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Jona Grümbel, Rüdiger Goldhahn, Martin Feneberg, [Yuichi Oshima](https://orcid.org/0000-0001-8293-4891), Adam Dubroka, Manfred Ramsteiner

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[Band gaps and phonons of quasi-bulk rocksalt ScN](https://mdr.nims.go.jp/datasets/cd92f0a9-f7dd-4e1b-bbf1-9c83ca6d60b6)

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Band gaps and phonons of quasi-bulk rocksalt ScNJona Grümbel,∗ Rüdiger Goldhahn, and Martin FenebergInstitut für Physik, Otto-von-Guericke-Universität Magdeburg, Universitätsplatz 2, 39106, Magdeburg, GermanyYuichi OshimaResearch Center for Electronic and Optical Materials,National Institute for Materials Science , 1-1 Namiki, Tsukuba, Ibaraki 305-0044, JapanAdam DubrokaDepartment of Condensed Matter Physics, Masaryk University, Kotlá°ská 2, 611-37 Brno, Czech RepublicManfred RamsteinerPaul-Drude-Institut für Festkörperelektronik (PDI), Hausvogteiplatz 5-7, 10117, Berlin, GermanyScN is an emerging transition metal nitride with unique physical properties arising from thed-electrons of Sc. In this work we present the results of optical characterization techniques spectro-scopic ellipsometry, Raman spectroscopy, and photoluminescence measurements of a 40 µm thick,fully relaxed, and only weakly n-type doped (n = 1.2 × 1018 cm−3) ScN �lm deposited by halidevapor phase epitaxy (HVPE) on r-sapphire substrate. Spectroscopic ellipsometry yields an indirectbandgap of 1.1 eV while the lowest direct interband transition is observed at Eg,opt = 2.16 eV in thedielectric function. A broad luminescence feature at 2.15 eV is observed, matching this transition.We derive an estimate for the exciton binding energy (EbX ≈ 14meV) as well as the Born e�ec-tive charges Z∗Sc = −Z∗N = 3.78. In the infrared spectral region we observe a strong phonon anda weak plasmon absorption. We precisely determine the transverse optical phonon eigenfrequency(ωTO = 340.7 cm−1), the high frequency dielectric constant (ε∞ = 8.3) and the static dielectricconstant (εstat = 29.5). Raman measurements using various excitation energies show resonantmulti-phonon scattering up to 6LO (6th order overtone for longitudinal optical (LO) phonons) forexcitation above the optical band gap (ELaser > Eg,opt), where the allowed 2LO scattering is thedominant scattering mechanism for all excitation energies. Their characteristic parameters deter-mined from Lorentzian line shape �tting yield ωLO = 681 cm−1 and an increased broadening andreduced asymmetry for higher LO scattering order n.I. INTRODUCTIONScN is a transition metal nitride with rocksalt (rs) crystalstructure (Fm3̄m) as the only stable and wurtzite (wz) struc-ture as a metastable phase [1]. It is a promising material forcertain applications due to its fundamental characteristics[2]. For example, giant polarization charge densities werepredicted for (111)rs-ScN/(0001)wz-GaN interfaces [3] andan improvement of crystalline quality in epitaxial wz-GaN�lms with rs-ScN interlayers has been achieved [4]. Recently,the ternary alloy system wz-ScxAl1-xN, which is stable upto 25-35% AlN mole fraction [5, 6], attracts high researchinterest due to piezo- [7, 8] and ferroelectric properties[9, 10] enabling e.g. wz-ScxAl1-xN-barrier HEMT structuresvia PA-MBE growth [11]. As a counterpart to wz-AlN,rs-ScN is the binary base material for ternary rs-AlxSc1-xN,which is under current investigation as well [6, 8, 12] andstable up to ≈55% ScN mole fraction [6].Already early theoretical studies [13, 14] concluded thatrs-ScN is an indirect semiconductor with its valence bandmaximum(VBM) located at the Γ-point and the conductionband minimum(CBM) located at the X-point of the Bril-louin zone, which is con�rmed also by more recent studies[15�18]. Some of the �rst experimental attempts includingcrystal growth and optical characterization were performedby Dismukes et al. [19], Travaligni et al. [20], and by Gallet al. [15, 21]. In the past, a very high unintentional free∗ jona.gruembel@ovgu.deelectron concentration usually masked the intrinsic proper-ties of rs-ScN regardless of the growth technique. However,in the last 15 years there were new attempts to grow rs-ScN�lms with high crystal quality, mainly by halide/hydridevapor phase epitaxy (HVPE) [19, 22], sputter epitaxy[23�26] even at room temperature conditions [27], andmolecular beam epitaxy (MBE) [28�30], going hand in handwith improved control of the unintentionally introducedfree electrons. Sputter grown samples typically exhibitcarrier densities higher than 1 × 1020 cm−3 [17, 23, 24],MBE grown sample are reported to achieve 5 × 1018 cm−3[31]. Oshima et al. [22] achieved record 1.2 × 1018 cm−3 byHVPE. The origin of the unintentional doping is attributedto nitrogen vacancies [31�33] and oxygen impurities [34, 35].It was already shown by Dismukes et al. [19] and Oshimaet al. [22] that the thickness of the rs-ScN layer has amassive impact on the structural quality and therefore dom-inantly determines the carrier concentration. These highunintentional carrier concentrations still remain one of thegreatest challenges in growth and characterization of rs-ScN.For application in electrical and optical devices, knowledgeof the optical constants of a material is crucial. Also, phononand luminescence properties may yield relatively quick andnon-destructive characterization of semiconductors. Thiswork provides solid optical parameters, i.e. band gap values,phonon eigenfrequencies and broadenings, optical constantsincluding precisely determined static and high frequency lim-its, and Born e�ective charges of quasi-bulk ScN. Knowledgeof these parameter for a bulk-like single crystal sets a basisfor understanding and design of thin �lms and heterostruc-mailto:jona.gruembel@ovgu.de2Figure 1: Numerically determined, exact-exchange-basedquasiparticle bandstructure of rs-ScN from Ref. 16 andmain critical point transitions.tures. Our results reveal several di�erences to state of the artScN thin �lms, most striking the enhanced above-bandgapabsorption, giant amplitude and narrow linewidth of the IRactive phonon mode, and strong multiple phonon Ramanscattering up to 6th order. Those parameters partially standin contrast to the properties of traditional III-V semiconduc-tors.II. EXPERIMENTALFor simpli�cation we now use the notation ScN instead ofrs-ScN. In this study we investigate a (100) oriented, ≈40 µmthick ScN �lm deposited by HVPE on r-plane sapphire[22]. X-ray di�raction (XRD) full widths at half maximum(FWHM) values are 0.07◦ and 0.34◦ for the (200) and the(131) re�exes, respectively, indicating relaxation and lowdislocation densities. The free carrier concentration of oursample is determined by Hall e�ect measurements withvan-der-Pauw geometry to be n = 1.2 × 1018 cm−3 at roomtemperature, the corresponding mobility is 264 cm2 V−1 s−1.The origin of the free electrons is not clear, however it ismuch below the theoretical calculated degeneracy thresholdof ≈ 3 × 1019 cm−3 [18]. Therefore the sample representsone of the best ScN �lms currently available. We use opticalcharacterization techniques, namely spectroscopic ellipsom-etry (SE) in the infrared (IR) and near infrared (NIR)− ultraviolett (UV) spectral range, Raman spectroscopy[including photoluminescence (PL)], and IR re�ectivity.Raman spectra were excited by laser wavelengths of either632.8 nm, 532.1 nm, or 472.9 nm. A discussion of spectralresolutions and detailed experimental setups is reported inthe supplement.III. THEORETICAL MODELSThe space group of rocksalt is Fm3̄m, the point group4m 3̄ 2m . Due to the rocksalt structure with two atoms perunit cell , only 6 phonon branches exist in ScN, wherethree of them are optical. The eigenfrequencies at theΓ-point are predicted to be 632 cm−1(78.4meV) for thelongitudinal optical (LO) phonon and 365 cm−1(45.3meV)for the doubly degenerate transverse optical (TO) phononmode [36]. Experimental results suggest 2ωTO ≈ ωLO[ωLO =686 cm−1 (85.1meV), ωTO =346 cm−1 (42.9meV)][37] at the Γ-point, which constitutes an even larger LO-TOsplitting than theoretically predicted [36]. While �rst orderRaman scattering in rs-structured crystals is symmetryforbidden, second and higher order processes are in gen-eral allowed [38], but exhibit a relatively weak scatteringe�ciency. One way to overcome the small e�ciency of nthorder phonon scattering is to choose an incident photonenergy Ei, for which an outgoing resonance condition isful�lled, i.e. choosing an excitation energy above the opticalband gap (ELaser > Eg,opt). The resonance enhancement ofmultiple phonon scattering in polar materials is expected tobe particularly large for LO phonons due to the so-calledFröhlich mechanism [39].Due to the non-vanishing dipole-moment under vibrationof Sc+- and N--ions the TO phonon mode is IR-active, ex-hibiting the symmetry T1u. Additionally, in the IR spectralregion one has to take into account the free carrier absorptionfor the given carrier concentration (n > 1018 cm−3). For asingle IR-active phonon mode and a Drude contribution thedielectric function for ℏω ≪ Eg,opt is described byε(ω) = ε∞ +S′ω2TOω2TO − ω2 − iγTOω− ω2Pω2 + iγPω(1)where S′ = εstat − ε∞ and εstat /ε∞ are the low-/high-frequency limits of the ε(ω), respectively. Here, with thepresence of a plasmon absorption, εstat is the limit ε(ω → 0)without the Drude contribution. The plasma frequency ωPis given byω2P =ne2ε0m∗e,opt(2)where m∗e,opt is the optical e�ective mass [40] and n the con-centration of free electrons in the conduction band. For ScNthe approximation of a constant ε∞ does not hold satisfac-torily, therefore we use the model by Shokhovets et al. [41]:εvis(ω) = 1 +2π[Ag2ln(E2h − (ℏω)2E2g − (ℏω)2)+AhEhE2h − (ℏω)2](3)We follow the notation of ref. [42]. Within this model ε∞ isgiven by ε∞ = εvis(ω → 0) and ε∞ in eqn. (1) is replaced byεvis from eqn. (3). Additionally, the LO-TO-splitting andε∞ yield the Born e�ective charges Z∗, given by [43, 44]ω2LO − ω2TO =(Z∗e)2ε0ε∞V0µ(4)where Z∗ = Z∗Sc = −Z∗N ful�lls the required sum rule, V0 isthe primitive unit cell volume, and µ = MScMN/(MSc+MN)the reduced mass. The lattice constant of strain-free ScN iswell known to be a = 4.505Å [29].To describe the imaginary part of the dielectric functionaround the fundamental absorption edge we use the model3(a) (b)(c) (d)Figure 2: Measured ellipsometric parameters (a) Ψ and (b) ∆ for three di�erent incident angles (grey solid) andcorresponding point-by-point dielectric function model �t results (red solid) for IR-SE and UV-SE. (c) measured IRre�ectivity (red solid), model �t (black solid), and calculated re�ectivity from point-by-point �tted ε1 and ε2 (red dashed)and (d) pseudo dielectric functions ⟨ε1⟩ (blue) and ⟨ε2⟩ (orange) from UV-SE.by Elliott et al. [45]. For the exciton continuum we haveε(con)2 (ω) =Cℏω1 + erf[ℏω−Egγg]1− exp[−2π√| EbXℏω−Eg|] + εo� (5)where EbX denotes the exciton binding energy, γg is theempirical width of the exciton continuum absorption, C aconstant taking into account the transition matrix elementand Eg the bandgap energy [42]. The constant o�set εo�is added to improve the �t results as discussed later. Inaddition, di�erent electronic transitions are assigned tovan-Hove singularities in the joint density of states (JDOS).From the electronic band structure shown in Fig. 1, we canassume a M0 critical point (CP) for the direct X-transition(at ≈ 2 eV), a M1 CP for the direct Γ-transition (at ≈ 4 eV)and aM0 CP for the direct Γ′- or X ′-transition (at ≈ 5.5 eV)to the second conduction- or valence band, respectively.For di�erent types of CPs di�erent line shapes of ε(ω) areexpected.IV. RESULTSA. Ellipsometric angles and pseudo-dielectric functionThe ellipsometric angles Ψ and∆ shown in Figs. 2a and 2bare converted to the so-called pseudo-dielectric function ⟨ε⟩,partially shown in Fig. 2d. Ψ and ∆ are the polarizationangle and phase shifts that emerge from the re�ection oflight with a distinct polarization at an interface. For a cubiccrystal, they are linked to the diagonal Fresnel coe�cientsrjj byρ =rpprss= tan(Ψ)ei∆ (6)4and with to pseudo-dielectric function by⟨ε⟩ = sin2 Φ[1 + tan2 Φ(1− ρ1 + ρ)2]. (7)where Φ is the incident angle. ⟨ε⟩ would be identical to εin case of an isotropic, semi-in�nite, and perfectly smoothsample.For photon energies < (1.1 ± 0.1) eV the data setsobtained with di�erent angles of incidence do not mergeto a single ⟨ε⟩. This threshold can be interpreted as theenergy position, where incoherent interface re�ectionsbecome relevant, i.e. the energy of the indirect band gapwhich is found between Γ and X points of the Brillouinzone. This indirect band gap energy of (1.1 ± 0.1) eV is ingood agreement with earlier results [15, 16, 18, 46]. Dueto incoherent backside re�ections in the transparent region[0.089 eV(720 cm−1)−1.1 eV] the point-by-point �t does notyield reliable results, which is obvious from Figs. 2a and 2b.Therefore we exclude this spectral range from the analysisof point-by-point �tted dielectric functions. The o�set inΨ and ∆ between IR-SE and UV-SE data is caused bydi�erent spot sizes.B. NIR−UV dielectric functionTo obtain the dielectric function of ScN, we apply asimple bulk model without taking into account the sub-strate including the ScN layer and an obligatory roughnesse�ective medium layer for the NIR−UV spectral range(UV-SE), which is 8 nm thick and has a layer/void ratioof 50%. Point-by-point-�tting of the complex refractiveindex of the ScN layer yields the real and imaginary partsof the dielectric function, which are shown in Fig. 3b for theNIR-UV spectral range (point-by-point �t results are shownin Figs. 2a and 2b). This dielectric function is decomposedinto di�erent empirical functions (generalized parametricsemiconductor oscillators provided by the analysis softwareWVASE32) exhibiting the typical characteristics of di�erentcritical point transitions. In Fig. 3b these contributions areshown as well.The characteristic energies of these oscillators are com-pared to the band structure calculated by Qteish et al. [16](Fig. 1) and a very good qualitative agreement is found.The fundamental absorption edge of ScN is located at theX-point of the Brillouin-zone in agreement to Gall et al.[15] and Haseman et al. [47] but in contrast to Saha et al.[24]. The energetic ordering of the main transition featuresin the dielectric function (Fig. 3b) corroborates this fact:At ≈ 2 eV we �nd a M0 like transition, at ≈ 4 eV a M1 typetransition, and again a M0 type transition at ≈ 5 eV. Theband structure (Fig. 1) reveals the same ordering: the lowestdirect CP transition occurs at the X-point (dEjoint/dk > 0for all directions, hence M0 CP) and a second direct CPtransition at the Γ-point (dEjoint/dk < 0 only for ΓX-direction, hence M1 CP). The third CP transition could beassigned to two di�erent points: (i) VB(Γ) to second CB(Γ)or (i) second VB(X) to CB(X). Possibly they both appearat around the same energy. The remaining contributionsto our model are a general higher energy contribution (Fig.3b, blue dotted) and a small background like contributiondescribing the indirect ΓX transition (Fig. 3b, yellowdotted).A quantitative analysis of the dielectric function forE > 1.1 eV reveals the fundamental absorption edge atEg = 2.16 eV with a width of γg = 76meV from Elliott'smodel (eqn. (5)). Applying Shokhovets' model (eqn. 3) weobtain Ag = 7.1 and Ah = 27.4 eV which precisely yieldsε∞ = 8.3 (Eg = 2.16 eV and Eh = 5.20 eV were �xed).The �tted curves and the real and imaginary parts of thedielectric function are displayed in Fig. 3b. Shokhovets'model was applied only to ε1 for E < 2 eV. Elliott's modelis valid only for a single M0 type VB to CB transition.Therefore, the �t was applied to the spectral region of ε2(ω),where all other transitions have ε2 ≈ 0, which is the case forE < 2.7 eV (see Fig. 3b). What still remains is the indirectabsorption edge contribution, which we approximate by aconstant o�set εo� in eqn. (5). Although we do not observeany discrete exciton state, we obtain the exciton bindingenergy EbX = 14meV as an estimate. For the transitionenergies EΓ and EΓ′ we determine the in�ection points ofε2 to be EΓ = 3.75 eV and EΓ′ = 5.20 eV in good agreementwith the electronic band structure shown in Fig. 1.Further, we observe a relatively high absolute ε2 abovethe fundamental bandgap (ε2 ≈ 7 at 3 eV) which yields anabsorption coe�cient α = 3.4 × 105 cm−1 at 3 eV, whichis signi�cantly larger than that of e.g. GaN [48] or othercommon III-V nitrides at ≈ 1 eV above the absorptiononset. Overall, our observations are similar to those of Dinhet al. [49] qualitatively, but our absolute amplitudes of ε1and ε2 are larger by a factor of ≈ 1.3 − 1.5. Additionally,we can derive the Born e�ective charges from our ε∞ andlater on determined ωLO,TO. We have Z∗Sc = −Z∗N = 3.81(eqn. (4)), which is well above the expected ionization levelsof 3/-3 for Sc/N respectively, but signi�cantly lower thanit was theoretically predicted [50]. This hints towards astrong bonding hybridization, leading to an admixture of N2p and Sc 3d states in the highest occupied valence band,which was already shown by theoretical calculations [16].The same behaviour was observed for the related rs-CrN byboth, theory [51] and experiment(Z∗ = 4.4) [43].C. IR dielectric functionIn the IR spectral range, a broad reststrahlenbandarising from the phonon absorption and a free carrierabsorption for ω < 200 cm−1 is observed from IR re-�ectivity measurements (Fig. 2c). From the model �t[eqns. (1) and (3)] we determine Drude parameters ofωP = 1200 cm−1 and γP = 250 cm−1, yielding an e�ectiveelectron mass of m∗e = 0.07me[eqn. (2)]. This e�ectiveelectron mass is well below various theoretical calculated[16, 18, 50] and experimentally determined [17, 46] values[mDOS ≈ (0.35± 0.05)me]. In Fig. 2c it is obvious, that theapplied model does not match the data well, especially forwave numbers below 250 cm−1. Therefore, we conclude thatthe Drude formalism currently does not hold satisfactorilyfor free electrons in ScN and the determined plasmonparameters are not trustworthy. Evaluation of the IR-SE5(a) (b)Figure 3: (a) Real (blue) and imaginary (orange) part of the point-by-point �tted dielectric function derived from IR-SEand Lorentz-model �t (black lines). (b) Real (blue) and imaginary (orange) parts of the point-by-point �tted dielectricfunction derived from UV-SE, Elliott model �t to ε2 (black line), Shokovets model �t to ε1 (red line), and di�erent modeloscillators (colour dotted). The reference line indicates the upper bound (2.7 eV) of the area, where only the directX-transition exhibits ε2 ≫ 0.data (see Figs. 2a and 2b) yields more accurate results, butdue to the limited spectral range, the plasmon absorption isnot detectable.The point-by-point �tted dielectric function shown in Fig.3a shows a strong phonon absorption with a maximum ofε2 ≈ 1700 and the re�ectivity calculated from this dielectricfunction matches the measured re�ectivity well(Fig. 2c). Asimilar value of ε2 was reported before [52] and hints towardsa partially ionic bond in ScN, which was already theoreticallypredicted in 1971 by Weinberger et al. [13]. A Lorentz �t[eqn. (1) without the Drude contribution] including our �xedεvis(ω) [eqn. (3)] from the UV-SE yields a TO-frequency ofωTO = 340.7 cm−1, broadening γTO = 3.7 cm−1, an am-plitude S = 21.2 and hence εstat = 29.5. This broaden-ing γTO is about twice the selected spectral resolution (seesupplement). In comparison to common III-V nitride semi-conductors such as GaN the oscillator strength of the TOphonon and hence εstat is very high, and thus semiconduct-ing ScN is a so called high-k dielectric. The determined TOfrequency (ωTO = 42.24meV) matches well with the exper-imentally determined phonon dispersion of Uchiyama et al.(ωTO(Γ + δk) = 42.9meV) [37], but is in contrast to severaltheoretical calculations [36, 50] and other experiments [52].D. Raman and PL spectraFor Raman and PL measurements we employed threedi�erent incident laser wavelengths: 472.9 nm (2.62 eV),532.1 nm (2.33 eV), and 632.8 nm (1.96 eV). In Fig. 4athe Raman spectra obtained with di�erent excitationwavelengths are shown. These spectra are measured witha better resolution than photoluminescence (see supple-ment). For all three incident laser energies the allowed [38]second-order scattering by two LO phonons (2LO peak) isthe dominant scattering process with ω2LO ≈ 1370 cm−1.Although �rst order scattering is Raman-forbidden, weobserve weak �rst order Raman scattering for excitationenergies of 2.33 eV and 2.62 eV. Assigning the multiple (nthorder) phonon scattering peaks has to be done carefullyfor ωLO ≈ 2ωTO and hence signals can be undistinguish-able. The Raman spectrum at an incident laser energyof 2.62 eV shows nLO scattering up to 4LO (see Fig. 4a,blue line). In the same �gure, nTO signals are labeled forodd n. Due to ωLO ≈ 2ωTO these Raman signals couldeither be (2n − 1)TO or nLO+TO peaks. We observe twodi�erent �rst order TO related peaks at ≈ 336 cm−1 and≈ 415 cm−1 with 2.62 eV excitation. They can be assignedto TO(Γ) and TO(X) in good agreement with previousexperimentally determined values at Γ (ωTO = 346 cm−1)and at X (ωTO = 408 cm−1) points of the Brillouin zone [37].Changing the laser energy to 2.33 eV yieldsELaser ≈ Eg,opt + 2ELO and hence nearly perfect criti-cal point resonance for the 2LO (and 4TO) scattering.Therefore, all other signals exhibit relatively small inten-sities. For excitation in the transparent region at 1.96 eV,the condition for the enhancement of multiple order phononscattering by outgoing resonances is not ful�lled anymore.Indeed, while we still observe a dominant 2LO peak, nohigher order scattering is found anymore (see Fig. 4a,red line). Additionally, we observe a broad contributioncovering various narrower signals around 700 cm−1. Theorigin of this broad contribution is not known yet. Becausewe do not expect �rst order scattering for the non-resonantexcitation at 1.96 eV, we tentatively assign the two featuresat ≈ 690 cm−1 and ≈ 830 cm−1 as 2TO(Γ) and 2TO(X)rather than �rst order LO scattering. The 2TO(X) is alsoweakly visible at other incident laser energies.For a quantitative analysis, line shape �ts are performedusing standard Lorentzian type functions. Due to theluminescence signal, which is located directly at the position6(a) (b)Figure 4: (a) Room temperature Raman spectra at three di�erent excitation wavelength and (b) Raman and PL spectrafrom 5K−293K at an incident laser energy of 2.62 eV.of the 2LO line, the spectrum for ELaser = 2.33 eV is impos-sible to �t unambiguously and with 1.96 eV excitation weobserve only second order scattering. Therefore, we chooseto model only data recorded with ELaser = 2.62 eV. Resultsare summarized in Tab. I and �t details are reported inthe supplement. From Tab. I the dependence of the n-LObroadening γ on the LO-order n is obvious. We observeincreasing broadening with higher scattering order n, whilethe broadening values for the nTO lines scatter around≈ 40 − 100 cm−1. An important result is the LO eigen-frequency obtained from �tting the �rst order LO signal.We have ωLO = 684.5 cm−1 in good agreement with earlierexperiments (ωLO = 686 cm−1) [37, 52], but in contrastto theoretical calculations (ωLO ≈ 630 cm−1) [36, 50] atthe Γ-point. The phonon lifetime can easily be derived asthe inverse phonon broadening as τLO = (2πγLO)−1. Wehave τLO = 0.2 ps, which is again in perfect agreementwith previous experimental results (τLO = 0.21 ps [37]).So in contrast to Dinh et al. [49], we rather conclude thatthe LO scattering takes place at the Γ-point due to both,momentum conservation and above discussed previous XRDresults [37]. The multiple odd number TO scattering linescorrespond to TO frequencies of ≈ 350 cm−1, which isbetween the frequencies of the �rst-order TO phonon lines(see Tab. I) indicating their origins as iTO(Γ) + jTO(X)(i + j = n) combination modes. The multiple even numberTO lines correspond to TO frequencies of ≈ 337 cm−1,which indicates their origin as nTO(Γ) lines.To investigate the photoluminescence signal, we scan alarger spectral range and apply lower temperatures downto 5K. These spectra demonstrate multi-phonon scatteringand luminescence in a single measurement, but do not allowprecise evaluation of the n-phonon peak positions due tothe decreased accuracy (see supplement). In Fig. 4b theRaman/PL spectra are presented from 1.9-2.6 eV for di�er-ent temperatures. We �nd a broad luminescence peak witha maximum at around ≈2.15 eV and multi-phonon Ramansignals up to 6LO and 9TO. Surprisingly, the center energyof the luminescence signal seems to decrease slightly withdecreasing temperature. Accordingly, the 6LO Raman lineexhibits a much larger intensity with respect to the lowerorder modes at low temperature (5K). This enhancementis caused by a better matching of the resonance conditionresulting from the slight decrease of the direct band gap.Comparing the luminescence peak to our ellipsometryresults we conclude that luminescence arises from directband-to-band recombination at the X-point. Concerningthe band structure shown in Fig. 1, the VB seems tobe only a saddle point and photo-generated holes couldeasily thermalize towards Γ. Our observation thus stronglyindicates a local VB maximum at the X-point. For a degen-erately doped ScN single crystal (nHall =2.2 × 1021 cm−3)Al Atabi et al. [46] already reported ARPES measurementsindicating such a local VB maximum at the X-point.V. CONCLUSIONSIn summary, we investigated a HVPE grown quasi-bulkrs-ScN single crystal and derived fundamental materialparameters which are listed in Tab. II (see supplement forerror analysis). UV-SE precisely yields an absorption edgeof Eg = 2.16 eV from an Elliott model �t as well as ε∞ = 8.3from Shokhovets model �t. Additionally, an estimate of theexciton binding energy of EbX = 14meV was extracted.IR-SE and IR re�ectivity showed a strong phonon and aweak free carrier (plasmon) absorption. Drude-Lorentz�tting yields ωTO = 340.7 cm−1, γTO = 3.7 cm−1, andεstat = 29.5.Checking the Lyddane-Sachs-Teller (LST) relation yieldsω2LOω2TOε∞εstat= 1.14±0.06, which is signi�cantly o� the expectedvalue of 1. Deriving the LO frequency from LST yieldsω(LST)LO = (640 ± 20) cm−1, which is much closer to theo-retically calculated values than our Raman result. Possiblereasons for this deviation are the large LO broadening,which is neglected in the LST relation, or the coupling of the7Table I: Characterization of single and multiple phonon resonant Raman scattering for an incident laser energy of 2.62 eV.Eigenfrequencies ω0/n, broadening parameters γ0, and signal-to-noise ratios snr were determined by Lorentzian line shape�tting.TO(Γ) TO(X) 2TO LO 3TO 4TO 2LO 5TO 6TO 3LO 7TO 8TO 4LOω0n(cm−1) 336±2 415±2 334.5±2 684.5±2 355.0±0.2 338.8±0.8 689.0±0.5 350.0±0.4 337.5±0.8 686±1 349.4±0.7 342.0±0.6 689±0.8γ0 (cm−1) 76±6 64±8 40±7 27±4 60±3 59±4 36±4 94±8 75±8 65±6 100±30 30±20 210±20snr 6.3±0.3 4.0±0.3 9±3 14±4 12.8±0.3 66±8 63±9 6.5±0.3 8±2 10±2 1.3±0.2 0.6±0.3 5.3±0.4Table II: Overview of results. Note that ωLO displays theeigenfrequency of the �rst order LO signal atELaser = 2.62 eV. For details about the experimentalaccuracy see supplement.parameter unit value accuracyωTO cm−1 340.7 ±0.03γTO cm−1 3.7 ±0.06εstat 29.5 ±0.5ε∞ 8.3 ±0.2ωLO cm−1 684.5 ±2γLO (τLO) cm−1 (ps) 27 (0.20) ±4 (±0.03)ω2LOω2TOε∞εstat1.14 ±0.06ω(LST)LO cm−1 640 ±20Z∗Sc = −Z∗N 3.81 ±0.05Z∗(LST)Sc = −Z∗(LST)N 3.50 ±0.2EbX meV 14 ±1EΓX eV 1.1 ±0.1Eg eV 2.16 ±0.002γg meV 76 ±3EΓ eV 3.75 ±0.02EΓ′ eV 5.20 ±0.03LO phonon mode with free charge carriers. Born e�ectivecharges are calculated as Z∗Sc = 3.81 and Z∗(LST)Sc = 3.5using ωLO and ω(LST)LO , respectively.The free carrier absorption could not be describedadequately by the Drude model. From Raman scatteringexperiments at di�erent excitation wavelengths we observede�cient multi-phonon scattering up to 4LO and 7TO, andeven 6LO and 9TO from temperature dependent combinedRaman/PL spectroscopy. The nLO and nTO positions andbroadening parameters are determined from asymmetric andsymmetric Lorentzian line shape �ts respectively, which de-scribe the spectra adequately for ELaser = 2.62 eV. The LObroadening parameter increases while the LO asymmetryparameter decreases with higher scattering order n and thedetermined �rst order LO-frequency is ωLO = 684.5 cm−1in good agreement with previous experiments [37, 52]. In acombined Raman and PL measurement we observed a broadluminescence signal at ≈ 2.15 eV which perfectly matchesthe UV-SE determined direct bandgap of 2.16 eV. From thiswe assume a possible local valence band maximum at theX-point in agreement with earlier ARPES measurements[46].VI. ACKNOWLEDGEMENTThis work was funded by the DFG within the frameworkof the priority programme 2312 (GaNius) under project FE1453/2-1. We acknowledge the support by the project Quan-tum materials for applications in sustainable technologies,CZ.02.01.01/00/22\_008/0004572, the Czech Science Foun-dation (GACR) under Project No. GA20-10377S and theCzechNanoLab Research Infrastructure supported by MEYSCR (LM2023051). We thank Patrick Rinke for providing theDFT data.[1] N. Takeuchi, Phys. Rev. B 65, 045204 (2002).[2] B. Biswas and B. Saha, Phys. Rev. B 3, 020301 (2019).[3] N. L. Adamski, C. E. Dreyer, and C. G. van de Walle, Appl.Phys. Lett. 115, 232103 (2019).[4] M. A. Moram, Y. Zhang, M. J. Kappers, Z. H. Barber, andC. J. Humphreys, Appl. Phys. Lett. 91, 152101 (2007).[5] C. Höglund, J. Birch, B. Alling, J. Bareño, Z. Czigány,P. O. Å. Persson, G. Wingqvist, A. Zukauskaite, and L. Hult-man, Journal of Applied Physics 107, 123515 (2010).[6] S. Satoh, K. Ohtaka, T. Shimatsu, and S. Tanaka, J. Appl.Phys. 132, 025103 (2022).[7] O. Ambacher, B. Christian, N. Feil, D. F. Urban, C. Elsässer,M. Prescher, and L. Kirste, J. Appl. Phys. 130, 045102(2021).[8] O. Ambacher, S. Mihalic, M. Yassine, A. Yassine, N. Afshar,and B. Christian, J. Appl. Phys. 134, 160702 (2023).[9] S. Fichtner, N. Wol�, F. Lo�nk, L. Kienle, and B. Wagner,Journal of Applied Physics 125, 114103 (2019).[10] N. Wol�, S. Fichtner, B. Haas, M. R. Islam, F. Niekiel,M. Kessel, O. Ambacher, C. Koch, B. Wagner, F. Lo�nk,and L. Kienle, J. Appl. Phys. 129, 034103 (2021).[11] K. Frei, R. Trejo-Hernández, S. Schütt, L. Kirste,M. Prescher, R. Aidam, S. Müller, P. Waltereit, O. Am-bacher, and M. Fiederle, Jpn. J. Appl. Phys. 58, SC1045(2019).[12] R. Deng, B. D. Ozsdolay, P. Y. Zheng, S. V. Khare, andD. Gall, Phys. Rev. B 91, 045104 (2015).https://doi.org/10.1103/PhysRevB.65.045204https://doi.org/10.1103/PhysRevMaterials.3.020301https://doi.org/10.1063/1.5126717https://doi.org/10.1063/1.5126717https://doi.org/10.1063/1.2794009https://doi.org/10.1063/1.3448235https://doi.org/10.1063/5.0087505https://doi.org/10.1063/5.0087505https://doi.org/10.1063/5.0048647https://doi.org/10.1063/5.0048647https://doi.org/10.1063/5.0170742https://doi.org/10.1063/1.5084945https://doi.org/10.1063/5.0033205https://doi.org/10.7567/1347-4065/ab124fhttps://doi.org/10.7567/1347-4065/ab124fhttps://doi.org/10.1103/PhysRevB.91.0451048[13] P. Weinberger, K. Schwarz, and A. Neckel, J. Phys. Chem.Solids 32, 2063 (1971).[14] A. Neckel, P. Rastl, R. Eibler, P. Weinberger, andK. Schwarz, J. Phys. C: Solid State Phys. 9, 579 (1975).[15] D. Gall, M. Städele, K. Järrendahl, I. Petrov, P. Desjardins,R. T. Haasch, T.-Y. Lee, and J. E. Greene, Phys. Rev. B 63,125119 (2001).[16] A. Qteish, P. Rinke, M. Sche�er, and J. Neugebauer, Phys.Rev. B 74, 245208 (2006).[17] R. Deng, P. Y. Zheng, and D. Gall, J. Appl. Phys. 118,015706 (2015).[18] S. Mu, A. J. E. Rowberg, J. Leveillee, F. Giustino, and C. G.van de Walle, Phys. Rev. B 104, 075118 (2021).[19] J. Dismukes, W. Yim, and V. Ban, Journal of Crystal Growth13-14, 365 (1972).[20] G. Travaglini, F. Marabelli, R. Monnier, E. Kaldis, andP. Wachter, Phys. Rev. B 34, 3875 (1986).[21] D. Gall, I. Petrov, L. D. Madsen, J.-E. Sundgren, and J. E.Greene, J. Vac. Sci. Technol. 16, 2411 (1998).[22] Y. Oshima, E. G. Víllora, and K. Shimamura, J. Appl. Phys.115, 153508 (2014).[23] J. M. Gregoire, S. D. Kirby, G. E. Scopelianos, F. H. Lee,and R. B. van Dover, J. Appl. Phys. 104, 074913 (2008).[24] B. Saha, G. Naik, V. P. Drachev, A. Boltasseva, E. E.Marinero, and T. D. Sands, J. Appl. Phys. 114, 063519(2013).[25] P. V. Burmistrova, J. Maassen, T. Favaloro, B. Saha, S. Sala-mat, Y. Rui Koh, M. S. Lundstrom, A. Shakouri, and T. D.Sands, J. Appl. Phys. 113, 153704 (2013).[26] B. Saha, M. Garbrecht, J. A. Perez-Taborda, M. H. Fawey,Y. R. Koh, A. Shakouri, M. Martin-Gonzalez, L. Hultman,and T. D. Sands, Appl. Phys. Lett. 110, 252104 (2017).[27] S. Chowdhury, R. Gupta, P. Rajput, A. Tayal, D. Rao,R. Sekhar, S. Prakash, R. Rajagopalan, S. N. Jha, B. Saha,and M. Gupta, Materialia 22, 101375 (2022).[28] A. R. Smith, H. A. H. AL-Brithen, D. C. Ingram, and D. Gall,J. Appl. Phys. 90, 1809 (2001).[29] M. A. Moram, Z. H. Barber, C. J. Humphreys, T. B. Joyce,and P. R. Chalker, J. Appl. Phys. 100, 023514 (2006).[30] D. Rao, B. Biswas, E. Flores, A. Chatterjee, M. Garbrecht,Y. R. Koh, V. Bhatia, A. I. K. Pillai, P. E. Hopkins,M. Martin-Gonzalez, and B. Saha, Appl. Phys. Lett. 116,152103 (2020).[31] H. A. Al-Brithen, A. R. Smith, and D. Gall, Phys. Rev. B70, 045303 (2004).[32] S. Kerdsongpanya, B. Alling, and P. Eklund, Phys. Rev. B86, 195140 (2012).[33] Y. Kumagai, N. Tsunoda, and F. Oba, Phys. Rev. Appl. 9,034019 (2018).[34] M. A. Moram, Z. H. Barber, and C. J. Humphreys, ThinSolid Films 516, 8569 (2008).[35] A. J. E. Rowberg, S. Mu, and C. G. van de Walle, J. Appl.Phys. 135, 125701 (2024).[36] T. R. Paudel and W. R. L. Lambrecht, Phys. Rev. B 79,085205 (2009).[37] H. Uchiyama, Y. Oshima, R. Patterson, S. Iwamoto, J. Sh-iomi, and K. Shimamura, Phys. Rev. Lett. 120, 235901(2018).[38] E. Burstein, F. A. Johnson, and R. Loudon, Physical Review139, A1239 (1965).[39] M. V. Abrashev, A. P. Litvinchuk, C. Thomsen, and V. N.Popov, Phys. Rev. B 55, R8638 (1997).[40] E. Baron, R. Goldhahn, M. Deppe, D. J. As, andM. Feneberg, Physical Review Materials 3, 104603 (2019).[41] S. Shokhovets, R. Goldhahn, G. Gobsch, S. Piekh, R. Lantier,A. Rizzi, V. Lebedev, and W. Richter, Journal of AppliedPhysics 94, 307 (2003).[42] M. Feneberg, J. Nixdorf, C. Lidig, R. Goldhahn, Z. Galazka,O. Bierwagen, and J. S. Speck, Phys. Rev. B 93, 045203(2016).[43] X. Y. Zhang and D. Gall, Phys. Rev. B 82, 045116 (2010).[44] X. Gonze and C. Lee, Phys. Rev. B 55, 10355 (1997).[45] R. J. Elliott, Phys. Rev. 108, 1384 (1957).[46] H. A. Al-Atabi, X. Zhang, S. He, C. chen, Y. Chen, E. Roten-berg, and J. H. Edgar, Appl. Phys. Lett. 121, 182102 (2022).[47] M. S. Haseman, B. A. Noesges, S. Shields, J. S. Cetnar, A. N.Reed, H. A. Al-Atabi, J. H. Edgar, and L. J. Brillson, APLMater. 8, 081103 (2020).[48] J. F. Muth, J. H. Lee, I. K. Shmagin, R. M. Kolbas, H. C.Casey, B. P. Keller, U. K. Mishra, and S. P. DenBaars, Appl.Phys. Lett. 71, 2572 (1997).[49] D. V. Dinh, F. Peiris, J. Lähnemann, and O. Brandt, AppliedPhysics Letters 123, 112102 (2023).[50] B. Saha, J. Acharya, T. D. Sands, and U. V. Waghmare, J.Appl. Phys. 107, 033715 (2010).[51] A. Herwadkar and W. R. L. Lambrecht, Phys. Rev. B 79,035125 (2009).[52] K. C. Maurya, D. Rao, S. Acharya, P. Rao, A. I. K. Pillai,S. K. Selvaraja, M. Garbrecht, and B. Saha, Nano Lett. 22,5182 (2022).https://doi.org/10.1016/S0022-3697(71)80383-9https://doi.org/10.1016/S0022-3697(71)80383-9https://doi.org/10.1088/0022-3719/9/4/008https://doi.org/10.1103/PhysRevB.63.125119https://doi.org/10.1103/PhysRevB.63.125119https://doi.org/10.1103/PhysRevB.74.245208https://doi.org/10.1103/PhysRevB.74.245208https://doi.org/10.1063/1.4923429https://doi.org/10.1063/1.4923429https://doi.org/10.1103/PhysRevB.104.075118https://doi.org/10.1016/0022-0248(72)90185-6https://doi.org/10.1016/0022-0248(72)90185-6https://doi.org/10.1103/PhysRevB.34.3876https://doi.org/10.1116/1.581360https://doi.org/10.1063/1.4871656https://doi.org/10.1063/1.4871656https://doi.org/10.1063/1.2996006https://doi.org/10.1063/1.4817715https://doi.org/10.1063/1.4817715https://doi.org/10.1063/1.4801886https://doi.org/10.1063/1.4989530https://doi.org/10.1016/j.mtla.2022.101375https://doi.org/10.1063/1.1388161https://doi.org/10.1063/1.2217106https://doi.org/10.1063/5.0004761https://doi.org/10.1063/5.0004761https://doi.org/10.1103/PhysRevB.70.045303https://doi.org/10.1103/PhysRevB.70.045303https://doi.org/10.1103/PhysRevB.86.195140https://doi.org/10.1103/PhysRevB.86.195140https://doi.org/10.1103/PhysRevApplied.9.034019https://doi.org/10.1103/PhysRevApplied.9.034019https://doi.org/10.1016/j.tsf.2008.05.050https://doi.org/10.1016/j.tsf.2008.05.050https://doi.org/10.1063/5.0198147https://doi.org/10.1063/5.0198147https://doi.org/10.1103/PhysRevB.79.085205https://doi.org/10.1103/PhysRevB.79.085205https://doi.org/10.1103/PhysRevLett.120.235901https://doi.org/10.1103/PhysRevLett.120.235901https://doi.org/10.1103/PhysRev.139.A1239https://doi.org/10.1103/PhysRev.139.A1239https://doi.org/10.1103/PhysRevB.55.R8638https://doi.org/10.1103/PhysRevMaterials.3.104603https://doi.org/10.1063/1.1582369https://doi.org/10.1063/1.1582369https://doi.org/10.1103/PhysRevB.93.045203https://doi.org/10.1103/PhysRevB.93.045203https://doi.org/10.1103/PhysRevB.82.045116https://doi.org/10.1103/PhysRevB.55.10355https://doi.org/10.1103/PhysRev.108.1384https://doi.org/10.1063/5.0119628https://doi.org/10.1063/5.0019533https://doi.org/10.1063/5.0019533https://doi.org/10.1063/1.120191https://doi.org/10.1063/1.120191https://doi.org/10.1063/5.0164058https://doi.org/10.1063/5.0164058https://doi.org/10.1063/1.3291117https://doi.org/10.1063/1.3291117https://doi.org/10.1103/PhysRevB.79.035125https://doi.org/10.1103/PhysRevB.79.035125https://doi.org/10.1021/acs.nanolett.2c00912https://doi.org/10.1021/acs.nanolett.2c00912 Band gaps and phonons of quasi-bulk rocksalt ScN Abstract Introduction experimental theoretical models results Ellipsometric angles and pseudo-dielectric function NIR-UV dielectric function IR dielectric function Raman and PL spectra Conclusions Acknowledgement References