Raman- and Infrared-Active Phonons in Nonlinear Semiconductor AgGaGeS₄

Abstract

AgGaGeS₄ is an emerging material with promising nonlinear properties in the near- and mid-infrared spectral ranges. Here, the experimental phonon spectra of AgGaGeS₄ single crystals synthesized by a modified Bridgman method are presented. The infrared absorption spectra are reported. They are obtained from the fitting of reflectivity to a model dielectric function comprising a series of harmonic phonon oscillators. In the Raman spectra, several modes are registered, which were not detected in previous works. The analysis of the experimental vibrational bands is performed on the basis of a comparison with reported data on structurally related binary, ternary, and quaternary metal chalcogenides. The temperature dependence of the Raman spectra between room temperature and 15 K is also investigated.

1. Introduction

In recent years there has been a growing interest in the applications of near- and mid-infrared optical devices such as sensors, thermal imagers, rangefinders, medical equipment, and recording and information processing devices. Until now, several commercially available nonlinear materials (AgGaS₂, AgGaSe₂, CdGeAs₂, and ZnGeP₂) have been typically utilized for these purposes [1,2,3,4,5,6]. However, these compounds no longer completely meet all requirements of a new generation of devices for modern applications. For example, despite their high efficiency of nonlinear conversion, AgGaS₂ and AgGaSe₂ compounds exhibit a relatively small radiation damage threshold, while ZnGeP₂ shows quite strong two-photon absorption in the spectral range of around 2 μm. CdGeAs₂ is expected to become an excellent frequency conversion material owing to its large nonlinear optical coefficient, but it is difficult to grow as single crystals of the required size and quality to find a suitable pump laser source due to the small (mid infrared) bandgap. These deficiencies of traditional compounds have stimulated the search for new materials with better-suited properties. One of the materials that has attracted the attention of researchers is orthorhombic AgGaGeS₄, which can alternatively be described as a AgGaS_2–GeS₂ solid solution [7,8,9,10,11,12,13,14,15,16,17]. Even though this compound was first synthesized in 1980s [7], its thorough investigation was initiated only much later [8,9,10,11,12,13,14,15,16,17]. As a novel nonlinear optical crystal, AgGaGeS₄ possesses a quite large nonlinear optical coefficient (d₃₁ = 15 pm/V), a wide transmission range (0.5–11.5 μm), and a high laser damage threshold (50 MW⋅cm⁻² at 1.064 μm, τ = 10 ns); it is also environmentally friendly [8,9,10,11,12,13,14,15,16]. However, in addition to these obvious benefits, there are a number of issues that must be overcome for its commercial use. One of these issues is structural heterogeneity.

Currently, several methods are used to obtain AgGaGeS₄ crystals [15,16,17,18,19,20]. However, all of them produce polycrystalline rather than single-crystal samples, which might limit their practical applications. The challenge of producing single crystals is complicated by the fact that the single crystals must be obtained at a certain component composition (ratio) of AgGaS₂ and GeS₂, optimal for a high radiation damage threshold and nonlinear optical coefficients. Even though AgGaGeS₄ crystals have been known for several decades, there are only a very limited number of Raman scattering studies [12,18] and, to the best of our knowledge, no reports of far-infrared phonon spectra of this material.

In this report, we investigate single crystals of AgGaGeS₄, synthesized using a modified Bridgman method as reported earlier [10,15,16,17]. We performed experimental studies of phonon spectra using Raman and infrared reflection spectroscopies, supported by first-principles density functional theory (DFT) calculations. Particularly, earlier Raman studies are extended here by polarization-dependent, low-temperature, and low-frequency (below 100 cm⁻¹) measurements. We also report and analyze the results of infrared reflection spectroscopy in the phonon frequency range.

2. Experiment

The AgGaGeS₄ crystals studied were obtained using a modified Bridgman method (Figure 1); the details of the synthesis and structural studies by X-ray diffractometry were reported in detail previously [10,15,16,17].

Raman scattering spectra were obtained using a triple-monochromator Raman spectrometer DILOR XY with λ_exc = 514.5 nm of an Ar⁺ laser (in a macroscopic configuration, laser spot diameter ~300 μm) and using a Xplora micro-Raman system with λ_exc = 532, 638, or 785 nm solid-state lasers, at a spectral resolution of about 2 cm⁻¹ and laser power below 1 mW; temperature-dependent measurements were performed in a closed-cycle He cryostat (Oxford Instruments, Abington, UK).

Unpolarized infrared spectra were obtained using a Bruker 80v FTIR spectrometer in reflectance mode. A Au film was used as a mirror reference. The angle of incidence was set to 45°. The spectral dependence of the dielectric function was extracted via fitting of the reflectance to a model dielectric function, comprising a series of harmonic phonon oscillators.

Theoretical calculations of the electronic ground state of “ordered” AgGaGeS₄ were performed within the generalized gradient approximation of the density functional theory, as implemented in the CASTEP code [21] and successfully employed for numerous compound semiconductor crystals [22,23,24,25,26,27,28].

3. Results and Discussion

On the basis of the previous successful application of the density functional theory (DFT) lattice dynamics calculations to a wide variety of quaternary metal chalcogenides [22,23,24,25,26,27,28], which showed a very good correlation with the experimental phonon spectra, we attempted the same calculations to AgGaGeS₄. Here, however, an important note has to be made with respect to some specific details of the AgGaGeS₄ crystallographic structure, shown in Figure 2. Experimental structural investigations clearly showed that Ag and S atoms occupy general position sites (16b) within the Fdd2 (no. 43) space group of AgGaGeS₄ [15]. Cations Ga and Ge, however, occupy 16b and 8a positions, and both of these specific positions reveal “mixed occupancy”: 0.5 Ga + 0.5 Ge. Moreover, some Ag deficiency was also established experimentally [29]. These structural features complicate DFT calculations and do not allow the “standard” lattice dynamics DFT calculations [21] to be performed.

It is obvious that the main structural building units are GaS₄, GeS₄, and distorted AgS₄ tetrahedra [15]. The unit cell of the material is rather large as it contains 12 formula units (Z = 12). It is known, however, that a smaller primitive cell is sufficient to perform the classification of the vibrational modes. Group theoretical site symmetry analysis of the Brillouin zone-center normal vibrations of AgGaGeS₄ within the point group C_2v yields the following:

Γ_tot = 16A₁ + 16A₂ + 17B₁ + 17B₂;

(1)

Γ_ac = A₁ + B₁ + B₂;

(2)

Γ_IR = 15A₁(z) + 16B₁(x) + 16B₂(y);

(3)

Γ_R = 15A₁(xx,yy,zz) + 16A₂(xy) + 16B₁(xz) + 16B₂(yz).

(4)

Here, the selection rules for infrared (IR) and Raman (R) spectra are indicated in brackets. As the space group is non-centrosymmetric, A₁, B₁, and B₂ phonons are active in both Raman and infrared spectra, while A₂ modes are accessible in Raman spectra only.

Figure 3 shows the polarization-dependent Raman spectra obtained at T = 300 K. The spectra were deconvoluted using Lorentzian line shapes in order to the extract phonon line parameters (position and width). All spectra show the most intense characteristic band at 322 cm⁻¹ and a slightly weaker one at 359 cm⁻¹. There are also a number of lines in the spectra at lower frequencies, below 50 cm⁻¹, which are registered for AgGeGaS₄ for the first time in this work (because this low-frequency range was not covered in other studies [18,19,20]). The performed polarized measurements allowed us to separate fully symmetric A₁ modes, active in parallel scattering polarizations, particularly (xx), from A₂ modes, which are active in the crossed-polarized scattering geometry (xy).

Table 1. Experimental phonon frequencies of AgGaGeS₄ from this study in comparison with experimental results on related sulfides from other works. Note that polarized Raman measurements probe A₁(LO) and A₂ phonons, while unpolarized IR reflectivity measurements are sensitive to A₁, B₁, and B₂ phonons. The most intense experimental modes are marked in bold.

AgGaGeS4			AgGeGaS4	AgGaS2	Pb2GeS4	Ag2S	GeS2
This Work			[18]	[29,30,31,32,33]	[28,32]	[33]	[32,33]
A1(LO), Raman	A2, Raman	IR (TO/LO)
					25	23
	29				27
				36	33
					43	42
44					46	44
					57
					61	62
				65		65
71					71
		77/79			81
	84
	84			85
				95
	101		106
109		115/116	109		110
	126	127/130	126	125	130–133		127
140		145/146	146		148
					150
165				159
		177/180		190	178,185
		206/211			204
				212
				224	225
				237
					248	243
					253		254
				275, 298
322		325/336	323	321
			338	334			335
			355				355
359			359	364	360, 363
				368	368		366
		365/385	385		375		374

summarizes the frequency position of all Raman and IR modes observed experimentally for AgGeGaS₄ in the present work and also lists experimental Raman data from [18], which were registered only above 100 cm⁻¹. As can be seen from a comparison of the presented sets of frequencies, our study not only extends the range of detected phonon modes to the low-frequency range, but also reveals several new modes in the range studied in [18], particularly at 165, 177, 180, 206, and 211 cm⁻¹ (see Table 1).

In view of the principal difficulties with performing DFT calculations of an appropriate crystal structure for the AgGeGaS₄ compound, we see it as most reasonable to analyze its phonon spectrum through a comparison with the experimental phonon frequencies of related binary and ternary metal sulfides, which comprise the same structural blocks consisting of S and Ag or Ga or Ge. This is the reason for presenting in Table 1 the corresponding sets of experimentally observed phonon frequencies of AgGaS₂ [29,30,31], Pb₂GeS₄ [26,32], Ag₂S [33], and GeS₂ [32,33]. A comparative analysis of the vibrations in the latter compounds with those observed for AgGeGaS₄ allows several conclusions to be made.

First of all, we make a reasonable assumption that the frequencies of the same vibrations (of the same structural blocks) in different compounds (listed in Table 1) should not differ by more than several percent. Within this expected “tolerance”, for 20 of 24 modes of AgGeGaS₄, a corresponding frequency can be found in the spectra of compounds collected for comparison. Most of the AgGeGaS₄ modes are apparently related to vibrations of the GeS₄ tetrahedra (modes at 71, 79, 109, 127, 146, 177, 180, 206, 336, 359, and 365 cm⁻¹), because they correlate with corresponding frequencies of Pb₂GeS₄ and GeS₂. The AgGeGaS₄ modes at 84, 126, 211, 322, and 336 cm⁻¹ are most likely related to vibrations in the GaS₄ tetrahedra, as they are also present in the AgGaS₂ spectrum. The vibration at 44 cm⁻¹ could be related to Ag–S vibrations, because this peak is present in the spectrum of Ag₂S.

From the comparison of the (normalized) first-order and second-order Raman spectra measured at different λ_exc (Figure 3), one can conclude that the stronger relative intensity of features around 640 and 740 cm⁻¹ at resonant excitation by λ_exc = 532 nm (Figure 3b, inset) can be related to enhanced second-order scattering of the 322 and 359 cm⁻¹ modes. This additionally confirms the assignment of the latter to LO modes [22,23,24,25,26,27]. In a similar way the slight increase in scattering intensity in the range of 400–430 cm⁻¹ can be interpreted as an enhancement of combinational modes involving the 322 and 359 cm⁻¹ LO modes and lower-frequency LO vibrations, i.e., 44 and 109 cm⁻¹ (Table 1).

Given that the temperature-dependent properties of AgGaGeS₄ crystals are an object of interest [12,20], we performed temperature-dependent Raman scattering measurements from T = 15 K to 265 K in 10 K increments (Figure 4). As the temperature decreases, there is a smooth shift of modes toward higher frequencies (up to 4 cm⁻¹ for the highest-frequency modes) due to the lattice anharmonicity (phonon–phonon interactions) [34]. No additional features appear in the spectra. Notably, the low-frequency modes (below 110 cm⁻¹) reveal much smaller shifts, which is related to the reduced number of phonon scattering (decay) channels.

Lastly, the infrared reflectance spectrum of the AgGaGeS₄ single crystal shown in Figure 5 reveals several spectral features with the most intense ones above 300 cm⁻¹. In order to extract information on the spectral dependence of dielectric function, we performed fitting of reflectance to a model dielectric function in the form of a series of harmonic phonon oscillators:

$$\epsilon \left(\omega \right)={\epsilon }_{\infty }+{\displaystyle \sum }_{k=1}^n{S_{\mathit{Tk}}}^2/\left({{\omega }_{\mathit{Tk}}}^2-{\omega }^2-i{\gamma }_{\mathit{Tk}}\omega \right),$$

(5)

where ${\epsilon }_{\infty }$ is the high-frequency dielectric constant, while ω_Tk, γ_Tk, and S_Tk are the oscillator mode frequency, its strength, and its damping, respectively. The software package from [35] was utilized. It is known that the maxima in the spectrum of the imaginary part of dielectric function Im(ε) correspond to transverse optical (TO) mode frequencies (marked in black in the lower panel of Figure 5), while maxima of the loss function Im(−1/ε) define the position of longitudinal optical (LO) modes. All obtained numerical data are listed in Table 1.

4. Conclusions

We report the results of an experimental investigation of polarized Raman and infrared vibrational spectra of AgGaGeS₄ single crystals. The analysis of the main features in the experimental vibrational spectra was performed by comparing them with reported data on structurally related binary, ternary, and quaternary metal chalcogenides. For the first time, experimental Raman spectra were obtained for the spectral region (<100 cm⁻¹), and the bands registered there were assigned to the corresponding vibrational modes. Several new modes were found in the range studied earlier, particularly at 165, 177, 180, 206, and 211 cm⁻¹. Optical properties in the infrared spectral range were determined by fitting experimental reflectivity spectra to a model dielectric function, comprising a series of phonon oscillators. It was established that the majority of the observed modes are related to vibrations of GeS₄ tetrahedra, several modes are most likely related to GaS₄ tetrahedra, and only the mode at 44 cm⁻¹ is largely due to vibrations involving Ag. Upon a temperature decrease to 15 K, a smooth shift of modes toward higher frequencies was observed (up to 4 cm⁻¹ for the highest-frequency modes) due to the lattice anharmonicity (phonon–phonon interactions).