Thermoelectric properties and electronic structure of Cr(Mo,V)Nx thin films studied by synchrotron and lab-based X-ray spectroscopy

Chromium-based nitrides are used in hard, resilient coatings, and show promise for thermoelectric applications due to their combination of structural, thermal, and electronic properties. Here, we investigated the electronic structures and chemical bonding correlated to the thermoelectric properties of epitaxially grown chromium-based multicomponent nitride Cr(Mo,V)Nx thin films. Due to minuscule N vacancies, finite population of Cr 3d and N 2p states appear at the Fermi level and diminishes the band opening for Cr0.51N0.49. Incorporating holes by alloying V in N deficient CrN matrix results in enhanced thermoelectric power factor with marginal change in the charge transfer of Cr to N compared to Cr0.51N0.49. Further alloying Mo isoelectronic to Cr increases the density of states across the Fermi level due to hybridization of the (Cr, V) 3d and Mo 4d-N 2p states in Cr(Mo,V)Nx. The hybridization effect with reduced N 2p states off from stoichiometry drives the system towards metal like electrical resistivity and reduction in Seebeck coefficient compensating the overall power factor still comparable to Cr0.51N0.49. The N deficiency also depicts a critical role in reduction of the charge transfer from metal to N site. The present work envisages ways for enhancing thermoelectric properties through electronic band engineering by alloying and competing effects of N vacancies.


Introduction
[9] Conventional thermoelectric materials such as tellurides and antimonides are used to harvest thermoelectric power from waste energy, [10][11][12] but are limited because of scarcity and toxicity of the constituent elements. 13,14An emerging class of alternative materials are transition metal nitrides, in particular those based on ScN and CrN. 15,16With a thermoelectric power factor of 1.5-5 mW m -1 K -2 and relatively low thermal conductivity of 2-4 W m -1 K -1 due to strong spinlattice coupling, 17,18 CrN is comparable to the conventional Bi2Te3 and PbTe. 1,19Thermoelectric properties, i.e., Seebeck coefficient (S), electrical conductivity (σ) and thermal conductivity (κ) are strongly coupled and hence hard to optimize.1][22][23] The generalized findings are valid for chromium based multicomponent nitrides compared to binary CrN, manifesting higher hardness, 24 thermal stability 25 and enhanced thermoelectric performances. 26wever, the thermoelectric performances are strongly correlated to the electronic structure of the final compound.Theoretical band structure calculations reveal a local and sharp increase of the density of states (DOS) near the Fermi level (EF) for any thermoelectric materials. 27Hence, to gain improved power factor (S 2 σ), the DOS should be as large as possible around EF for increased σ and as asymmetric as possible to achieve best S. 28 It occurs due to the resonance of either the valence or conduction band of the host semiconductor with an energy level of the localized atom in the compound and can to a first approximation be explained by the Mott equation. 21,27here, kB = Boltzmann constant, q = charge, and T = absolute temperature.The expression for σ(E) is given by, 21 σ(E) = n(E)qµ(E) ………….(2)   Here, n(E) = charge carrier density and µ(E) = mobility of the charge carrier.The charge carrier density is related to the DOS g(E) and Fermi function f(E) as, 21 n(E) = g(E)f(E) …………….(3)   Furthermore, theoretical approaches for strongly-correlated-electron systems like CrN indicate that induced defects (metal/N vacancies) lead to an increase in the DOS along with shift in the EF affecting the band opening. 29This in turn affects the thermoelectric power factor S 2 σ. 29,30 Among different alloying elements (e.g., Sc, V, Al, Mo, W) in CrN, V alloying resulted in enhanced thermoelectric properties of Cr1-xVxN in both bulk and thin films, due to increased hole concentration. 31,32While alloying heavier Mo atoms, isoelectronic to Cr, would not alter the electronic properties substantially but rather affect thermal transport properties by increased phonon scattering. 33nsequently, in the present study attempts were made to synthesize epitaxial CrN, Cr1-xVxN and Cr(Mo,V)N thin films.To the best of our knowledge, no literature on such complex chromium-based multicomponent nitride Cr(Mo,V)Nx has been reported so far.Since probing electronic structure in any thermoelectric material is primordial for further improvement of transport properties, below the EF, the DOS were probed by synchrotron-based resonant inelastic X-ray scattering (RIXS) (partial-DOS) complementary to lab-based valence band spectroscopy (VBS) (total-DOS).RIXS study on correlated chromium nitride-based system is non-existent, maybe due to poor energy resolution in earlier times. 34The valence band below the EF was also studied using lab-based X-ray photoelectron spectroscopy (XPS) which is highly surface-sensitive with overlapping spectral features.In addition, above the EF synchrotron-based X-ray absorption (XAS) measurements were performed probing the unoccupied states in the conduction band.To investigate the thermoelectric properties, electrical resistivity and Seebeck coefficient of the samples were measured at room temperature.Thus, the structural, electronic, and thermoelectric correlations were systematically and quantitatively studied for CrN and Cr1-xVxN thin films.Later, we qualitatively delve into the more complex systems of chromium-based multicomponent nitride Cr(Mo,V)Nx thin films.

Experimental details
CrN, Cr1-xVxN and a series of Cr(Mo,V)Nx thin film samples were deposited on single-side polished c-plane sapphire (0001) substrates using reactive dc magnetron sputtering in an ultrahigh-vacuum deposition system described elsewhere. 35The substrates were left electrically floating at a deposition temperature of 600°C.Depositions were performed using three magnetrons, each with > 99.7 % pure metal targets, and in an atmosphere of Ar and N2.The gas composition was fixed at 40 % Ar and 60 % N2.The CrN reference was deposited at 0.32 Pa and 22 sccm Ar, while the rest of the samples were deposited at 0.40 Pa and 28 sccm Ar, due to difficulty in sustaining the plasma of all three targets ignited at lower gas flow.More detailed description of depositions and more in-depth characterization can be found elsewhere. 36therford backscattering (RBS) measurements were performed at Uppsala University using 2 MeV 4 He + ion beam. 37Backscattered ions were detected at a scattering angle of 170°.
Channeling effects in the substrates and samples were minimized by adjusting the equilibrium incidence angle to 5° with respect to the surface normal and perform multiple-small-randomangular movements within a range of 2° during data acquisition.Atomic concentrations were extracted from the spectra using the SIMNRA simulation program. 38e X-Ray Diffraction (XRD) measurements were performed in Bragg-Brentano-mode (θ-2θ) using a PANalytical X'Pert Pro diffractometer system, with a Cu-Kα source operated at 45 kV and 40 mA.The incident optics was a Bragg-Brentano module with 0.5° divergence slit and a 0.5° anti-scatter slit, while the diffracted optics included a 5.0 mm anti-scatter slit, a 0.04 rad Soller slit, a Ni-filter, and an X'Celerator detector.Detailed structural analysis using pole figures and transmission electron microscopy is described elsewhere. 36he soft X-ray absorption near-edge structure (XANES) at Cr 2p, N 1s, Mo 3p and V 2p were measured at the SPECIES beamline equipped with an elliptically polarizing undulator (EPU61) and a plane grating monochromator (PGM), at the MAX IV Laboratory, Lund, Sweden.The XANES spectra were measured at 20° grazing incidence with 0.1 eV resolution using total electron yield (TEY) and total fluorescence yield (TFY), simultaneously.The combination of drain current and NEXAFS detector enabled to acquire both surface and bulk sensitive information simultaneously.For normalization of the data, a 4 µm thick Au reference foil was scanned in the same energy range as the samples over each absorption edge.
The RIXS spectra were also measured at SPECIES beamline with a high-resolution Rowlandmount grazing-incidence grating spectrometer 39,40 with a two-dimensional multichannel detector with a resistive anode readout.The Cr 2p and N 1s RIXS spectra were recorded using a spherical grating with 1200 lines/mm of 5 m radius in the first order of diffraction.During the Cr 2p and N 1s RIXS measurements, the energy resolutions of the beamline monochromator were 0.45, and 0.2 eV, respectively.The spectrometer resolutions were 0.4 for Cr 2p and 0.3 eV for N 1s spectra.All measurements were performed with a base pressure lower than 6.7×10 −7 Pa.In order to minimize self-absorption effects 41 the angle of incidence was 20° from the surface plane during the emission measurements.The x-ray photons were detected parallel to the polarization vector of the incoming beam to minimize elastic scattering.
The hard X-ray XANES and EXAFS measurements were performed at Cr K-edge in fluorescence mode at the BALDER beamline 42 at MAX IV.For reference and energy calibration, both XANES and EXAFS were performed on a 5 µm thick Cr foil (K-edge at 5989 eV) in transmission mode.The energy scans were done using a Si (111) double crystal monochromator and either a 7-element silicon drift detector (X-PIPS, from Mirion Technologies for fluorescence signal) or ionization gas detector filled with Ar, N2 and He gases (for transmission signal) were used to measure the signals.A hexapod sample holder was used to mount the samples which were placed at an incidence and exit angle of 45° from the source and the detector, respectively in fluorescence mode.However, in the transmission mode the Cr foil was fixed at 90° incidence angle.For both XANES and EXAFS, the energy scans were repeated three times for each sample, at an energy interval of 0.25 eV and 0.5 eV with an integration time of 0.02 s.For fitting the EXAFS spectra, scattering lengths of the photoelectron and the phase shift were calculated using the FEFF9 code 43,44 considering the body centered cubic (bcc) and NaCl rocksalt-type B1 structure of Cr (COD-ID 5000220) and CrN (COD-ID 1010974), respectively.The data processing was done using the Visual Processing in EXAFS Researches (VIPER) software 45 and three scans for each spectrum from the 7 channels of the detector were analyzed and summed in the software to generate the final spectrum for each sample.A modified Victoreen polynomial function was used for the pre-edge normalization and a smoothing spline function was used for the post-edge background correction of the XAFS spectra.The k 2 -weighted back Fourier Transform (FT) spectra were fitted in the range of 0-13.5 Å -1 after extracting from the forward FT spectra within R-φ = 1-3 Å.
Core-level XPS measurements were performed in an Axis Ultra DLD instrument, Kratos Analytical (UK), using monochromatized Al-Kα radiation (1486.6 eV).The base pressure during analysis was ~1.3×10 -7 Pa.Prior to measurements, samples were sputter etched for 10 minutes using 0.5 keV Ar + ions incident an angle of 70° from the surface normal.The area affected by the Ar + beam was 3×3 mm 2 , while the analysis area was 0.3×0.7 mm 2 (centered in the middle of the etched crater).All spectra are charge referenced by setting the low energy DOS cut-off at 0 eV.For Cr0.44Mo0.08V0.06N0.42 and Cr0.45Mo0.09V0.07N0.40sample, an electron flood gun was used to neutralize the charge accumulation on the sample surface due to low electrical conductivity.Complementary to p-DOS, the total DOS was probed using valence band spectroscopy (VBS).
The sheet resistances of the samples were measured using a standard four-point-probe set-up (Jandel Model RM3000) at room temperature (~300 K) with equidistant probes with spacing of 1 mm each and a tip radius of 100 µm.The electrical resistivities (ρel) of the samples were then calculated taking into consideration the film thickness 46 as deduced from the XRR measurements (Table S1 in supplementary information). 47The Seebeck coefficients were also measured at room temperature using a home-built thermoelectric measurement setup. 48The setup was equipped with two Peltier heat sources for creating a temperature gradient in the sample and two K-type thermocouples for measuring the temperature.The two electrodes are made of Cu and are in contact with the sample in an area of approximately 9×1 mm 2 in which the Ktype thermocouples are present. of Mo in the metal site and an increase in the V content from 6 to 8%.All the samples contain negligible amount of oxygen which is less than the detection limit (~1 atomic %) of the instrument.A plausible explanation for the higher degree of N deficiency within the Cr(Mo,V)Nx series compared to Cr0.51N0.49and Cr0.50V0.03N0.47 is explained below (see section 3.2.1).  Figure 1(a) shows θ-2 XRD patterns of Cr0.51N0.49,Cr0.50V0.03N0.47 and Cr(Mo,V)Nx epitaxial thin films, described in more details elsewhere. 36For all samples, the (0001)-oriented Al2O3 substrate provides a template for twin-domain epitaxial cubic growth of the thin films along [111] direction. 49With increase in alloying-element concentration of V and incorporation of Mo in the CrN matrix, the lattice parameter gradually decreases as evident from the shift of the 111 and 222 peaks to higher diffraction angles.Up to the highest alloying element concentration, a single-phase cubic NaCl structure is retained, with no indication of any secondary phases.The 111 peaks of each sample were fitted using pseudo-Voigt functions and the lattice parameters determined from the 111 peak positions are listed in Table I.It can be inferred from the present study that addition of V increases the solid solubility limit of Cr(Mo,V)Nx preventing phase segregation of Mo2N as observed by Quintela et al in bulk Cr1-xMoxN (at x ≥ 0.025). 33For Cr0.51N0.49, the lattice parameter corroborates well with literature values around 4.15-4.18Å. 49 Note the presence of Laue oscillations (see Figure 1(b)) in all the samples, indicating high crystallinity.

X-ray diffraction
The atomic radii of Cr, V, Mo, and N are 140, 135, 145 and 65 pm, respectively.It is known that with nitridation of Cr, phase transition from Cr (bcc) → β-Cr2N (hcp) → CrN (rocksalt) occurs. 50For stoichiometric CrN, the N atoms occupy 100% of the interstitial octahedral sites of the metal lattice.Earlier studies show alloying with V or Mo results in an increase in the lattice parameter provided the Cr atoms are substituted by the metal atoms in bulk CrN. 31,33evertheless, our RBS results confirm the presence of N vacancies in all the samples.Thus, decrease in the lattice parameter stems from the volume contraction caused by the insufficient N occupancy.Similar observations have been reported for N deficient CrN thin films. 50lthough the metal content is considerably more than 50% (and N content is reduced from 47 to 39%) of the lattice site, the B1 rocksalt structure is still retained, instead of transformation to hcp Cr2N.Within the Cr(Mo,V)Nx samples, the reduction in the lattice parameter follows the    The fitting of FT χ (R) of the Cr foil is shown and discussed in the supplementary information (Figure S1). 47Single scattering theory with the first two nearest neighbor scattering paths from the Cr absorber atom were considered for fitting the FT χ (R) spectra.The first two shells extended in 0.7-3.1 Å (see Figure 2(a)) correlate to the Cr-N and Cr-Cr bond distances at around 1.55 and 2.45 Å.The scattering phase shift in EXAFS is typically 0.5 Å at lower (R-φ) from the obtained fitted values since χ (k) ∝ sin (kR+φ) in k-space. 52The atomic pair distances (Rabsorber-neighbor) obtained from the fitting are RCr-N = 2.08 (±0.04) and RCr-Cr = 2.92 (±0.01)Å.The RCr-N value is in excellent agreement while RCr-Cr is slightly at a lesser value compared to the XRD data (R'Cr-N = 2.079 and R'Cr-Cr = 2.941).This local information may differ from the macroscopically averaged information acquired from XRD.
The fitting reveal values of NCr-N = 4.85 (±1.5) and NCr-Cr = 10.6 (±1.1) in the first and second coordination shell, respectively.Contrary to our RBS results, from EXAFS, the N deficiency around the first coordination shell for Cr0.51N0.49sample cannot be stated within the error bar of the present study.Fitting of the RBS data yields an overall substoichiometry in nitrogen if the elemental distributions are assumed to be homogeneous.Local inconsistencies from the stoichiometry can be probed using EXAFS which typically extends up to 5 Å from the Cr absorber atom.EXAFS fitting further suggests locally less occupancy of Cr atoms in the second coordination shell.Figure 3(a) shows normalized Cr K-edge XANES spectra of Cr0.51N0.49,Cr0.50V0.03N0.47 and Cr(Mo,V)Nx samples.The observed features are labelled as A-E.For comparison, a reference Cr foil was also measured and shown in the supplementary information (Figure S2). 47Note that all the samples display a weak pre-edge feature, shown in Figure 3(a) as a shaded region labeled A. This is assigned to a single core electron excitation from the 1s core orbital to the unoccupied 3d valence states of the Cr absorber atom partially hybridized with the 2p valence states of the neighboring N atoms and is electric dipole allowed (∆l = ±1).The EF lies around the pre-edge, which is indicated in the inset of Figure 3(a) (also in the magnified view of Figure 3(b)).
Above the Fermi energy, EF, the higher-energy feature labeled B is attributed to 1s → 4s transitions of the Cr absorber atom, with partial contribution from 2p-3s-3p states of the nitrogen ligand.This makes the electric dipole transition allowed (∆l = ±1) as observed for different transition metal compounds. 54Around this region, the absorption edge (E0) also appears (indicated in the inset of Figure 3(a)) and the positions for all the samples are listed in Table I.The E0 gradually shifts to the lower photon energy from Cr0.51N0.49to Cr0.44Mo0.09V0.08N0.39.This is attributed to the reduced core-hole screening of the Cr ions from Cr0.51N0.49to Cr0.44Mo0.09V0.08N0.39leading to reduction in the charge transfer from Cr to N. The trend in the samples can be well corroborated to the different electronegativities of the transition elements present in the samples with 1.63 (V), 1.66 (Cr), 2.16 (Mo), and 3.04 (N) in Pauling scale.
As seen from XRD, the samples crystallize in cubic rocksalt NaCl structure (Fm3 ̅ m).This structure is known to have a periodic ABCABC stacking sequence.Such a stacking sequence in the presence of a nitrogen ligand environment gives rise to an intense white line (a sharp intense peak in the near edge) feature labeled C. Hence, such observation is a fingerprint for the typical characteristics of transition metal nitrides crystallized in NaCl structure.Features labeled C and D arises due to core electron transition from 1s → 4p obeying the electric dipole transition rule.The occupancy of electrons in the unoccupied 4p orbitals of the Cr absorber reflects an inverse trend in the intensity around feature C. Feature E is resultant of the constructive interference of the outgoing photoelectron from the Cr absorber and backscattered photoelectron wave function from the neighboring N atoms.
A magnified view of the electronic DOS around EF of the normalized Cr K-edge XANES spectra is shown in Figure 3(b).In contrast to stoichiometric CrN, 55 non-vanishing Cr 3d t2g non-bonding and Cr 3d eg anti-bonding states with partial contribution from N 2p states arise around the EF.This is due to the N vacancy mediated defects for the substoichiometric Cr0.51N0.49 in the present study and is consistent with previous band structure calculations. 29The vacancy in the N site led to occupancy of electrons back to the metallic spin up Cr 3d t2g nonbonding states pushing the EF inside the conduction band.The increase in the DOS around EF with alloying (also indicated around EF in the inset of Figure 3(a)) is governed by the cumulative effect of alloying elements and N vacancies.The effect is strongly correlated to the change in the thermoelectric properties of the samples (discussed in Section 3.4 below).   ] and indicates hybridization strength. 57However, no significant changes in the 10Dq values between Cr0.51N0.49and Cr0.50V0.03N0.47 are observed in the present study within the energy resolution limit.For the Cr(Mo,V)Nx system, an overlap between the N K-edge (401.6 eV) and the Mo M3,2 -edges (spread over 392 -410 eV), 58 makes it complicated to analyze the N K-edge after addition of Mo.Due to the low fluorescence yield at the Mo M3,2-edge, 59 the N K-edge dominates the XANES spectra.The noticeable suppression of features G and H are caused by the band smearing of unoccupied Mo 4d states due to the opening of the Mo 3p→4d dipole allowed transition channel.The broadening also overshadows the relative chemical shifts of E0 between the samples.

Soft X-ray Absorption
Similar to the Cr L-edge spectra, the same trend can be observed in the V L-edge spectra, where the L3 and L2 features start appearing for Cr0.50V0.03N0.47 and becomes prominent for the Cr(Mo,V)Nx samples.However, in a simple electronic picture with higher V alloying, V should contribute with more 3d states.Simultaneously more electrons should be drawn from V to N because of the lower electronegativity, provided the N content is constant.Although at first glance it may appear simple, the presence of three transition metals with a gradual reduction of N/Me ratio is a complex system.A smaller number of available N 2p states enforces a competition of the charge transfer from one of the metals to N and back to the other metal site, especially within the Cr(Mo,V)Nx series, depending on the electronegativities of the metals.This affects the intensity distribution, and therefore no definite trend within the Cr(Mo,V)Nx system can be observed from all the absorption edges.Figure 5 shows the Cr 2p, N 1s, Mo 2p, V 2p, and Mo 3d XPS core level spectra normalized to the highest intensity.Cr 2p core level spectra (see Figure 5(a)) reveal the spin-split doublet peaks 2p3/2 and 2p1/2.For Cr0.51N0.49and Cr0.50V0.03N0.47, the peaks 2p3/2 and 2p1/2 are centered at around 574.4 and 583.9 eV.An asymmetry around the main 2p3/2 peaks is noted which arises in the Cr photoelectron spectrum owing to the multiplet structure due to unpaired electrons. 60round the broadened 2p1/2 peaks, such effect is less pronounced due to the Coster-Kronig effect. 61For Cr(Mo,V)Nx samples, no notable peak shifts can be observed compared to Cr0.51N0.49and Cr0.50V0.03N0.47.This indicates no significant change in the valence charge distribution of Cr ions after alloying which is contrary to the observed absorption edge shift in Cr K-edge XANES spectra.Thus, the deviation can be understood in the difference of the probed volume in both the measurements.However, reduction in peak broadening and peak asymmetry can be observed with Mo and increasing V alloying concentrations.

X-ray
In Figure 5(b), the N 1s and Mo 2p3/2 partially overlapping peaks are shown.The dotted lines show the reference position of the N 1s spectra for CrN, VN and MoN, respectively. 62For all samples, including even Cr0.51N0.49, the N 1s peak shifts to lower BE from the reference value reported for stoichiometric CrN (396.9 eV).This is due to the N substoichiometry (N/metal ratio is 0.96), which results in that each N atom has on average more Cr neighbors.That can lead to both (i) higher negative charge density on each Cr atom, and (ii) better screening of the core hole left after photoemission.Both effects result in the peak shift to lower BE.A gradual shift of N 1s core level spectra to the higher BE side can be seen for Cr0.50V0.03N0.47 and Cr(Mo,V)Nx samples.The observation is in line with the same trend of shift from reference samples.Thus, the shift is due to gradual reduction of N content in the non-metal site and addition of other transition metals i.e., Mo and V in the CrN matrix.The result implies reduction in the charge state of N.Although it should be noted that in XPS there is a probability of preferential sputtering of N during sputter cleaning of the sample surface.
V 2p core-level spectra shown in Figure 5(c) reveal no significant peak shifts.The only visible change is the reduction in peak asymmetry that takes place with increasing V content.Mo 3d core-level spectra (see Figure 5(d)) from Cr0.44Mo0.08V0.06N0.42 and Cr0.45Mo0.09V0.07N0.40films are identical.A shift to the lower BE side (~0.2 eV) can be noted in the Mo 3d spectrum from the Cr0.44Mo0.09V0.08N0.39sample.As the corresponding N 1s peak shifts to higher BE (see Figure 5(b)) this corroborates a reduced charge transfer from metal to N atoms.
The ζsp value of 9.5 and 7.7 eV is obtained for Cr 2p and V 2p XPS core level spectra.A discrepancy of 1.4 eV for Cr and 1.2 eV for V, among the ζsp values between the XAS and XPS measurements can be noted.This is due to excitation of the electrons to different final states involved in both the processes.Considering 2p 6 3d n as the ground state, the final states for XAS and XPS are 2p 5 3d n+1 and 2p 6 3d n , respectively.It leads to variable exchange and Coulomb interaction between the transition states involved resulting in such discrepancy. 63theoretical total-density of states calculations (Figure 6 (b), (c) and (d)) reveal contribution from the different states in the valence band spectra.Figure 6 shows valence band spectra for the Cr0.51N0.49,Cr0.50V0.03N0.47 and the Cr(Mo,V)Nx samples with their indicated EF.In the supplementary information, the theoretical total-DOS calculations are shown in Figure S3. 47Note that double layer antiferromagnetic ordering with a Hubbard parameter U=3 was considered in the calculations. 64The calculations were used to identify the hybridization contributions and their positions in the valence band spectra.

Valence Band Spectroscopy
In contrast to stoichiometric CrN known to exhibit a narrow band gap, 55,65 finite DOS around EF in the present study is attributed to the presence of N vacancies in Cr0.51N0.49thin film sample.From previous studies it is known theoretically that N vacancies induce n-type behavior in the DOS. 29However, in this study the x-ray width is ~0.3 eV.Feature Q arises mainly due to the contribution from the Cr 3d states hybridized with N 2p states, whereas feature R around 5 -8 eV is an effect from Cr 3d states hybridized to N 2p states with partial contribution from Cr 3p states.The shoulder (at 6.5 eV) arises as intense as the main feature J (5.2 eV) and appears as a doublet. 66The contribution of feature S is mostly dominated by N 2s states with a small contribution from Cr 3d states.For Cr0.50V0.03N0.47 sample, the features of the valence band spectra reciprocate similar trend like Cr0.51N0.49.However, calculated total-DOS reveals essential contribution from both Cr 3d and N 2p states with partial contribution from V 3d states for feature Q in this sample. 32Feature R unveils hybridization of N 2p states with (Cr,V) 3d and small contribution from Cr 3p states.Feature S is contributed due to the hybridization of N 2s states with marginal contribution from Cr 3d states.
For Cr(Mo,V)Nx samples, the main contribution of the features is due to the hybridization of the following states: -Feature Q at around 0.8 -1.6 eV: N 2p states -Cr 3d, V 3d and primarily Mo 4d states.
Here, a band smearing across feature Q is due to overlap of the broadened 4d wavefunctions of Mo with (Cr,V) 3d wavefunctions leading to delocalization of the valence band.The effect is also pronounced around feature R with diminished doublet feature as was observed for Cr0.51N0.49and Cr0.50V0.03N0.47.For feature S, a shift to lower BE (0.5 eV) can be observed for Cr(Mo,V)Nx samples compared to Cr0.51N0.49and Cr0.50V0.03N0.47.Cr L-edge N K-edge  The peak maxima in the XAS data were used to determine the photon energies for the emission measurements.Cr 2p RIXS on a Cr thin metal film is shown in the supplementary information (Figure S4) to obtain insight on the partial-DOS and a comparison between Cr and Cr0.51N0.49. 47The Cr 2p RIXS spectra represents the sd-DOS of the occupied Cr states of the valence band following the Cr 3d4s → 2p3/2,1/2 dipole transitions (∆l = ±1).

Resonant Inelastic X-ray
The spectra excited at 576.3 eV (resonant) show doublet features in the valence band region.In contrast, the spectra excited at 583.8 (resonant) and 625 eV (non-resonant) exhibit four features.For all samples, we attribute these features in the valence band region as L3 and L2 emission with a t2g-eg sub splitting.The most intense L3 emission at 576.3 eV and L2 emission at 583.8 eV are due to excitation at the 2p3/2 and 2p1/2 absorption edges.The feature at the lowest emission energy arise primarily due to 3d t2g orbitals, with partial N 2p contribution, whereas at higher emission energy, the 3d eg orbitals with admixture of N 2p orbitals dominates. 64,67 576.3 eV excitation energy, the relatively large distance of the band maxima from the crossover of the RIXS and XAS spectra of this bond region is an indication of strong covalent bonding between Cr and N.However, the doublet feature is less pronounced for the Cr(Mo,V)Nx samples with reduced bandwidth.It indicates a decrease in the Cr 3d -N 2p hybridization with reduced states leading to less covalent bonds.For 583.8 excitation energy, a reduced intensity of the Cr(Mo,V)Nx samples is observed compared to the Cr0.51N0.49,and the Cr0.50V0.03N0.47 samples, in-line with the reduced atomic % of Cr from our RBS measurements (see Table I).At non-resonant 625 eV excitation energy, the L3/L2 branching ratio increases from 1.9 for Cr0.51N0.49to 4.4 for Cr0.44Mo0.09V0.08N0.39.Quantitatively, the significantly higher L3/L2 ratio for the Cr0.44Mo0.09V0.08N0.39sample compared to the statistical ratio (2:1) is due to the more effective Coster-Kronig process in conducting systems compared to more localized electrons with less conduction of Cr0.51N0.49sample. 68e N 1s RIXS spectra representing the partial-DOS of N valence region follows the 2p → 1s dipole transitions.The N 1s RIXS spectra excited of all the samples at resonant photon energy of 397.3 eV exhibits a main peak centered around 389.9 eV composed of primarily N 2p states, in agreement with band structure calculations. 69We interpret the low-energy emission shoulder at ~388 eV below the main peak as N 2s-2p hybridization.A higher-energy shoulder at ~393.6 eV is also observed attributed to N 2p states hybridized with Cr 3d states in line with theoretical density functional theory calculations. 55The intensity of this shoulder is highest for the Cr0.51N0.49and the Cr0.50V0.03N0.47 samples due to more directional bonds and more charge withdrawal from Cr and V to N when there is no Mo content.For the Cr(Mo,V)Nx samples containing Mo, the number of hybridized N 2p states around the crossover region are significantly higher.This in turn affects the electrical resistivity within the samples as discussed in the next section.Contrary to the Cr 2p RIXS, most excitation-energy dependent changes in the N 1s RIXS are only observed in the high-energy shoulder, while there are only minor changes in the main peak.This is a signature of delocalized N 2p states compared to the more localized Cr 3d states.) 2/3 …………..(4)

Seebeck Coefficient and Electrical Resistivity
Combining equation ( 4) and ( 2), Seebeck coefficient and electrical conductivity are interrelated.For Cr0.51N0.49,presence of small amount of N vacancies results in S value of -93 µV K -1 at room temperature which is at least 3 times higher than earlier reports without any post deposition treatment. 17,49Rather ρ and thermoelectric power factor S 2 σ value also seems to be at per with stoichiometric bulk CrN. 71We attribute the enhanced performance is due to the presence of sharp and local increase in the DOS near EF in the VBS spectra (see Figure 6) in line with the estimated theoretical band structure calculations. 21For Cr0.50V0.03N0.47,S remains nearly same but the abrupt decrease in the ρ value is correlated to the increased population across the EF, as seen from our XANES and VBS study (See Figure 3(b) and 6) resulting 6 times higher value in power factor compared to Cr0.51N0.49.However, for Cr(Mo,V)Nx series, a large reduction in electrical resistivity with typical metal like S values originates from the strong hybridization of the N 2p-(Cr,V) 3d states with Mo 4d states inducing higher DOS across the EF as evidenced from our RIXS, XAS and VBS studies (See Figure 7(a)).Moreover, a strong coupling between Mo 4d and N 2p states near the Fermi level weakens the Cr 3d-N 2p electronic correlations driving it far from Mott insulator. 33However, the power factor of Cr(Mo,V)Nx series is still comparable to Cr0.51N0.49which we attribute to the N substoichiometry.

Conclusions
In summary, we systematically studied the effect of V and/or Mo alloying in the CrN matrix, with substoichiometric N as revealed by our RBS study.For the first time we successfully synthesized epitaxial single phase Cr(Mo,V)Nx multicomponent nitride.The addition of V stabilizes the cubic phase retention in this complex system despite the presence of higher atomic % of Mo.Even minuscule N substoichiometry led to diminished band gap in Cr0.51N0.49  Figure S1 shows the real part of the Fourier Transform (FT) moduli χ (R) and the corresponding best fit as a function of radial distance (R-φ) for Cr foil and Cr0.51N0.49thin film sample.As shown in Figure S1, the first two nearest neighbor Cr-Cr subshells constitute the first maxima in the FT spectra distributed over 1-3 Å in the (R-φ) range for the reference Cr foil.The corresponding best fits are tabulated in Table S2.For Cr0.51N0.49sample, the first two shells extended in 0.7-3.1 Å correlate to the Cr-N and Cr-Cr bond distances at around 2.08 and 2.92 Å.A clear distinction between the FT spectra and the fitting parameters confirms the body centered cubic crystal structure of Cr foil and NaCl rocksalt structure of Cr0.51N0.49.  Figure S2 shows the XANES spectra of reference Cr foil and Cr0.51N0.49thin film sample.In the present case, we approximated the absorption energy values typically around 50% of the edge jump, corresponding to the inflection point (feature A).The higher absorption energy shift of Cr0.51N0.49compared to reference Cr foil indicates higher oxidation state of Cr in Cr0.51N0.49.The shift stems from the higher core hole screening of Cr ions in Cr0.51N0.49due to charge transfer from Cr to N atoms as opposed to Cr 0 in Cr foil.The XANES spectra of Cr foil present different features compared to the nitride sample.This can be understood in terms of the different crystal structures owing to different local bonding environment of the nitride samples compared to the metallic Cr foil.Pure Cr exhibits body centered cubic crystal structure with a single stacking sequence, as it is not a closed packed structure.The Cr0.51N0.49crystallize in cubic rocksalt NaCl-type structure (Fm3 ̅ m), with a periodic ABCABC stacking sequence.Such a stacking sequence in the presence of a nitrogen ligand environment gives rise to an intense white line feature B. It arises due to 1s → 4p dipole transitions, compared to the less pronounced feature of metallic Cr foil.Here, the Cr foil has a lower intensity than Cr0.51N0.49.Charge transfer leads to higher empty unoccupied states in the 4p orbitals of Cr0.51N0.49than Cr metal which results in higher intensity around feature B and C. Figure S3 shows the theoretical partial and total density of states (DOS) calculations (Figure S3 (a), (c) and (e)) revealing contribution from the different electronic states from -20 eV below to 15 eV above the Fermi level.Figure S3 (b), (d) and (f) shows the B1 NaCl rocksalt-type crystal structure of the theoretically calculated CrN, CrVN and CrVMoN.The electronic structure calculations were performed within a density-functional-theory framework and the projector augmented wave (PAW) method 2 as implemented in the Vienna ab initio simulation package(VASP) 3,4 .LDA 5 with a combination of a Hubbard Coulomb term (LDA+ U) 6,7 was used for treating electron exchange-correlation effects.The Hubbard terms U=3 eV 8 was applied to the Cr 3d, V 3d and Mo 4d orbitals.The energy cutoff for plane waves included in the expansion of wave functions was 400 eV.The CrN cell contained 32 Cr atoms and 32 N atoms, the CrVN cell contained 28 Cr atoms, 4 V atoms and 32 N atoms while the CrVMoN contained 28 Cr atoms, 2 V atoms, 2 Mo atoms and 32 N atoms.Sampling of the Brillouin zone was done using a Monkhorst-Pack scheme 9 on a grid of 5×5×5 (64-atom supercells) k points.The calculations were only used to identify the hybridization contributions in the valence band spectra.Note in the theoretical calculations stoichiometric crystal system are considered.However, our thin film samples exhibited N substoichiometry in Cr0.51N0.49,Cr0.5V0.03N0.47 and Cr(Mo,V)Nx samples.The details of the hybridized states have been compared to the experimentally obtained valence band spectra and discussed therein.Figure S4 shows Cr 2p RIXS measured at 576.3, 583.8, and 625.0 eV photon energies, respectively and Cr L3,2 XAS data of the Cr foil and Cr0.51N0.49thin film sample.The Cr L3,2 RIXS spectra follows the 3d4s → 2p3/2,1/2 dipole transitions and the peak maxima in the XAS data were used to determine the photon energies for the emission measurements.As observed in the RIXS data, Cr metal has an intense peak at ~3 eV below EF due to metal bonding with a bandwidth of 4 eV that is narrower than for Cr0.51N0.49.At 583.8 and non-resonant 625 eV excitation energy, Cr thin film shows L3 and L2 features due to spin-orbit split of Cr 3d states contrary to Cr0.51N0.49.Due to hybridization of N 2p states with Cr 3d states, additional crystal field splitting t2g-eg takes place around the L3 and L2 features in Cr0.51N0.49.

Figure 2 (
Figure2(a) shows the real part of the Fourier Transform (FT) moduli χ (R) and the corresponding best fit as a function of radial distribution distance (R-φ) for Cr0.51N0.49thin film.The fitting of FT χ (R) of the Cr foil is shown and discussed in the supplementary information (FigureS1).47Single scattering theory with the first two nearest neighbor scattering paths from the Cr absorber atom were considered for fitting the FT χ (R) spectra.The first two shells extended in 0.7-3.1 Å (see Figure2(a)) correlate to the Cr-N and Cr-Cr bond distances at around 1.55 and 2.45 Å.The scattering phase shift in EXAFS is typically 0.5 Å at lower (R-φ) from the obtained fitted values since χ (k) ∝ sin (kR+φ) in k-space.52The atomic pair distances (Rabsorber-neighbor) obtained from the fitting are RCr-N = 2.08 (±0.04) and RCr-Cr = 2.92 (±0.01)Å.The RCr-N value is in excellent agreement while RCr-Cr is slightly at a lesser value compared to the XRD data (R'Cr-N = 2.079 and R'Cr-Cr = 2.941).This local information may differ from the macroscopically averaged information acquired from XRD.

Figure 2 (
Figure 2(b) shows distinct variation in the intensity of oscillations of Cr0.51N0.49,Cr0.50V0.03N0.47 and highest alloyed Cr0.44Mo0.09V0.08N0.39samples around the first and second coordination shell (up to 3Å).The maximum intensity is observed at around 2.45 Å for Cr0.51N0.49and it gradually decreases with increasing alloying concentrations.The peak area of the radial distribution distance is correlated to the coordination number.53Therefore, it can be inferred that for Cr0.51N0.49, the local coordination (N and next nearest Cr atoms) is the maximum for Cr absorber leading to highest intensity in both the shells.

Figure 3 :
Figure 3: Normalized Cr K-edge XANES spectra of Cr0.51N0.49,Cr0.50V0.03N0.47 and Cr(Mo,V)Nx thin film samples in different alloying concentrations.The inset shows the first order derivative of the absorption spectra with respect to the photon energy.EF represents the Fermi level, and E0 represents the absorption edge of the samples (a).The magnified view of the same normalized Cr K-edge XANES spectra near the pre-edge region indicating EF is shown for Cr0.51N0.49,Cr0.50V0.03N0.47 and Cr(Mo,V)Nx samples (b).

Figure 7 (
Figure 7(a) shows Cr 2p RIXS, Cr L3,2-edge XAS data and Figure 7(b) shows N 1s RIXS, N Kedge XAS data, respectively of the Cr0.51N0.49,Cr0.50V0.03N0.47 and the Cr(Mo,V)Nx thin film samples.The peak maxima in the XAS data were used to determine the photon energies for the emission measurements.Cr 2p RIXS on a Cr thin metal film is shown in the supplementary information (FigureS4) to obtain insight on the partial-DOS and a comparison between Cr and Cr0.51N0.49.47The Cr 2p RIXS spectra represents the sd-DOS of the occupied Cr states of the valence band following the Cr 3d4s → 2p3/2,1/2 dipole transitions (∆l = ±1).

Figure S3 .
Figure S3.The partial and total-density of states calculated by Density Functional Theory and lattice structure of CrN (a, b), CrVN (c, d), and Cr(Mo,V)N (e, f) system.

Table I .
Details of metal film composition obtained from RBS.The lattice parameters were calculated from the 111 peaks of each sample.The absorption edges around the Cr K-edge spectra are also listed.03N0.47 to Cr0.44Mo0.09V0.08N0.39 for the lowest N containing film.The sample Cr0.51N0.49and Cr0.50V0.03N0.47 are used as reference while the other three samples contain around 8 -9% 51end of B1 MoNx (4.20 -4.27 Å)/hcp MoN (a = 5.72 Å, c = 5.60 Å) → fcc Mo2N (4.16 -4.19 Å)51with reduction in the N content.Since, the lattice parameters of fcc Mo2N and rocksalt CrN matches closely, addition of Mo leads to half occupancy of N in the non-metal site (approaching Mo2N) resulting in more N deficiency in Cr(Mo,V)Nx samples compared to Cr0.51N0.49and Cr0.50V0.03N0.47.
53, Cr0.50V0.03N0.47 and highest alloyed Cr0.44Mo0.09V0.08N0.39samplesaround the first and second coordination shell (up to 3Å).The maximum intensity is observed at around 2.45 Å for Cr0.51N0.49and it gradually decreases with increasing alloying concentrations.The peak area of the radial distribution distance is correlated to the coordination number.53Therefore, it can be inferred that for Cr0.51N0.49, the local coordination (N and next nearest Cr atoms) is the maximum for Cr absorber leading to highest intensity in both the shells.For Cr0.50V0.03N0.47 sample, the intensity of the first shell remains unaltered in comparison to Cr0.51N0.49.However, 3% alloying of V leads to substitution of few Cr atoms with V and is reflected in less Cr-Cr bonds seen from a reduced intensity around the second shell.For Cr0.44Mo0.09V0.08N0.39sample, presence of less Cr-N and Cr-Cr bonds are evident from the radial distribution spectra compared to rest of the samples.This is due to the bond formation of Cr absorber atom with V and Mo atoms which substituted few Cr atoms in the metal site.Consequently, due to substoichiometry of N as observed from our RBS results, the resultant Cr-N bonds also reduce.Locally, the less directional Cr-Cr bond length reduces for Cr0.44Mo0.09V0.08N0.39 compared to rest of the samples demonstrating similar trend as our XRD results.This is attributed to the presence of N vacancies due to transition from covalent to metallike character.
503.3 Electronic structure of unoccupied and occupied states3.3.1 X-ray Absorption Near Edge Spectroscopy

Table II .
The Seebeck coefficient, electrical resistivity, and power factor of the samples.

properties and electronic structure of Cr(Mo,V)Nx thin films studied by synchrotron and lab-based X-ray spectroscopy
due to lesser N 2p states available to accommodate the electrons and instead return to the metal site shifting the Fermi level towards the conduction band.For Cr0.50V0.03N0.47,less N content and marginal alloying of V leads to lower hybridization of the Cr 3d-N 2p states revealing lower electrical resistivity without altering the Seebeck coefficient.This results in overall improvement of the thermoelectric power factor.Hence, it can be inferred that presence of N deficiency up to a critical limit still retains good thermoelectric properties.Later, in Cr(Mo,V)Nx series, combined effect of N substoichiometry and contribution of Mo 4d hybridized to N 2p states weakens the Cr 3d-N 2p electronic correlations driving it far from Mott insulator.It is governed by crossover of significant density of states across the Fermi level compared to Cr0.51N0.49and Cr0.50V0.03N0.47 exhibiting metal-like resistivity.The N substoichiometry also leads to a reduction in the charge transfer from metal to N site.The reduced Seebeck coefficient of Cr(Mo,V)Nx stems from presence of broadened Mo 4d wavefunctions which drives it away from sharp and local increase in the density of states just below the Fermi level.Thus the present study shows potential of Cr(Mo,V)Nx as a thermoelectric material which are strongly correlated to the density of states present near the Fermi level.The study motivates further research on N-stoichiometric Cr(Mo,V)N with lower alloying concentration of Mo for enhancement of the thermoelectric properties.The Fourier transform moduli χ(R) as a function of radial distance (R-φ) and the corresponding best fits for metallic Cr foil and Cr0.51N0.49thin film sample.

Table S2 .
The different structural metrical parameters obtained after fitting the FT spectra from 0-13.55 Å -1 in kregion and 1-3 Å in the (R-φ) region.Here, N1 and N2 = first and second nearest neighbor co-ordination, R1 and R2 = atomic pair distance of the first and second neighbors i.e., Cr-N and Cr-Cr in case of CrN, 1 2 and 2 2 = Debye Waller factor obtained from fitting of the first shell for Cr-foil and from first and second shell for Cr0.51N0.49sample.