In Brillouin light-scattering (BLS) measurements of an ion-milled Si(001) surface grating with grating wavelength Lambda(G) =0.35 mu m, we have observed numerous high-order zone-folded surface acoustic modes between the second and third zone boundaries associated with the grating. A surprisingly intense signal from a zone-folded longitudinal resonance was observed in the absence of direct hybridization with the Rayleigh modes. The relative intensities of all of the modes have been calculated by allowing for coupling between modes related by up to two grating reciprocal-lattice vectors, and for a grating profile with nonzero first and second Fourier amplitudes. The Fourier amplitudes inferred from the BLS measurements and calculations agree very well with those obtained from a direct measurement of the grating profile using atomic-force microscopy

Amoddeo, A.

Caputi, L. S.

Dutcher, J. R.

Giovannini, L.

Lee, Sukmock

Marvin, A. M.

Nizzoli, F.

Ross, J. D.

Stegeman, G. I.

Wang, Z.

English

University of Central Florida (UCF): STARS (Showcase of Text, Archives, Research & Scholarship)

University of Central Florida STARS Faculty Bibliography 1990s Faculty Bibliography 1-1-1994 Light-Scattering Observation Of Surface Acoustic Modes In High-Order Brillouin Zones Of A Si(001) Grating Sukmock Lee University of Central Florida L. Giovannini J. R. Dutcher F. Nizzoli G. I. Stegeman University of Central Florida See next page for additional authors Find similar works at: https://stars.library.ucf.edu/facultybib1990 University of Central Florida Libraries http://library.ucf.edu This Note is brought to you for free and open access by the Faculty Bibliography at STARS. It has been accepted for inclusion in Faculty Bibliography 1990s by an authorized administrator of STARS. For more information, please contact STARS@ucf.edu. Recommended Citation Lee, Sukmock; Giovannini, L.; Dutcher, J. R.; Nizzoli, F.; Stegeman, G. I.; Marvin, A. M.; Wang, Z.; Ross, J. D.; Amoddeo, A.; and Caputi, L. S., "Light-Scattering Observation Of Surface Acoustic Modes In High-Order Brillouin Zones Of A Si(001) Grating" (1994). Faculty Bibliography 1990s. 3102. https://stars.library.ucf.edu/facultybib1990/3102 Authors Sukmock Lee, L. Giovannini, J. R. Dutcher, F. Nizzoli, G. I. Stegeman, A. M. Marvin, Z. Wang, J. D. Ross, A. Amoddeo, and L. S. Caputi This note is available at STARS: https://stars.library.ucf.edu/facultybib1990/3102 PHYSICAL REVIEW B VOLUME 49, NUMBER 3 15 JANUARY 1994-ILight-scattering observation of surface acoustic modes in high-order Brillouin zonesof a Si(001) gratingSukmock Lee'Center for Research and Education in Optics and Lasers, University of Central Florida, Orlando, Florida 32826L. GiovanniniDipartimento di Fisica, Uniuersita di Ferrara, Via Paradiso 12, I-44100 Ferrara, ItalyJ. R. DutcherDepartment ofPhysics, University of Guelph, Guelph, Ontario, Canada NIG 2%1F. NizzoliDipartimento di Fisica, Uniuersita di Ferrara, Via Paradiso 12, I-44100 Ferrara, ItalyG. I. StegemanCenter for Research and Education in Optics and Lasers, University of Centra! Florida, Orlando, Florida 32826A. M. MarvinDipartimento di Fisica Teorica, Uniuersita di Trieste, Strada Costiera 11, I-34014 Miramare-grignano, ItalyZ. WangDepartment ofPhysics, University of Guelph, Guelph, Ontario, Canada N1G 2WIJ. D. RossCenter for Research and Education in Optics and Lasers, University of Central Florida, Orlando, Florida 32826A. Amoddeo and L. S. CaputiDipartimento di Fisica, Universita della Calabria, 1-87036Arcavacata di Rende (CS), Italy(Received 11 October 1993)In Brillouin light-scattering (BLS) measurements of an ion-milled Si(001) surface grating with gratingwavelength AG =0.35 pm, we have observed numerous high-order zone-folded surface acoustic modesbetween the second and third zone boundaries associated with the grating. A surprisingly intense signalfrom a zone-folded longitudinal resonance was observed in the absence of direct hybridization with theRayleigh modes. The relative intensities of all of the modes have been calculated by allowing for cou-pling between modes related by up to two grating reciprocal-lattice vectors, and for a grating profile withnonzero first and second Fourier amplitudes. The Fourier amplitudes inferred from the BLS measure-ments and calculations agree very well with those obtained from a direct measurement of the gratingprofile using atomic-force microscopy.Recently, Brillouin light-scattering (BLS) measure-ments of a shallow surface grating on a Si(001) wafer'with grating wavelength AG=0. 25 IMm have revealed arich variety of grating-related features: zone folding ofthe Rayleigh mode, a gap in the Rayleigh mode disper-sion for the phonon wave vector corresponding to thefirst grating zone boundary, and the unexpected observa-tion of hybridization between the Rayleigh mode and thelongitudinal resonance within the second grating zone.All of the grating-related features were explained quanti-tatively in a calculation of the normal modes and the BLSsurface ripple cross section for a shallow grating on anopaque material. With the assumption of a cosinusoidalgrating profile, excellent agreement between the mea-sured and calculated BLS spectra was obtained both formodes with frequencies below and above the transversethreshold, corresponding to the discrete and continuousspectrum, respectively. This implies that the couplingbetween the discrete modes and the continuum occurs al-most entirely via the fundamental periodicity of the grat-ing, as specified by the first Fourier amplitude of the grat-ing profile.In this paper, we describe an extension of this originalwork to a larger period grating (AG =0.35 pm), which al-lows us to measure spectra between the second and thirdgrating zone boundaries. We have observed numerouszone-folded surface acoustic modes, including the obser-vation of a zone-folded longitudinal resonance in the ab-sence of direct hybridization with the Rayleigh modes.This latter observation is indeed unexpected because it iswell known that the longitudinal resonance cannot be ob-served with BLS on the flat Si surface, and this mode hasbeen observed for the AG =0.25 pm Si(001) grating onlyin the presence of a strong coupling with the Rayleigh0163-1829/94/49(3)/2273(4)/$06. 00 49 2273 1994 The American Physical Society2274 SUKMOCK LEE et al. 49mode. ' Our observations for the A& =0.35 pm gratingdescribed in this paper are qualitatively different fromthose reported previously. The BLS calculation ofGiovannini, Nizzoli, and Marvin has been extended toallow for coupling between modes with wave vectors re-lated by up to two grating reciprocal-lattice vectors, andfor a grating profile with nonzero first and second Fourieramplitudes. We find that the anomalously large scatter-ing intensity for the zone-folded longitudinal resonance isconfirmed by the calculation. In fact, excellent agree-ment is obtained between the experimental relative modeintensities for all of the modes observed in each of theBLS spectra and those calculated using the first andsecond Fourier amplitudes determined from BLS mea-surements of the first and second grating zone-boundarygaps. In addition, the Fourier amplitudes determinedfrom the BLS data are in very good agreement with thoseobtained from a direct measurement of the grating profileusing atomic-force microscopy.The calculation of the normal modes of the grating andthe ripple scattering cross section corresponding to eachof these modes for a cosinusoidal grating profile has beendescribed by Giovannini, Nizzoli, and Marvin. This cal-culation is valid for shallow gratings, since the Rayleighhypothesis and a perturbative expansion to first order inthe corrugation strength were used. To allow the properdescription of all of the phonon modes with wave vectorsbetween the second and third grating zone boundaries,this calculation has been extended to include the first twoFourier components: the grating profile g(x) is specifiedbyg(x) =2(Gcos(Gx)+2(2Gcos(2Gx),where g„Gare the Fourier amplitudes of the surface cor-rugation. Equation (1) can be used to describe symmetricgrating profiles. In Eq. (1), the fundamental grating wavevector, or grating reciprocal-lattice vector G is defined as2'/AG, such that the dispersion curves for the Rayleighmode and longitudinal resonance are periodic in wavevector with period G. The first and second Fourier am-plitudes gG and (2G, respectively, are primarily related tothe measured frequency gaps of the Rayleigh mode at thefirst and second grating zone boundaries. ' In ourtheoretical approach, the first zone-boundary gap de-pends only on gG, while the second gap depends on bothgzG (which gives the main contribution because of themixing of two Rayleigh modes) and gG (due to the mixingof the Rayleigh mode with the continuum). To calculatedispersion relations and spectra for wave vectors betweenthe second and third grating zone boundaries, it is neces-sary, in principle, to include the effects due to the thirdFourier amplitude (3G. However, for the grating dis-cussed below, we have found that the first two Fourieramplitudes give the only relevant contributions for thefrequency and wave-vector ranges corresponding to theBLS data presented below. From a physical point ofview, the calculation accounts for coupling betweenmodes with wave vectors related by kG and +2G. Forthe calculation of the BLS cross section, both the direct-scattering process and indirect-scattering process in-volving light diffraction through the first two Fourier am-plitudes of the corrugation have been taken into account.The Si(001) grating, with the grating grooves parallelto the Si [100] direction, was prepared using the tech-niques described in Ref. 1. The grating period was deter-mined to be AG =0.349 pm by accurate measurement ofthe first-order-diffracted beam deflection. The BLS ex-periments were performed at room temperature using aSandercock-type high contrast, tandem (3+3 passes)Fabry-Perot interferometer. 100 mW of p-polarizedlight from a single mode Ar+ laser (A, =5145 A) was fo-cused onto the grating surface using a f /1. 4 (f =50 mm)lens. Diffusely scattered p- and s-polarized light was col-lected by the same lens using a 180' backscatteringgeometry. A narrow slit was placed in the collectedbeam, offset slightly from the beam center, to avoidartificial splitting of the BLS peaks. ' The plane of in-cidence of the light was along the [010] direction of theSi(001) crystal, perpendicular to the grating grooves.A BLS spectrum collected for a phonon wave-vectorvalue of Ql =2.373 X 10 cm ' (angle of incidence8;=78' and scattering angle 8, =75') is shown in Fig.1(a). The large peak at 18 GHz corresponds to lightscattering from the Rayleigh mode that would be ob-served for a flat surface. In addition, there are smallerpeaks at 4.6, 7.9, and 9.2 GHz, which correspond to lightscattering from modes which exist and are observed be-cause of the presence of the surface grating. Because ofits very low frequency, the peak at 4.6 GHz sits on theedge of the background due to the very large elastic-scattering peak at 0 GHz. The character of each of thesemodes can be understood from a plot of the frequency-dispersion curves.In Fig. 2 are shown the frequency-dispersion curves for0~ ~CP4)EAlOEOOL(bj(c)Aij IA-20 —10 0 10 20Frequency (GHz)FIG. 1. Brillouin light-scattering spectra for the Si(001) grat-ing with AG =0.35 pm, for a phonon wave vector of 2.373 X 10'cm '. (a) Experimental spectrum, collected using 100 mW oflaser power, and 50.9 s of counting time per data point; (b) spec-0trum calculated using Fourier amplitudes of gG =12& A and0 0gzG =40 A; and (c) spectrum calculated using gG =125 A and4G =o.49 LIGHT-SCA I IERING OBSERVATION OF SURFACE ACOUSTIC. . . 22752520—N& 15-lJtDa. 10-tDLL2.0I I I }2.2 2.4Qi} (10 cm ')2.6FIG. 2. Frequency-dispersion curves for the Si(001) gratingwith AG =0.35 pm between the second and third grating zoneboundaries. The open and solid circles correspond to data, withthe solid circles corresponding to the BLS spectra shown in 1(a).The solid and dashed curves represent the dispersion of thezone-folded Rayleigh mode and longitudinal resonance, respec-tively, calculated using the theory described in the text.the Rayleigh mode and the longitudinal resonance of theSi(001} grating for phonon wave vectors between thesecond and third grating zone boundaries. The data cor-responding to the BLS spectrum of Fig. 1(a}are shown assolid circles. The curves correspond to the periodic zonescheme representation of the Rayleigh mode and longitu-dinal resonance. Data and curves are limited to the thirdgrating zone which corresponds to the actual phononwave vectors probed in BLS experiments. These curveshave been calculated using the first and second Fourieramplitudes gG =125 A and gzG =40 A that gave the bestfit to BLS measurements of the first and second zone-boundary gaps b f& =0.4 GHz and b fr=0. 8 6Hz, re-spectively. These Fourier amplitudes have been fittedalso by considering the behavior of the peak intensitiesnear the grating zone-boundary gaps. Actually, for wavevectors close to the zone boundaries, the mode intensitiesdepend strongly on Qi, i.e., on the incident and scatteringangles 8; and 8, . The intrinsic experimental uncertaintyin the determination of 8, of 0.2S produces a typicaluncertainty in the determination of b,f& and b,fz of+15%. We estimate that our determinations of gG andgzG are described by the same +15% uncertainty. Themeasurement of b,fz at the second grating zone boundarywas complicated by the presence in the collected scat-tered light of an intense beam due to first-orderdiffraction from the grating. %'e found that it was possi-ble to block this small diameter (3 mm) beam with a smallmask inserted into the collected scattered light. For thisgrating, the depth is determined primarily by gG,' the cor-rugation strength (2$G)/AG =0.07 corresponds to thesma11 roughness limit, as for the grating discussed inRefs. 1 and 2.In Fig. 2, the highest frequency branch of the disper-sion curves corresponds to the Rayleigh mode branchthat would be observed for a flat Si(001) surface (Sat-surface-like Rayleigh mode). The lowest frequencybranch corresponds to the Rayleigh mode branch whichhas been shifted in wave vector by +6 (+6 Rayleighmode}. The intermediate frequency branch with negativeslope corresponds to the Rayleigh mode branch whichhas been shifted in wave vector by +26 (+26 Rayleighmode). The intermediate frequency branch with positiveslope corresponds to the longitudinal resonance branchwhich has been shifted in wave vector by +6 (+6 longi-tudinal resonance). Therefore, for the BLS spectrumshown in Fig. 1(a), the peaks correspond to, in order ofincreasing frequency, a +6 Rayleigh mode, a +6 longi-tudinal resonance, a +26 Rayleigh mode, and the flat-surface-like Rayleigh mode. Associated with each Ray-leigh mode branch is a transverse threshold which has afrequency that is about 10% larger than that of the Ray-leigh mode. For mode frequencies above the lowesttransverse threshold, the modes are no longer discreteand are called "leaky" modes with respect to the contin-uum, since they can decay into bulk modes. Therefore, inthe spectrum of Fig. 1(a), only the lowest frequency +6Rayleigh mode is discrete. The +6 longitudinal reso-nance and the +26 Rayleigh mode are both leaky withrespect to the +6 continuum, and the flat-surface-likeRayleigh mode is leaky with respect to both the +6 andthe +26 continua. Note that the dispersion relations ofthe leaky modes have been taken from the correspondingmaxima in the calculated BLS spectra.As can be seen in Fig. 2, the +6 longitudinal reso-nance is observed for wave vectors up to 7% less than thewave vector corresponding to the gap between the +6longitudinal resonance and the +26 Rayleigh mode,with differences between the two mode frequencies of upto 3.5 GHz. This is in dramatic contrast to the observa-tions of Dutcher et al. , ' in which the +6 longitudinalresonance was observed only for wave vectors within+3% of the wave vector corresponding to the largestmixing of the +6 longitudinal resonance and the flat-surface-like Rayleigh mode, with differences between thetwo mode frequencies of less than l 6Hz.In Fig. 1(b) a spectrum is shown calculated using theFourier amplitudes given above. All of the peaks ob-served in the BLS experiment also appear in the calculat-ed spectrum, and the agreement between the experimen-tally observed and calculated relative scattering intensi-ties of the modes is excellent. The effect of including thesecond Fourier component can be seen by comparing thecalculated spectrum in Fig. 1(b) to the calculated spec-trum in Fig. 1(c), for which the second Fourier amplitudehas been set equal to zero. Not surprisingly, the relativeintensity of the Rayleigh mode near 9 GHz that is shiftedin wave vector by +26 is very sensitive to the secondFourier amplitude. Note that with gzG=O, the +26Rayleigh mode is marked by the presence of a dip insteadof a peak. This is due to destructive interference effectsin the surface phonon power spectrum occurring throughmodes coupled by g. Also, the linewidth of the fiat-49SU«MPC« ~ '22761.259oeo3o25) image of thee Si(001)sco e(AFM 'arisonmic-force microsshown a compface. In the inseer endicular totheFM lited usingg gpom litudes determin=60 A.-fit Fourier a p u=135 A and g, ~Ge absence of direct hy-R„lihWe find eode intensi 'set of rsLSb't ""thd d dlitudes obtaine inFourier amp eand AFM data.e financial supportgrs ratefu yn ineeringnces d E 'Natural Scie.D. and S.f Canada (J.Re Ricerca Scien 'A.M.M. , A.A. , ant't te ProgramScience Research Inst' u' h increasing 026'a leigh mode inc~ of the mode wreases witithsurface-»kethe "leakjnto ether withthe increaseThis effect, gs torespect to te of the cross sh respect tohe+ectlp»dependencef t»s mode w&tthe;n the intensitymodes.a decrease1 w-frequencyd ctly usingasured irethe intens' 'pfile wasAFM measuThe grating P(AFM). Te 111 (Di-e microscoPya NanoscoPatomic fprcet in ajr usingt fprce mode.ere carried pu'the constantt~-ments wrating &n. jth the opruments opcantilevergjfal Instruercial »3N4was equippedIt combines a ch AFM micros.1 d radiuscal lever technjqb tips with a yph ratingard Nanopro,uare area of t gwith standart 3pp'A sqData were ac-f curvatur e of abputa side.] 358 pm pnconnected0ned that was' ital processorwas scanne11 sing a djgit pdjgitized im-uired automr and it was sf the gratingmatica y u.tpred asal comp«erral eriod' ja persoX256 grid. Sever ph shown in F&g.s with a 25fprce microg ph gratingages'the atom&cseen».er en icd' glar to t ecan beFM line scan p p3 together wit h the3 A single Ainset to Fjg~nd Fpurier's shown as anfirst and secorooves Jsrofile calcu.=60+5er1 t d with~h t givethgrating P'135+5 A and 02Grosie Th«amP1itudes (Gh the measuredh single 1ineent with er estimates app yThe AFM pa]] asyroAFM imagexce t for a smascan of the1 d profile, e pt g groovesthe calcu atepf th e graduced byr the bottoml defined bmetry Pb described byresent nearprpfinpt eva lues determininedwhich canf the (G an 2Gt is remark-ement oFM data '1) The agreeindepende t ythe approximat opfil with the s™e, consider g h true grating ponfidenceaducing the deh Eq (1), and i gof the Si(001)nsjpn g&ven yLS propertiethat we understanu tofour i ed'fferent sur-we have observed ple BLS spectrum coed observation o ai ' . The unexpecteS (001) grating.Inha University, In-rtment of Physics, adress: Departmen. G.'Present ad .- 51 Korea.G. J. cM Laughlin, BB. Hillebrands,r S. Lee, iev. Lett. 68,g' F N' ol'L. Giovannini,Ph s. e.1572 (1992).F Nizzoli an3V. Bortolani,39 (1978).mun. 26, 547 (1978).~ . . Loudon, andN. E Glass, Rl' and A M Marvinck, in Lig ter-Verlag,d G. Giint erCardona andp. 173.

Light-Scattering Observation Of Surface Acoustic Modes In High-Order Brillouin Zones Of A Si(001) Grating

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Light-Scattering Observation Of Surface Acoustic Modes In High-Order Brillouin Zones Of A Si(001) Grating

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