Abstract:
Compositional dependencies of the optical properties of as-deposited
amorphous As40S60, As40S35Se25
and As40Se60 prepared by thermal evaporation, have been
studied. The direct analysis proposed by Swanepoel has been successfully employed
and it has allowed us to determine the average thickness
INTRODUCTION
The optical properties of chalcogenide glasses, for example excellent transmittance in the infra-red region, continuous shift of the optical absorption edge and values of refractive index ranging between 2.0 and 3.5, as well as the strong correlation between the former properties and the chemical composition, explain the growing interest in these semiconducting materials for the manufacture of filters, anti-reflection coatings and, in general, a wide range of optical devices[1-4]. This underlines the importance of the characterization of these glassy materials through the determination of their optical constants, refractive index and extinction coefficient, as well as the corresponding optical band gaps. Great efforts have been made to develop the mathematical formulation describing the transmittance and reflectance of different optical systems[5-12].
This study will use the straightforward method proposed by Swanepoel[6], which is based on the use of the extremes of the interference fringes of transmission spectrum for calculation the refractive index and film thickness in both weak absorption region and transparent region and will use transmission spectrum and reflection spectrum for calculation the extinction coefficient in the strong absorption region. As to the method for determining the refractive index of thin films, we must consider that, if the optical thickness of the film is sufficient to generate several interference extremes and also the higher thickness helps us to avoid us the effect of film thickness on the optical constant of thin films.
MATERIALS AND METHODS
Bulk chalcogenide samples were prepared according to the conventional melt-quenched technique. The high-purity elements were weighted and placed together in a precleaned and out gassed silica ampoule, which has been evacuated to a pressure of about 10-3 Pa and then, sealed. The synthesis was performed in a rocking furnace at a temperature of approximately 900oC, for about 24 h. After the synthesis, the melt was cooling water-quenched, resulting in a bulk glass of the required chemical composition, As40S60, As40S35Se25 and As40Se60. The glass thin films were deposited by evaporating the bulk chalcogenide samples from a resistance heating quartz glass crucible onto clean glass substrates kept at room temperature, using a conventional coating unit (Denton Vacuum DV 502 A) and a vacuum of about 2x 10-6 Torr. The evaporation rate as well as the film thickness was controlled using a quartz crystal DTM 100 monitor. The mechanical rotation of the substrate holder (≈ 30 rpm) during deposition produced homogeneous film. The temperature rise of the substrate due to radiant heating from crucible was negligible. Small fluctuations in the measured transmittance (≈ 1.0 %) of studied films confirm their homogeneity. The amorphous state of the as-deposited films was checked using Philips X-ray diffractometry (1710).
The measurements of transmittance and reflectance were carried out using a double-beam (Shimadzu UV-2101 combined with PC) computer-controlled spectrophotometer, at normal incidence of light and in a wavelength range between 400 and 2500 nm. Without glass substrate in the reference beam, the measured transmittance spectra were used to calculate the refractive index and the average film thickness of three different glass compositions As40S60, As40S35Se25 and As40Se60 thin films.
Preliminary theoretical considerations: Consider the optical system consists of chalcognide glass thin films evaporated onto thick, finite, transparent substrates. The homogeneous film has thickness d and complex refractive index n = n – ik, where, n is the refractive index and k the extinction coefficient, which can be expressed in terms of the absorption coefficient α by the equation: k = αλ/4π. The thickness of the substrate is several orders of magnitude larger than d and its index of refraction is s. The system is surrounded by air with refractive index n0 = 1. Taking all the multiple reflections at the three interfaces into account, it can be shown that in the case k2<< n2 the expression for the transmittance T for normal incidence is given by[6,8,13].
| (1) |
Where, A = 16n2s, B = (n + 1)3(n + s2), C = 2(n2 – 1)(n2 – s2), D = (n – 1)3(n – s2), φ = 4πnd/λ and χa(λ), the absorbance, is given by the formula χa = exp (–αd).
Moreover, the values of the transmission at the extremes of the interference fringes can be obtained from Eq. 1 by setting the interference condition cos φ = +I for maxima and cos φ = –1 for minima. From these two new formulae, many of the equations that provide the basis of the method in use are easily derived[8].
RESULTS AND DISCUSSION
Calculation of the refractive index and film thickness: According to Swanepoel’s method, which is based on the idea of Manifacier et al.[5] of creating the envelopes of interference maxima and minima (Fig. 1), a first, approximate value of the refractive index of the film n1, in the spectral region of medium and weak absorption, can be calculated by the expression:
| Fig. 1: | Three typical transmission T(λ) and reflection R(λ)
spectrum for three different composition thin films of As40S60,
As40 S35 Se25 and As40
Se60, TM and Tm according to the text.
Ts(λ) and Rs(λ) are the transmission and reflection of uncoated
substrate |
| Table 1: | Values of λ, TM and Tm for the three different composition thin films of amorphous As–S corresponding to transmission spectra of Fig. 1; the underline values of transmittance are the values calculated by orgin program. The calculated values of refractive index and film thickness are based on the envelope method |
| (2) |
Where:
Here, TM and Tm, are the transmission maximum and the corresponding minimum at a certain wavelength λ. Alternatively, one of these values is an experimental interference extreme and the other one is derived from the corresponding envelope; both envelopes were computer-generated using the origin version 7 program using more than one procedure. On the other hand, the necessary values of the refractive index of the substrate are obtained from the transmission spectrum of the substrate, Ts using the well-known equation[14]:
| (3) |
The values of the refractive index n, as calculated from Eq. 2 are shown in Table 1. The accuracy of this initial estimation of the refractive index is improved after calculating d, as will be explained below. Now, it is necessary to take into account the basic equation for interference fringes
| (4) |
Where, the order numbers m is integer for maxima and half integer for minima. Moreover, if nel and ne2 are the refractive indices at two adjacent maxima (or minima) at λ1 and λ2, it follows that the film thickness is given by the expression:
| (5) |
The values of thickness d of different composition samples determined by this equation are listed as d1, in Table 1. The last values usually deviate considerably from the other values and must consequently be rejected. The average value of d1, corresponding to the three films of different composition are listed in Table 1. This value can now be used, along with n1, to calculate the order number mo for the different extremes using Eq. 4.
| Fig. 2: | Refractive index dispersion spectra for the three different composition thin films |
The accuracy of d can now be significantly increased by taking the corresponding exact integer or half integer values of m associated to each extreme (Fig. 1) and deriving a new thickness, d2 from Eq. 4, again using the values of n1. The values of d2 found in this way have a smaller dispersion (σ1 > σ2). It should be emphasized that the accuracy of the final thickness is approximately 1% (Table 1). With the exact value of m and the very accurate value of Eq. 3 can then be solved for n at each λ and thus, the final values of the refractive index n2 are obtained (Table 1). Figure 2 shows the dependence of n on wavelength for three different composition thin films of As40S60, As40S35Se25 and As40Se60 chalcogenide glass thin films. This figure illustrates that the change in the n values was related to the change in the concentration of S at the expense of Se content, i.e., the values of n increase towards As40Se60 over the entire spectral range studied, Ramirez-Mato et al.[20] and González-Leal et al.[22] have observed similar dependence on As–S, As–S–Se and As–Se cholegoenide glass system. This increase is related to the increased polarizability of the larger Se atoms atomic radius, 115 pm), in comparison with S atoms (atomic radius, 100 pm).
Now, the values of n2 can be fitted to a reasonable function such as the two-term Cauchy dispersion relationship, n(λ) = a + b/λ2, which can be used for extrapolation the whole wavelengths[15] (Fig. 2). The least squares fit of the three sets of values of n2 for the three different composition samples listed in Table 1, yields n = 2.304 + 68218/ λ2 for As40S60 sample, n = 2.467+81962/ λ2 for As40S35Se25 sample and n = 2.688 + 73372/λ2 for As40Se60 sample.
The energy dependence of n of amorphous materials can be fitted to the Wemple and DiDomenico dispersion relationship, that is single-oscillator model[16]:
| Fig. 3: | Plot of refractive index factor (n2 – 1)-1 versus E2 for spectra for the three different composition thin films |
| (6) |
Where, E0 is the single-oscillator energy and Ed the
dispersion energy. By plotting (n2 – 1)-1 versus
E2 (Fig. 3) and filled the data to a straight line,
E0 and Ed can be determined from the intercept, E0/Ed
and the slope, –1/E0Ed. The values obtained for dispersion
parameters Ed, Eo and for static refractive index n (o) (i.e. extrapolated to
hvv 0), for three different compositions thin films. Eo is considered
as an average energy gap to a good approximation, it varies in proportion to
the Tauc gap
| (7) |
Where, Nc is the effective coordination number of the cation nearest neighbour to the anion, Za is the formal chemical valency of the anion, Ne is the effective number of valence electrons per anion and β is a two-valued constant with the either an ionic or a covalent value (βi = 0.26±0.03 eV and βc = 0.37±0.04 eV, respectively). The dispersion energy Ed increases with increasing Se content. Taking into account Eq. (7) and assuming that the parameters Ne = (40 x 5 + 60 x 6)/60 = 28/3 and Za = 2 retain the same values along this particular composition, it would seen reasonable to ascribe the trend observed in the values of Ed to an increase in the effective cation coordination number, Nc. On the other hand the possible influence of the parameter β on the increase observed for the oscillator strength should be also mentioned.
| Table 2: | Values of the single-oscillator energy Eo, dispersion energy Ed, refractive index at (hv v 0) and Tauc optical gap Eoptg |
| Fig. 4: | Plot of l/2 against n/λ to calculate the order number
and film thickness for spectra for the three different composition thin
films |
Thus, the nature of the chemical bonding could change towards being less ionic with increasing Se content. Nevertheless, according to Paulings’ electronegativities, the ionicity of an As–S bond is ≈ 8% while in the case of an As–Se bond it is ≈ 4%. Therefore β is considered to be a constant, with the covalent value βc = 0.37±0.04 eV.
The agreement of the different parameters Ed, Eo and n(o) are reported in this work with those of Gonzαlez-Leal et al.[22]. The values of single-oscillator energy Eo, dispersion energy Ed and static refractive index n(o) for the three different composition thin films are listed in Table 2.
Furthermore, a simple complementary graphical method for deriving the values of m and d, based on Eq. 4 was also used. This expression can be rewritten for that purpose as:
| (8) |
Where, l = 0, 1, 2,…..and m, is the first extreme. Therefore, plotting l/2 against n/λ yields a straight line with slope 2d and cut-off on the vertical axis of –m1. Figure 4 shows this plot, in which the values obtained for d and m1 are displayed for three different composition thin films.
Determination of the extinction coefficient and optical band gap: The spectral dependence of the optical Transmittance (T) and Reflectance (R) of the investigated sample can be obtained using double beam spectrophotometer. The absorption coefficient α can be obtained from the experimentally measured values of R and T according to the following expression[19]:
| (9) |
Where, d is the sample thickness. In order to complete the calculation of the optical constants, the extinction coefficient is estimated from the values of a and λ using the already mentioned formula k = αλ/4π. Figure 5 shows the dependence of k on wavelength for different samples of thin films.
Finally, the optical band gap will be found from the calculated values of a To that end, it should be pointed out that the absorption coefficient of amorphous semiconductor.
| Fig. 5: | The extinction coefficient k against wavelength λ for spectra for the three different composition thin films |
| Fig. 6: | The dependence of (α. hv)1/2 on photon energy
hv for spectra for the three different composition thin films, from which
the optical band gap |
In the high-absorption region (a = 104 cm-1), assuming parabolic band edges and energy-independent matrix elements for interband transitions, is given according to Tauc[1] by the following equation:
| (10) |
Where, K is constant which depends on the transition probability and
CONCLUSIONS
The optical properties of as-deposited amorphous three different composition
thin films of As40S60, As40S35Se25
and As40S60 chalcogenide glass prepared by thermal evaporation,
have been determined from their corresponding transmission and reflectance spectrum,
measured at normal incidence. The envelope method suggested by Swanepoel has
successfully been applied to films with higher thickness, with a reasonable
number of interference fringes. This optical method makes it possible to determine
the refractive index and average thickness with an accuracy of about 1%. It
has been found that the refractive index increases with increasing Se content
over the entire spectral range studied. The increase in refractive index is
related to the increased polarizability, of the larger Se atoms, in comparison
with S atoms. The subsequent fitting of the refractive index to the Wemple-DiDomenico
relationship for obtaining the dispersion parameters. The optical band gap is
appropriately fitted to the non-direct transition model proposed by Tauc[1],
in the strong-absorption region of investigated films. The results indicate
that the values of Eo and
ACKNOWLEDGMENTS
Sincere gratitude for Prof. Abd El Salam Abou Sehly, Faculty of Science, Al Azhar university, Assiut, Egypt and for Prof. N. Afifi, Faculty of Science, Assiut University, Egypt, for their great support and helpful discussion.