#### 3.2. X-ray Diffraction Analysis

An X-ray diffractogram of CdTe thin films is shown in

Figure 3. Thin films exhibit two cubic phases with lattice parameters (

a) of 6.48 and 6.28 Å for both planar and microstructured film cases (ICDD data base PDF 03-065-0890 and 03-065-1046). The main phase with a lattice constant of 6.48 Å is in good agreement with that reported for the CdTe bulk [

32]. However, a minority second phase was also observed with a lattice parameter that differed by 0.20 Å with respect to the main one. This may be due to the kinetic energy of the ablated particles due to the laser Gaussian spatial profile of the laser beam and the recrystallization process during the deposition process.

The interplanar distance

d_{hkl} was calculated from the peak positions and the Bragg’s law:

where

λ is the incident X-ray wavelength;

θ is the angle of incidence, and n is the order of diffraction. The cubic system follows the relation:

which allows us to obtain the Miller indices (

hkl) of the lattice planes. For the phase 1 (

a = 6.4775 Å), the respective prominent peaks correspond to reflections from the (111), (220), (311), and (331) planes and, for phase 2 (

a = 6.28 Å), from (111), (220), and (400).

From the diffraction selection rules, when h + k, h + l, and k + l are even numbers, a zinc blended structure was obtained. Diffraction peaks for other compounds, such as metallic Cd, Te, or their oxides states, were not observed.

The crystallite size (D) in the CdTe films was estimated from Scherrer equation:

where

β is the line broadening at full width at half maximum intensity (FWHM). The calculated crystallite sizes are 11.4 ± 4 nm, thereby indicating the nanocrystalline nature of the film.

Hence, the deposited CdTe thin films are polycrystalline in nature due to the presence of sharp structural peaks, with a zinc blended structure and preferential orientation in the (111) plane.

#### 3.3. Raman Spectroscopy

CdTe Raman spectra were recorded for the planar substrate using a 532 nm excitation wavelength in the frequency range of 100–200 cm

^{−1}. Measured peaks were fitted with a Lorentzian profile, to investigate the quality of CdTe synthesized films. Results shown in

Figure 4 display three emission peaks. The first at 121 cm

^{–1} corresponding to the A1 mode of the tellurium Raman active peak [

33]. The second one at 140 cm

^{–1} was assigned to a combination of the tellurium peak E and the transversal optic (TO) phonon of the CdTe located at 139 and 141 cm

^{–1}, respectively [

34]. The third observed peak, located at 167 cm

^{–1}, is associated with the CdTe longitudinal optical (LO) phonon.

Spectra measured on the microstructured silicon substrates were obtained by using a 780 nm excitation wavelength in the range of 100 to 1000 cm

^{−1} (see

Figure 5). For these samples, the laser was focused in two different spatial regions: on top of the film surface (a) and inside the ablated holes (b), to verify the presence of CdTe over the whole microstructured substrate. For both regions, Raman spectra show a peak at 167 cm

^{−1}, which corresponds to the CdTe LO phonon [

35]. Additionally, it can be observed that the first harmonic at 335 cm

^{−1} and, subsequently, the second, third, and fourth harmonics at 501, 667, and 834 cm

^{−1}, respectively. These results are in agreement with those reported in [

36,

37,

38]. Furthermore, the characteristic peak of silicon at 520 cm

^{−1} [

39] was also detected.

#### 3.4. Optical Properties

The energy absorbed by the films was determined from reflectance measurements as a function of the wavelength R(λ) (see

Figure 6). As expected, the reflectance presents a series of maxima and minima values due to light interference caused by the reflection on both interfaces of the film. For the planar film, a minimum around 585 nm was observed, which is in agreement with the theoretical expected values using the Fresnel equations for a 245 nm thick CdTe film on a silicon substrate [

40]. Furthermore, the minimum reflectance value expected was about 0.24, which is slightly higher than the measured value. This small deviation with the predicted values can be attributed to a non-homogenous layer. On the other hand, results show that the reflectance of planar films is up to 1.5-fold larger than the values obtained for microstructured thin films. The reduction in the measured reflectance for microstructured substrates can be attributed to light reabsorption of reflected light inside the burned holes [

31].

The absorption coefficient

α, was determined from the experimental results by using Beer’s law:

where

d is the film thickness. Here, the sample optical absorbance

A(

λ) is given by

where

T(

λ) is the transmittance through the film. However,

T(

λ) could not be experimentally measured since the substrate is opaque. Thus, the transmission can be calculated by using the Fresnel equations for a thin film formed on a planar substrate [

41]. In our case, the light travels from air with a refractive index

n_{0} and through the CdTe film with thickness d and transmitted to the silicon substrate; the film and the substrate have complex refractive indexes

n_{1} −

i k_{1} and

n_{2} −

i k_{2}, respectively.

Figure 7a shows a diagram of the light path with the substrate have infinite thickness being assumed. From the Fresnel equations for the transverse electric s and magnetic p components it is possible to obtain [

41]

where

r_{jk} and

t_{jk} are the amplitude of reflection and transmission coefficients at each interface, correspondingly. The values for the complex refractive index n and k for the substrate and the film have been obtained from the experimental data reported in [

42,

43].

The amplitude transmission coefficient is obtained from the sum of all of the transmitted waves:

The phase variation between the surface and the interface

β can be written as

Since the infinite series

$y=a+ax+a{x}^{2}+a{x}^{3}+\cdots $, is reduced to

$y=a/(1-x)$ and from Equation (6),

r_{10} = −

r_{01}; then, substituting into Equation (8), it is possible to write

Thus, the amplitude transmission coefficients for p- and s-polarized waves are expressed by

and the transmittance for p-and s-polarized waves is given by

The incidence and transmission angles at each interface can be obtained by applying Snell’s law, and the total transmittance

T through

Since, for the microstructured case, all of the involved dimensions are much larger than the incident wavelengths, it is possible to use the same ray analysis. The top of the microstructured surface is planar and

T could be obtained as above; the difference to

T is due to the laser produced craters. We consider an increment of the area due to the holes as

$\frac{{A}_{walls}}{{A}_{planar}+{A}_{walls}}$. For simplicity, we have assumed that the crater has a conical shape (see

Figure 2b), as depicted in

Figure 7b. Accordingly, the above analysis can be used by adding a term to take into account these new areas, considering the change in the angle of incidence as shown in the figure.

Hence, the amplitude transmission coefficient for the p component could be written as:

Thus, from Equation (13)

T has been obtained and replaced in Equations (4) and (5) to calculate the absorption coefficient

α as a function of the wavelength (see

Figure 8). For both, planar and microstructured substrates, the transmittance was calculated averaging the obtained values when the incidence angle was varied from the normal incidence by up to 70°.

It was observed that the transmittance decreases to values near zero as the extinction coefficient for CdTe grows [

43]. Calculated data for films grown on planar substrates are in agreement with experimental data published elsewhere, taking into account the employed film thickness [

44]. Hence, these results verify the accuracy of the refractive indices used in the simulations. Since the reflectance of films on microstructured substrates is lower than those obtained using the planar configuration (see

Figure 6), then higher values for the transmittance are predictable, as those shown in

Figure 8a. Furthermore, larger values for the absorption coefficient was obtained for films deposited over microstructured substrates, in the whole visible range with values, exceeding by 10% those obtained in planar films (

Figure 8b). This enhancement could be attributed to a reduced reflectance due to a larger absorption area of the modified substrate and that the light travels a longer path throughout the film.

From the absorption coefficient data, the energy band gap

E_{g} can be obtained through

where

h is the Plank constant, ν is the photon frequency, and A is a constant. The exponent n depends on the material transition type and could be 0.5 for a direct transition and 2 for an indirect one. In this work

n = 0.5 since CdTe presents a direct transition as reported in [

1].

Figure 9 shows the Tauc plots obtained from the experimental data. The energy band gap could be calculated by extrapolation of the linear fit at the absorption limit

α = 0 [

45].

The obtained values for the band gap were 1.44 ± 0.02 eV for films deposited on planar and microstructured substrates. Here, it is expected that the same optical band gap for films deposited on treated and untreated substrates will be obtained, since X-ray diffraction results exhibited the same crystalline structure. Furthermore, the obtained value is in agreement with previously-reported data [

9,

46,

47].

A better comparison between both kinds of films can be obtained by dividing the optical absorption coefficient obtained for microstructured substrates by the planar ones.

Figure 10 shows that microstructured films absorb 10% more on average, in comparison with films grown on planar substrates, with a maximum value of 16% at ca. 456 nm.

The absorption coefficient depends on the absorbance, which strongly depends on the used surface modification. Therefore, the obtained value could be further enhanced by increasing the absorption area. This can be accomplished by increasing the density of holes and their depths and reducing the hole diameters. However, according to the employed model, the array periodicity does not change the obtained absorptance. A similar result was reported elsewhere [

48,

49], where theoretical models were used to compare the quantum efficiency for periodic and randomly-textured thin films.