Introduction

Laser-based micromachining is a valuable technique that facilitates the miniaturization and alteration of materials at the microscale [1]. This approach can be employed to produce a variety of components applicable in fields such as micro-optics, micro-electronics, and micro-biology, as well as industries focused on renewable energy, automotive, aerospace, and more [1, 2]. Surface microstructuring is a progressive branch of materials engineering. Due to the efforts made, various routes for the formation of microlenses on the surface of glasses have been discovered with application to image processing and optical fiber bonding. As an alternative route to the presented direct laser writing, surfaces are modified employing hot-embossing by heating the surface through a stamp, e.g. [3, 4], additive printing technology of optical material with lower resolution and limit in optical quality, e.g. [5], self-assembly of microparticles on the surface, e.g. [6] or by multi-step soft lithography and wet etching techniques, see e.g. [7]. The direct laser writing (DLW) method offers several benefits over other micromachining/microstructuring techniques. These advantages include (a) non-contact modification, with no contamination of the material surface, (b) a one-step, environmentally friendly process, offering an alternative to methods like chemical etching, and (c) the ability to modify materials by selectively removing different compounds through varied laser illumination durations, wavelengths, and/or power densities [2].

Chalcogenide glasses have several advantages that make them suitable for micromachining/microstructuring using DLW. (a) They can be prepared in multiple forms, including bulk samples, thin films, and fibers, offering flexibility for diverse applications. (b) These glasses exhibit high infrared transparency, higher values of linear and nonlinear refractive indexes, and comparably low glass transition temperatures, melting temperatures, and bond energies. This makes them ideal for various optical, optoelectronic, and electrical devices operating in the near and mid-IR regions [8, 9]. (c) Chalcogenide glasses are also often photo-sensitive, aiding in localized surface modifications using the DLW technique, e.g. photo-induced volume changes like photo-expansion [10, 11], photo-contraction [12, 13] or ablation [14, 15], commonly used in glassy surface microstructuring and forming concave or convex microlenses and their arrays [13, 16,17,18].

Ge–Sb–S glasses are well-established glassy systems. Consequently, several of their attributes, including glass-forming ability [19,20,21], density [22,23,24], structure, e.g. [25,26,27,28,29], optical [22, 30, 31], thermal [22,23,24, 30, 32], electrical [24, 30] or mechanical [22] properties, have been investigated. Additionally, this glassy system is devoid of any toxic elements at low concentrations. Yet, only a limited number of studies have explored the photo-induced surface alterations, with particular attention to some chemical compositions from the Ge–Sb–S glassy system. These include: (a) Formation of microlenses on the surface of (GeS2)0.74(Sb2S3)0.26 when illuminated by a CW 532 nm laser, attributable to the local thermal expansion of the overheated material [33]. (b) Formation of smooth microcraters due to increased viscous flow, as well as microcraters surrounded by a notable number of ejected particles because of explosive boiling, both observed on the surface of bulk glassy Ge0.35Sb0.10S0.55 using a CW laser emitting at 785 nm [34]. (c) Formation of microcraters on the bulk samples and thin films through ablation under pulsed laser illumination ((GeS2)0.3(Sb2S3)0.7, illuminated by a 5 ns pulsed laser emitting at 213 nm) [35].

The objective of this study is to investigate the formation of microlenses on the surface of Ge–Sb–S bulk glasses using a CW laser emitting at 532 nm. Additionally, the research evaluates how chemical composition affects the characteristics and properties of the resulting microobjects/lenses. The chemical compositions studied include a stoichiometric set of glasses represented by (GeS2)1−x(Sb2S3)x (x = 0–0.88), and two sets of samples with a constant amount of either Ge or Sb, represented as GexSb0.17S0.83−x, where x = 0.13–0.24, and Ge0.18SbxS0.82−x, with x = 0.03–0.10.

The created microlenses have been analyzed in terms of key parameters crucial for potential applications, such as fundamental dimensions and focal length. Given the variations in the chemical composition of the glasses studied, the continuous-wave laser emitting at 532 nm enables an examination of the influence of over-band gap, near-band gap, and sub-band gap photons on microlens formation.

Experimental

Three sets of bulk glasses of Ge–Sb–S system were prepared, i.e. (a) stoichiometric compositions (GeS2)1−x(Sb2S3)x, x = 0–0.88; (b) set with constant amount of Sb: GexSb0.17S0.83−x, x = 0.13–0.24; and (c) glasses with constant Ge amount: Ge0.18SbxS0.82−x, x = 0.03–0.10.

The compositions we prepared and examined are based on the glass-forming ability of Ge–Sb–S glasses as per Ref. [21] and are depicted in the part of ternary Ge–Sb–S diagram in Fig. 1. The black star in Fig. 1 signifies the composition (GeS2)0.66(Sb2S3)0.34, approximately Ge0.18Sb0.18S0.64. This composition is consistent across all three glass sets we studied. We synthesized each glass from pure elements: Ge (5N, Alfa Aesar, Germany), Sb (5N, VHG Labs, United Kingdom), and S (> 4N, Sigma-Aldrich, USA), utilizing the traditional melt-quenching method in a sealed, evacuated quartz ampoule. The mixture, with a weight aligned to the elemental ratios (around 10 g total), was placed in a rocking electric furnace. It was gradually heated up to a final reaction temperature of 950 °C. Once the melt reached this reaction temperature, we maintained its homogenization for 2 h. The resulting glass was then procured by cooling the ampoule in water. To eliminate internal stresses in the glasses post-synthesis, we annealed them at temperatures roughly 50 °C below their respective glass transition temperatures.

Figure 1
figure 1

The part of ternary diagram Ge–Sb–S showing the chemical compositions of the prepared glasses: black circles represent the stoichiometric set (GeS2)1−x(Sb2S3)x, x = 0–0.88, blue empty cubes correspond to the set GexSb0.17S0.83−x, x = 0.13–0.24, and red solid cubes signify the set Ge0.18SbxS0.82−x, x = 0.03–0.10. The black star indicates the composition (GeS2)0.66(Sb2S3)0.34, i.e. ≈ Ge0.18Sb0.18S0.64, which is consistent across all three analyzed sets. The drawn dotted (magenta) and dashed (olive) lines illustrate the glass forming regions according to Ref. [21].

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The samples for all optical measurements were prepared to a thickness of approximately 1.4 mm, with both surfaces polished to optical standards. For the final polishing, we used a suspension of Al2O3 with a grain size of 50 nm in ethylene glycol, resulting in a Root Mean Square of Residual Roughness (RMS-RR) [36] of about 4–5 nm.

The crystalline phase’s absence in the prepared glasses was confirmed through Powder X-ray Diffraction Analysis using a D8-Advance diffractometer (Bruker AXE, Germany) equipped with Bragg–Brentano θ–θ geometry (40 kV, 30 mA), Cu Kα radiation, and a secondary graphite monochromator. The real chemical composition of the glasses and the formed microlenses was verified with a JSM 5500-LV (Jeol, Japan) featuring an energy-dispersive X-ray (EDX) analysis detector (GRESHAM Sirius 10, Japan) and an accelerating voltage of 20 kV. The X-ray characteristic photons formation depth varies between ≈ 2.1 and 3.2 µm, depending on the chemical composition. EDX analysis was performed using the value of spot size parameter < 50 with magnification 4000×  for a maximum time 3 min to avoid the possible changes of materials/microlenses by the action of primary electrons. Optical properties were assessed using UV/Vis Spectroscopy with a Perkin-Elmer Lambda 12 instrument (USA). The glass transition temperature (Tg) for the examined glasses (in powder form) was determined using a Differential Scanning Calorimeter Diamond (Perkin-Elmer, USA), applying a heating rate of 10 °C min−1 within a 50–500 °C temperature range. The coefficient of thermal expansion (CTE) below Tg was determined using rectangular bulk samples (typically 10 × 5 × 2 mm3) at a heating rate of 10 °C min−1, measured with a Thermomechanical Analysis (TMA CX 04R, R.M.I, Czech Republic). The thermal conductivity of selected samples (κ) was obtained by measuring heat capacity cp and thermal diffusivity k using a laser flash system LFA 457 (Netzsch, Germany), for more information on the determination of κ see e.g. Ref. [37]. Microlenses were created by exposing the sample surfaces to a continuous-wave laser at λ = 532 nm. The illumination set-up was equipped with a microscope objective (60× magnification, 0.85 numerical aperture) producing a laser beam diameter of approximately 40 µm and a maximum power density of 190 W cm−2, for an exposure time of 600 s. Raman spectra of the glasses and the formed microlenses were recorded using the Raman Spectrometer Dimension-P2 (Lambda Solution, USA) with an emission at 785 nm. The reduced Raman spectra were derived from the Gammon-Shuker equation [38]. The topography of non-illuminated glassy surfaces and created micro-objects was assessed using a Digital Holographic Microscope DHMR1000 (Lynceé Tec, Switzerland) operating at 785 nm in reflection mode. Nanoindentation measurements were conducted using the TI 950 TriboIndenter (Hysitron, Netherlands) equipped with a Berkovich-type diamond tip (maximum force: 300 µN).

Results and discussion

Characterization of examined glasses

No traces of crystalline phases were detected in the examined glasses by XRD analysis within its detection limit. Table 1 presents the actual chemical composition of the prepared glasses. It also displays the energy values (E03) corresponding to an absorption coefficient (α) of 1000 cm−1, used here as the optical band gap width. Additionally, the table lists the optical penetration depths (dp) for excitation light (λ = 532 nm), calculated as dp532 nm = 1/α532 nm [33], as well as the glass transition temperature values (Tg).

Table 1 List of the essential optical (expressed as optical band gap E03 value and optical penetration depths at λ = 532 nm, i.e. Eph = 2.33 eV (dp532 nm)) and thermal properties (glass transition temperature, Tg) of the evaluated Ge–Sb–S glasses: ●—stoichiometric set (GeS2)1−x(Sb2S3)x, x = 0–0.88, □—set GexSb0.17S0.83−x, x = 0.13–0.24, and ■—Ge0.18SbxS0.82−x, x = 0.03–0.10
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From Table 1, it can be observed that the values of both E03 and dp532 nm decrease as the Sb2S3 content in stoichiometric (GeS2)1−x(Sb2S3)x increases aligning well with the findings in Refs. [22, 30]. For non-stoichiometric compositions, the values of both parameters diminish with reduced sulfur content. Furthermore, dp532 nm values span a broad range, from hundreds of nanometers to millimeters (see Table 1). Thus, the effect of varied dp532 nm values on the material’s response to illumination should be considered.

The glass transition temperature (Tg) was identified as the midpoint of the observed endothermic effect on DSC curve. It is important to highlight that the Tg value likely influences the formation of micro-objects, particularly during continuous-wave illumination. During this illumination, the conversion of absorbed light to heat and a subsequent rise in the local sample temperature have been noted, e.g. in [10, 33]. The values of Tg of stoichiometric compositions significantly decrease with Sb2S3 content which is in agreement with [22, 28, 30]. This decrease is attributed to the lower rigidity of the glassy network as a result of substitution of GeS4/2 tetrahedra by SbS3/2 trigonal pyramids [28]. In both sets of non-stoichiometric glasses, Tg values decrease with the increase in sulfur content. This is related to a weakened glassy structure, most probably due to formation of structural units with –S–S– bridges like, e.g., S3Ge–S–S–GeS3, S2Sb–S–S–GeS3 units, as well as the formation of S8 rings (see Raman spectra in Supplementary materials for more details).

Direct laser writing by CW 532 nm laser

The samples, polished to the optical quality, were illuminated by CW laser (532 nm), using various laser power densities up to 190 W cm−2 for 600 s. Depending on the chemical composition of examined glasses, certain laser power densities induced localized volume expansions on the glass surface. These expansions remained in place after the laser was switched off. As a result, microlenses were formed, which remained stable under ambient conditions, as depicted in the SEM image in Fig. 2a.

Figure 2
figure 2

a SEM image of a microlens created on the surface of (GeS2)0.66(Sb2S3)0.34 using FL = 105 W cm−2 for 600 s illumination and b the topographical profiles of microlenses (solid line) and “dimple” deformed microlenses (dashed line, explained in the text) created on the surface of stoichiometric (GeS2)0.66(Sb2S3)0.34.

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The microlenses were analyzed using digital holographic microscopy to study their topography (Fig. 2b). A key metric for characterizing them was their height (h). As depicted in Fig. 2b (solid lines), for the (GeS2)0.66(Sb2S3)0.34 glass, the height increases with the increasing laser power density (FL), reaching up to 730 nm at FL = 105 W cm−2. This increase in height follows a linear trend on a logarithmic scale of laser power density, aligning well with the empirical relationship between h and ln FL as mentioned in e.g. [33, 39]:

$$h = \alpha_{{{\text{eff}}}}^{ - 1} \cdot \ln \frac{{F_{L} }}{{F_{{{\text{th}}}} }},$$
(1)

where \(\alpha_{{{\text{eff}}}}^{ - 1}\) represents the effective optical penetration depth and Fth denotes the threshold power density necessary for the microlenses formation.

When the laser power density exceeds 105 W cm−2, the formed microlenses start to exhibit deformation, evidenced by a reduction in their height. This reduction in height (h) results in a deviation from the linear trend in the relationship between h and ln FL. We attribute these deformations to the increased overheating of the illuminated region. Greater overheating amplifies viscous flow [40], which likely influences the changes in the height and shape of the formed microlenses. Surface tension in the molten microlenses is also expected to play a significant role. At the peak laser power density used (FL = 190 W cm−2), the formerly symmetrical shape of the microlenses is altered, with a noticeable dimple forming. This altered microlens shape presents two asymmetrical peaks, probably caused by the Gaussian-like laser beam, which overheats the material most intensely at the center of the illuminated region. Additionally, an expansion in the width of the micro-object was noted.

In this text, we focus on the formation of microlenses that exhibit a regular shape consistent with the linear segment of the h versus ln FL relationship. Several methods were employed to understand the mechanisms underlying their formation. Figure 3 displays the EDX spectra, normalized to the S–Kα signal (2.307 keV). The chemical composition of the fabricated microlenses appears to be nearly identical to that of the non-illuminated surface, within experimental error margins, as shown in the results for stoichiometric (GeS2)0.66(Sb2S3)0.34 (Fig. 3a) and for sulphur-rich Ge0.13Sb0.17S0.70 (Fig. 3b). In addition, no deformations of microlenses and non-illuminated areas were detected by DHM after EDX analysis which confirms that the samples have not been affected by accelerating electrons during EDX analysis. Figure 4a provides typical Raman spectra for both microlens and non-illuminated samples for the two chemical compositions: (GeS2)0.66(Sb2S3)0.34 and Ge0.13Sb0.17S0.70 glasses. Notably, the Raman spectra for the microlenses and the non-illuminated surfaces are virtually indistinguishable, considering the experimental error. This suggests that illumination does not induce photo-chemical changes, such as the proposed photo-oxidation believed to cause photo-expansion in Ge–Ga–S bulk glasses [41]. Similarly, no photo-structural changes were identified in either stoichiometric or non-stoichiometric glasses.

Figure 3
figure 3

The comparison of EDX spectra of the highest formed microlens with non-illuminated surface (marked as non-ill) for a stoichiometric (GeS2)0.66(Sb2S3)0.34 and b sulphur-rich Ge0.13Sb0.17S0.70 bulk glasses.

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Figure 4
figure 4

The comparison of a Raman spectra of microlens and non-illuminated surface for stoichiometric (GeS2)0.66(Sb2S3)0.34 and sulphur-rich Ge0.13Sb0.17S0.70 and b histogram illustrating the mechanical properties (contact depth, nanoindentation hardness) for microlens and non-illuminated surface of stoichiometric (GeS2)0.66(Sb2S3)0.34 bulk glass, all for the highest formed microlenses.

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Finally, the nanoindentation hardness, as determined by the Oliver–Pharr model [42], was compared between the microlens and the non-illuminated surface. Figure 4b displays a histogram showing the contact depth to which the indenter was pressed for both the microlens and the non-illuminated (GeS2)0.66(Sb2S3)0.34 glass surfaces. The indenter penetrated to a greater contact depth (hc) on the microlens surface (hc = 51.9 ± 0.2 nm) compared to the non-illuminated surface (hc = 47.7 ± 0.1 nm). This increased contact depth for the microlens is associated with a 6.2 rel% reduction in nanoindentation hardness compared to the non-illuminated surface (Hind ≈ 2.87 ± 0.02 GPa for the microlens and ≈ 3.06 ± 0.01 GPa for the non-illuminated surface).

Based on our findings, we hypothesize that the microlenses, i.e. local volume expansions, form on the surface of all examined glasses probably by thermal mechanism without any significant contribution of other factors (photo-oxidation, photo-structural changes), i.e. by a frozen-in the thermal volume expansion of locally overheated materials similarly as was observed for different chalcogenide glasses or even oxide glasses [10, 33, 43]. The stability of microlenses over time and temperature has been studied in our previous works on both Ge–Sb–S and heavy metal oxide glasses. In the case of (GeS2)0.74(Sb2S3)0.26 glass [33] we observed the stability of the same microlens for 2000 h (almost 3 months) at room temperature and the height decreased in units of %. When the temperature was increased to Tg value, the microlenses disappeared and the surface was reconstructed. In the case of microlenses on PbO–Ga2O3 glasses, stability was demonstrated even after 9 months (undetectable changes in height from 1607 to 1605 nm after 9 months; see Fig. S5 in [43]). We assume that the formed microlens represents a “frozen” state, similar to rapidly cooled glass, where the rate of cooling prevents crystallization, although devitrification or macroscopic changes on topography can only occur after an extremely long time at temperatures under Tg.

Microlenses formation and the parameters characterizing microlenses shape

The parameters utilized for examining microlens formation on Ge–Sb–S glass surfaces are detailed in Table 1 and 2. Microlenses do not form on binary chalcogenide GeS2 glass when illuminated at 532 nm, an expected outcome given that the photon energy of the employed light (Eph = 2.33 eV) is substantially below the E03 value, as shown in Table 1. Under these conditions, an insufficient number of photons are captured within the sample, the absorbed energy being insufficient to trigger the glass's photo-expansion.

Table 2 Parameters used for assessing the role of chemical composition in microlenses formation for Ge–Sb–S bulk glasses: coordination number (<CN>) and optical band gap (E03), threshold power density needed for the microlenses formation (Fth), maximal obtained microlenses height (hmax), and the laser power density used for the obtaining hmax (Fmax h)
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On the other hand, microlenses formation was successfully induced on the surface of the other sample sets, where E03 ranges 1.87–2.86 eV (Table 1) covering illumination by over-band gap (Eph > E03, i.e. 2.33 eV > E03), band-gap (E03 ≈ 2.33 eV) and sub-band gap photons (Eph < E03, i.e. E03 > 2.33 eV).

For the characterization of microlens formation, we utilize the maximum height achieved by the microlenses (hmax) at a given laser power density (Fmax h) and the threshold power density required for microlens formation (Fth), see Table 2. Table 2 also presents the mean coordination number for the examined glasses. This parameter serves as an indicator of sample rigidity/flexibility and facilitates the comparison of glasses with varied chemical compositions. The mean coordination number (<CN>) of each GexSbySz sample was calculated as <CN> = x · NGe + y · NSb + z · Ns, where the coordination numbers NGe, NSb and NS are assumed to be 4, 3 and 2, respectively [44].

The dimensions of the fabricated microlenses, such as height and diameter, are crucial for their potential applications. They influence the microlenses' curvature radius and their effective focal length, in conjunction with the refractive index of the material/microlens [5].

The diameter of microlenses, as derived from our experiments, primarily depends on the laser beam diameter. Consequently, in our experiments, the microlenses diameter, dmicrolens, was typically 40 µm or slightly lower, aligning well with the used laser beam diameter. The chemical composition of the sample did not significantly alter the microlenses' diameter.

In contrast, the heights of the microlenses under our tested conditions appear to correlate with the chemical composition, specifically through E03. The maximum microlens heights (hmax) observed span a wide range, from tens to hundreds of nanometers, even when considering glasses with similar coefficients of thermal expansion (CTE, detailed for several stoichiometric glasses in the Supplementary materials, Table S1). For instance, a stoichiometric glass with x = 0.88 exhibited an hmax of just 80 nm and a CTE below Tg of approximately 12.1 ppm K−1. In contrast, the glass with x = 0.34 presented an hmax of 730 nm and a CTE of about 11.3 ppm K−1 below Tg (refer to Table 2 and S1). Therefore, our findings suggest that the decisive factor determining the maximal height of microlenses, even among glasses with comparable CTE values, appears to be the E03 value, which ranged between 1.87 and 2.97 eV in our study.

In Fig. 5, we illustrate the relationship between hmax and the coordination number (<CN>) of the examined glasses. It is evident that the <CN> values, which represent network rigidity, do not correlate with the observed hmax variations. Glasses with nearly identical <CN> values can exhibit markedly different hmax values. For instance, the stoichiometric glass with x = 0.51 and the sulphur-rich Ge0.16Sb0.18S0.66 composition share the same <CN>. Yet, the latter composition shows a hmax value that is more than double (approx. 410 nm compared to about 180 nm). The highest microlenses were observed for the stoichiometric glass with x = 0.34 (hmax = 730 nm, <CN> = 2.54). Only marginally smaller was the hmax for the sulphur-rich non-stoichiometric Ge0.19Sb0.10S0.71 glass, i.e. hmax ≈ 700 nm, <CN> = 2.48. Consequently, the influence of stoichiometry versus non-stoichiometry on hmax appears to be of minor significance in our observations, see Fig. 5, where there’s no discernible trend in hmax concerning the stoichiometry or non-stoichiometry of the glasses.

Figure 5
figure 5

The dependency of a the maximal height of microlenses (hmax) created on the surface of various Ge–Sb–S glasses and b the optical penetration depth of the used light (dp532 nm) on the coordination number (<CN>): (1) black circle—stoichiometric set of samples (GeS2)1−x(Sb2S3)x, x = 0–0.88; (2) red cube—Ge0.18SbxS0.82−x, x = 0.03–0.10; (3) blue empty cube—GexSb0.17S0.83−x, x = 0.13–0.24; black star (1–3)—composition shared across all three investigated sample series, i.e. (GeS2)0.66(Sb2S3)0.34 ≈ Ge0.18Sb0.18S0.64. The dotted line serves only as a guide for the eyes.

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The dependences of hmax on Tg and dp532 nm values (see Table 1) were also analyzed. Initially, for the stoichiometric set of glasses, Tg values rise with increasing <CN> (indicating an increase of tetrahedral structural units), because both these parameters are associated with the strengthening/rigidity of the glassy network. However, hmax displays a different trend in its dependence on <CN> when compared to the Tg versus <CN> relationship for stoichiometric samples. As depicted in Fig. 5a (black circles and black star), hmax values ascend with a rise in <CN>, reaching a peak at <CN> = 2.54. Subsequently, however, as <CN> values continue to rise further, there’s a pronounced decline in hmax values.

The main parameter influencing the hmax value in the examined Ge–Sb–S glasses appears to be optical penetration depth of the used light, denoted as dp532 nm. The volume of expandable material—contributing to microlenses' formation—is presumably determined by dp532 nm, given a constant laser beam diameter. It’s worth mentioning that the actual depth employed for the microlenses' formation might be slightly higher than the dp532 nm value (equal to 1/α532 nm), especially considering the lengthy exposition time of 600 s. The relationship between dp532 nm and the peak microlenses height can be summarized as:

(a) Glasses with hmax < 200 nm exhibit two distinct dp532 nm behaviors, potentially elucidating the observed responses to illumination in these materials. Certain glasses from this group have an E03 value (Table 1) significantly exceeding the energy of the employed photons (Eph = 2.33 eV). This means sub-band gap photons undergo only minimal absorption. Consequently, the optical penetration depth of the light used significantly surpasses the material’s thickness: dp532 nm > 2.1 mm, relative to dmaterial ≈ 1.4 mm. An example is (GeS2)0.92(Sb2S3)0.08 (<CN> = 2.63), which has a hmax of merely 100 nm (as shown in Fig. 5). In such instances, the laser power density provided isn’t potent enough to trigger notable photo-expansion throughout the material. The amount of absorbed energy is low and it disperses across the sample’s entire thickness being insufficient to cause significant thermal overheating and/or photo-structural changes. Therefore, the resulting microlenses are small, in this case ≈ 100 nm, see the hmax values in Table 2 and Fig. 5.

For glasses where the E03 value is either comparable to or lower than Eph (refer to Table 1 and Fig. 5), a similar behavior is evident. The dp532 nm values are notably low, typically in the range of hundreds of nanometers or just a few micrometers. Consequently, the light employed is confined to a minuscule volume near the surface. As a result, photo-expansion is triggered only within this limited volume, leading to the formation of small microlenses with a maximum hmax value of ≈ 200 nm.

(b) In contrast, the highest microlenses, exhibiting hmax values ranging 410–730 nm under the given experimental conditions, were observed in glasses with dp532 nm values spanning approx. 40–550 µm, see the dashed rectangles shown in both Fig. 5a, b. In these cases, the photon energy of the light used is between 0.84 and 0.95 of the E03 values. While this remains near sub-band gap light, its photon energy closely aligns with the band gap or E03 of the relevant glasses. Under such conditions, the light is predominantly absorbed in localized or defect states within the Urbach edge. Given the sample thickness and dp532 nm value, a sufficient amount of energy is absorbed and transformed into volume expansion. This significant impact of near sub-band gap light on the height of the microlenses has also been noted in other chalcogenide glasses, e.g. As2S3 [11], Ge–As–S [45] or Ge–As–Se [46].

Moreover, we observed that the peak hmax value (x = 0.34) for the stoichiometric set of glasses closely aligns with the highest probability of Ge–S–Sb linkages (y = 60, as denoted in Ref. [29], equating to 60 mol% of GeS2, in comparison to our glass containing 66 mol% of GeS2). Notably, the highest microlenses on the surface of the Ge–As–S glassy system were detected in the (GeS2)0.59(As2S3)0.41 composition [45]. This is analogous to our findings, as it essentially matches the highest likelihood of the proposed Ge–Ch–P linkages (where Ch represents chalcogen and P signifies pnictogen) as mentioned in [29]. Based on these results, we suppose that the unique structural characteristics of these compositions might influence microlenses formation and impact their maximal height.

Kutálek et al. [45] measured photo-induced expansion of Ge–As–S glass in-situ using thermomechanical analysis. They detected two forms of photo-expansion: temporary and permanent, where the temporary expansion was observed only during the illumination, but after the illumination ceased, only the permanent expansion remained at the ambient temperature. We hypothesize that microlens formation primarily takes place above Tg, where viscous flow intensifies. Consequently, the transition time from the undercooled liquid to the glassy state during the cooling process may influence the balance between temporary and permanent volume shifts, thereby affecting the resultant microlens heights. Zallen [47] highlighted that eutectic compositions require the least time to transition from a melt to a glassy state during the cooling process. The composition with x = 0.34 is close to the eutectic point of the GeS2–Sb2S3 glassy system (see Ref. [5] in [29]). Thus, we suppose that the distinct cooling behavior of eutectic compositions might impact the balance between temporary and permanent photo-expansion, potentially explaining the maximum microlens height observed for glass with x = 0.34.

The threshold power density of microlenses formation (F th)

The threshold power density of microlenses formation (Fth, mentioned in Section "Direct laser writing by CW 532 nm laser") is another important parameter characterizing the creation of microlenses through illumination. This parameter denotes the maximum absorbed laser power density before the sample surface incurs damage/modification. Thus, to form microlenses, one must employ a laser power density exceeding the threshold power density.

The dependence of Fth value on <CN> for the examined glasses is illustrated in Fig. 6. For the binary GeS2 glass (<CN> = 2.66), microlenses formation was absent, attributable to the insufficient laser power density in tandem with the highest dp532 nm and Tg among the glasses analyzed, as detailed in Table 1. For Sb2S3 rich glasses, i.e. <CN> = 2.42 (x = 0.88) and 2.45 (x = 0.70), the heights of the microlenses were notably minimal, and we did not observe clear linear dependence on logarithm of laser power density (according to the Eq. (1) in Section "Direct laser writing by CW 532 nm laser"). Thus, under the experimental conditions applied to these compositions, determining the threshold power density was unfeasible.

Figure 6
figure 6

Correlation between the mean coordination number (<CN>) and the threshold power density required for microlenses formation (Fth) for Ge–Sb–S glasses upon 532 nm illumination: (1) black circles—stoichiometric set of samples (GeS2)1−x(Sb2S3)x, x = 0–0.88; (2) red cubes—Ge0.18SbxS0.82−x, x = 0.03–0.10; (3) blue empty cube—GexSb0.17S0.83−x, x = 0.13–0.24; black star—sample composition/intersection of all three examined samples sets, i.e. (GeS2)0.66(Sb2S3)0.34 ≈ Ge0.18Sb0.18S0.64, n.d.—not determined, see text for detailed explanation.

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The Fth values for the remaining samples are depicted in Fig. 6. In these cases, <CN> is not an appropriate parameter for correlating with Fth. Figure 6 illustrates distinct Fth versus <CN> relationships for each set of samples studied. Specifically, an upward trend of Fth in relation to an increase in <CN> was noted for the stoichiometric set of (GeS2)1−x(Sb2S3)x glasses, x = 0.08–0.51. This contrasts with the varied behaviors observed for both non-stoichiometric sets, as shown in Fig. 6. We believe this discrepancy arises because the concept of <CN>, derived from constraint theory [44, 48, 49], represents only the mechanical rigidity of the glassy network. However, this parameter does not consider binding energies and the roles of structural units. For example, a stoichiometric glass (x = 0.51) favoring SbS3/2 and GeS4/2 structural units has a <CN> value of 2.50, identical to that of a sulfur-rich glass Ge0.16Sb0.18S0.66, which is also expected to contain S–S bonds. Therefore, a meaningful correlation between Fth and <CN> is only evident when one type of structural unit is substituted for another, as mentioned above. Generally, the <CN> parameter was employed merely to simplify comparisons of glasses with varying Ge, Sb, and S compositions.

To explain the effect of chemical composition on the behavior of Fth, we employed the subsequent assumption: It is commonly accepted that the energy from absorbed photons elevates the sample’s temperature, leading to the formation of microlenses due to the localized thermal expansion of the overheated material. As a result, the optical and thermal properties of the examined glasses, including optical penetration depth, glass transition temperature, viscosity, thermal conductivity, and heat capacity, can significantly influence microlens formation. The roles of individual parameters can be described as follows:

  1. (a)

    The glass transition temperature (Tg) is typically associated with the cross-linking and strengthening of the glass structure, which impacts surface modification. Moreover, the temperature-dependent viscosity of the resulting undercooled liquid also affects surface modification. Higher viscous flow, which facilitates surface shaping, is more evident above Tg.

  2. (b)

    Our experiments indicate that the optical penetration depth (dp532 nm), given a consistent laser beam diameter, can serve as a parameter to estimate the extent of overheating during illumination, subsequently leading to the formation of microlenses.

  3. (c)

    In our experiments, as a first approximation, we assumed that the heat capacity of the material (cp) represents the amount of energy required to be locally absorbed to significantly overheat the illuminated volume of the material. As for thermal conductivity (κ), it can be said that it influences the rate of heat transfer and dissipation from the illuminated spot to its surroundings. Both parameters, therefore, influence the extent of overheating.

For stoichiometric samples, both parameters κ and cp diminish as the SbS3/2 structural units content increases, as detailed in Table S1 in the Supplementary materials. Concurrently, a rise in the SbS3/2 structural units content results in a reduction of the optical penetration depth of the utilized light, coordination number, and glass transition temperature, as shown in Table 1 and 2. This trend aligns with the fragility behavior of undercooled liquids, which, when heated above Tg, also demonstrates an increase with the augmenting SbS3/2 structural units content [32]. In other words, as temperature increase, the viscosity just above Tg alters more rapidly for Sb2S3-rich glasses. In summary, the cumulative effect of these observations can account for the varying Fth values observed across the examined stoichiometric samples. For instance, the Fth value decreases with the decreasing <CN> value, corresponding to a rise in Sb2S3 content up to x = 0.51. For glass with x = 0.51, the minimal laser power density is required to trigger microlenses formation (Fig. 6 and Table 2), because a reduced volume of material (with a low dp532 nm) is required to adequately heat up to a relatively low Tg of the material. Additionally, a lesser quantum of energy absorption is needed to heat the sample, given that energy dissipation into the non-illuminated surroundings is also reduced, given the low values of cp and κ in comparison to glasses with a higher GeS2 concentration.

For Sb2S3-rich glasses, while we couldn't determine the exact Fth value, microlenses were successfully created at relatively high FL values > 50 W cm−2 (hmax < 100 nm). In stoichiometric glass compositions, the influence of chemical composition on the laser power density required for microlens formation appears to have a non-monotonous trend, with the minimum Fth observed for a composition where x = 0.51. We hypothesize that the elevated FL values needed for microlenses formation in Sb2S3-rich glasses (x = 0.70 and 0.88) are primarily related to the dp532 nm values, which are merely in order of tens or hundreds of nanometers (Table 1). In these glasses, light is predominantly absorbed within a small volume just beneath the surface. As a result, a portion of the generated heat might disperse across the glass surface-to-air interface, reducing local material overheating. This implies a greater FL is required to achieve adequate overheating and subsequent local volume expansion or microlenses formation. Furthermore, a potential correlation may exist between the highest likelihood of Ge–S–Sb linkages and Fth, as both parameters show a similar reliance on the chemical composition in stoichiometric glass series [29].

Based on the results shown in Fig. 6 and Table 1, we assume that the combination of dp532 nm and Tg predominantly influences the values of Fth. Consequently, we tried to compare Fth values for some selected glasses from all three sets of Ge–Sb–S glasses in order to demonstrate the possible effect of Tg and dp532 nm on Fth.

(a) As an example, we consider stoichiometric (GeS2)0.49(Sb2S3)0.51 (<CN> = 2.50, dp532 nm ≈ 3 µm, Tg = 265 °C), sulphur-rich Ge0.18Sb0.03S0.79 (<CN> = 2.39, dp532 nm ≈ 3.8 mm, Tg = 193 °C) and sulphur-poor Ge0.24Sb0.16S0.60 (<CN> = 2.64, dp532 nm ≈ < 0.1 µm, Tg = 327 °C) glasses and compare their Fth values with dp532 nm and Tg (see Fig. 6 and also Table 3 for better clarity). It is clearly visible that all selected glasses differ in all dp532 nm, <CN> and Tg, see Table 3. The highest Fth value was observed for Ge0.18Sb0.03S0.79 glass, i.e. Fth ≈ 87 W cm−2, despite its lowest Tg value. The reason for this behavior is high value of dp532 nm, which is significantly higher (≈ 2.7 times) than the thickness of the material. Thus, only a small part of used light is absorbed in the sample and a relatively high energy/laser power density has to be used to create a microlens.

Table 3 Demonstration of the effect of Tg and dp532 nm on the values of Fth by comparison of selected Ge–Sb–S glasses: (a) glasses with different <CN>, Tg, dp532 nm, (b) glasses with comparable <CN> and Tg, and (c) glasses with comparable value of dp532 nm
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The lowest Fth was determined for stoichiometric (GeS2)0.49(Sb2S3)0.51, with values of dp532 nm and Tg in the middle of the examined ranges (Table 3). Relatively high laser power densities (Fth ≈ 21 W cm−2) have to be applied to induce microlenses formation on the surface of sulphur-poor Ge0.24Sb0.16S0.60 glass, probably due to a significantly higher Tg. In addition, in the case of dp532 nm, values are in order of only tens or hundreds of nanometers, the induced temperature rise may be partially mitigated by heat dissipation into the air, which could also contribute to a higher Fth for this glass.

(b and c) For glasses with comparable values of either Tg and dp532 nm, the second divergent parameter appears to prevalently influence the value of Fth, e.g. (GeS2)0.49(Sb2S3)0.51 and Ge0.19Sb0.10S0.71 have practically the same value of Tg ≈ 265 °C and significantly differ in dp532 nm (≈ 3 µm for (GeS2)0.49(Sb2S3)0.51 versus ≈ 550 µm for Ge0.19Sb0.10S0.71), see Table 3. The different optical penetration depth therefore resulted in more than 5.3 times higher Fth value for glass with higher dp532 nm, i.e. for Ge0.19Sb0.10S0.71. Likewise, for glasses with comparable dp532 nm values, higher Fth values are typically observed for glasses with higher Tg, see e.g. results obtained for Ge0.19Sb0.10S0.71 and (GeS2)0.82(Sb2S3)0.18 in Table 3.

Based on the presented results, it is evident that glasses with greater optical penetration depth (dp), particularly when dp > dmaterial, and a high Tg tend to require a higher Fth value for microlenses formation. This implies that a higher laser power density is necessary to induce microlenses formation in such glasses. For glasses with similar values of these parameters, considering additional factors like κ, cp, and the material structure can be useful.

Effective focal length of formed microlenses

Convex microlenses formed by illumination, often resulting from local photo-expansion of the illuminated material, are notably researched for their potential use in diverse optical and/or photonic devices. For such applications, a suitable characterization of the created microlenses is desirable, particularly regarding their effective focal length (fe).

In Table 4, key parameters essential for the potential use of microlenses are detailed, including their height, diameter, full width at half maxima (FWHM), radius of curvature (Rc), and focal length (fe). The parameters are specified for the highest microlenses developed on the surface of (GeS2)0.66(Sb2S3)0.34 glass. The calculations of Rc and fe were performed as in Ref. [5]. The linear refractive index of the glass (n0) was estimated to be ≈ 2.47 for (GeS2)0.66(Sb2S3)0.34 glass at λ = 1064 nm, based on data presented by Petit et al. [22]. The height of the selected microlenses ranges from 0.43 to 0.73 µm, while their diameters lie between 31.1 and 35.2 µm. The full width at half maximum (FWHM) for these microlenses is confined to a narrow range of 10.1–12.1 µm. Notably, Rc values show minimal variation for the discussed microlenses, i.e. ≈ 210 µm for the highest and 280 µm for the lowest microlens. A similar trend is evident for the effective focal lengths, with fe values in the range ≈ 145–190 µm (see Table 4). Therefore, these microlenses hold potential for device miniaturization, as their fe values lie in the order of hundreds of micrometers.

Table 4 Characteristics for selected microlenses formed on the surface of bulk (GeS2)0.66(Sb2S3)0.34 glass: used laser power densities (FL), microlenses height (h), diameter (D), full width at half maximum (FWHM), radius of curvature (Rc) and focal length (fe)
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Conclusion

This work focused on the microlenses formation on the surface of three sets of bulk Ge–Sb–S glasses by direct laser writing technique (CW laser with λ = 532 nm). Using a combination of EDX analysis, Raman spectroscopy and Nanoindentation—coupled with our previous findings [45]—it appears that the formation of microlenses results from thermal overheating of the illuminated section of the material. According to our results, the chemical composition was identified as the primary factor influencing the formation and attributes of the microlenses (maximum achieved microlenses height (hmax) and threshold power density required to induce the microlenses formation (Fth)). The value of hmax seems to be predominantly influenced by optical penetration depth of the used light (dp532 nm), with some contribution of the glassy structure given by its chemical composition. High microlenses (400–730 nm) were formed especially for glasses having dp532 nm in order of tens or hundreds of micrometers. The highest microlenses (h ≈ 730 nm) were found on the stoichiometric glass with a composition of (GeS2)0.66(Sb2S3)0.34. This can be attributed to its proximity to the eutectic in the GeS2–Sb2S3 system and the increased probability of Ge–S–Sb structural bonds.

The threshold power density values (Fth) for microlenses formation are primarily influenced by dp532 nm and the glass transition temperature (Tg), with the glassy structure, largely determined by its chemical composition, also playing a role. While additional thermal parameters, such as heat capacity and thermal conductivity, have potential impacts, their effects are difficult to assess since they interrelate and influence each other. Our results indicate that glasses with great dp532 nm values (often matching or exceeding the sample’s thickness) and elevated Tg values are likely to show higher Fth values, meaning more energy must be supplied to induce microlenses formation. The lowest Fth values are typically observed for glasses with dp532 nm values in the range of single or tens of micrometers. Conversely, dp532 nm values in the range of hundreds of nanometers or less may increase Fth, likely due to heat loss at the surface/air interface during illumination. In other words, the balance between the energy used (or the heat produced) and the heat lost to the surroundings can significantly influence the overheating of the illuminated region, and consequently, the threshold power density essential for microlenses formation induction.

Since the appropriate effective focal length of the formed microlenses is critically important, we note that under our experimental conditions, the highest microlenses formed on the (GeS2)0.66(Sb2S3)0.34 glass surface showed effective focal length values of 145–190 µm.