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Abstract
This work reports trends for the electronic band edge, the transmission window, infrared active structural signatures, and ultra-high measurement density of the real refractive index from their electronic band edge out to 14 µm for the GexAsySe(100-x-y) glass family where Se(100-x-y)>Se60. This region of the ternary glass family has electronic band edges reported from 1.28 eV to 1.69 eV, optical shortwave cutoffs from 720 nm to 920 nm. Completing the transmission window is the longwave cutoff caused from the measured two-phonon infrared active structural signatures with a reported range from 15.85 µm to 18.42 µm. The refractive index dispersion is calculated with over 100 direct measured data points and are fit using a 3-term 6-variable Sellmeier equation with a R2 better than 0.99999999.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Non-oxide chalcogenide glasses are still in continual need of development as optical materials. These materials find use in fiber optics [1–3], memory materials [4,5], photonic devices [6–8], and traditional optical systems [9–12], all of which have aspects of their field that are limited by the currently available glasses and the limited availability of their optical properties. From a scientific perspective, chalcogenide materials can form glasses in large elemental ratios due to the chalcogen (S, Se, Te) being the glass former and not a stoichiometric compound. The combination of the allowance of homopolar bonds in the glass formation region and that many chalcogenide glasses are comprised of tetrels and pnictogens to accompany the chalcogens leads to the full range of glass dimensionality in the system. The chalcogens, being two-coordinated, are 1-dimensional structural units, the pnictogens are three-coordinated and create planar like structures from 2-dimensional structural units, and the tetrels are four-coordinated and are 3-dimensional structural units. This work explores the germanium arsenic selenide (Ge-As-Se) elemental ternary glass family which will inherently evaluate the dimensionality of the glassy matrix across the glass family.
Many papers that cover chalcogenide glass property trends tend to isolate a single tie-line in composition space be it a binary, ternary, or a component that is being substituted with another. [12–19] Isolating a tie-line is valuable but understanding the driving reason behind a trend can be difficult without additional data. This leads many researchers to analyze data from multiple sources and techniques which can have inherent off-sets from instrumental, sample, and operator differences.
The current work will show the full glass forming region of the Ge-As-Se glass family. This is one of the most common chalcogenide glass families studied due to the large glass forming region and the fact that the majority of the currently commercially available chalcogenide glasses can be found in this ternary directly or are derivatives of it. This work will focus on compositions that have 60% or higher atomic selenium content and aims to study the impact of composition on the optical properties such as the electronic band edge, the transmission window, infrared structural features, and the index of refraction.
The index of refraction as a function of wavelength for the Ge-As-Se glass family has very few compositions that have a complete dispersion curve created from more than a handful of wavelength measurements in the transmission window, and so we hope that this paper provides a valuable resource for optical designers working in the infrared space. An attempt was made to use the electronic band edge and the calculated single-phonon absorption edge as poles in the Sellmeier fitting equation, but this yielded unsatisfactory results, indicating once again that the Sellmeier equation should be used only for data fitting purposes rather than conveying any description of the physical reality underpinning the dispersion in this glass family. Future work will develop a stretched exponential function for these poles, with the aim of providing this missing physical insight.
2. Experimental details
The glass-forming region of the germanium arsenic selenide ternary, GexAsySe(100-x-y), was determined by systematically melting composition at x- and y-increments of 10 atomic percent and is shown by the black line in Fig. 1(a). The black squares in Fig. 1(a) indicate the fourteen glass samples studied in this paper, chosen because glasses with less than 60% selenium exhibit distinctly different optical behavior due to the presence of Ge-Ge and/or As-As bonds because of the chalcogen deficiency. [20] Glasses were formed by first batching 20 g of elemental materials, in the appropriate ratio, into a clean, water-free fused silica tube under ultra-high-purity argon glove box conditions. Following batching, the tubes were evacuated using a rotary vane pump and sealed using a gas-oxygen torch to create melting ampoules. Ampoules were rocked overnight in a tube furnace at 750-950 °C to ensure homogeneity and then quenched with forced air or water for some lower Tg glasses.
Fig. 1. (a) A ternary diagram of the samples measured in this paper and the glass-forming region, and (b) the mean coordination number of the samples studied.
As will be shown below, many of the properties of these glasses are not strict functions of the elemental composition but are more often correlated with the mean coordination number of the system. Figure 2(b) shows a close-up view of the ternary of fourteen glasses studied in this paper. The red dotted lines show the mean coordination number,
Fig. 2. (a) Tauc plots showing the linear extrapolation of the direct and indirect band edge calculated from the data in the inset, which is the shortwave cutoff for the As40Se60 glass, and (b) variation in the indirect electronic band edge as a function of composition.
, which is calculated by:
The refractive index of each of these glasses was measured using an M3MSI minimum deviation refractometer. To capture the full spectral range, the system uses either a tungsten or a glow-bar light source which is passed through a monochrometer for wavelength selection, and combination of Si, InGaAs, and cooled MCT detectors combine to give the system a spectral range of 0.38–14 µm. The system can achieve an accuracy of better than $1\; x\; {10^{ - 4}}$ refractive index units on large wedge samples, but due to the small laboratory scale of the samples investigated we have assigned a system error of $2\; x\; {10^{ - 3}}$ to all measured data.
Table 1. Indirect and direct band edges (in eV and nm), mean coordination numbers, short- and longwave cutoffs of all measured compositions
The transmission spectra for the electronic band edge was measured on an Essentoptics Photon RT UV/Vis spectrometer and the data was gathered using their software, Photon Soft v3.14.4.8. Scans were made in the 400-1800 nm range for all samples at 0° AOI.
The transmission spectra for the multi-phonon edge of the transmission window and structural data was measured on a Perkin Elmer Frontier Optica Fourier Transform Infrared Spectrometer (FTIR). Transmission scans were from 2 µm – 25 µm with a resolution of 4 cm-1 and 64 accumulations. The reflectance measurements, with a 10° near normal reflectance accessory, utilize the same instrument and scan window with a 16 cm-1 resolution and 128 accumulations.
3. Results and discussions
3.1 Electronic band edge
Figure 2(a)’s inset shows an example of the short-wave band edge of the As40Se60 composition where the transmission of the material drops to zero due to the total absorption of photons above the electronic band edge of the material. This figure shows the total (as opposed to internal) transmission; the baseline of ∼60% transmission is due to Fresnel reflection losses from the faces of the sample due to the high refractive index.
In order to standardize the calculation of the band-edge position, Tauc plots [22] were created based on the measured Vis/NIR transmission of each of the fourteen samples of which the inset in Fig. 2(a) is a representative. Tauc plots are created by converting the wavelength axis to photon energy (hν) in eV and converting transmission axis to the photon energy multiplied by absorption coefficient raised to the power of ½ or 2, for indirect band edge calculations and the direct band edge calculations respectively. The absorption coefficient was calculated by using the Beer-Lambert equation and the sample thickness. By extrapolating the linear region of the middle portion of the curve to the ordinate axis, the photon energy of the electronic band edge can be calculated. Figure 2(a) shows the direct and indirect band edge extrapolation for As40Se60. The difference in direct vs. indirect band edge calculation comes from the inherent nature of the direct band edge calculation which samples the lower wavelengths or higher energy section of transmission measurement. The glasses in this study all yielded higher direct band edge values over their indirect values and are listed in Table 1.
Figure 2(b) shows the variation of the indirect electronic band edge with composition in the Ge-As-Se ternary glass family. Plotting the direct electronic band edge showed the same trends as the indirect calculations. For consistency with the units in the rest of the paper, the band edge is shown in nanometers rather than eV. Table 1 contains the values in both sets of units.
For all but one of the compositions, the band edge shifts to shorter wavelengths with increasing mean coordination number <r > . Utilizing a Pearson correlation between the electronic band edge and the average coordination number yielded a strong correlation coefficient of 0.8. As will be seen throughout this paper, the Ge40Se60 composition is an outlier due to its overconstrained network in combination with the overabundance of Ge in the alloy, creating Ge-Ge homopolar bonds in the network.
3.2 Transmission window
Figure 3(a) shows an example of the As-Se binary materials transmission window using the spectra from the Vis/NIR and FTIR. It should be noted that there is an extrapolated data region between the two spectra from the two instruments from 1.8 µm to 2 µm. Values for the optical shortwave and longwave cutoff points were determined by converting the transmission spectrum to absorbance, subtracting the minimum value of the absorbance spectrum across the entire spectrum to get a near approximation of the internal absorbance, normalizing to 1 cm thickness to obtain absorption coefficient spectrum, and using the absorption coefficient value of 1 at the electronic band edge for the shortwave cutoff and at the multiphoton edge for the longwave cutoff. Figures 3(b) and 3(c) show the trends across the ternary space for the shortwave and longwave cutoff respectively, with the discrete values reported in the Table 1. The shortwave trend is very similar to the electronic band edge calculated by the Tauc plots. This is expected because it is the material’s band edge that controls those values, and variations in the trend could be due to the shortwave cutoff being more susceptible to fluctuations in sample preparation.
Fig. 3. (a) Transmission window of the As-Se binary tieline, (b) variation of the shortwave cutoff with composition, and (c) variation of the longwave cutoff with composition
This work will focus on the structural signatures that make up the multi-phonon edge in later sections, but there are impurity and structural features in the FTIR transmission spectra. The feature in Fig. 3(a) at 2.9 µm is associated with OH bonds, the feature at 4.5 µm is associated with Se-H bonds, the feature at 6.3 µm is associated with OH bonds, and the feature at 13.5 µm is associated with Se-Se bond [23].
3.3 FTIR structural information
The absorption coefficient spectra are also used to get structural information from the Infrared-active vibrational modes in the glasses. To show how we utilize the structural information for the Ge-As-Se ternary, SiO2 glass will be used as an example. Figure 4(a) shows the transmission and reflectance measurement of SiO2 glass measured from 2 µm – 12 µm. The transmission measurement has absorption features from 3.75 µm to 4.75 µm before the absorption is too great for the instrument’s detector. For materials with refractive index’ discussed in this paper, the difference between a 10° near normal reflectance in air and normal incidence reflectance in a vacuum is calculated to be less than 1%, this is considered negligible for this work and the measurements were treated as normal incidence. These assumptions also allow reflectance to be related to the dielectric constant in the form of Eq. (2).
Where $\varepsilon $ is the dielectric constant, and R is the measured reflectance. The relationship in Eq. (2) means the distinct poles or sharp increases in reflectance can be attributed to fundamental vibrational modes in the material. Therefore, in the case of the SiO2 glass, the transmission absorption features at the multi-phonon edge are not where the fundamental vibration modes are. Instead, the transmission scan’s absorption features appear to be two-phonon vibrational absorptions. To further verify the two-phonon relationship, the transmission values were translated by a factor of two in wavelength. The absorption features in the translated transmission now align well with the fundamental vibrational modes measured in reflectance.Fig. 4. (a) FTIR transmission and reflectance features with a translated transmission spectrum of SiO2 glass and (b) FTIR reflectance of As40Se60
Figure 4(b) is an example of a reflectance measurement in this ternary space using As40Se60, and it does not show any fundamental vibrational features in the measurement range. All compositions were measured in reflectance, and like the As40Se60, none of them had a fundamental vibrational frequency in the measurement range. Therefore, we will evaluate the structural features that cause the longwave cutoff as two-phonon vibrations.
Figure 5 shows structural features that can be found between 15 µm and 25 µm from the measurement. This window corresponds to frequencies from 400 cm-1 to 666 cm-1, and when translated to single phonon energy is 200 cm-1 to 333 cm-1. Figure 5 has all of the plots with the measured wavelength on the bottom x-axis, but the top x-axis is in ½ frequency space from the measured frequency to correlate to the single phonon and fundamental frequency of the vibrational feature. It should also be noted that the single phonon vibration frequency space aligns very well with the range of Raman spectroscopy measurements for these glasses [24,25] Due to the some of the measurements nearing the limits of the detector, a Savitzky-Golay smoothing function was applied to the spectra to remove high-frequency dark noise. Figure 5(a) shows the As-Se binary system where the absorption coefficient increases as a function of arsenic content. With the assumption that the structures available are Se-Se homopolar bonds and stoichiometric As-Se3/2 structural units, this evolution shows that the As-Se3/2 unit has stronger infrared-active vibrations compared to those of the Se homopolar bonds. The As-Se3/2 peak (or culmination of multiple peaks) is centered at a measured 20.6 µm and a translated fundamental frequency of 243 cm-1. Similarly, with the Ge-Se binary in Fig. 5(b), if the dominant structures are the Se homopolar bonds and stoichiometric Ge-Se2 structures, the Ge-Se2 structure has the stronger infrared-active signature. The Ge-Se2 structures have a peak (or culmination of peaks) measured at 17.75 µm and a number of peaks that make up the measured signal between 20–21.5 µm which corresponds to fundamental vibrational frequencies of 281 cm-1 and a range from 250–232 cm-1 respectively. For the Ge-Se system the Ge40Se60 occupies the Se-deficient space beyond stoichiometry, exhibiting Ge-Ge homopolar bonds. In this study, where there is only one clear composition, Ge40Se60, with expected Ge homopolar bonds, there was not a clear structural signature in the evaluated window. Table 2 lists the compositions, including single crystal germanium, the largest possible value of excess atoms from stoichiometric GeSe2-As2Se3 based on a 100 atom count, and the calculated homopolar bonds/atom.
Fig. 5. FTIR absorbance features of (a) the As-Se binary tieline, (b) the Ge-Se binary tieline and calculated proportional Ge-Ge signal for Ge40Se60, (c) the 90% Se tieline and Se-Se bond features, (d) the 80% Se tieline, (e) the 70% Se tieline, (f) the 60% Se tieline
Table 2. Excess atom from stoichiometry and the homopolar bonds per atom for each composition.
The most overconstrained and Se deficient glass in this work is the Ge40Se60 and some of the properties make it seem anomalous to the trends of Se 60% and higher glasses. The scanned structural signature was difficult to identify a clear Ge-Ge signature, but it is expected that it is there. Other work have proposed a Se3/2-Ge-Ge-Se3/2 ethane like unit. This not only has homopolar bonds but is a 1-dimentional unit and could be linked to form chain like structures in the glass. If this is true, it could help explain the anomalous properties found in the Ge40Se60 [26,27]. In an attempt to identify a Ge-Ge homopolar signature, a calculated signal for the Ge40Se60 composition was constructed using the infrared signature of single crystal germanium. The Ge-Ge signal in Fig. 5(b) was created by using a ratio of the calculated Ge-Ge bonds per cm3, via Eq. (3), for single crystal germanium and Ge40Se60.
Identification of a signature from the Se homopolar bonds was done by taking the 90% Selenium compositions and subtracting a ratio factored (RF) stoichiometric or near-stoichiometric signature. The RF is determined by the ratio of the pnictogen or tetrel in the binary system. The residual could be considered the Se-Se contribution. The 90% selenium signatures in Fig. 5(c) show the difference of the two binaries, and the RF subtracted curves show that there is a Se-Se infrared active signature. Both subtracted curves show a signature around a measured 20.2 µm which correlates to a fundamental frequency of 247 cm-1. This aligns well with previous findings in literature [23]. The Se features are not directly on top of each other, and this could be due to the excess selenium that is still in the Ge30Se70 and it not being a perfectly stoichiometric composition.
The 80% Se series’ infrared signatures in Fig. 5(d) is the first series with a ternary composition and shows a combination of the two binary compositions. The 70% Se spectra in Fig. 5(e) continue to show the ternary evolution from one binary to the other. The 60% Se spectra in Fig. 5(f) show a nice binary to binary evolution for the 281 cm-1 feature, but the less so for the features in the 250 cm-1 to 233 cm-1. The lack of a clear trend in this region could be one or both of the following: with the exception of As40Se60, all of the compositions are both selenium deficient and overconstrained, and some of these samples were nearing the detectors limit and had more noise in the second region of interest.
3.4 GeAsSe dispersion curves
The refractive index dispersion for each of the samples was fit using a three-term, six variable, Sellmeier equation of the form:
where n is the refractive index, $\lambda $ is the wavelength in microns, and ${B_i}$ and ${C_i}$ are fitting parameters. In this formalism, the Ci can be considered as the poles of the dispersion and the ${B_i}$ the coupling strength to those poles. As seen below, this form of Sellmeier equation does not adequately account for the physics of the light-matter interaction and so the ${B_i}$ and ${C_i}$ should be considered only as fitting parameters rather than representative of physical realities.Figure 6(a) shows the measured refractive index data for the As40Se60 composition as well as the best fit of Eq. (4) to the data. Error bars have been omitted for clarity of presentation, but it should be remembered that we assign an error of $2\; x\; {10^{ - 3}}$ to all measured refractive index data due to the laboratory scale of the samples.
Fig. 6. (a) an example of the As40Se60 glass measured and fit refractive index curves, (b) refractive index fits for each of the studied samples, and (c) the change in refractive index at 10 µm as a function of composition.
Initially, we attempted to use the values of the electronic and single-phonon band edges (Table 1) for the poles created by ${C_1}$ and ${C_3}$ in Eq. (4). These fits yielded very poor results, most of them not converging to a solution, and none with an acceptable coefficient of determination (R2) value. To achieve the optimal fits of Eq. (4) to the measured data, a Levenberg Marquart iteration algorithm was first used to create a best-guess solution which was subsequently fed as a starting guess into an Orthogonal Distance Regression iteration algorithm to converge upon the best fit. All fits achieved this way showed an R2 better than 0.99999999. The fitted curves for each of the compositions studied here is shown in Fig. 6(b) and the associated fitting parameters are listed in Table 3.
Table 3. Sellmeier fits of the studied compositions
Figure 6(b) shows that the glass with the highest refractive index in this family is As40Se60 binary and that the lowest index is at the Ge30Se70 binary. As shown in Fig. 2(b), the Ge40Se60 binary is consistently an outlier given its very highly overconstrained network (<r > = 2.8). To help clarify the compositional trends shown in Fig. 6(b), Fig. 6(c) shows the refractive index of all of the measured compositions at 10 µm. This representation flattens out some of the interesting curvatures exhibited by the fits in Fig. 6(b) but allows the reader to see how the ratio of As to Ge in the glass directly impacts the resultant refractive index, with the increase in arsenic raising the index. This is a physical property that does not correlate to average coordination number, the visual trend in Fig. 6(c) is perpendicular to the average coordination lines in Fig. 1(b).
3.5 Structural and optical correlations
When using the structural information to identify the structural feature with the shortest wavelength or highest frequency (which would control the longwave cutoff), the trends in Fig. 3(c) from the data in Table 1 is explainable. For the As-Se binary, while the Se-Se bond is the shortest wavelength at 20.2 µm, it’s infrared active signature is so small, that it is the intensity and breadth of the As-Se3/2 signature at 20.6 µm that controls the longwave cutoff. With the Ge-Se binary and the ternary compositions, the strength of the Ge-Se2 signature at 17.75 µm or 281 cm-1 control the rest of the trend in the longwave cutoff in the evaluated region of this glass family.
4. Conclusions
This work reported a comprehensive refractive index, optical transmission window, electronic band edge, and infrared active structural signatures for the majority of the excess selenium region of the germanium arsenic selenium glass forming region while also including additional 60% selenium tie line compositions. The measurement techniques utilized in this work did not show evidence of large-scale phase separation via scattering trends in the transmission measurements or clear additional features in the IR-active structural signals.
For the most of the measured and analyzed trends in this work, the Ge40Se60 composition is found to be anomalous in this material set. The highest level of bonding constraint, along with Ge homopolar bonds is the leading cause of this sample’s pattern deviation. If the previously proposed Se3/2-Ge-Ge-Se3/2 ethane-like units are assumed, this structure reverses the dimensionality of the glassy network back to a one-dimensional structure as well. Such a drastic change in structure could explain the anomalous properties for this composition. To better understand the trends of the some of the properties, the Ge40Se60 was excluded from interpretation.
The electronic band edges and shortwave cutoff calculations had expected similar trends due to both being controlled by the electronic transitions near the band edge. With the removal of the Ge40Se60 composition due to reasons explained above, the remaining compositions had a Person correlation coefficient of 0.8 to average coordination number, which is a strong to very strong correlation. With large, 10 percent, increments in compositional space and the small data set, a higher correlation is preferred for determining a controlling mechanism of a property, but it should not be ignored.
The longwave cutoff was explained via the infrared active structural units measured at the proposed two-phonon vibrational frequencies. The Ge-Se2 peak at 17.75 µm affected the longwave cutoff the most, followed by the As-Se2 feature at 20.6 µm. Reflectance spectroscopy was used as evidence towards the two-phonon signatures. The two-phonon signatures were used to identify the simple stoichiometric structural units, As-Se3/2, Ge-Se2, and Se-Se in the glasses.
To evaluate the trends in the refractive index, the Ge40Se60 composition is once again discarded. Once this composition was removed, the two binaries exhibited monotonic evolutions in refractive index, but were not linear. The refractive indexes in the ternary space on the iso-selenium content tie-lines also have monotonic evolutions and almost all data points show a linear relationship on those tie-lines.
Funding
Rochester Precision Optics LLC.
Disclosures
The authors declare no conflicts of interest
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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