Raman spectroscopy and lattice dynamics calculations of tetragonally-structured single crystal zinc phosphide (Zn3P2) nanowires

Earth-abundant and low-cost semiconductors, such as zinc phosphide (Zn3P2), are promising candidates for the next generation photovoltaic applications. However, synthesis on commercially available substrates, which favors the formation of defects, and controllable doping are challenging drawbacks that restrain device performance. Better assessment of relevant properties such as structure, crystal quality and defects will allow faster advancement of Zn3P2, and in this sense, Raman spectroscopy can play an invaluable role. In order to provide a complete Raman spectrum reference of Zn3P2, this work presents a comprehensive analysis of vibrational properties of tetragonally-structured Zn3P2 (space group P42/nmc) nanowires, from both experimental and theoretical perspectives. Low-temperature, high-resolution Raman polarization measurements have been performed on single-crystalline nanowires. Different polarization configurations have allowed selective enhancement of A1g, B1g and Eg Raman modes, while B2g modes were identified from complementary unpolarized Raman measurements. Simultaneous deconvolution of all Raman spectra with Lorentzian curves has allowed identification of 33 peaks which have been assigned to 34 (8 A1g + 9 B1g + 3 B2g + 14 Eg) out of the 39 theoretically predicted eigenmodes. The experimental results are in good agreement with the vibrational frequencies that have been computed by first-principles calculations based on density functional theory. Three separate regions were observed in the phonon dispersion diagram: (i) low-frequency region (<210 cm−1) which is dominated by Zn-related vibrations, (ii) intermediate region (210–225 cm−1) which represents a true phonon gap with no observed vibrations, and (iii) high-frequency region (>225 cm−1) which is attributed to primarily P-related vibrations. The analysis of vibrational patterns has shown that non-degenerate modes involve mostly atomic motion along the long crystal axis (c-axis), while degenerate modes correspond primarily to in-plane vibrations, perpendicular to the long c-axis. These results provide a detailed reference for identification of the tetragonal Zn3P2 phase and can be used for building Raman based methodologies for effective defect screening of bulk materials and films, which might contain structural inhomogeneities.


Introduction
Among the II-V compounds, zinc phosphide (α-Zn 3 P 2 , hereafter referred to as Zn 3 P 2 ), an earth-abundant, environmentally friendly and low-cost semiconductor, has gained attention as a promising absorber candidate for the next generation of thin-film photovoltaics (PV) [1][2][3]. With merits such as a direct band gap of 1.5 eV, a high absorption coefficient of 10 4 -10 5 cm −1 , and carrier diffusion lengths of ∼10 μm, zinc phosphide is a very suitable material for solar energy applications [4][5][6][7][8][9]. However, even with all these benefits, the conversion efficiencies are still far from reaching the 31% predicted from the Shockley−Queisser limit [10]. In fact, the record solar cell, with a conversion efficiency of ∼6%, was produced 40 years ago [11], and since then there has not been any significant scientific breakthrough. Despite the highly promising result at that time, research on Zn 3 P 2 recessed mostly due to technical challenges in fabricating high-quality material with controllable doping, surface passivation and clean interfaces, all of which are crucial for highefficiency devices.
One major challenge in the synthesis of high-quality Zn 3 P 2 is its rather large crystallographic unit cell [11] when compared to other PV materials, along with its high coefficient of thermal expansion [12,13]. All of these increase heterointerface defect densities when grown epitaxially on commercially available substrates. Major progress has recently been made in this regard, where growth of highly crystalline Zn 3 P 2 was achieved using innovative nanofabrication methods (i.e. selective area epitaxy) [14][15][16]. However, fine-tuning of the material's functional properties through doping and defect engineering still remains a challenge. This is mostly due to the complex structure of Zn 3 P 2 characterized by empty sites in the cubic zinc sublattice dispersed throughout a tetragonal lattice, which, besides providing ample opportunities for material design, also results in a higher probability for formation of intrinsic defects during synthesis (i.e. phosphorus interstitials in the empty zinc sites). While some amounts of intrinsic defects are beneficial for the doping and recombination characteristics of the Zn 3 P 2 , large concentrations of defect complexes can lead to limiting minority charge carrier lifetimes and enhance recombination processes [6,17,18]. Defects can also have an effect on the net band gap variations and cause localized band gap or electrostatic potential fluctuations, which can lead to a change in the bulk diffusivity and indirectly affect the optoelectronic properties [18,19]. This is why controlled defect engineering and doping play a significant role in achieving high-efficiency devices based on Zn 3 P 2 . Thus, a thorough assessment of Zn 3 P 2 , in terms of crystalline quality, defect identification and quantification, and homogeneity is of the foremost importance for the future development of this technology. In particular, developing predictive synthesis-structure-property relationships are crucial for effective design of materials with enhanced functional properties as absorbers for high-efficiency devices.
Raman spectroscopy can play an important role in this context. Besides being a fast and non-destructive technique, it is also one of the most suitable tools for determining the crystal structure and quality of semiconductors. This is due to the intensity, shape and position of Raman peaks being strongly influenced by the presence of structural inhomogeneities in the material. These include both point defects, such as vacancies, interstitials, and anti-sites, and other structural disorders, like dislocations or grain boundaries. Clear variations in Raman spectral features with the changes in the composition, processing conditions and doping can be observed for many materials [20][21][22][23][24][25][26]. However, in order to be able to use Raman spectroscopy as a suitable tool for defect identification, it is necessary to have reliable reference Raman spectra of the material, with detailed identification of all peaks and their vibrational origin. This can greatly help in building Raman based methodologies which can be later used for further development of materials in the PV field.
In this work, we provide a reference Raman spectrum of single-crystalline Zn 3 P 2 , with a complete analysis of all Raman active modes from both experimental and theoretical perspectives. To the best of our knowledge, this is the first comprehensive theoretical analysis of the lattice vibrations in Zn 3 P 2 along with a concise comparison with experimental results in terms of phonon symmetries and frequencies. So far, the most complete experimental Raman analysis of Zn 3 P 2 was performed by Pangilinan et al [27]. However, this work contained a few inconsistencies in terms of the number of observed modes and their symmetry assignment. Later on, Hanuza et al provided data on the vibrational modes in zinc phosphide by reflectance spectroscopy [28]. The identification of the modes was supported by a molecular model of a simplified Zn 3 P 2 structure with 18 atoms out of the 40 present in the Zn 3 P 2 unit cell, which resulted in a somehow qualitative assessment of the vibrations in the structure. On the other hand, density functional theory (DFT) calculations of Zn 3 P 2 have primarily been dealing with the prediction of the electronic band structure [29], defects [30,31] and growth mechanisms [32,33], rather than the phonon analysis.
This work provides high-resolution polarization-resolved Raman scattering measurements. The experiments have been performed on the basal (010) plane of single crystal nanowires in high-symmetry polarization conditions. Together with the detailed deconvolution of the Raman spectra with Lorentzian curves, this has allowed the identification of 33 Raman peaks. The experimental results are consistent with the vibrational frequencies that have been computed by firstprinciples calculations based on DFT. Furthermore, calculations of the phonon density of states (PDOS) (elemental and total), as well as the phonon dispersions provide a microscopic understanding of the experimentally observed phonon lines, in addition to the assignment to the specific lattice eigenmodes. These results can be used as a reference for identification of the Zn 3 P 2 phase, as well as for building Raman based methodologies for effective defect screening of bulk materials and films that might contain structural inhomogeneities.

Material preparation
The Zn 3 P 2 nanowires were epitaxially grown in a Veeco GENxplor molecular beam epitaxy (MBE) system on InP (100) substrates. They were grown via a In-catalyzed vaporliquid-solid method. The In was generated through a 5 min Zn pre-deposition prior to growth, which reacted with the substrate to form the catalyst droplet. The analyzed samples were then grown at a manipulator temperature of 250°C and a P/Zn ratio of 1.45 for four hours (Zn base flux3.4 -10 7 Torr). Additional details on the growth can be found in [14,34].

Characterization
The morphological properties of the nanowires were characterized by scanning electron microscopy (SEM) with a Zeiss Merlin microscope operated at 3 kV. (Scanning) Transmission electron microscopy (S/TEM) and energy-dispersive x-ray spectroscopy (EDX) studies were performed using an FEI Talos transmission electron microscope operating at 200 kV. For TEM analysis, the nanowires were transferred to a copper grid covered by holey-carbon by gently scraping it across the substrate surface with a cotton swab.
Micro-Raman spectroscopy was realized in the backscattering configuration on a Zn 3 P 2 nanowire at 12 K. The 532 nm line of a Coherent Sapphire SF optically pumped semiconductor laser was used for excitation. The beam was focused on the sample with a microscope objective with a numerical aperture of 0.75, resulting in around 1 μm diameter spot size, and reached radiant fluxes on the order of 150 μW at the surface. A linear polarizer and a half-waveplate were used to control the polarization of the incident beam, while the scattered light was filtered through a linear polarizer. Before entering the spectrometer, a half-waveplate oriented the light polarization parallel to the entrance slit. The signal was analyzed with a TriVista triple spectrometer with 900, 900 and 1800 mm −1 gratings in subtractive mode and a Princeton Instruments liquid nitrogen cooled multichannel CCD PyLoN camera. The polarization direction is described by the angle it makes with the direction of the long axis of the nanowire. For Raman analysis, the nanowires were transferred to a silicon wafer by gently brushing the growth substrate against it.

Lattice dynamics calculations
The first-principles calculations of the electronic ground state of the tetragonally structured Zn 3 P 2 were performed within the local density approximation using Ceperly-Adler functional [35,36], as implemented in the CASTEP code [37]. Norm-conserving pseudopotentials were used. The cutoff energy for the plane wave basis was set to 600 eV. A selfconsistent-field (SCF) tolerance better than 10 −7 eV per atom and the phonon SCF threshold of 10 −12 eV per atom were imposed. Prior to performing calculations, the structure was relaxed so that forces on atoms in the equilibrium position did not exceed 2 meV Å −1 and the residual stress was below 5 MPa. Experimentally determined lattice parameters from [38] were used as a starting point. An integration over the Brillouin zone was performed over a 3×3×2 Monkhorst−Pack grid in reciprocal space.

Results and discussion
A sketch of the crystal structure of Zn 3 P 2 is depicted in figure 1. It exhibits tetragonal symmetry with the space group P4 2 /nmc (D h  with Zn atoms filling 3/4 of the tetrahedral voids. Each P atom is surrounded by 6 Zn atoms at the corners of a distorted cube while the metal atoms are surrounded by 4 P atoms at the vertices of a distorted tetrahedron. The ordered unoccupied tetrahedral voids lead to a decrease in lattice symmetry and the significant extension of Zn 3 P 2 unit cell when compared to the zinc-blende or fluorite building blocks. The experimentally determined lattice parameters are a=b= 8.0785 Å and c=11.3966 Å [38].
Group theory analysis predicts the following set of irreducible representations for the structure P4 2 /nmc (D h where a, b, c, d, and e are the Raman tensor elements. In order to experimentally determine the positions of the Raman active modes, high-resolution Raman polarization measurements were performed on a Zn 3 P 2 nanowire, of which SEM micrographs are presented in figure 2. The nanowires present a square cross-section that decreases in area along the nanowire axis. At the top we find the indium droplet that catalyzes the growth. The Raman measurements were carried out at approximately one-third of the length of the nanowire from the wide base. The nanowire width is at least 100 nm along the whole structure and more than 600 nm at the location of the measurement. Consequently, phonon confinement effects are negligible, and the measured spectrum is equivalent to that of the bulk material. Selective area electron diffraction measurements on the nanowires in TEM have confirmed the formation of monocrystalline Zn 3 P 2 phase with P4 2 /nmc tetragonal symmetry, and allowed identification of the nanowire growth orientation as [001], with the c crystal axis perpendicular to the substrate [14]. It should be noted that the roughness on the nanowire surface is not due to crystallographic defects but rather microfaceting as the (101) facets have a lower surface energy than (100) facets, and thus the surface has the same crystalline orientation as the core of the nanowire and does not affect the Raman spectrum. The compositional assessment, performed by STEM-EDX, indicated the formation of Zn-rich wires with Zn/P=2.3 compared to stochiometric Zn/P=1.5. The extra Zn is probably accommodated at the empty Zn sites in the lattice, and therefore it should not affect the positions of the main Raman modes expected for this crystal structure. Further, a homogenous distribution of Zn and P with no phase segregation is observed from the compositional maps shown in figure 3. This confirms that only peaks from the Zn 3 P 2 phase are expected in the Raman spectra.
Raman measurements were performed on a nanowire with the [001] growth direction being parallel to the substrate (figure 2(c)), indicating (010) crystallographic plane as the basal plane.
Based on these conditions, the angular dependence of the Raman mode intensity is given by:  Based on the angular dependencies of Raman modes intensity from table 1, three polarization geometry configurations were chosen for selective activation of specific phonon symmetries in the Raman spectra, thus allowing easier identification of the peak characteristics. The chosen polarization geometries correspond to the maximum or minimum Raman response of the lattice, in terms of the A 1g, B 1g and E g modes. Raman measurements in parallel configuration with q =  90 allow selective enhancement of only the A 1g modes, while for q =  0 both A 1g and B 1g modes are expected. On the other side, polarization measurements in the perpendicular configuration with q =  90 will selectively enhance only the E g modes. Finally, unpolarized Raman measurements were performed in order to identify B 2g vibrations. Figure 4 presents the Raman spectra of Zn 3 P 2 measured at 12 K under different polarization configurations using 532 nm excitation. Low-temperature measurements were chosen due to the increase in the phonon lifetime in the material, which results in better defined Raman peaks. This allows for a repeatable and reliable spectrum deconvolution as it decreases the overlap between Raman lines. The standard Porto notation has been utilized for labeling of the measurements, where á-ñ Y ZX Y | | denotes the incoming radiation along the −y-axis being polarized along the z-axis with the backscattered (y) light polarized along x. It should be noted that in case of the á-ñ Y ZX Y | | polarization configuration, Figure 4. Raman spectra of Zn 3 P 2 in polarized and unpolarized configurations measured at 12 K using 532 nm excitation wavelength. The polarization geometry is indicated above each spectrum, along with the labels of the specific phonons that are allowed in these conditions. The lines under each spectrum show comparison between the Raman peak positions obtained experimentally by the deconvolution of the spectra with Lorentzian curves (labeled Exp), and from the lattice dynamics calculations based on DFT (labeled DFT). besides the allowed E g modes, the appearance of extra peaks is observed with closely matching positions and characteristics of A 1g modes. The activation of forbidden A 1g modes under this measurement geometry can be explained by a possible breakdown of selection rules. For example, planar native defects in the form of stacking faults with the direction of growth in the c axis, which are often found in layered materials due to very low formation energy, could activate forbidden modes [25,[42][43][44]. Additionally, the breakdown of selection rules can be activated by the photonic nature of the light-nanowire interaction, which can modify the light polarization inside the nanowire [45][46][47][48].
Raman spectra were deconvoluted with a minimum number of Lorentzian components, allowing identification of a total of 33 peaks from the four different Raman measurement configurations. A representative deconvolution of the Raman spectra of Zn 3 P 2 , along with details regarding the deconvolution procedure and identification of the peaks can be found in the supporting information (available online at stacks.iop.org/NANO/32/085704/mmedia). It should be noted that all linewidths of the peaks are narrow and similar in values, pointing to their nature as one-phonon modes. Table 2 lists the Raman frequencies of all peaks obtained from the deconvolution, the symmetry assignment based on the polarization conditions, comparison with calculated phonon modes, as well as previously reported experimental results [27]. Table 2 indicates an excellent agreement (within 2% difference) between the experimentally observed peaks and the theoretically predicted Raman frequencies. Minor disagreement in the Raman peak positions between the experimental and the theoretical results is expected, due to approximations applied during the calculations.
While the peak positions have shown excellent agreement between this work and the results reported in the literature, we would like to point out several inconsistencies regarding their symmetry assignment. In particular, 9 modes out of 26 modes from [27] do not match the proposed symmetry assignment with the identification performed in this work. These peaks are highlighted in table 2 by providing the literature's symmetry assignment in parenthesis next to the peak position. One possible reason for the mismatch could be closeness in peak position for different types of modes, which, along with some breakdown in selection rules due to the defects present in the crystal, as reported in [27], could result in the appearance of forbidden modes in the Raman spectra, and consequently lead to misinterpretation. Additionally, we also point out that the proposed mode assignment in [27] is based solely on experimental results, while this work is supported by both theoretical calculations and polarization measurements.
A more detailed analysis of the Zn 3 P 2 phonons can be obtained from the calculated phonon dispersion along highsymmetry directions of the Brillouin zone, which is presented in figure 5, along with the total and elemental PDOS. Three separate regions can be identified in the phonon dispersion diagram: (i) a low-frequency region (<210 cm −1 ) which is dominated by Zn-related vibrations, (ii) an intermediate region (210-225 cm −1 ) which represents a true phonon gap with no observed vibrations, and (iii) a high-frequency region (>225 cm −1 ) which is attributed mainly to P-related vibrations. The observation of the phonon gaps seems typical for II-V compounds, as similar features were observed for ZnP 2 and CdP 2 [49]. Additionally, it was noted that the position and shape across the Brillouin zone of those phonon bandgaps seems virtually independent of the cations (Zn or Cd). This Figure 5. DFT-calculated phonon dispersion along high-symmetry directions of the tetragonal Zn 3 P 2 structure. On the right the partial phonon density of states is presented: zinc atoms in blue-gray, phosphorous in pink, and total in black. feature could be further exploited for thermoelectric applications, for example. It is also important to point out that the tetragonal Zn 3 P 2 does not possess any optical phonons above 365 cm −1 . This is the consequence of Zn 3 P 2 being structurally more similar to ternary and quaternary chalcogenides where anions, similar to cations, are all tetrahedrally coordinated [23,26,50].
Finally, atomic displacements of the Raman modes were calculated to provide the visualization of the corresponding atom motions. Figure 6 shows representative vibrational patterns. As expected from the PDOS, the vibrational patterns are mostly dominated by either Zn (<200 cm −1 ) or P motions (>225 cm −1 ). E g -symmetry modes represent primarily in-plane vibrations, perpendicular to the long c-axis of the crystal lattice (160, 316 and 344 cm −1 ). On the other hand, non-degenerate modes involve mostly atomic motion along the c-axis. The A 1g mode centered at 200 cm −1 , for example, corresponds to compression of Zn layers towards P atoms at 4c and 4d Wyckoff positions. The A 1g mode at 287 cm −1 involves breathing-like vibrations of P atoms around the vacancy at 8e Wyckoff position. On the other hand, the A 1g mode at 337 cm −1 involves asymmetric stretching vibrations along the c crystal axis of P atoms at 4c and 4d positions. Other modes exhibit more complicated vibrational patterns, which can involve both in and out of plane motions of atoms, as shown in figure 6.

Conclusions
In conclusion, this work provides a reference Raman spectrum of tetragonally-structured Zn 3 P 2 , with the complete analysis of all Raman active modes from both experimental and theoretical perspectives. High-resolution Raman scattering measurements that were performed under different polarization configurations on the basal (010) plane of single crystal nanowires, together with the detailed deconvolution of the Raman spectra with Lorentzian curves, have allowed identification of 33 Raman peaks out of 39 even parity vibrational modes. The experimental results are in good agreement with the vibrational frequencies that have been computed by first-principles calculations based on DFT. Further calculations of the PDOS (elemental and total), as well as the phonon dispersions allowed for a better understanding of the experimentally observed phonon lines, as well as the assignment to the specific lattice eigenmodes. In particular, three separate regions were observed in the phonon dispersion diagram: (i) a low-frequency region (<210 cm −1 ) which is dominated by Zn-related vibrations, (ii) an intermediate region (210-225 cm −1 ) which represents a true phonon gap with no observed vibrations, and (iii) a highfrequency region (>225 cm −1 ) which is attributed to primarily P-related vibrations. These results can be used as a reference for identification of the Zn 3 P 2 phase, as well as for building Raman based methodologies for effective defect screening of bulk materials and films, which might contain structural inhomogeneities.