Spectroscopic ellipsometry characterization of spin-coated Ge₂₅S₇₅ chalcogenide thin films

Structure model and material optical constants

Two sets of samples were prepared by the same spin-coating procedure on different substrates. As shown in Fig. 1 (left column), a sample model used to analyze the raw ellipsometry data consists of i) a semi-infinite glass substrate, ii) a homogenous, isotropic layer representing the Ge₂₅S₇₅ film, iii) surface roughness and iv) air as the ambient medium. Analogously in Fig. 1 (right column), a sample model consists of i) a crystalline silicon substrate, ii) a SiO₂ layer, iii) a homogenous, isotropic layer representing the Ge₂₅S₇₅ film, iv) surface roughness and v) air as the ambient medium.

Fig. 1:

Sketch of the optical models used to fit the ellipsometry data.

For ellipsometry and reflectivity measurements of samples on glass substrates, their backside was roughened to avoid unwanted backside reflection. Optical constants of the glass substrate were obtained by measurement of an uncoated glass substrate. In case of Si substrate backside reflection was treated in the WVASE32 software numerically. Possible thickness nonuniformity was modeled in the WVASE32 software as well.

Optical constants of Si and SiO₂ in the NIR – VIS – UV range were taken from the literature [24]. Optical constants of Si and SiO₂ layer in the MIR part of spectra was obtained by measurement of an uncoated SiO₂/Si substrate.

In this work, different model dielectric function, TL or CL model describing SWAE and sum of Lorentz or Gauss oscillators representing absorption in middle infrared part of spectra will be used and compared. Therefore model dielectric function used for the Ge₂₅S₇₅ films consists of several contributions:

Surface roughness is modeled by a Bruggeman type effective medium approximation [25] with 50% of voids and 50% of Ge₂₅S₇₅. With the aim to improve reliability of obtained results, multi sample analysis has been employed with simultaneous use of samples spin-coated onto glass substrate and onto silicon substrate in the fitting procedure.

Figure of merit and quality of the fit

The change of the polarization state is usually expressed by two parameters, amplitude ratio ψ and phase shift Δ, that are defined using the Fresnel reflection coefficients for p- and s- polarized light:

Spectroscopic ellipsometry is an indirect optical characterization method, where the measured values ψ_exp and Δ_exp are compared to the values calculated from the model. In the model structure, the model dielectric function which define optical constants of the layers and their thicknesses are assumed, and corresponding values of ψ_mod and Δ_mod belonging to the proposed model structure are calculated. In this way, the optical parameters of studied layers, such as complex refractive index (which includes refractive index as the real part and extinction coefficient as the imaginary part) together with geometrical properties (such as thickness of the layer and surface roughness) can be calculated.

In our case, the measured spectroscopic ellipsometry parameters, ψ^exp and Δ^exp fitted against the designed model in the spectral range from 0.05 eV to 6 eV using the mean square error (MSE) given in the following expression:

where N is the number of measured pairs of ellipsometric parameters ψ^exp and Δ^exp and M represents the total number of fitted parameters. σψ,iexp and σΔ,iexp are then the estimated experimental error of ψ^exp and Δ^exp, respectively. Ellipsometric data measured for all three angles of incidence 50°, 60° and 70° were used in the fit simultaneously. Moreover, multi sample analysis consisting the Ge₂₅S₇₅ films with the same optical constants parametrization on two different substrates were used in the fit. Data from optical reflectivity and optical transmission were used in the fit as well with the use of MSE in the similar manner as described in eq. 5.

Figure 2 shows the comparison of ellipsometry parameters, ψ (circles) and Δ (triangles) for an AOI of 70° in the spectral range from 0.05 to 0.8 eV (MIR part of spectrum) for Ge₂₅S₇₅ as-prepared onto Si substrate (left column) and for Ge₂₅S₇₅ as-prepared onto glass substrate (right column).

Fig. 2:

Measured values of ψ (circles) and Δ (triangles) for as-prepared Ge₂₅S₇₅ sample in the MIR part of the spectrum for sample deposited onto Si substrate (left column) and for sample deposited onto glass substrate (right column). The best fit for the angle of incidence 70° is shown by solid lines.

Based on proposed model described in details later, transmission and reflectivity could be calculated and used in the fit as well. Sufficient fit quality of the transmission and reflectivity data can be seen at Fig. 3. Incorporation of the transmission data into the fit improve reliability of calculated optical constants especially in the region close to the bandgap.

Fig. 3:

Measured values of transmission (symbols, left column) and reflectivity (symbols, right column) for t90 sample in the NIR-VIS-UV part of the spectra for sample deposited onto glass substrate. The best fit is shown by solid lines.

Film thickness and surface roughness

Measurement of the uncoated SiO₂/Si substrate revealed a native SiO₂ layer thickness of 2 nm. Measured thicknesses of Ge₂₅S₇₅ films are summarized in Table 1.

Although thickness of the films deposited onto glass substrate and onto Si substrate slightly differs, its dependence on annealing temperature is similar. The similar huge thickness decrease (approximately to the half) caused by annealing temperature as in the studied case has been reported previously for As₂S₃ spin-coated layers [26] and was explained by releasing of organic residues and by the glass densification.

In our previous paper [8] good agreement between surface roughnesses determined by spectroscopic ellipsometry on the samples prepared on soda-lime glass substrate and surface roughnesses determined by AFM was shown. Moreover AFM scans do not reveal any signs of seeding of crystallites. As can be seen from Table 1 surface roughness is only slightly dependent on the used substrate. Increase of surface roughness with the annealing temperature observed on both used substrates is connected with releasing of alkyl ammonium germanium salts residue from the films together with decreasing of film thickness.

Thicknesses of the films obtained by CL model are nearly the same within experimental error less than 1%. The values of thickness nonuniformity obtained by the fit of measured depolarization parameter are presented in the Table 1 and reflect possible wedging of the film.

It is worth to mention that stoichiometry of the samples is slightly changing. The gradual decrease of the sulfur content with increasing annealing temperature has been observed (see Fig. 7 at Ref. [8]). The composition after annealing at 240°C obtained by EDS measurement is Ge_29,1S_70,9.

Refractive index and extinction coefficients of Ge₂₅S₇₅ in wide spectral range

Figure 4 shows determined wide spectral range dispersion of the refractive index, n, and extinction coefficient, k, of Ge₂₅S₇₅ films annealed on different temperature. In the NIR-VIS-UV region (0.5<E<6.0 eV) all samples show a broad profile of refractive index with a peak moving towards lower photon energies (red shift) with the increasing annealing temperature. The refractive index is increasing with the annealing temperature suggesting densification of glass structure at elevated annealing temperatures. It is probable that as-prepared samples exhibits residual tensile stress and with the increasing annealing temperature stress relaxation takes place influencing refractive index as well. Although existence of the nano pores in the spin-coated Ge₂₃Sb₇S₇₀ thin films [27] and in ion sputtered TaO₅ coatings [28] were reported in the literature there is no direct evidence of nano pores in studied films.

Fig. 4:

Determined Ge₂₅S₇₅ refractive index n (left column), and extinction coefficient k (right column), as a function of photon energy in the wide spectral range. Indication of spectral ranges where different models [Mott-Davis, Wemple-DiDomenico (WDD)] are used (left), indicate the different oscillators used (right).

In the NIR-VIS-UV region, SWAE is present. The onset of SWAE is moving toward lower photon energies consistently with described shift of refractive index peak with the exception of t240 sample. Relationship between real (refractive index n) and imaginary (extinction coefficient k) part of complex refractive index is described by Kramers–Kronig relations [29], [30]. The extinction coefficient of all samples is ~0 in the visible spectrum.

In the MIR region (0.05<E<0.5 eV), optical active absorptions either from alkyl ammonium germanium salts residues or from absorption of photons by phonons are present.

In the following sections the wide spectral range of Ge₂₅S₇₅ refractive index and extinction coefficient will be divided into three parts (as shown in Fig. 4) where different models (Mott-Davis, Wemple-DiDomenico) will be applied to get more physical insight.

Effect of annealing temperature on the refractive index dispersion data

The effect of annealing temperature on the refractive index dispersion data in the semi-transparent part of spectra below the bandgap (0.5<E<2.5 eV) is further investigated using a Wemple-DiDomenico model [31], [32]. The refractive index data can be fitted in this spectral range to the single oscillator expression

where E is the photon energy, E₀ is the energy of the effective dispersion oscillator and E_d is the dispersion energy. From linear regression of dependence (n²−1)⁻¹ against E² (as shown in Fig. 5), the parameters E_d and E₀ could be calculated.

Fig. 5:

Dependence of 1/(n²−1) as a function of square photon energy obtained from ellipsometry (symbols) and linear fit of this data (solid lines) according to Wemple-DiDomenico model.

The parameter E_d, which is a measure of the intensity of the inter-band optical transition, is related to other physical parameters of the material through the following empirical relationship [31], [32],

where N_c is the effective coordination number of the cation nearest-neighbor to the anion, Z_a is the formal chemical valence of the anion, N_e is the effective number of valence electrons per anion and β is a two valued constant with either an ionic or covalent value (β_ionic=0.26±0.03 eV and β_covalent=0.37±0.04 eV).

Figure 6 shows the variation of E_d and E₀ as a function of annealing temperature of the Ge₂₅S₇₅ films. E_d is ~14 eV for annealing temperatures below 120°C and ~17 eV for higher annealing temperatures. In spite of eq. 7, increase of E_d could be explained both by increase of β and by increase of N_e. These findings supports results obtained from Raman measurements [8] and could be explained by alkyl ammonium germanium salt releasing from the structure and thermo-induced polymerization connected with changes of local arrangement. Annealing temperature about 150°C is sufficient for the majority of these changes.

Fig. 6:

Wemple-DiDomenico parameters E_d and E₀ as a function of annealing temperature.

E ₀ is ~7.3 eV for as-prepared film and is decreasing with annealing temperature. Parameter E₀ is associated with distance of centroids of valence and conduction band and therefore with optical bandgap (E0≈1.5+1.25Egopt) [33], [34]. From the decrease of the parameter E₀ with increasing annealing temperature, the decrease in the optical bandgap (red shift) could be deduced. Red shift of optical bandgap with increasing annealing temperature is described for other spin-coated systems e.g. [35] and was explained by increasing density of the spin-coated film reflecting increasing of film refractive index.

Effect of annealing temperature on the optical bandgap

According to the Mott and Davis [36], [37] and Tauc [38] models, the width of the localized states near the mobility edges depends on the degrees of disorder and defects present in the amorphous structure, in particular, differences in coordination number in amorphous state with respect to crystalline state [39], [40].

For photon energies (2.0 eV<E<6.0 eV) SWAE is observed. As mentioned previously, Tauc-Lorentz oscillator or Cody-Lorentz oscillators are used to model the band edge region.

For majority of amorphous semiconductors, the optical absorption in the vicinity of the SWAE obeys the Tauc relationship [38]:

where α=4πkλ is absorption coefficient, E is the energy of the incident photon, B is a constant and Egopt is the optical energy gap.

In order to obtain parameters from previous equation, dependence in the form of (αE)^1/2 as a function of photon energy E is depicted at Fig. 7 (left) for Tauc-Lorentz oscillator and at Fig. 7 (right) for Cody-Lorentz oscillator. The Tauc model (eq. 8) is used to describe its linear part (left, lines). Parameter B can be calculated as B=4πσminncΔE [37], where σ_min is the minimum metallic conductivity usually assumed as constant ≈350 Ω⁻¹cm⁻¹, n is the refractive index, c is the free space velocity of light and ΔE_c=ΔE_v=ΔE is the width of localized states near valence band mobility edge can be taken as a measure of a disorder.

Fig. 7:

(αE)^1/2 as a function of photon energy (symbols, left column) obtained using Tauc-Lorentz oscillator and its linear part described by Tauc model (solid lines, left column). (αE)^1/2 as a function of photon energy obtained using Cody-Lorentz oscillator (symbols, right column).

Influence of the annealing temperature leads to the considerable changes in the sample disorder (the change of parameter B^1/2). The width of localized states can be compared with as-prepared sample for all measured samples as (ΔE_tx/ΔE_as-prepared)=(B_as-prepared/B_tx)/(n_tx/n_as-prepared). Table 2 summarizes the change of the slope of SWAE, values of the refractive index for 3.0 eV used for calculation of ΔE ratio together with the results of this calculation.

From these results (Table 2), shrinking of the width of localized states due to annealing temperature can be observed. Annealing temperature 240°C decrease disorder in the material approximately to 1/3 in comparison with as-prepared sample.

The comparison of TL and CL oscillator is depicted at Fig. 7 (left column Tauc-Lorentz, right column Cody-Lorentz oscillator). The main difference is that CL parametrization allows optical transitions in the bandgap (tail states) and dependence of (αE)^1/2 as a function of photon energy is not linear above the bandgap. Generally the results obtained by CL model are very close to that obtained by TL model. For comprehensive discussion of these two oscillators parameters of TL model together with MSE are summarized in the Table 3, parameters of CL model together with MSE in the Table 4.

As can be seen from Table 4, CL model exhibits serious difficulties when use for the fitting of SWAE of studied samples. For example parameter E_t describing optical transitions in the bandgap has to be fixed or has significant error in the case of nearly all studied samples. Taking into account that CL parametrization have seven free parameters and TL only four free parameters and that the MSE for CL model is generally higher than for TL model it is more accurate to use Tauc-Lorentz oscillator for the studied samples.

Among all presented parameters usually value of parameter Egopt is of special importance because it determines range of the transparency. From the transmission measurements Egopt is usually obtained as interception of linear part of dependence of (αE)^1/2 as a function of photon energy E with the energy axis. In the TL parametrization this parameter is included (see eq. 1). Parameter Egopt (TL) obtained from TL model [15], [16] is presented in the Table 3 and can compared with parameter Egopt (CL) obtained from CL model (see eq. 2) [17].

Consistently both parameters Egopt (TL) and Egopt (CL) are generally decreasing with annealing temperature as expected from parameter E₀ (see Fig. 6) with exception of the last sample t240. On vacuum deposited samples, blue shift of optical bandgap was reported [9], [10] leading us to the idea that in our case two mechanism can be proposed for studied spin-coated samples a) decomposition of alkyl ammonium germanium salt molecules connected with decreasing of film thickness and increase of film density and b) thermo-induced structural polymerization. The former influence red shift of E_g, the later blue shift [9], [10], [35]. Very likely both of these mechanisms take part, decomposition of alkyl ammonium germanium salt molecules prevails for lower annealing temperatures, thermo-induced polymerization takes pronounced place for higher annealing temperatures. Moreover stress relaxation induced by annealing temperature could be presented as well.

Effect of annealing temperature in the MIR part of spectra

As was mentioned earlier, in the MIR part of spectra, optically active absorptions of alkyl ammonium germanium salts and absorptions of photons by phonons are present. Usually Lorentz oscillators are used for this type absorption. In case of amorphous materials, gauss oscillator can be used instead. The refractive index comparison of both oscillators used for the sample annealed at the lowest (as-prepared) and the highest (t240) temperature is depicted at Fig. 8. Usage of both oscillators leads to very similar results. For amorphous samples, use of gauss oscillator is usually preferred allowing to model broader absorption peak (Gaussian widening of the Lorentz oscillators).

Fig. 8:

Comparison of refractive index in MIR part of spectra calculated by Gauss and Lorentz oscillators.

Refractive index, respectively extinction coefficient of all studied films obtained using Gauss oscillators are depicted in the Fig. 9.

Fig. 9:

Determined Ge₂₅S₇₅ refractive index n (left column), and extinction coefficient k (right column), as a function of photon energy in MIR part of spectra.

From the results of Raman measurement described in our previous paper [8] some of these absorptions (especially that close to 3000 cm⁻¹) can be associated with alkyl ammonium germanium sulfide salts molecules. As we shown [8] intensity of this particular absorption matches well with results of EDS analysis and therefore infrared ellipsometry could be used as alternative method for determine of quality of annealed spin-coated films. Described intensity of absorption peak close to 3000 cm⁻¹ is still not negligible even for the highest annealing temperature used (240°C) suggesting that n-butylamine is difficult to be removed completely from the spin-coated films as was similarly reported in the literature in the case of spin-coated films using propylamine [35], [41], [42]. Presence of n-butylamine in the annealed films could be alternatively observed from comparison with the data reported for the bulk Ge₂₅S₇₅ [43] where n (632.8 nm)=2.132 and E_g=2.47 eV. From our measurements even for annealing temperature 240°C: n (632.8 nm)=1.993 (see Fig. 4) and E_g=3.13 eV (see Table 3) both still far from the bulk data.