1. Introduction

The ε-polytype gallium selenide (GaSe) crystal promises efficient optical frequency conversion based on second order nonlinearity over a large wavelength range between 0.7895 and 5640 μm except for the phonon limited gap between 38.4 and 58.2 μm [1–4]. The performance potential of GaSe is due to outstanding physical properties. Its wide transparency window between 0.62 and 20 μm for non-polarized light at negligible loss level [5] continues at wavelengths ≥50 μm [6,7]. Other attractive physical properties are very high second order nonlinear susceptibility (d₂₂ = 54 pm/V) and large birefringence (0.35 at 10 μm) [5].

These properties have led to extensive in-lab use of GaSe for mid-IR and THz generation but have not allowed it to achieve the ubiquity of other nonlinear materials such as ZnGeP₂ in commercial and industrial applications. This is because GaSe is difficult to grow and process as large, high optical quality single crystal samples (absorption coefficient α≤0.1-0.2 cm⁻¹) [8,9], due to its layered structure with weak inter-layer Wan-der-Waals type bonding [2]. The crystal cleaves readily along the ‹001› plane. With careful preparation it is possible to produce optical quality surfaces along this direction which is orthogonal to the c-axis. Access to other crystallographic directions is hampered, as GaSe is too soft to be cut and polished to optical quality. Its hardness has been measured as close to 0 on the Mohs’ scale [5]. Limited optical quality of grown GaSe crystals is caused by technologically weakly controlled defects: point defects (mainly Ga vacancies) and micro-defects (Ga precipitates, voids or bubbles, stacking disorders, broken layers and dislocations) [10,11], as well as by significant two-photon absorption for near IR pump (≈0.5 cm/GW at 0.755-0.875 μm [12,13]). As a result, only the intensive peak of exciton absorption for e-wave, and strong anisotropy of absorption coefficients for o- (α_o) and e-wave (α_e) at the short-wave edge (α_e>α_o) have been sufficiently studied by original measurement techniques [14–16]. Other available data on the optical properties of GaSe that have been published in over 1300 papers [17] are related mainly to o-wave and are highly scattered, presumably dependent on technological state of the art, on the measurement facilities, and on the length of crystals studied.

An earlier paper reports the measured absorption spectrum in the THz range for o-wave in a cleaved GaSe sample [6]. Due to processing difficulties only limited data are as yet available on α_e or absorption anisotropy in the THz range [15, 19–21] and at the long-wave mid-IR edge where α_e is several times larger than α_o [17,18]. However, a common feature of available data on THz absorption in polarized light is significant predominance of α_o over α_e [4,22,23], moreover their magnitudes and spectral behavior are significantly different. Values of α_o as large as 70-250 cm⁻¹ are reported for the spectral range 0.5-3 THz in [24], as well as 40-100 cm⁻¹ [25], 5-15 cm⁻¹ [26,27] and down to 0.5-8 cm⁻¹ [7,27–29]. These data are up to several orders higher than the values theoretically estimated by [30] which are mistakenly reproduced in a well cited paper [31]. Values from [30] are reproduced correctly in [26]; but as was established later, had been underestimated by up to three times [7]. It was found that α_o spectra show an intense phonon absorption peak at 0.59 THz [7,26–28,32] and two wide absorption bands at 1.0 THz [27,28,32,33] and 2.5 THz [27,28,33]; and that α_o increases with frequency. Data on the main dispersion features reported in [18,28,33] are in good agreement. Some details of the fine structure in o-wave THz absorption can be found in [27]; weakly resolved fine structure can also be identified in [19]. Specific features of the α_o and α_e spectra can also be estimated from the spectral dependency of power produced by difference frequency generation in GaSe crystal [3,4,31,34]. It is evident that extremely poor mechanical properties, limited optical quality, and inconsistent data on other physical properties, have impeded utilization of GaSe crystals.

Sulfur (S-) doping of GaSe appears to be an efficient method of controlling physical properties of the crystal by means of sulfur concentration. Mechanical properties improve significantly due to substitution of gallium vacancies by sulfur atoms that in turn reduce the stacking faults. As a result, the lattice structure strengthens enough to be cut and polished in arbitrary direction, especially if the crystal is first prepared by setting in a polymer matrix that shrinks slightly during polymerization [35]. Simultaneously, the mid-IR optical absorption coefficient decreases by a factor of 2-3 [13,36,37], while the optical damage threshold increases fivefold at the optimal mixing ratio, as reported in [13,36], and optical properties in the THz range are improved [23]. The short-wave transparency edge of GaSe:S crystals shifts towards shorter wavelengths, thus reducing the two-photon absorption for the near-IR pump [36] and causing changes in phase matching conditions that improve frequency conversion efficiency [38]. Composition-dependent changes in the phonon absorption spectrum for o-wave were reported in [21,32] but were not confirmed by other researchers [20]. According to the majority of available data, GaSe:S crystals possess improved optical properties that increase frequency conversion efficiency in mid-IR and THz ranges 3-15 times [13,23,36,38–40]. This would make possible out-of-doors applications. On the other hand, negative effects of S-doping on the optical damage threshold and on frequency conversion efficiency were also reported [20,41], that reflect doping-induced degradation in optical quality.

Due to difficulties in accessibility and limited processing capability, absorption spectra (i.e. absorption anisotropy properties) for e-wave in GaSe:S crystals in the THz range have only been studied for 6 [42] and 7 [20] mass% of sulfur. In these studies and from measurements at fixed frequencies [4,23] it was established that α_o>α_e at THz frequencies as it is in the pure GaSe crystal. This difference in absorption loss leads to higher efficiency of THz e-wave generation. It was also predicted and confirmed experimentally that the uncommon ee→e type of interaction can be realized in both pure and S-doped GaSe crystals [20,42].

Successful design of THz sources calls for adequate data on absorption spectra and anisotropy over the entire transparency range including the THz range in pure and S-doped GaSe as a function of sulfur concentration. Correct data are a crucial factor in selecting the most efficient type of three-wave interactions and in maximizing the frequency conversion efficiency. In the present work, we report for the first time to our knowledge detailed THz time-domain spectroscopy (THz-TDS) measurements of o- and e-wave absorption spectra and absorption anisotropy in the 0.3-4.0 THz range for GaSe:S (1.1, 2.5, 5, 7 and 11 mass%) crystals. For this study, improved quality crystals were grown using a modified synthesis and vertical Bridgman growth method with heat field rotation [8,35].

Two types of GaSe:S samples were fabricated. The first type was cleaved from as-grown boules, i.e. it had faces orthogonal to the c-axis, so that a beam traversing the sample traveled parallel to the c-axis. The second type was mechanically processed as described in reference [35].

2. Crystal characterization

Surface roughness was measured by a Probes HOMMEL-ETAMIC T1000 (JENOPTIK AG, Germany) profilometer. Cleaved surface of GaSe:S ‹001› is automatically flat with roughness ≤0.15 nm. For cut and polished 1-mm thick samples the measured surface roughness varies from 75 nm for GaSe:S (11 mass%) to 220 nm for GaSe samples. Regions of local defects (mainly scratches and cracks along the growth layers) were observed on polished surfaces. It was found that the surface finish of these extremely easily cleaved samples is suitable for THz-TDS study if their thickness is ≥1 mm. Thinner samples possess high concentrations of cracks and are useless for the study.

Scanning electron microscopy (SEM Quanta 200 3D (FEI, Netherlands) microscope) in combination with energy-dispersive X-ray spectroscopy (EDAX ECON VI microanalyzer) were used to measure Ga, Se and S contents as well as the distribution of components in the crystals (Fig. 1).

 

Fig. 1 EDX spectra revealing the increment of sulfur content in the crystals grown from the melt containing 1.1% (a), 2.5% (b) 5% (c) and 11 mass % (d) of sulfur.

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For the pure GaSe no peaks of other elements except Ga and Se were observed in the energy-dispersive X-ray spectrum indicating the high purity of the materials. The average atomic ratio was Se∕Ga = 51.13∕48.87, i.e. close to the stoichiometric ratio with a small Ga deficit that is well within the homogeneity range 47.8-49.6 at.% [43]. Analyses of doped crystals showed a gradual increment of sulfur concentration in the crystals with doping level. The absolute concentration of S measured for the samples in Fig. 1 was 0.8, 1.9, 4, and 9 mass% of S. The discrepancy between the initial concentration in the melt and the measured content in the crystal may be explained both by the inaccuracy of EDX method and by segregation occurring phenomenon arising in the growth of solid solution crystals. However the samples in this work are labeled in accordance with the initial sulfur concentration. Transmission electron microscopy (CM12 (Philips, Netherlands) microscope) using selected area electron diffraction (SAED) was employed in analyzing the structures. These data confirmed the presence of the same ε-type structure in all our samples.

UV-visible-near-IR transmission spectra were recorded by a Cary 100 Scan (Varian Inc., Australia) spectrophotometer over the spectral range of 190-900 nm with a spectral resolution of 0.2-4 nm and wavelength accuracy of ± 1 nm. NIR transmittance shows a short-wave edge shift of GaSe:S spectra with sulfur concentration which agrees well with the known data [38]. It was found that optical losses in the grown crystals within the maximum transparency window are well below 0.1 cm⁻¹, and therefore are too low to be accurately measured by the instrument used.

3. Absorption properties in the THz range

Absorption spectra of the grown crystals in the THz band were measured using the THz-TDS at NPL, UK, described in detail elsewhere [44,45]. This spectrometer used a standard configuration incorporating a femtosecond laser, four off-axis parabolic mirrors, a biased GaAs emitter, and electro-optic detection with a ‹110› ZnTe crystal and balanced Si photodiodes. The frequency resolution was 3.75, 7.5 or 15 GHz, depending on the sample, with a linearly polarized THz beam. The grown crystal samples were placed at the focus of the THz beam such that they interacted with the incident radiation in either $\overrightarrow{E}┴\overrightarrow{c}$ (o-wave) or _{$\overrightarrow{E}$$\parallel$$\overrightarrow{c}$}(e-wave) geometry for both cleaved and cut & polished crystals, where E is the electric field vector of the incident THz light.

The frequency-dependent refractive indices n(ν) and absorption coefficients α(ν) of the samples were calculated for o- and e-waves from the Fourier Transform data using the well-known relations [46]:

The modulation in the spectra caused by reflection echoes was removed by a smoothing algorithm. It may be easily distinguished from absorption features by its regular sinusoidal form and frequency spacing (50-100 GHz), depending on the sample thickness.

Metrology issues and solutions in THz-TDS: noise, errors and calibration were accounted in accordance with algorithms presented elsewhere [47]. To exclude mistaken treating of spectral oscillations arising from reflection echoes as phonon absorptionlines, absorption spectra were measured with different spectral resolution. First, the well-known rigid mode phonon absorption peak E'⁽²⁾ at 0.59 THz [29,32,48] was studied.

It is seen in Fig. 2 that spectral oscillations due to reflection echoes are independent of spectral resolution of THz-TDS in difference to phonon absorption peak E'⁽²⁾ whose intensity increases up to the reported magnitude while its spectral bandwidth decreases to published values [32]. In fact, etalon oscillations are also dependent on resolution. But in this case resolution is much smaller than oscillation spacing. In contrast to etalon oscillations, phonon resonances at 0.59 THz are much narrower and more intense, as seen in Fig. 2.

 

Fig. 2 Absorption spectra of the rigid layer phonon mode E'⁽²⁾ at 0.59 THz with different spectral resolution.

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Examples of the measured absorption spectra for o- and e-wave are depicted in Fig. 3.In addition, dispersion of the o-wave absorption coefficient in a semi-insulating GaAs wafer was also measured as a reference material to confirm the accuracy of the THz-TDS measurement. In Fig. 3(a) it is seen that the absorption coefficient of the GaAs wafer agrees well with the known data [49]. The maximum measurable absorption coefficient [50] is also included in Fig. 3, showing limits of the measurement bandwidth. Absorption curves may be assumed to be accurate up to the limit of the dynamic range as denoted by the (αd)_max (red dash-dot curve).

 

Fig. 3 Absorption spectra for o- (a) and e-waves (b) in the grown crystals. Dashed lines show cut & polished crystals whereas solid lines denote cleaved samples. The dash-dot line marks the limit of dynamic range for the THz-TDS used.

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Absorption coefficients for cleaved crystals doped with 2.5 and 5 mass% of sulfur are smaller than those reported for the best quality GaSe crystal [20,28]. Moreover, it was found that GaSe:S (2.5 mass%) possesses the lowest absorption coefficient among all the grown crystals, confirming a positive effect of the doping, and consistent with the published data on optimal S-content [13].

It was established that the measured THz absorption for cut & polished crystals is strongly influenced by a number of factors. Among them are incorporated particles of polishing powder, inaccuracy in the crystal thickness measurement, as well as wedge-sampling, local deformations, and crystal tilt relative to the THz beam (crystal faces should be normal to the beam axis) which results in greater reflection losses and extended optical path through the crystal. In the case of crystals cut orthogonally to the c-axis, the crystal must be accurately oriented with its c-axis either parallel or perpendicular to the THz beam polarization; an intermediate angle will produce a time-domain trace combining signals from both o-wave and e-wave, and will give rise to a spectrum containing oscillation artefacts. Comparisons between the absorption spectra of different crystal compositions are further hampered by changes in the phonon structure.

The characteristic phonon absorption peak at 0.59 THz in GaSe disappears in the absorption spectra of GaSe:S (2.5 and 5 mass%) crystals in Fig. 3(a). Instead, a peak appears at 1.8 THz, shifting towards higher frequencies with the increase of sulfur concentration. This type of phonon transformation was also reported in [51]. It should be noted that accurate measurement of the 0.59 THz phonon peak requires sufficiently high frequency resolution due to its narrow width, estimated as <2.5 GHz (FWHM).

In Fig. 3(a) it is seen that absorption spectra for o-wave for cleaved and cut & polished GaSe crystals possess similar spectral features, as do those for cleaved and cut & polished GaSe:S (11 mass%) crystals; however, cut & polished crystals exhibit higher absorption losses than cleaved ones. The main phonon absorption peaks are centered at the frequencies of 0.59, 1.0, 2,5 and 3.5 THz. The phonon absorption peak at around 1.8 THz shifts toward higher frequencies and grows in intensity with increasing mixing ratio, as is well-known from the literature [27,28,32]. The differences in magnitudes of the absorption coefficients for pairs of GaSe and GaSe:S (11 mass%) crystals that are cut & polished as compared with cleaved appear to be frequency-independent. This implies that optical losses in these samples are not caused by scattering originating from polishing quality or by absorption by residues of the polishing medium, as those should be frequency-dependent. Indeed, the evidence indicates that higher optical losses in cut & polished samples originate in surface defects related to polishing. It may be proposed that the excess loss is due to increased interface reflections arising from changes in the refractive index caused by incorporated particles of the polishing powder.

Absorption spectra for e-wave in cut & polished crystals were found to be most strongly affected by the perturbing factors, which as a consequence makes it impossible to perform a quantitative analysis of the data. Some recorded spectra are presented in Fig. 3(b) where it is seen that among crystals that have been polished with fine powder, doped crystals possess the highest optical quality. Their e-wave absorption coefficients are 2-3 times lower than those for o-wave, in good agreement with the published data [4,20,23,38,42]. Once again it is seen that a GaSe crystal polished with coarse polishing powder has an order of magnitude higher loss coefficient than a similar crystal polished with fine powder (9-μm versus 0.8-1.2 μm). For the first time, an intense absorption peak centered at 1.1 THz (37 cm⁻¹) is clearly observed in the GaSe spectrum recorded with the spectral resolution of 3.75 GHz; whilst it is barely seen at 15 GHz resolution. It was found that its intensity and spectral bandwidth vary with spectral resolution similarly to those for phonon absorption peak at 0.59 THz. Although an indication of this peak can be seen in the data presented in reference [20], it was not identified as such. It was, however, also observed in one GaSe sample and identified as phonon absorption peak [52]. Therefore, we propose that the consistently observed peak at 1.1 THz should be acknowledged as a new phonon absorption peak and should be taken into account in the design of THz devices [21]. In the frequency band 0.3-2.0 THz the absorption coefficient for e-wave in GaSe:S crystals with high (7, 11 mass%) S-concentrations is nearly frequency independent. The phonon peak around 2.5 THz is common for both GaSe and GaS crystals, so that it remains even in heavily S-doped GaSe. For preliminary estimation of THz generation efficiency in GaSe within 0.3-3.5 THz range we recommend simple approximations of absorption coefficients for o- (α_o) and e-wave (α_e) as follows:

4. Conclusion

High optical quality GaSe:S (1.1, 2.5, 5, 7 and 11 mass%) compounds were produced by modified synthesis method, and centimeter-sized sulfur-doped crystals were grown by a modified vertical Bridgman method with heat field rotation. Physical origins were identified explaining contradictions and scatter in the available THz absorption data in pure and doped GaSe. These were found to be: crystal growth, sample fabrication and polishing techniques, quality of the sample surface, accuracy of the crystal thickness measurement, accuracy of the crystal alignment relative to the THz beam axis and polarization direction, and spectral resolution. Predominance of o-wave absorption was confirmed for all crystal compositions. An optimal mixing ratio for the highest optical quality crystal was estimated as 2.5 mass% of sulfur. Nearly frequency-independent absorption was observed in the 0.3-2 THz range. A phonon absorption peak for e-wave centered at 1.1 THz was observed for the first time. Both o- and e-wave absorption coefficients as well as absorption anisotropy were observed to decrease with increasing sulfur concentration. It is concluded that e-wave THz generation is preferable in GaSe:S (up to 11 mass%)