate plane. The optical absorption data indicate an allowed direct inter – band transition near the absorption edge with optical energy gap varies continuously from 2.9 eV to 3.6 eV.Part of the optical data was fitted to an indirect type transition to determine the indirect optical energy gap which also varies continuously from 2.2 eV to 3.1 eV . Both energy gaps show thickness dependences, which can be explained qualitatively by a thickness dependence of the grain size through the decreasing of the grain boundary barrier height with grain size.


1-Introduction
CdI 2 is an important compound having a layered structure with a hexagonal unit cell held with neighbring layers by Van derWaals forces, in which each hexagonal sheet of Cd atoms sandwich between two similar sheets of I atoms, the Cd atoms being octahedrally coordinated [1].As many as 200 polytypes of CdI 2 material are recorded [2].Recent studies have revived interest in cadmium iodide films [3][4][5].The optical absorption data fit best to direct band to band transition indicating a direct band gap, a smaller indirect band gap can also be near the absorption edge.The optical absorption measurement carried out on CdI 2 single crystal samples were fitted to an indirect energy gap of 3.2 eV while the reflectivity spectra reveal a direct transition at 3.8 eV.The band structure calculation show the presence of both direct and indirect band gaps, the difference between the two is only about 0.3-0.6 eV [6][7][8][9][10][11]. Material modification such as grain size, morphology etc, can be achieved by bombarding CdI 2 single crystals and thin films with laser radiation or highly kinetic ions (plasma), where CdI 2 crystals showed a linear variation of energy gap with intensity of laser radiation (0 to 125 mW) and decreasing in the energy gap value from (3.28 to 3.11 eV).The effect of plasma irra- diation on poly type (002) oriented CdI 2 stoichiometric film was found to change the orientation to (110), decre-ase in grain size and residual stress.The iodineiodine distance in the unit cell could be responsible for the change in Eg with stress [12,13].The report on the structure of CdI 2 films show that thinner films (<100 nm) are amorphous and thicker films tend to crystallize [2][3][4][5], it is also known that CdI 2 films grown at substrate temperature less than 300 k are amorphous and these either grown or annealed above 300 k polycrystalline [14].
In this paper we tried to correlate the variation in the band gap of evaporated films with different thickness with the optical properties.

2-Experimental:
The CdI 2 films were grown on glass substrates at room temperature by thermal evaporation at a pressure better than 10 -6 Torr (BALZERS BAE 080) using a molybdenum boat .The start-ing material was analar grade powder 99.999% pure stoichiometric material, which was pelletized for evaporation.Film thickness was measured after evaporation by optical interfero-meter method, using He-Ne Laser λ= 0.632 μm and the thickness were determined using the formula: Where: x is fringe width, ∆x is the distance between two fringes and λ is the wavelength of the laser light.Films up to 100 nm were completely transparent and become translucent for higher thicknesses .The films of thickness below 50 nm were nonuniform, and above 600 nm peel off from the substrate.To determine the nature of the growth and the structural characteristics of CdI 2 film, x-ray diffraction measurement has been done and compared with the ASTM cards, using (Philips PW-1840 X-ray diffractometer of λ= 1.54 Ả from Cu-Kα).Optical transmission measured using a double beam spectrophotometer (Cecile CE 7200 spectrophotometer, by Aquarius Company).

Results and discussion 3 3-1 Structural Investigation:
The structural properties of the CdI 2 films were studied using XRD irrespective of the films thickness.The XRD result shows that the films are polycrystalline.Figure (1) shows diffraction spectrum scan over a rang of 10 о ≤2Ө≤ 50 о ,from which it is clear that our X-ray diffraction data is in agreement with ASTM No.(12-574).Table (1) summarize the calculated parameters for XRD.The total absence of ( 001), (101),or(111) reflection, the high degree of orientation with the basal plane parallel to substrate and c-axis normal to the substrate plan can be seen as indication of a good agreement with earlier study [15].However, another less intensity reflection plane(110) have been observed with 250 nm thick films.
This indicates a slight misalignment among the grains .We have determined the average grain size from the full width at half maximum (FWHM) of the most intense peak using the Scherre formula [16]: Where ΔӨ is the full width at half maximum (FWHM) of XRD peak appearing at the diffraction angle Ө, A the shape factor depends on the crystalline shape, and generally it is 1.Fig. (2) shows the average grain size as a function of films thickness, from this curve we could conclude the following points: a-For thickness less than 250 nm the thickness have no influence on grain size.
b-For thickness greater than 250 nm the grain size increased with a ratio of 0.13.
By comparing this result with these of Fig. (1) if is clear that such variation with grain size is due to the prwdominated orientations.At thickness<250 nm both planes (002),( 004 Optical transmition and absorption spectra of various thickness films were obtained and analyzed in wavelength from 350-900 nm at room temperature Fig. 3 and Fig. 4. The absorption coefficient α was calculated by [17]: Where A is the absorbance and t the film thickness.The samples show a high absorption coefficient (α > 10 5 cm -1 for λ< 400 nm, 10 4 cm -1 for λ > 400 nm).
The dependence of α on hν near the band edge is shown in Fig. 5.It is clear that the value of α increases with increasing photon energy.In a crystalline or Polycrystalline material both direct or indirect optical transition is possible depending on the band structure of the material.In general absorption coefficient is related to the photon energy by following equation [17]:

. (4)
Where A is constant depending on transition probability Eg is the band gap of the material and n has different values depending on the nature of the absorption process.
The usual method of determining energy gap is to plot a graph between (α h ν) 1/n and hν and look for that value of n which gives best linear curve in the absorption edge region.Plotting (α h ν) 1/ n versus h ν for CdI 2 films of various thickness shows that the best fit was obtained for n =1/2, indicating a direct type of allowed transition as shown in Fig. 6.The part of the optical absorption data near the tail of the direct absorption edge have to be replotted as (αhν) 1/2 vs hν to determine indirect gap as shown in Fig. 7.Table (2) summarizes the optical direct and indirect band gap, average grain size for CdI 2 films with different thickness.Our value of Eg(direct) of 3.6 eV determined for thicknesses ≤150nm agrees well with the predicted value of 3.8 eV from band structure calculation [9].However, both type of band gaps showed thickness dependence as shown in table (2) which gives also the grain size.
In general, thickness dependence of band gap can a rise due to one or combined effect of ( 1) the change in barrier height due to change in grain size in polycrystalline films.(2) A large density of dislocation for thickness > 150 nm.The decreasing of energy gaps with grain size for CdI 2 as shown in Fig. 8.However, both energy gaps show thickness dependence as shown in Fig. 9.

Conclusion
1.The optical absorption data indicate a direct type of inter-band transition near the absorption edge yielding a direct optical energy gap varies continuously from 2.9 eV to 3.6 eV.
2. Part of the optical data was fitted to an indirect type of transition to determine the indirect optical energy gap varies continuously from 2 eV to 3.1 eV.
3. The direct and indirect band gap of CdI 2 films decreasing with film thickness can be attributed to grain size dependent grain boundary barrier height, at least for film thickness > 150 nm.
4. The lattice parameter c of hexagonal structured CdI 2 films shows a wavy dependence on film thickness in the rang 150 -600 nm, the films show c-axis alignment normal to substrate plan for film thickness up to about 250 nm.

Figure 1 :
Figure 1: X-ray diffraction patterns and Miller indices of CdI 2 films prepared with different thickness.

Figure 2 :Figure 3 :
Figure 2: Variation of grain size with thickness of CdI 2 films.

Figure 4 :Figure 5 :
Figure 4: The optical absorption spectra of CdI 2 films of different thickness.

Figure 6 :Figure 7 :Figure 8 :
Figure 6: Photon energy dependences of the absorption coefficient squared for CdI 2 films with different thickness to determination of Eg (direct).

and Optical Band Gap of CdI 2 Film
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Band Gap of CdI 2 Film Table (1) analysis of the XRD study of CdI 2 films
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Table ( 2) direct and indirect optical band gap, average grain size of CdI 2 films of different thickness Thickness (nm) Eg(eV) direct Eg(eV) indirect
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