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Dependence of optical properties on the thickness of amorphous Ge30Se70 thin films
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Dependence of optical properties on the thickness of amorphous Ge30Se70 thin films Ahmed S. Solieman a,b,∗ , Mohamed M. Hafiz c , Abdel-hamid A. Abu-Sehly c , Abdel-naser A. Alfaqeer c a
Physics Department, Faculty of Science, Taibah University, PO Box 344, Madina, Saudi Arabia b Physics Department, Faculty of Science, Al-Azhar University, Assiut, Egypt c Physics Department, Faculty of Science, Assiut University, Assiut, Egypt
Abstract In order to calculate the optical properties of evaporated Ge30 Se70 thin films and their relation to thickness, amorphous Ge30 Se70 thin films of different thicknesses were deposited by thermal evaporation at a base pressure of 7.5 × 10−6 Torr at room temperature. The optical transmission and reflection spectra of all films were measured in the wavelength range of 0.2–2.5 m. Efficient parameterization of the spectral dependence of the optical constants of amorphous Ge–Se thin films was obtained by applying a suitable dielectric function model. The O’Leary, Johnson and Lim (OJL) model, based on joint density of states functions, was used to analyze the optical spectra. The best fit was obtained by configuring the film as two layers, the top layer consisting of bulk Ge30 Se70 material embedded in air medium containing different volumes of voids. Therefore, the OJL model coupled with the Bruggeman effective-medium approximation model were used to determine the optical constants of the Ge30 Se70 thin films. The photon energy dependence of the dielectric function, ε = εr − iεi of the investigated films is presented. The film thickness, absorption coefficient α, refractive index n, extinction coefficient k, static refractive index n(0) and optical band gap Eg were deduced. We found that increasing the film thickness increased the direct optical energy gap and decreased the refractive index. © 2014 Taibah University. Production and hosting by Elsevier B.V. All rights reserved. Keywords: Ge30 Se70 films; OJL model; Dielectric function; Drude model; Band gap energy; Thickness
1. Introduction Chalcogenide glasses have attracted much scientific interest because of their potential application in various solid-state devices [1–3]. As they are multipurpose ∗ Corresponding author at: Physics Department, Faculty of Science, Taibah University, PO Box 344, Madina, Saudi Arabia. Tel.: +966 597326140; fax: +966 48454770. E-mail address: [email protected] (A.S. Solieman). Peer review under responsibility of Taibah University
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materials, chalcogenide semiconductors have been used to fabricate several technologically important devices such as infrared detectors, electronic and optical switches and optical recording media [4]. The exceptional optical properties, low phonon energy, optical transparency in infrared regions, intensive luminescence of doped chalcogenides in near and mid-infrared regions, high linear and non-linear index of refraction, photoinduced changes of refractive index and absorption edge make them suitable candidates for the fabrication of integrated optical devices and fully optical signal processing [4,5]. Most of these properties are, however, strongly affected by the compositions of chalcogenide semiconducting glasses [5,6]. GeSe glasses are important chalcogenide semiconductors, with numerous promising applications [7–9]. Research on GeSe glass has been carried out for
Please cite this article in press as: A.S. Solieman, et al. Dependence of optical properties on the thickness of amorphous Ge30 Se70 thin films, J. Taibah Univ. Sci. (2014), http://dx.doi.org/10.1016/j.jtusci.2014.01.002
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decades, to determine rigidity percolation, glass transition and the short and intermediate range order of the structure [10–12]. Wahab et al. [8] investigated the AC conduction mechanism and photodarkening phenomenon of amorphous Ge30 Se70 films prepared by thermal evaporation, and Sleekx et al. [13] reported thermalinduced bleaching in amorphous Ge30 Se70 films prepared by plasma-enhanced chemical vapour deposition. Ge30 Se70 can be readily prepared in either glass or crystalline form. What is difficult is to fabricate highly homogeneous multicomponent chalcogenide thin films. Several techniques have been explored for preparing thin films. The thermal vacuum evaporation technique is widely used for depositing Ge30 Se70 thin films because of its simplicity and the possibility of controlling thickness and uniformity. Green thermal evaporated films are, however, not homogeneous and not in an equilibrium state due to the volatility of the components [14]. The optical properties of a deposited Ge30 Se70 film prepared by thermal evaporation must therefore be investigated. For samples of thickness ranges that represent interference fringes in the reflection–transmission spectrum, full information on the optical constants and thickness can be obtained from spectra in either a dielectric function model or by directly solving Maxwell equations. The aim of this work was thus to calculate the optical properties of evaporated Ge30 Se70 thin films and to investigate the relation to their thickness. 2. Experimental procedures Ge30 Se70 films of different thicknesses (66–475 nm) were deposited on glass substrates by thermal evaporation, and the transmission and reflection spectra of the films were measured at wavelengths of 0.2–2.5 m. The optical transmission and reflection spectra were analyzed simultaneously by applying O’Leary, Johnson and Lim (OJL) model with the Bruggeman effective-medium approximation (BEMA) model. The optical dielectric response of the films, such as their dielectric functions ε = εr − iεi , their refractive index, N = n + ik, and the optical band gap (Eg) dependent on the absorption coefficient (α) were obtained. The classical melt-quenching technique was used to prepare bulk chalcogenide Ge30 Se70 glass. Appropriate amounts of highly pure (99.999%) germanium and selenium were heated together in an evacuated silica tube at a temperature of approximately 1200 K for about 24 h. Then, the melt was cooled by waterquenching, resulting in a bulk glass of the required chemical composition, Ge30 Se70 . The Ge30 Se70 thin films were deposited with a thermal evaporation coating
unit on microscopic slides at room temperature. The slide substrates, 1.1 mm thick, were carefully cleaned ultrasonically in acetone and ethanol for 30 min and then rinsed with deionized water. The desired amount of the material was evaporated from a tungsten boat, which was heated by passing a high current (100 A) under a base vacuum of 7.5 × 10−6 Torr. Mechanical rotation of the substrate holder (about 30 rpm) during deposition ensures the homogeneity and thickness uniformity of the films. Temperature rise of the substrate due to radiant heating from the crucible was negligible. The optical transmission spectra were measured at normal incidence in a double-beam spectrophotometer (Shimadzu 3150 UV–VIS-NIR) of 0.1 nm resolution. The transmittance, T(λ), and reflectance, R(λ), spectra of the films were recorded over the spectral range 0.2–2.5 m. The film thicknesses were measured with a mechanical stylus profilometer (Dektak). 3. Results and discussions The optical transmission and reflection spectra of a-Ge30 Se70 films with different thicknesses in the wavelength range 0.2–2.5 m are shown in Fig. 1. The curves show the typical features of a-Ge30 Se70 films [15–18]. The transmission spectrum was divided into a transparent region, where T(λ) is ≥90%, and a strong absorption region, where T(λ) drops to 0%. In the transparent region, very thin layers (<108 nm) showed no interference features but appear with thin films measuring ≥108 nm. The complex dielectric function (ε = εr − iεi ) of any material defines the response of the material to electromagnetic waves and depends on the photon energy, E, or wavelength, λ. The real and imaginary parts of ε (εr and εi ) are related to the refraction index n and the extinction coefficient k by the relations: εr = n2 − k2 , and εi = 2nk. Therefore, the complex dielectric function of a material and its variation with wavelength is used to interpret the transmission features and/or reflection spectra of semiconductor films. Various dielectric function models describe the optical properties of many amorphous and crystalline semiconductor materials. Although there are several models [19–23], the OJL model [24] is widely used for modelling the optical properties of amorphous semiconductors based on the density of states (DOS) function. The Drude model is used to describe free carrier transitions. The optical susceptibilities obtained by applying such models were used to calculate the real and imaginary parts of the dielectric function in the Kramers–Kronig relation, from which the absorption coefficient (α) and the real (n) and imaginary (k)
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Fig. 1. Transmission and reflection spectra of a-Ge30 Se70 films of thicknesses of (a) 66–234 nm and (b) 316–475 nm. Table 1 Values of OJL and BEMA model parameters, film thicknesses (measured and fitted) and deviation of all a-Ge30 Se70 films of different thicknesses. Thickness (nm)
66 108 159 202 234 316 334 392 475
Drude model
OJL model
ωp (eV)
Γ (eV)
Mass (cm−1 )
EgOJL (eV)
opt Egd
BEMA model
0.29 0.34 0.32 0.42 0.43 0.52 0.55 0.54 0.68
0.36 0.30 0.31 0.302 0.299 0.3009 0.188 0.144 0.031
4.38 4.07 5.771 5.59 6.12 6.54 6.83 6.42 7.25
1.95 1.98 2.09 2.11 2.14 2.15 2.25 2.35 2.44
2.29 2.31 2.34 2.37 2.39 2.40 2.41 2.42 2.45
(eV)
opt Egind
2.01 2.1 2.08 2.07 2.05 2.04 2.03 2.09 2.20
(eV)
f 0.56 0.58 0.63 0.72 0.75 0.80 0.81 0.84 0.87
OJL, O’Leary, Johnson and Lim; BEMA, Bruggeman effective-medium approximation.
parts of the refractive index were obtained. For nonhomogeneous thin films, however, several powerful effective medium approximation models can be used, such as the Maxwell–Garnett [25] or Bruggeman [26] model. We have used the OJL model to determine the optical constants of evaporated a-Se films by fitting only their transmission spectra [27]. In another study, we used OJL, Drude and BEMA models to analyze the optical properties of nanocrystalline In2 O3 :Sn films [28], solgeldeposited In2 O3 films [29] and evaporated AsS films [30]. In the OJL model, the shape of the conduction and valence band DOS are mathematically defined as a function of energy, predominantly by the parameters E0 (defining the gap between the band edges), mass (a scaling factor determining the shape of the DOS) and gamma (reflecting the width of the exponential band tails). The fit parameters of the OJL interband transition model are the gap energy EgOJL (eV) (the gap between the band edges), the tail state exponent of the valence band γ (band tail width in cm−1 ), the mass of the transition (relate to the DOS shape in cm−1 ) and the decay factor (cm−1 ), which
decrease the imaginary part to zero at high frequencies. The combination of the OJL and BEMA models is referred to as the OB model hereafter. To improve the fit, different film–substrate configurations were used. The best fit was obtained when the film was configured as glass substrate–bulk Ge30 Se70 layer of thickness d/surface layer representing the roughness of thickness drough . Initial values for the OB model parameters d and drough were inserted with the background value of the refractive index. Automatic fitting is used to minimize any deviation between the calculated and experimental data by varying the fit parameters (model parameters and film thickness). The downhill simplex method is applied until an optimal fit is obtained. The deviation is given by squaring the difference of the simulated and measured values, D=
m TEXp (λi ) − T [n(λi ), k(λi ), d, λi ]2 . i=1
In our earlier work [28], the dielectric functions of the microscopic glass substrates were obtained from a sum
Please cite this article in press as: A.S. Solieman, et al. Dependence of optical properties on the thickness of amorphous Ge30 Se70 thin films, J. Taibah Univ. Sci. (2014), http://dx.doi.org/10.1016/j.jtusci.2014.01.002
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Fig. 2. Measured and fitted transmittance and reflectance spectra of a-Ge30 Se70 films of different thicknesses.
of Kim’s oscillators [31]. The measured and fitted optical spectra of the substrate were in excellent agreement, and the obtained dielectric function of the glass substrate was saved in a database. The transmittance and reflection spectra of all films fit well with the OB model. The model parameters and thicknesses of different layers are used as free fit parameters; their values are listed in Table 1. For all T and R spectra, the positions and amplitude of the interferences as well as the value and curvature of the band gap energy fit very well. As an example, Fig. 2 shows the measured and fitted transmittance and reflectance spectra of GeSe films with thicknesses of 159 nm and 316 nm. The measured and calculated values of film thickness agreed well, indicating that the OB model is adequate to describe the properties of this coating. The relative percentage error between the experimental, Fiexp (λ), and the calculated, Fcalc (λ), points of T and
R Ei = (Fiexp − Fcalc (λ))/Fiexp × 100, were found to be lower than 1% in the region of high transparency and about 5% in the region of strong absorption. The deviation of calculated from experimental data ranged from 0.65 to 1.91 (Table 1). The real and imaginary parts of dielectric function spectra obtained from the OB model are shown in Fig. 3. The εi (E) spectra showed a broad-peak structure, which is typical of amorphous semiconductors due to the breakdown of crystal periodicity in the amorphous state. The same feature was observed by Innami et al. [32] for a Se film deposited on an Si substrate at room temperature by vacuum evaporation. The thicker film had the higher peak, indicating that the surface is very clean, that there is dielectric discontinuity between the samples and ambient air, and that the highly accurate behaviour of the dielectric function spectrum is similar to that of the bulk material. This is deduced
Fig. 3. Real and imaginary parts of the dielectric functions of a-Ge30 Se70 films of different thicknesses.
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Fig. 4. (a) Real part of the refractive index (n) and (b) extinction coefficient (k) of a-Ge30 Se70 films of different thicknesses as a function of wavelength.
from the simple criterion “biggest is the best” [33], which is applicable to both crystalline and amorphous semiconductors. The Jellison–Modine model [34] proposes an expression of εi (E) for the optical constants of amorphous tetrahedral semiconductors combining Tauc joint DOS and Lorentz calculation. The Lorentz term 2
−1
E[(E2 − Eo2 ) + C2 E2 ] predicts a decrease in optical density at higher energy and a single broad peak of εi (E) spectrum at E ∼ E0 . This spectrum is typically observed in tetrahedral amorphous semiconductors. To verify the goodness of ε values obtained by fitting the optical spectra in the OB model, we computed the corresponding refractive index. In the OJL model, the refractive index n as a function of energy is determined mainly by the parameter ‘mass’, which determines the shape of the conduction and valence band DOS. Fig. 4(a) shows the spectral dependence of refractive index (n) for different film thicknesses. It is clear that the refractive index decreases with increasing thickness of the film. This behaviour can be attributed to the long-range order in thicker films, disorder increasing with increasing film thickness. At long wavelengths, close to zero frequency, n decreases from 2.5 for a 66-nm film thickness to 2.1 for a thicker film of 475 nm. This was confirmed by increasing the value of the mass parameter and increasing the volume fraction (f) with increasing film thickness (Table 1). The value of the refractive index n is, however, still in the amorphous range, lower than that of crystalline film. The refractive index at zero frequency, no , of semiconductors such as Ge, Si and the III–V compounds is typically somewhat larger in the amorphous state than in the crystalline state. The imaginary part of the refractive index or extinction coefficient (k) is plotted as a function of wavelength, as shown in Fig. 4(b).
At higher photon energy, the absorption coefficient (α) is given as a function of photon energy (hν) [35], opt r by αhν = A(hν − Eg ) where A and r are physical constants that depend on the material properties, and opt Eg is a parameter that has been called optical band gap energy. It is found that r = 2 and 1/2 for most crystalline semiconductors and many amorphous semiconductors, r = 3 for some complicated glasses and r = 1 for relatively simple glasses, such as a-Se [36,37]. The absorption coefficient (α) of a-Ge30 Se70 films was deduced from optical spectra in the parameters of the OJL model by Kramers–Kronig analysis. The values opt opt of Egd and Egind for our a-Ge30 Se70 films of different thicknesses were obtained by plotting (αhν)2 and (αhν)1/2 versus hν, respectively, as shown in Fig. 5. As the film thicknesses increased from 66 to 475 nm, the valopt ues for the direct band gap energy Egd increased from 2.29 to 2.45 eV, while the values for indirect band gap opt energy Egd increased from 2.01 to 2.20 eV. The values of the fitted parameter of the OJL model (EgOJL )ranged from 1.95 to 2.44 eV for thicknesses of 66 to 475 nm. The opt opt values of the optical band gap energy (Egd and Egind ) and that obtained as a fitted parameter in the OJL model (EgOJL ) were similar (Table 1). O’Leary studied the optical absorption in GaAs and a-Si:H in a model based on the DOS functions and calculated the joint DOS (and hence the absorption coefficient) as a function of photon energy [38,39]. He concluded that the optical band gap, determined by plotting a typical Tauc equation, depends on the spread of the opt tail states. When the tail spreads widely, the value of Eg opt is lower than that of Ec − Ev , and Eg = Ec − Ev only when the tail is absent. Table 1 shows that the value for the optical band gap (fit parameter EgOJL ) is close to that opt for Egind at lower film thickness (66–234 nm) and close
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Fig. 5. (a) (αhν)2 and (b) (αhν)1/2 vs photon energy (E) for a-Ge30 Se70 films of different thicknesses. opt
to the value of Egd for thicker films (316–475 nm). This indicates that increasing the film thickness decreases the tail state spread and thus increases the optical band gap. In addition, there was some correlation between the OJL parameters EgOJL and mass: higher values for mass are found with higher EgOJL values. This correlation was reported by Gordijna et al. [40] for c-Si:H films. The values for the band gap energy of Ge30 Se70 films are in good agreement with the reported values for GeSe2 films [41,42]. An indirect band gap energy of 2.0 eV was obtained for Ge0.28 Seo.72 by Bakr [43], and a value of 2.03 was obtained for GeSe3 by Reyes et al. [44]. El Metwally et al. [16] obtained direct and indirect optical band gap values of 2.02 eV and 1.98 eV, respectively, for thermally evaporated a-Ge30 Se70 thin films. Ananth Kumar et al. [15] studied the effect of thickness on the optical band gap of deposited and annealed thermal evaporated GeSe films. They found that the values of the indirect optical gap (Eg) for deposited films ranged from 1.4 eV to 2.47 eV for films of 511–1022 nm, and that for films annealed at 200 ◦ C for 2 h varied from 1.72 eV to 2.66 eV for film thicknesses of 511–1022 nm. The band gap energy for the deposited 511-nm film was 1.482 eV, while that for the thicker film (1022 nm) was 2.475 eV. 4. Conclusion Amorphous Ge30 Se70 films of thicknesses of 66–475 nm were prepared by vacuum evaporation under pressure of 7.5 × 10−6 Torr on microscopic glass slides. XRD patterns confirmed the amorphous state of deposited films of different thicknesses. A model combining the OJL and Brugmann models was used successfully to fit the transmission and reflection spectra of the evaporated a-Ge30 Se70 films simultaneously. The values for the dielectric function in the 0.45–4.0 eV
photon energy range were in good agreement with those previously published for a-Ge30 Se70 films. At long wavelengths, close to zero frequency, the refractive index (n) decreased from 2.5 for a 66-nm film to 2.1 for a 475-nm film. The optical band gap EgOJL (OJL fit opt parameter) is close to the indirect Egind att lower film opt
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Please cite this article in press as: A.S. Solieman, et al. Dependence of optical properties on the thickness of amorphous Ge30 Se70 thin films, J. Taibah Univ. Sci. (2014), http://dx.doi.org/10.1016/j.jtusci.2014.01.002
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ScienceDirect Journal of Taibah University for Science xxx (2014) xxx–xxx
Dependence of optical properties on the thickness of amorphous Ge30Se70 thin films Ahmed S. Solieman a,b,∗ , Mohamed M. Hafiz c , Abdel-hamid A. Abu-Sehly c , Abdel-naser A. Alfaqeer c a
Physics Department, Faculty of Science, Taibah University, PO Box 344, Madina, Saudi Arabia b Physics Department, Faculty of Science, Al-Azhar University, Assiut, Egypt c Physics Department, Faculty of Science, Assiut University, Assiut, Egypt
Abstract In order to calculate the optical properties of evaporated Ge30 Se70 thin films and their relation to thickness, amorphous Ge30 Se70 thin films of different thicknesses were deposited by thermal evaporation at a base pressure of 7.5 × 10−6 Torr at room temperature. The optical transmission and reflection spectra of all films were measured in the wavelength range of 0.2–2.5 m. Efficient parameterization of the spectral dependence of the optical constants of amorphous Ge–Se thin films was obtained by applying a suitable dielectric function model. The O’Leary, Johnson and Lim (OJL) model, based on joint density of states functions, was used to analyze the optical spectra. The best fit was obtained by configuring the film as two layers, the top layer consisting of bulk Ge30 Se70 material embedded in air medium containing different volumes of voids. Therefore, the OJL model coupled with the Bruggeman effective-medium approximation model were used to determine the optical constants of the Ge30 Se70 thin films. The photon energy dependence of the dielectric function, ε = εr − iεi of the investigated films is presented. The film thickness, absorption coefficient α, refractive index n, extinction coefficient k, static refractive index n(0) and optical band gap Eg were deduced. We found that increasing the film thickness increased the direct optical energy gap and decreased the refractive index. © 2014 Taibah University. Production and hosting by Elsevier B.V. All rights reserved. Keywords: Ge30 Se70 films; OJL model; Dielectric function; Drude model; Band gap energy; Thickness
1. Introduction Chalcogenide glasses have attracted much scientific interest because of their potential application in various solid-state devices [1–3]. As they are multipurpose ∗ Corresponding author at: Physics Department, Faculty of Science, Taibah University, PO Box 344, Madina, Saudi Arabia. Tel.: +966 597326140; fax: +966 48454770. E-mail address: [email protected] (A.S. Solieman). Peer review under responsibility of Taibah University
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materials, chalcogenide semiconductors have been used to fabricate several technologically important devices such as infrared detectors, electronic and optical switches and optical recording media [4]. The exceptional optical properties, low phonon energy, optical transparency in infrared regions, intensive luminescence of doped chalcogenides in near and mid-infrared regions, high linear and non-linear index of refraction, photoinduced changes of refractive index and absorption edge make them suitable candidates for the fabrication of integrated optical devices and fully optical signal processing [4,5]. Most of these properties are, however, strongly affected by the compositions of chalcogenide semiconducting glasses [5,6]. GeSe glasses are important chalcogenide semiconductors, with numerous promising applications [7–9]. Research on GeSe glass has been carried out for
Please cite this article in press as: A.S. Solieman, et al. Dependence of optical properties on the thickness of amorphous Ge30 Se70 thin films, J. Taibah Univ. Sci. (2014), http://dx.doi.org/10.1016/j.jtusci.2014.01.002
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decades, to determine rigidity percolation, glass transition and the short and intermediate range order of the structure [10–12]. Wahab et al. [8] investigated the AC conduction mechanism and photodarkening phenomenon of amorphous Ge30 Se70 films prepared by thermal evaporation, and Sleekx et al. [13] reported thermalinduced bleaching in amorphous Ge30 Se70 films prepared by plasma-enhanced chemical vapour deposition. Ge30 Se70 can be readily prepared in either glass or crystalline form. What is difficult is to fabricate highly homogeneous multicomponent chalcogenide thin films. Several techniques have been explored for preparing thin films. The thermal vacuum evaporation technique is widely used for depositing Ge30 Se70 thin films because of its simplicity and the possibility of controlling thickness and uniformity. Green thermal evaporated films are, however, not homogeneous and not in an equilibrium state due to the volatility of the components [14]. The optical properties of a deposited Ge30 Se70 film prepared by thermal evaporation must therefore be investigated. For samples of thickness ranges that represent interference fringes in the reflection–transmission spectrum, full information on the optical constants and thickness can be obtained from spectra in either a dielectric function model or by directly solving Maxwell equations. The aim of this work was thus to calculate the optical properties of evaporated Ge30 Se70 thin films and to investigate the relation to their thickness. 2. Experimental procedures Ge30 Se70 films of different thicknesses (66–475 nm) were deposited on glass substrates by thermal evaporation, and the transmission and reflection spectra of the films were measured at wavelengths of 0.2–2.5 m. The optical transmission and reflection spectra were analyzed simultaneously by applying O’Leary, Johnson and Lim (OJL) model with the Bruggeman effective-medium approximation (BEMA) model. The optical dielectric response of the films, such as their dielectric functions ε = εr − iεi , their refractive index, N = n + ik, and the optical band gap (Eg) dependent on the absorption coefficient (α) were obtained. The classical melt-quenching technique was used to prepare bulk chalcogenide Ge30 Se70 glass. Appropriate amounts of highly pure (99.999%) germanium and selenium were heated together in an evacuated silica tube at a temperature of approximately 1200 K for about 24 h. Then, the melt was cooled by waterquenching, resulting in a bulk glass of the required chemical composition, Ge30 Se70 . The Ge30 Se70 thin films were deposited with a thermal evaporation coating
unit on microscopic slides at room temperature. The slide substrates, 1.1 mm thick, were carefully cleaned ultrasonically in acetone and ethanol for 30 min and then rinsed with deionized water. The desired amount of the material was evaporated from a tungsten boat, which was heated by passing a high current (100 A) under a base vacuum of 7.5 × 10−6 Torr. Mechanical rotation of the substrate holder (about 30 rpm) during deposition ensures the homogeneity and thickness uniformity of the films. Temperature rise of the substrate due to radiant heating from the crucible was negligible. The optical transmission spectra were measured at normal incidence in a double-beam spectrophotometer (Shimadzu 3150 UV–VIS-NIR) of 0.1 nm resolution. The transmittance, T(λ), and reflectance, R(λ), spectra of the films were recorded over the spectral range 0.2–2.5 m. The film thicknesses were measured with a mechanical stylus profilometer (Dektak). 3. Results and discussions The optical transmission and reflection spectra of a-Ge30 Se70 films with different thicknesses in the wavelength range 0.2–2.5 m are shown in Fig. 1. The curves show the typical features of a-Ge30 Se70 films [15–18]. The transmission spectrum was divided into a transparent region, where T(λ) is ≥90%, and a strong absorption region, where T(λ) drops to 0%. In the transparent region, very thin layers (<108 nm) showed no interference features but appear with thin films measuring ≥108 nm. The complex dielectric function (ε = εr − iεi ) of any material defines the response of the material to electromagnetic waves and depends on the photon energy, E, or wavelength, λ. The real and imaginary parts of ε (εr and εi ) are related to the refraction index n and the extinction coefficient k by the relations: εr = n2 − k2 , and εi = 2nk. Therefore, the complex dielectric function of a material and its variation with wavelength is used to interpret the transmission features and/or reflection spectra of semiconductor films. Various dielectric function models describe the optical properties of many amorphous and crystalline semiconductor materials. Although there are several models [19–23], the OJL model [24] is widely used for modelling the optical properties of amorphous semiconductors based on the density of states (DOS) function. The Drude model is used to describe free carrier transitions. The optical susceptibilities obtained by applying such models were used to calculate the real and imaginary parts of the dielectric function in the Kramers–Kronig relation, from which the absorption coefficient (α) and the real (n) and imaginary (k)
Please cite this article in press as: A.S. Solieman, et al. Dependence of optical properties on the thickness of amorphous Ge30 Se70 thin films, J. Taibah Univ. Sci. (2014), http://dx.doi.org/10.1016/j.jtusci.2014.01.002
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Fig. 1. Transmission and reflection spectra of a-Ge30 Se70 films of thicknesses of (a) 66–234 nm and (b) 316–475 nm. Table 1 Values of OJL and BEMA model parameters, film thicknesses (measured and fitted) and deviation of all a-Ge30 Se70 films of different thicknesses. Thickness (nm)
66 108 159 202 234 316 334 392 475
Drude model
OJL model
ωp (eV)
Γ (eV)
Mass (cm−1 )
EgOJL (eV)
opt Egd
BEMA model
0.29 0.34 0.32 0.42 0.43 0.52 0.55 0.54 0.68
0.36 0.30 0.31 0.302 0.299 0.3009 0.188 0.144 0.031
4.38 4.07 5.771 5.59 6.12 6.54 6.83 6.42 7.25
1.95 1.98 2.09 2.11 2.14 2.15 2.25 2.35 2.44
2.29 2.31 2.34 2.37 2.39 2.40 2.41 2.42 2.45
(eV)
opt Egind
2.01 2.1 2.08 2.07 2.05 2.04 2.03 2.09 2.20
(eV)
f 0.56 0.58 0.63 0.72 0.75 0.80 0.81 0.84 0.87
OJL, O’Leary, Johnson and Lim; BEMA, Bruggeman effective-medium approximation.
parts of the refractive index were obtained. For nonhomogeneous thin films, however, several powerful effective medium approximation models can be used, such as the Maxwell–Garnett [25] or Bruggeman [26] model. We have used the OJL model to determine the optical constants of evaporated a-Se films by fitting only their transmission spectra [27]. In another study, we used OJL, Drude and BEMA models to analyze the optical properties of nanocrystalline In2 O3 :Sn films [28], solgeldeposited In2 O3 films [29] and evaporated AsS films [30]. In the OJL model, the shape of the conduction and valence band DOS are mathematically defined as a function of energy, predominantly by the parameters E0 (defining the gap between the band edges), mass (a scaling factor determining the shape of the DOS) and gamma (reflecting the width of the exponential band tails). The fit parameters of the OJL interband transition model are the gap energy EgOJL (eV) (the gap between the band edges), the tail state exponent of the valence band γ (band tail width in cm−1 ), the mass of the transition (relate to the DOS shape in cm−1 ) and the decay factor (cm−1 ), which
decrease the imaginary part to zero at high frequencies. The combination of the OJL and BEMA models is referred to as the OB model hereafter. To improve the fit, different film–substrate configurations were used. The best fit was obtained when the film was configured as glass substrate–bulk Ge30 Se70 layer of thickness d/surface layer representing the roughness of thickness drough . Initial values for the OB model parameters d and drough were inserted with the background value of the refractive index. Automatic fitting is used to minimize any deviation between the calculated and experimental data by varying the fit parameters (model parameters and film thickness). The downhill simplex method is applied until an optimal fit is obtained. The deviation is given by squaring the difference of the simulated and measured values, D=
m TEXp (λi ) − T [n(λi ), k(λi ), d, λi ]2 . i=1
In our earlier work [28], the dielectric functions of the microscopic glass substrates were obtained from a sum
Please cite this article in press as: A.S. Solieman, et al. Dependence of optical properties on the thickness of amorphous Ge30 Se70 thin films, J. Taibah Univ. Sci. (2014), http://dx.doi.org/10.1016/j.jtusci.2014.01.002
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Fig. 2. Measured and fitted transmittance and reflectance spectra of a-Ge30 Se70 films of different thicknesses.
of Kim’s oscillators [31]. The measured and fitted optical spectra of the substrate were in excellent agreement, and the obtained dielectric function of the glass substrate was saved in a database. The transmittance and reflection spectra of all films fit well with the OB model. The model parameters and thicknesses of different layers are used as free fit parameters; their values are listed in Table 1. For all T and R spectra, the positions and amplitude of the interferences as well as the value and curvature of the band gap energy fit very well. As an example, Fig. 2 shows the measured and fitted transmittance and reflectance spectra of GeSe films with thicknesses of 159 nm and 316 nm. The measured and calculated values of film thickness agreed well, indicating that the OB model is adequate to describe the properties of this coating. The relative percentage error between the experimental, Fiexp (λ), and the calculated, Fcalc (λ), points of T and
R Ei = (Fiexp − Fcalc (λ))/Fiexp × 100, were found to be lower than 1% in the region of high transparency and about 5% in the region of strong absorption. The deviation of calculated from experimental data ranged from 0.65 to 1.91 (Table 1). The real and imaginary parts of dielectric function spectra obtained from the OB model are shown in Fig. 3. The εi (E) spectra showed a broad-peak structure, which is typical of amorphous semiconductors due to the breakdown of crystal periodicity in the amorphous state. The same feature was observed by Innami et al. [32] for a Se film deposited on an Si substrate at room temperature by vacuum evaporation. The thicker film had the higher peak, indicating that the surface is very clean, that there is dielectric discontinuity between the samples and ambient air, and that the highly accurate behaviour of the dielectric function spectrum is similar to that of the bulk material. This is deduced
Fig. 3. Real and imaginary parts of the dielectric functions of a-Ge30 Se70 films of different thicknesses.
Please cite this article in press as: A.S. Solieman, et al. Dependence of optical properties on the thickness of amorphous Ge30 Se70 thin films, J. Taibah Univ. Sci. (2014), http://dx.doi.org/10.1016/j.jtusci.2014.01.002
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Fig. 4. (a) Real part of the refractive index (n) and (b) extinction coefficient (k) of a-Ge30 Se70 films of different thicknesses as a function of wavelength.
from the simple criterion “biggest is the best” [33], which is applicable to both crystalline and amorphous semiconductors. The Jellison–Modine model [34] proposes an expression of εi (E) for the optical constants of amorphous tetrahedral semiconductors combining Tauc joint DOS and Lorentz calculation. The Lorentz term 2
−1
E[(E2 − Eo2 ) + C2 E2 ] predicts a decrease in optical density at higher energy and a single broad peak of εi (E) spectrum at E ∼ E0 . This spectrum is typically observed in tetrahedral amorphous semiconductors. To verify the goodness of ε values obtained by fitting the optical spectra in the OB model, we computed the corresponding refractive index. In the OJL model, the refractive index n as a function of energy is determined mainly by the parameter ‘mass’, which determines the shape of the conduction and valence band DOS. Fig. 4(a) shows the spectral dependence of refractive index (n) for different film thicknesses. It is clear that the refractive index decreases with increasing thickness of the film. This behaviour can be attributed to the long-range order in thicker films, disorder increasing with increasing film thickness. At long wavelengths, close to zero frequency, n decreases from 2.5 for a 66-nm film thickness to 2.1 for a thicker film of 475 nm. This was confirmed by increasing the value of the mass parameter and increasing the volume fraction (f) with increasing film thickness (Table 1). The value of the refractive index n is, however, still in the amorphous range, lower than that of crystalline film. The refractive index at zero frequency, no , of semiconductors such as Ge, Si and the III–V compounds is typically somewhat larger in the amorphous state than in the crystalline state. The imaginary part of the refractive index or extinction coefficient (k) is plotted as a function of wavelength, as shown in Fig. 4(b).
At higher photon energy, the absorption coefficient (α) is given as a function of photon energy (hν) [35], opt r by αhν = A(hν − Eg ) where A and r are physical constants that depend on the material properties, and opt Eg is a parameter that has been called optical band gap energy. It is found that r = 2 and 1/2 for most crystalline semiconductors and many amorphous semiconductors, r = 3 for some complicated glasses and r = 1 for relatively simple glasses, such as a-Se [36,37]. The absorption coefficient (α) of a-Ge30 Se70 films was deduced from optical spectra in the parameters of the OJL model by Kramers–Kronig analysis. The values opt opt of Egd and Egind for our a-Ge30 Se70 films of different thicknesses were obtained by plotting (αhν)2 and (αhν)1/2 versus hν, respectively, as shown in Fig. 5. As the film thicknesses increased from 66 to 475 nm, the valopt ues for the direct band gap energy Egd increased from 2.29 to 2.45 eV, while the values for indirect band gap opt energy Egd increased from 2.01 to 2.20 eV. The values of the fitted parameter of the OJL model (EgOJL )ranged from 1.95 to 2.44 eV for thicknesses of 66 to 475 nm. The opt opt values of the optical band gap energy (Egd and Egind ) and that obtained as a fitted parameter in the OJL model (EgOJL ) were similar (Table 1). O’Leary studied the optical absorption in GaAs and a-Si:H in a model based on the DOS functions and calculated the joint DOS (and hence the absorption coefficient) as a function of photon energy [38,39]. He concluded that the optical band gap, determined by plotting a typical Tauc equation, depends on the spread of the opt tail states. When the tail spreads widely, the value of Eg opt is lower than that of Ec − Ev , and Eg = Ec − Ev only when the tail is absent. Table 1 shows that the value for the optical band gap (fit parameter EgOJL ) is close to that opt for Egind at lower film thickness (66–234 nm) and close
Please cite this article in press as: A.S. Solieman, et al. Dependence of optical properties on the thickness of amorphous Ge30 Se70 thin films, J. Taibah Univ. Sci. (2014), http://dx.doi.org/10.1016/j.jtusci.2014.01.002
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Fig. 5. (a) (αhν)2 and (b) (αhν)1/2 vs photon energy (E) for a-Ge30 Se70 films of different thicknesses. opt
to the value of Egd for thicker films (316–475 nm). This indicates that increasing the film thickness decreases the tail state spread and thus increases the optical band gap. In addition, there was some correlation between the OJL parameters EgOJL and mass: higher values for mass are found with higher EgOJL values. This correlation was reported by Gordijna et al. [40] for c-Si:H films. The values for the band gap energy of Ge30 Se70 films are in good agreement with the reported values for GeSe2 films [41,42]. An indirect band gap energy of 2.0 eV was obtained for Ge0.28 Seo.72 by Bakr [43], and a value of 2.03 was obtained for GeSe3 by Reyes et al. [44]. El Metwally et al. [16] obtained direct and indirect optical band gap values of 2.02 eV and 1.98 eV, respectively, for thermally evaporated a-Ge30 Se70 thin films. Ananth Kumar et al. [15] studied the effect of thickness on the optical band gap of deposited and annealed thermal evaporated GeSe films. They found that the values of the indirect optical gap (Eg) for deposited films ranged from 1.4 eV to 2.47 eV for films of 511–1022 nm, and that for films annealed at 200 ◦ C for 2 h varied from 1.72 eV to 2.66 eV for film thicknesses of 511–1022 nm. The band gap energy for the deposited 511-nm film was 1.482 eV, while that for the thicker film (1022 nm) was 2.475 eV. 4. Conclusion Amorphous Ge30 Se70 films of thicknesses of 66–475 nm were prepared by vacuum evaporation under pressure of 7.5 × 10−6 Torr on microscopic glass slides. XRD patterns confirmed the amorphous state of deposited films of different thicknesses. A model combining the OJL and Brugmann models was used successfully to fit the transmission and reflection spectra of the evaporated a-Ge30 Se70 films simultaneously. The values for the dielectric function in the 0.45–4.0 eV
photon energy range were in good agreement with those previously published for a-Ge30 Se70 films. At long wavelengths, close to zero frequency, the refractive index (n) decreased from 2.5 for a 66-nm film to 2.1 for a 475-nm film. The optical band gap EgOJL (OJL fit opt parameter) is close to the indirect Egind att lower film opt
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Please cite this article in press as: A.S. Solieman, et al. Dependence of optical properties on the thickness of amorphous Ge30 Se70 thin films, J. Taibah Univ. Sci. (2014), http://dx.doi.org/10.1016/j.jtusci.2014.01.002