J. Appl. Phys. 125, 175701 (2019); https://doi.org/10.1063/1.5093809 125, 175701

© 2019 Author(s).

Strain related relaxation of the GaAs-like Raman mode selection rules inhydrogenated GaAs1−xNx layers

Cite as: J. Appl. Phys. 125, 175701 (2019); https://doi.org/10.1063/1.5093809Submitted: 25 February 2019 . Accepted: 13 April 2019 . Published Online: 01 May 2019

E. Giulotto , M. Geddo , M. Patrini , G. Guizzetti , M. S. Sharma, M. Capizzi , A. Polimeni, G.

Pettinari, S. Rubini, and M. Felici

Strain related relaxation of the GaAs-like Ramanmode selection rules in hydrogenated GaAs1−xNx

layers

Cite as: J. Appl. Phys. 125, 175701 (2019); doi: 10.1063/1.5093809

View Online Export Citation CrossMarkSubmitted: 25 February 2019 · Accepted: 13 April 2019 ·Published Online: 1 May 2019

E. Giulotto,1,a) M. Geddo,1 M. Patrini,1 G. Guizzetti,1 M. S. Sharma,2 M. Capizzi,2 A. Polimeni,2

G. Pettinari,3 S. Rubini,4 and M. Felici2

AFFILIATIONS

1Dipartimento di Fisica, Università degli Studi di Pavia, Via Bassi 6, I-27100 Pavia, Italy2Dipartimento di Fisica, Sapienza Università di Roma, Piazzale A. Moro 2, I-00185 Roma, Italy3National Research Council, Institute for Photonics and Nanotechnologies, Via Cineto Romano 42, I-00156 Roma, Italy4IOM-CNR Laboratorio TASC, SS14, Km. 163.5, 34149 Trieste, Italy

Note: This paper is part of the Special Topic on Highly Mismatched Semiconductors Alloys: From Atoms to Devices.a)enricovirgilio.giulotto@unipv.it

ABSTRACT

The GaAs-like longitudinal-optical (LO) phonon frequency in hydrogenated GaAs1−xNx (x = 0.01) layers—with different H doses andsimilar low-energy irradiation conditions—was investigated by micro-Raman measurements in different scattering geometries and comparedwith those of epitaxial GaAs and as-grown GaAs1−xNx reference samples. A relaxation of the GaAs selection rules was observed, to beexplained mainly on the basis of the biaxial strain affecting the layers. The evolution of the LO phonon frequency with increasing hydrogendose was found to heavily depend on light polarization, thus suggesting that a linear relation between strain and the frequency of the GaAs-like LO phonon mode should be applied with some caution. Moreover, photoreflectance measurements in fully passivated samples of identi-cal N concentration show that the blueshift of the GaAs-like LO frequency, characteristic of the hydrogenated structures, is dose-dependentand strictly related to the strain induced by the specific type of the dominant N-H complexes. A comparison of photoreflectance resultswith the finite element method calculations confirms that this dependence on the H dose is due to the gradual replacement of the N-2Hcomplexes responsible for the electronic passivation of N with N-3H complexes, which are well known to induce an additional and sizeablelattice expansion.

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I. INTRODUCTION

In GaAs1−xNx alloys, many properties are strikingly modifiedwith respect to those of GaAs, even at N concentrations as low as∼1%.1 In particular, the bandgap is markedly lowered, due to thestrong interaction between the states of the GaAs conduction bandbottom and the N-related localized states.2,3 Moreover, whenthe alloy is grown as a pseudomorphic layer on top of a GaAsbuffer, the sizeable reduction of the lattice parameter of GaAs1−xNx

due to N incorporation results in the development of a biaxialtensile strain.

Incorporation of hydrogen in GaAsN can quench the elec-tronic activity of nitrogen via the formation of N-nH (n = 2,3)

complexes, with the recovery of the GaAs bandgap.4 Several appli-cations have been devised to exploit such a bandgap tuning,5

including the realization of site-controlled, single-photon emittingnanostructures by spatially selective H irradiation6 and removal.7

Correspondingly, upon H incorporation, the lattice parameterincreases up to, or even beyond, the value of N-free GaAs. In thelatter case, compressive strain develops4 in the GaAsN layer. Byspatially selective hydrogenation, a strain profile engineering can beachieved, which allows for the modulation of the optical propertiesin GaAsN/GaAsN:H planar heterostructures.

Raman scattering from GaAs-like phonons has proved to bean effective tool in mapping the strain pattern, especially across the

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interface between GaAsN wires and their GaAsN:H barriers.8,9 Inparticular, a polarization-resolved Raman spectroscopy10–12 wouldbe crucial for mapping the evolution of the strain tensor acrossGaAsN/GaAsN:H wires of different orientations (a promise aspolarization-controlled light emitters13). However, a systematicstudy of the dependence of the Raman signals on the H dose andrelated strain is still missing in the literature.

The main goal of the present paper is an experimental com-parison of GaAs-like Raman scattering response in initially identi-cal GaAsN pseudomorphic layers both as-grown and irradiatedwith different hydrogen doses. Moreover, a photoreflectance (PR)line shape analysis near the split-off (SO) spectral feature hasallowed a quantitative estimate of the biaxial (compressive) strain14

in the growth plane of heavily hydrogenated samples. PR resultshave been then compared with the strain profiles computed via thefinite element method (FEM) calculations to establish a direct linkbetween the strain level/value and the spatial distribution of N-nHcomplexes in the material.

II. EXPERIMENTAL DETAILS AND MODELING

The investigated samples were obtained from a heterostructure(sample G535) consisting of a 100-nm-thick GaAs1−xNx layer (x =0.01) pseudomorphically grown at 500 °C by molecular beamepitaxy on top of a 500-nm-thick, undoped GaAs buffer depositedon a (001) GaAs substrate. The layer thickness was determined bymeans of reflection high-energy electron diffraction. By usingoptical characterization techniques, such as room temperature PRand photoluminescence (PL), the nitrogen concentration wasverified to be very close (within 1%) to its nominal value. Six piecesof the original sample were hydrogenated at 300 °C (100 eVion-beam energy, 20 μA/cm2 ion current and different hydrogena-tion times) with six different doses: 1.2c, 1.6c, 2.0c, 2.5c, 3.0c, and3.5c (here “c” indicates a H dose dH = 1.0 × 1018 ions/cm2). Thelowest H dose here employed—dH = 1.2c—nearly corresponds tothe amount of H needed to recover the emission spectrum and theenergy gap of pure GaAs, as assessed by PL and PR measurements,respectively. A bare GaAs epitaxial layer and an untreated GaAsNsample were also used as references for optical measurements.

Micro-Raman scattering experiments were performed in back-scattering configuration—with the incident beam directed alongthe z axis, normal to the growth plane—by using a Jobin-YvonLabram micro-spectrometer (equipped with a 100× objective and a1800 lines/mm grating for a spectral resolution of 1 cm−1) and acooled Si CCD detector. The exciting He-Ne laser beam (λ = 632.8 nm,spot diameter ∼0.7 μm) was attenuated to about 0.5 mW or lessto avoid dissociation of N-H complexes.15 Different scatteringgeometries were obtained by rotating the sample around thegrowth axis and by selecting the scattered light polarization with ananalyzer. In zinc-blende GaAs, scattering of longitudinal-optical(LO) phonons is allowed by selection rules in the z(x,y)-z and z(x0,x0)-z geometries, while it is forbidden in the z(x,x)-z and z(x0,y0)-zgeometries. Here, z and –z label the directions of the incident [001]and diffused [00−1] light, respectively; x = [100], y = [010], x0 =[110], and y0 = [1−10] indicate the light polarization of the incident(symbol on the left side in parentheses) and scattered (symbol onthe right side) light. Results for GaAs-like Raman spectra are

reported in the 260–300 cm−1 wave-number range. Wheneverspectra of appreciable intensities were recorded, the data were bestfitted by two Lorentzian line shapes, accounting for thetransversal-optical (TO) and LO modes. The uncertainty of LO fre-quencies resulting from fitting was of the order of 0.1 cm−1.

PR measurements were performed at near-normal incidencein the 1.1–1.9 eV range, with a spectral resolution of 1 meV. A stan-dard experimental apparatus was operated with a 100W halogenlamp as the probe source. The excitation source was provided by a20 mW Coherent He-Ne laser (λ = 632.8 nm; 1-mm spot diameter)chopped at 220 Hz. Further details on the PR apparatus can befound elsewhere.16

The biaxial strain value in the GaAsN growth plane was deter-mined by using a well-established analytical procedure,17 based onthe PR line shape analysis near the split-off (SO) energy band, andexploiting deformation potential theory18 results.

Finally, Raman and PR results were compared with those of atwo-step calculation, performed using the finite element method(FEM). The first step was based on the diffusion-reaction equationsintroduced in Ref. 19 and allowed for computing the concentrationprofile of the two N-H complexes responsible for N passivation—respectively labeled as N-2H and N-3H—depending on thenumber of H atoms involved in the complex.

As reported in Ref. 20, the N-2H species locally results in anear-perfect recovery of the lattice parameter of GaAs, whereas theN-3H species induces an additional lattice expansion, thus leadingto the emergence of a significant compressive strain. The computedconcentration profiles could then be used as the starting point forthe second step of FEM calculations, which exploited the knowl-edge of the effects that the formation of the two N-H complexeshas on the crystal lattice to compute the spatial distribution of thestrain tensor in the material. For a hydrogenation process per-formed on unpatterned samples—such as in our case—the strainremains biaxial throughout the epilayer, although its characterranges from tensile to compressive depending on the relative con-centration of the two N-H complexes.

The strain distribution obtained with this method can then beused to reproduce the behavior of any strain-dependent quantity,as described in Sec. III for Raman and PR responses.

III. RESULTS AND DISCUSSION

Raman scattering experiments in different polarization geome-tries require a careful analysis, since the GaAs selection rules relaxin strained GaAsN21 and GaAsN:H layers. On the ground of ourmeasurements, LO scattering in the z(x0,y0)-z geometry is forbiddennot only in epitaxial GaAs but also in GaAsN (sample G535untreated) and GaAsN:H (sample G535 hydrogenated withdifferent H doses at T = 300 °C). On the contrary, scattering in thez(x,x)-z geometry is forbidden only in epitaxial GaAs, not in all theother investigated samples.

Such a relaxation of Raman selection rules can be naturallyattributed to the biaxial strain in pseudomorphic GaAsN andGaAsN:H layers.14,20–22 In fact, a biaxial strain in the (001) growthplane lowers the Td point symmetry of cubic zinc-blende semicon-ductors to the D2d symmetry of the tetragonal system.23 Of course,this complicates the choice of the polarization geometry to be

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employed when performing Raman mapping experiments of non-conventional heterostructures, such as GaAsN wires8,9 in GaAsN:Hmatrices. Indeed, the feasibility of using Raman scattering to char-acterize the strain modulation in planar heterostructures, asobtained by spatially selective H irradiation, has been recently dem-onstrated for GaAsN/GaAsN:H wires oriented along the [110]direction.8,9 However, the extension of this approach to arbitrarilyoriented wires—whose optical polarization properties have alreadyshown a nontrivial dependence on the wire orientation related tothe crystallographic axes13—will require the knowledge of the fulldependence of the main Raman modes on the experimental polari-zation geometry. In general, a polarization analysis of the scatteredlight should be carried on.24

A. TO mode

The scattering of the TO mode from a GaAs (001) surface(at ∼270 cm−1) is always forbidden in backscattering,25 which isthe only geometry accessible to us. In accordance with selectionrules, in all our samples, no scattering of the TO mode hasbeen detected in the z(x0y0)-z scattering geometry, as exem-plified by full dots in Figs. 1(a), 1(c), and 1(e). In the z(x0x0)-zand z(xy)-z geometries, instead, scattering from the TO modewas detected in all samples, though much weaker than theprominent LO scattering; see open circles in Figs. 1(a), 1(c),and 1(e). Finally, in the z(xx)-z forbidden geometry, the inten-sity of the TO mode was vanishing in epitaxial GaAs [see fulldots in Fig. 1(b)], whereas it was clearly detectable in GaAsN[full dots in Fig. 1(d)] and competing in intensity with the LOline in GaAsN:H [full dots in Fig. 1(f )].

B. LO mode—Allowed

Let us now discuss the response of the GaAs-like LO mode tothe incorporation of N and H in the crystal, as assessed inthe allowed z(x0x0)-z scattering geometry. In untreated GaAsN[Fig. 1(c)], the mode redshifts with respect to GaAs [Fig. 1(a)]because of the tensile biaxial strain in the growth plane of pseudo-morphic GaAsN.20 On the contrary, a blueshift is measured inGaAsN:H 2.5c [Fig. 1(e)], as a consequence of the onset of a com-pressive biaxial strain at high hydrogen doses.10,14,20,22

In the spectra obtained in the allowed z(xy)-z geometry, theLO mode shows a rather weak redshift in the GaAsN sample [opencircles in Fig. 1(d)], while it has a more pronounced blueshift inGaAsN:H [open circles in Fig. 1(f )).

As PR results suggest (see below), the allowed geometries areboth suitable to describe strain inversion via a monotonic relationbetween the LO GaAs-like frequency blueshift and the compressivestrain value. Nevertheless, the biaxial strain seems to be betterreproduced by a linear relation in the z(x0,x0)-z geometry.

C. Photoreflectance results

In Fig. 2(a), room temperature PR spectra (dots) for thesamples with maximum and minimum hydrogen dose are com-pared. Solid lines represent the best fit to the SO structure per-formed by using the appropriate14,26 line shape model. For thecritical point (CP) energy and broadening parameters of the SO

band we obtained: E00 + Δ00 = 1.766 eV; Γ = 42 meV—for the 1.2c

dose—and E00 + Δ00 = 1.774 eV; Γ = 49meV—for the 3.5c dose. Inthe latter case, the observed blueshift (with respect to GaAs27) isΔE = 7 meV, and an average compressive in-plane strain εxxroughly equal to −0.8 × 10−3 can be estimated.17 This confirms theinversion of the native28 tensile strain, as usually observed inhydrogenated GaAsN structures.14,20,22 Moreover, the energy

FIG. 1. Raman spectra in the GaAs-like phonon range from epitaxial GaAs,GaAsN, and GaAsN:H 2.5c (c = 1018 ions/cm2) in different polarization geome-tries. For selected scattered light polarization [100], i.e., x, or [110], i.e., x0, theRaman spectrometer throughput was five times higher than for scattered lightpolarization [010], i.e., y, or [1−10], i.e., y0. The spectra are reported without cor-rection for instrument throughput. In each panel, the GaAs-like LO phonon peakfrequencies are indicated.

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position of the SO band increases by going from the sample withthe minimum H dose to that with the maximum dose, as evidentin Fig. 2(a), thus indicating a greater “compressive” strain in thelast sample.

In addition, a moderate increase in the broadening parameter(from 5% to 20%) is also observed for increasing H dose. Thiseffect can be better appreciated from the Franz–Keldysh oscillations(FKO)29 accompanying the spectral feature of the GaAs-like energygap. In fact, the increase in the fundamental gap broadeningparameter produces an increase in the FKO period and an FKOfaster extinction. As displayed in Fig. 2(a), for the smallest H dose,the period is shorter and we may count one more oscillation withrespect to the spectrum obtained for the maximum dose. It shouldbe noted that the observed line shape broadening is small withrespect to previously reported results,14,20–22 thus suggesting thatonly a modest additional lattice disorder is introduced in thesample due to the H irradiation; this is also confirmed by thehigher LO/TO intensity ratio30 observed here [see Raman spectrain Fig. 4(a)].

Here, it is important to note that for GaAs (and GaAsN), thelight penetration depth in the energy range of our spectra is of theorder of 200 nm or more and PR signals are expected to arise inpart also from the GaAs buffer layer. Nevertheless, the results ofour analysis are not affected. The reason for this is threefold: (i) InGaAs materials, the SO PR features usually exhibit very weak inten-sity29,31,32 with respect to the GaAs bandgap ones. (ii) The GaAsNlayer grown on the GaAs buffer further reduces the intensity of thesignal coming from the GaAs layer, and indeed, the spectrum ofthe untreated reference sample (GaAsN layer on GaAs buffer, notshown here) exhibits in addition to the E− and E+ features, typicalof dilute nitrides, an intense spectral feature due to the GaAsbandgap (near 1.43 eV) and a very weak feature (near 1.77 eV) dueto the GaAs SO band (similar to what is reported in Fig. 1 ofRef. 14). (iii) For the H-treated samples, the features due to theGaAsN layer (now GaAs-like) are stronger than those coming fromthe GaAs buffer layer and much broader, as it was usually found inH- or D-treated dilute nitrides.14,33,34

This accounts for a qualitative analysis of the FKO period toobtain information on the line shape broadening and justifies ourquantitative use of the GaASN:H SO features to extract biaxialstrain values.

Finally, we note that in the present case, the GaAs buffer isintrinsic and its optical properties should not change when a veryminor amount of H diffuses through it, as supported by theabsence in our samples of any PR signal different from those dueto GaAs or fully hydrogenated GaAsN.

In fact, hydrogen solubility in semiconductors is very low35

and should not lead to any sizable change in the optical properties,unless the semiconductor is heavily doped or defected.

The rather low lattice damage due to hydrogen irradiation,combined with the full N passivation observed for all but one ofthe H doses employed [as discussed below, the 1.2c sample showsevidence of a partially incomplete passivation, albeit the GaAsNbandgap spectral feature is missing from its PR spectra; seeFig. 2(a)], nicely suggests the possibility of fine-tuning the strainlaterally applied to GaAsN/GaAsN:H wires by irradiating their bar-riers with different H doses, while, at the same time, (i) keeping theenergy gap in the barriers unchanged (but for the effects of strain)and (ii) producing a modest lattice disorder. The possibility ofusing H irradiation to finely tune the amount of strain present inthe material is perhaps better illustrated in Fig. 2(b), which reports

FIG. 2. (a) Room temperature PR spectra for the samples with minimum (1.2c =1.2 × 1018 ions/cm2, open dots) and maximum (3.5c, full dots) H dose. (b) Detailsof PR spectra near the SO region for samples with H dose 1.2c (open dots) and1.6c (full dots). Arrows indicate the SO band energy positions, as obtained fromthe best fit of the corresponding spectral features (solid lines). The energy positionE0 + Δ0 of the GaAs SO band is also reported (vertical broken line). (c) Evolutionof the blueshift vs H dose for the SO energy band, as obtained from the analysisof the PR spectral features in differently hydrogenated samples (dots, left-handscale). The theoretical (i.e., estimated from the FEM calculations described in themain text) dependence of the εxx component of the strain tensor (right-handscale) on the H dose is also reported in the figure. The dashed curves wereobtained assuming that the H dose required to achieve full passivation (see maintext) be equal to dFPH = 1.2c (lower curve) or 2.0c (upper curve). The continuousline corresponds to the curve obtained for dFPH = 1.6c.

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the comparison between the PR spectra of the 1.2c and 1.6csamples (only the SO region is shown). The drastic evolution of thespectrum for such a relatively small difference in the H dose isactually indicative of a change in the “strain character” in the mate-rial, from moderately tensile (the “near-zero strain condition” inthe 1.2c sample) to compressive (for a 1.6c dose).

In Fig. 2(c), the measured SO band blueshift (right-handscale) is shown vs H irradiation dose. It increases rapidly withincreasing H dose, and its monotonic behavior tends to saturate forhigher doses. This must be related to the effects of different typesof N-nH complexes4,36 on the energy of the SO band. In fact, thelattice parameter characterizing the hydrogenated GaAsN layerstrictly depends on the dominant complex (N-2H or N-nH withn > 2, the former favored by soft H irradiation, typical of lowerdoses). For all the examined samples, indeed, a blueshift of the SOband was observed with the only exception of a sample of dose 1.2c[see Fig. 2(b)]. This result can be interpreted on the basis of alattice parameter of GaAsN:H very close to that of GaAs, as itwould happen in the presence of a prevailing concentration ofN-2H complexes.20 Nevertheless, the near-zero strain conditionevolves rapidly toward compressive strain as evidenced in Fig. 2(b).

D. FEM calculations

As noted in Sec. II, in fully passivated GaAsN epilayers, thedependence of strain on the H dose is entirely dictated by the dis-tribution of N-2H and N-3H complexes inside the material. Inprinciple, the N-2H and N-3H concentration can be estimated viaFEM simulations, providing us with a link between the microscopicarrangement of atoms in the material and the evolution of strainwith increasing H dose. In order to provide such insight, however,simulations must be properly “calibrated”: after defining a thresh-old value that the simulated concentrations of N-H complexesmust meet to qualify the GaAsN epilayer as “fully passivated,” wehave to ensure that the hydrogenation time required to reach thethreshold matches the experimentally determined one. For the sim-ulations discussed in this work, we deemed the sample as fully pas-sivated whenever the sum of the concentrations of N-2H andN-3H complexes exceeded 90% of the initial N concentration (x =0.01) through the entire epilayer depth. Of course, it is importantto note that the inherently subjective nature of such a calibrationprocedure will unavoidably muddle the comparison between exper-iments and simulations. On the one hand, indeed, the threshold wechose to define the achievement of full passivation in the simula-tions is, in and by itself, somewhat arbitrary; on the other hand, themethod employed to experimentally identify a fully passivated layer—based on optical spectroscopy techniques such as room tempera-ture PL and PR measurements—is also affected by a sizeable uncer-tainty. For example, it is highly likely that the presence of a thin(e.g., 10–15 nm) layer of nonpassivated material near the bottom ofthe hydrogenated epilayer would go unnoticed by optical spectro-scopy techniques: apart from its limited thickness, such a layercould be optically inactive due, for example, to (i) the large concen-tration of defects typically observed at the interface between ahighly mismatched layer and the substrate,37 or (ii) to theinhomogeneous effective nitrogen concentration in the layer, asso-ciated with the finite width of the edge of the H diffusion profile

(∼10–15 nm for a hydrogenation temperature of 300 °C, as shownin Ref. 19).

In order to account for the uncertainty inherent to our calibra-tion procedure, we performed three sets of simulations, calibrated tomeet the full passivation threshold at a H dose dFPH = 1.2c, 1.6c, and2.0c, respectively. As shown in Fig. 2(c), these simulations can beused to estimate the dependence of the average strain present inthe epilayer on the H dose, providing us with a range of values(identified by the area delimited by the dashed lines in the figure)that matches rather well with the experimental data, extracted fromthe measured shift of the SO band. The strain dependence ondH extracted from this simulation is displayed as a continuous blackline in the figure, whereas the dashed lines are associated withthe dFPH = 1.2c and 2.0c simulations, respectively.

However, a detailed analysis of the FEM simulations per-formed in this work can provide us with even more interestingglimpses of the relationship between the distribution of H inthe material and the estimated level of strain. Figure 3 is relativeto the simulation performed with dFPH = 1.6c, which provides thebest agreement with the experiments, as shown in Fig. 2(c).Figures 3(a)–3(d) display the evolution with increasing hydrogendose of the simulated concentration profiles of the N-2H andN-3H complexes, together with the spatial distribution of unpassi-vated nitrogen impurities. By design, when dFPH is set to 1.6c, a 1.2cdose is clearly insufficient to achieve full passivation (see panel a),and the sample is indeed characterized by the presence of a∼20 nm-thick layer of unpassivated GaAsN close to the GaAsbuffer layer. It is important to stress that an incomplete passivationis the only way to explain the slightly “tensile” strain value mea-sured in the 1.2c sample: in fully passivated GaAsN, indeed, strainmust range from zero—in the unphysical hypothesis that thesample be uniformly filled with N-2H complexes, in the absence ofN-3H complexes in the epilayer—to its (compressive) saturationvalue, εxx = 0.8 × 10−3, as obtained when N-3H complexes reach100% of the initial N concentration. Figures 3(e)–3(h), whichreport the distribution of the εxx component of the strain tensor inthe GaAsN:H epilayer for different H doses, confirm that such satu-ration value is reached for dH∼ 3.0c in our sample, as also sug-gested by the experiments [see Fig. 2(c)]. Furthermore, the straindistribution estimated for the 1.2c epilayer—see Fig. 3(e)—is con-sistent with the lack of any PR features related to the unpassivatedGaAsN layer in the sub-GaAs bandgap region of the spectrum. Thepresence of such a layer, indeed, results in a broad, weak plateau inthe tensile region of the strain distribution, which is unlikely toresult in any sharp PR feature, but definitely pushes the averagestrain toward a positive (i.e., tensile) value.

E. LO mode frequency shift and strain

Figure 4(a) highlights the increase in the LO mode frequencyand linewidth with increasing H dose in the z(x0x0)-z polarizationgeometry. In particular, as summarized in Fig. 4(b), the frequencyblueshift is consistent with that determined by the strain variationwith increasing H dose, as estimated from PR experiments andfrom FEM simulations. As far as the latter are concerned, the threecurves displayed in Fig. 4(b) show the LO mode frequencies

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estimated from the computed strain values, based on the formula11

ωLO ¼ ωGaAsLO þ ωGaAs

LO

2� (~K11 � εzz þ 2~K12 � εxx),

where ~K11 ¼ �1:7, ~K12 ¼ �2:4, and ωGaAsLO ¼ 292:5 cm�1, as

measured in our reference GaAs sample. The dashed lines are

relative to the simulations performed with dFPH = 1.2c and 2.0c,whereas the continuous line is based on the dFPH = 1.6c simula-tion, which once again yields the best comparison with theexperimental data (dashed bars). In terms of the LO mode linewidth,

FIG. 3. (a)–(d) Depth profiles of the concentration of unpassivated nitrogen(continuous line) and of the N-2H (dashed) and N-3H (dotted) complexesresponsible for N passivation, as estimated from FEM calculations performedassuming that dFPH = 1.6c (see main text). The depth is measured starting fromthe top surface of the epilayer. The four panels refer to different H doses (1.2c,1.6c, 2.0c, and 3.0c, from top to bottom). (e)–(h) Bar plots of the distribution ofthe εxx component of the strain tensor in the GaAsN:H epilayer. The dashedlines indicate the values of the average strain expected in an untreated GaAsN(N = 1 mol. %) sample and in a hydrogenated sample completely filled withN-3H complexes (labeled as GaAsN:H).

FIG. 4. (a) Spectra in the GaAs-like phonon range from GaAsN:H 1.2c (c =1018 ions/cm2, dots), 2.5c (circles), and 3.5c (triangles). (b) Comparison ofGaAs-like LO phonon frequency in two different polarization geometries(allowed: dashed bars; forbidden: solid bars), as resulting from a two-Lorentzianmodel fit, which accounts also for the nearby TO mode. The 110 allowedRaman shifts estimated from FEM simulations (see main text) are also shown.The dashed black curves delimiting the gray area were obtained assuming thatdFPH = 1.2c (lower curve) and 2.0c (upper curve). The continuous black curvewas obtained for dFPH = 1.6c.

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on the other hand, a Lorentzian fitting yields values of 4.7, 5.6,6.0, 6.8, 6.65 cm−1 in GaAs, GaAsN, and GaAsN:H 1.2c,2.5c, and 3.5c, in the order. This linewidth trend is compatiblewith a moderate increase in the lattice disorder for increasinghydrogen doses.

Tables I and II summarize the frequency values of GaAs-likeLO mode, obtained with incident [110] (i.e., x0) polarization(Table I) and incident [100] (i.e., x) polarization (Table II) in epi-taxial GaAs, GaAsN, and GaAsN:H (after hydrogenation atdifferent doses: 1.2c, 2.5c, and 3.5c). It appears that the generaltrends of the LO frequency in all the investigated samples are quitesimilar in the “allowed” geometries, z(x0x0)-z and z(xy)-z, wherein—as noted above—there is a good agreement with the expectedstrain dependence of the LO mode.

In Fig. 4(b), one may also appreciate the near-zero strain con-dition as evidenced by the nearly coincident values of the LO peakfrequency of the GaAs and 1.2c GaAsN:H samples in the allowed z(x0x0)-z geometry. Finally, we note that, if compared with PRresults, the Raman spectra reported here produce further supportto the frequently adopted choice of z(x0x0)-z polarization geometryto reproduce with a linear relation the frequency dependence ofstrain in III-V materials.8,38,39 Interestingly, however, this is insharp contrast with the trends observed in the forbidden z(xx)-zgeometry [see Table II and Fig. 4(b)], which are discussed inSec. III F.

F. LO mode—Forbidden

In GaAsN and GaAsN:H 2.5c, the intensity of the forbiddenLO scattering in z(xx)-z polarization geometry has an appreciableintensity, which allows us to observe an unmistakable frequencyredshift resulting from hydrogen irradiation: 289.6 cm−1 in GaAsN:H2.5c vs 290.4 cm−1 in GaAsN. This finding suggests that thedeformation potentials associated with the phonons probed in thisconfiguration may have an opposite sign with respect to thoseobtained in other, more conventional scattering geometries. Thishypothesis is supported by the values of the LO mode measured in

GaAsN:H 1.2c (290.1 cm−1) and GaAsN:H 3.5c (289.8 cm−1).Moreover, the scattering intensities in the forbidden geometry arevery low in the sample treated with the lowest H dose, a peculiaritywhich confirms the hint of vanishing strain provided by PR analy-sis. We point out that the LO line in this polarization geometry hasno counterpart in GaAs, where the signal is virtually absent.

No Raman scattering data are available in the literature for a[100] incident light polarization in GaAsN:H layers, to the best ofour knowledge. In our opinion, these results highlight the need toperform polarization-resolved Raman studies in order to correctlycapture the strain dependence of the phonon frequencies. This willbe particularly relevant for future/upcoming studies to be per-formed on GaAsN/GaAsN:H wires with different orientations withrespect to the [100] crystallographic axis.

IV. CONCLUSIONS

In summary, we investigated the GaAs-like Raman spectra asobtained in a backscattering geometry from GaAs1−xNx layers (x =0.01) both as-grown and irradiated with several different H doses.We found that, in a specific polarization arrangement, the selectionrules that hold for GaAs are relaxed. This effect can be ascribed tothe built-in strain in the layers. The frequencies of the LO mode inthe allowed geometries are consistent with a progressive evolutionfrom tensile strain in the as-grown sample to increasingly compres-sive in the hydrogenated samples, in nice agreement with predic-tions from FEM simulations. Analysis of photoreflectance dataconfirms this picture and indicates, in particular, that the strain isvanishing in the sample that received the lowest H dose. The defor-mation potential for the GaAs-like phonons in the forbidden scat-tering geometry implies decreasing frequencies for increasingcompressive in-plane strain, in contrast to observations in the otherscattering geometries. The present results will be applied to thedesign of Raman mapping experiments aimed at obtaining strainprofiles in GaAsN/GaAsN:H planar heterostructures, such asGaAsN wires variously oriented in GaAsN:H matrices.

ACKNOWLEDGMENTS

M.S., M.F., and A.P. acknowledge funding from the EuropeanUnion’s Horizon 2020 Research and Innovation Program under theMarie Skłodowska-Curie Grant Agreement No. 641899 (PROMIS),Regione Lazio Program “Progetti di Gruppi di ricerca” leggeRegionale n. 13/2008 (SINFONIA project, prot. n. 85-2017-15200)via LazioInnova spa., and SapiExcellence from Sapienza Universitàdi Roma.

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TABLE I. Frequencies of GaAs-like LO phonons obtained with [110] (i.e., x’) inci-dent polarization.

Scattered lightpolarization

GaAsreference(cm−1)

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1.2c Hdose(cm−1)

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TABLE II. Frequencies of GaAs-like LO phonons obtained with [100] (i.e., x) inci-dent polarization.

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Published under license by AIP Publishing.