Dissimilar gold nanoclusters at GaAs(0 0 1) surface: Formation chemistry, structure, and localized plasmons

Applied Surface Science 507 (2020) 144982

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Dissimilar gold nanoclusters at GaAs(0 0 1) surface: Formation chemistry, structure, and localized plasmons

T

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V.L. Berkovits , V.A. Kosobukin, V.P. Ulin, F.Yu. Soldatenkov, I.V. Makarenko, V.S. Levitskii, A.V. Nashchekin, P.A. Alekseev Ioffe Institute, 194021 Saint-Petersburg, Russia

A R T I C LE I N FO

A B S T R A C T

Keywords: Gold nanoclusters Semiconductor surface Formation chemistry Recrystallization Surface plasmons Reflectivity spectra

A procedure is developed for controlled creation of Au nanoclusters by annealing of a gold film deposited onto GaAs(0 0 1) crystal surface. The nanoclusters of Au are formed at GaAs surfaces covered by either a natural oxide layer or a monolayer of gallium nitride. Surface morphology of the Au/GaAs structures with Au nanoclusters is characterized by scanning probe diagnostics and localized plasmons of the nanoclusters are investigated by optical reflection spectroscopy. In annealing Au film dissimilar gold nanoclusters are found to occur on oxidized or nitridized GaAs(0 0 1) surface via chemical transformation or recrystallization of Au film, respectively. Gold nanoclusters of the two types cause resonant peaks in optical reflectance spectra at the energies of 1.6 eV and 2.15 eV. Using the data of optical spectroscopy and their theoretical analysis we assign the former peak to localized plasmons of prolate Au nanoclusters buried into GaAs crystal near its surface. Another peak at 2.15 eV is attributed to plasmons of oblate Au nanoislands appearing on nitride overlayer which prevents any chemical contact of Au with GaAs bulk. The asserted existence of Au nanoclusters in the bulk of GaAs crystal near its oxidized surface is expected to be helpful in elucidating the nature and structure of Ohmic Au-GaAs contacts.

1. Introduction Metal-semiconductor structures with metal nanoclusters supporting localized plasmons are of growing interest for both fundamental science and applications [1–5]. Especially advantageous are the nanoclusters of noble metals (Au, Ag) supporting high-quality localized plasmons, the gold clusters being rather stable chemically and physically. In the nanoclusters of gold, the long-lived localized plasmons are known to exist at the energies below 2.5 eV and to be suppressed at higher energies by interband transitions [1]. Generally speaking, the remarkable plasmonic properties of gold nanoclusters in optics have made them indispensable for applications in many fields. As the implicit applications of Au clusters (and Ag, too) should be mentioned the optoelectronics [2,3], optical enhancement effects [6,7], chemical and biological sensing [8], photovoltaics [9], nanophotonics [10], biology and medicine [11], etc. As to the combinations of gold nanoclusters with semiconductors, the activities of technology and research are focused notably on the silicon-based nanostructures with Au inclusions [3,12]. To exemplify, one could be referred to [12] for the preparation technology of Si-based nanostructures, and to [3] for some plasmon-assisted optoelectronic

⁎

effects in Au/Si structures. Of particular our interest is an observation [7] that metal (gold) nanoparticles aggregated on Si substrate are highly desirable than individual plasmonic nanoparticles for possible applications, like SERS-based biosensing. Although GaAs is believed to be a competitor of Si in optoelectronics, the knowledge about gold nanoclusters formed on the surface of GaAs seems to be very scarce in comparison with Au/Si systems. Concerning the creation and study of gold nanoclusters at AIIIBV semiconductor surfaces, apparently only a few works [13,14] could be pointed out. Technologically, this situation is probably because of ability of gold to react chemically with AIIIBV compounds and to diffuse atomically into the crystal bulk even at room temperature [15]. The two fundamental properties are the obstacles for controlled preparing Au nanocluster arrays on AIIIBV semiconductor surfaces when any conventional annealing of a thin Au film is used. Nevertheless, the issues concerning both chemical interaction of gold with GaAs surface and atomic diffusion of Au into GaAs bulk were somewhat investigated in the context of electrocontact phenomena, see [15] and references therein. As well, current interest to fabrication of Au nanoclusters on GaAs surface is related with Au droplets used as a catalyst in growing GaAs nanowires [16]. The formation mechanisms of such Au droplets

Corresponding author. E-mail address: [email protected]ffe.ru (V.L. Berkovits).

https://doi.org/10.1016/j.apsusc.2019.144982 Received 29 July 2019; Received in revised form 19 November 2019; Accepted 6 December 2019 Available online 09 December 2019 0169-4332/ © 2019 Elsevier B.V. All rights reserved.

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at the temperatures higher than 300 °C according to the chemical reaction

are studied both experimentally and theoretically [17–19]. But none of the cited works has dealt with plasmonics of Au nanoclusters created even on commonly used oxidized GaAs surfaces, to say nothing of peculiar nitridized GaAs surfaces. In the above context, this work is aimed at creating Au/GaAs(0 0 1) structures with gold nanoclusters and at optical detecting and studying the structure-conditioned localized plasmons. For this purpose, we develop a novel method of controllable preparation of Au/GaAs(0 0 1) structures with gold nanoclusters. Also, our intention is to clarify possible chemical mechanisms of Au nanoclusters formation at GaAs surfaces at high temperatures. The sizes and shapes of obtained clusters are characterized, their optical spectra are measured and analyzed to assign the observed spectral peaks to plasmons. The paper is organized as follows. The formation chemistry of Au nanoclusters on GaAs surfaces is introduced in Sec. 2, and the procedure of Au/GaAs samples preparation is described ibidem. In Sec. 3 the results of the structure diagnostics of gold nanocluster arrays are presented. The data of plasmonic spectroscopy of Au/GaAs structures and theoretical analysis of the spectra substantiating existence of two types of Au nanoclusters are presented in Sec. 4. At last, some consequences of interest for fundamental and applied physics of gold nanoclusters are suggested in Sec. 5.

Au + GaAs = Au(Ga) + (¼)As4↑.

(1)

This chemical process is provided by the high solubility of Ga in Au and by the above-mentioned volatility of As at temperatures higher than 300 °C [26,27]. To anticipate, reaction (1) leads to formation of nanoclusters presumably consisting of Au-Ga alloy buried into the GaAs substrate. This idea seems to be consistent with the observation of some intermetallic compounds of Au and Ga at Au/GaAs interfaces after their annealing at 300 °C [15]. In case II (creation of type-II Au clusters on nitridized GaAs surfaces), any chemical contact of Au film with GaAs substrate is preserved by the intermediate GaN monolayer. Under these conditions, the hightemperature behavior of Au film deposited on GaAs is expected to be similar to the behavior of Au layers deposited on glass [28] or quartz [29] substrates. From this viewpoint, annealing of a thin gold film should be accompanied by significant increasing the sizes of Au grains entering the film, cf. [28,29], which process can apparently lead to the disintegration of the Au film. At rather high temperatures the GaN interlayer can lose its continuousness through the relaxation process initiated by lattice mismatch between GaN and GaAs. Then, reaction (1) of Au with GaAs surface could occur through the holes in GaN monolayer giving birth to extra type-I Au clusters. However, in this case the amount of type-I clusters is expected to be relatively small since the total square of holes (reaction areas) is much smaller than the square of GaAs surface itself. In our study, the Au/GaAs structures of both types I and II are controlled by means of surface diagnostics and optical spectroscopy at all obligatory stages of sample preparing and measuring. Main attention is paid primarily to type-II Au clusters appearing only on nitidized GaAs (0 0 1) substrates. The interface diagnostics and the other experiments are performed at room temperature.

2. Formation chemistry and preparation of samples Usually, metal nanoclusters are prepared on solid surfaces by the methods including deposition of the metal on a substrate and further annealing of the formed structure. As a rule, evaporation of a metal by either electron beam [20] or intense light beam [21] is carried out before its deposition. In our work, to create Au nanoclusters on GaAs (0 0 1) surface the thermally evaporated gold is deposited as a thin Au film onto GaAs substrate, and then the obtained Au/GaAs structure is annealed. To prepare the structures, we make two principally different sets of GaAs substrates that are distinguished by the chemical state of the GaAs surface. One of the sets is represented by naturally oxidized surfaces GaAs(0 0 1), and here we specify such the commonly used surfaces as standard. Another set is our know-how set consisting of GaAs substrates undergone the chemical nitridization of GaAs surface in hydrazine-sulfide solution [22]. The chemical procedure removes the surface oxide layer and, instead, forms a chemically stable GaN monolayer. The latter protects the surface of GaAs crystal beneath against its oxidation and high-temperature chemical reaction of GaAs with Au film deposited afterwards. A detailed description of the nitridation procedure and the properties of nitridized GaAs surfaces is available in [23] and references therein. To add, the nitridation was demonstrated earlier to weaken the chemical interaction of deposited Au with GaAs crystal in Au/GaAs Shottky structures [24]. In order to get Au/GaAs structures of need, we use n-doped GaAs substrates. After cleaning the GaAs(0 0 1) surface and its chemical nitridation, if any, a gold film is formed on the surface in a vacuum chamber at the residual pressure of 10−7 Torr, the gold deposition rate being about 0.1 nm/s. The thickness of growing Au film controlled by a quartz-crystal oscillator adjacent to the sample is estimated to be about 10 nm. Then, the formed Au/GaAs structure is annealed ibidem at the temperature of 350 °C. The formation of Au nanoclusters under heating should proceed in accordance with one of the two different mechanisms depending on whether initial GaAs surface is (I) naturally oxidized or (II) nitridized. In case I (specified as creation of type-I Au clusters), GaAs surface is covered by an amorphous layer of mixed oxide Ga2O3*As2O3 with a layer of As atoms located at the oxide/GaAs interface. When annealed, the mixed oxide decomposes into separate oxides Ga2O3 and As2O3, the latter is volatile at temperatures above 300 °C, and so is the near-surface As [25]. After removal of both volatile components, the rest oxide layer becomes porous resulting in appearance of material contacts between deposited Au and GaAs substrate. In the contact areas, GaAs dissociates

3. Diagnostics of samples Surface morphology of our Au/GaAs structures is studied first by atomic force microscopy (AFM) with scanning probe microscope NtegrA AURA (NT-MDT). If a better resolution of the surface relief is of need, we use ultrahigh-vacuum scanning tunneling microscopy (STM) as realized in the microscope GPI-300 designed in Prokhorov GeneralPhysics Institute. For a nitridized GaAs surface with unannealed Au film, a typical AFM topography and its cross-section profile are presented in Fig. 1(a) and (b). The size of the surface area is 0.5 μm × 0.5 μm and the film thickness is about 14 nm. It is seen from Fig. 1(a) and (b) that the relief of as-deposited Au film before annealing is formed actually by grains whose lateral sizes are 15–25 nm, the on-surface distribution of grains being uniform on the average. Next, the effect of annealing on the structure of Au films deposited onto nitridized GaAs surface is illustrated by Figs. 2 and 3. It follows from comparison of the data presented in Figs. 2 and 3 with the AFM data of Fig. 1 that the annealing at 350 °C leads to significant increase of Au grain sizes. As a result of recrystallization, the initial Au grains are concluded to transform finally into type-II Au nanoclusters. The STM image of surface area 0.8 μm × 0.8 μm in Fig. 2(a) shows a typical topography of type-II Au nanoclusters formed on nitridized GaAs surface after annealing of 10 nm thick Au film at 350 °C during 15 min. The Au clusters are seen to appear at random on the substrate surface, their lateral sizes and heights estimated from the profile shown in Fig. 2(b) are in the ranges of 80–120 nm and 9–12 nm, respectively. These estimations evidence Au nanoclusters of type II to be oblateshaped islands. Fig. 3 presents AFM image of surface topography (a) and the related surface profile (b) for Au/GaAs structure prepared on surface-nitridized 2

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Fig. 2. (a) STM image measured for surface area 0.8 μm × 0.8 μm of Au/GaAs structure prepared on nitridized substrate and annealed at 350 °C during 15 min. (b) The profile of the surface along the dashed line. The on-surface gold nanoclusters are formed on Ga-N monolayer covering GaAs crystal surface.

conditions. To verify this idea demonstratively, we turn next to the data of optical spectroscopy obtained for differently prepared Au/GaAs (0 0 1) nanostructures. The optical spectroscopy distinguishes between the two types of Au clusters taking advantage of their plasmons as indicators. For optical experiments we choose Au/GaAs structures with the initial thickness of Au films about 10 nm.

Fig. 1. Surface-topography image (a) and the related surface profile (b) along the dashed line measured by Atomic Force Microscopy for unannealed Au/GaAs structure prepared on nitridized GaAs surface.

GaAs substrate after annealing at 350 °C during 30 min. The thickness of deposited Au film is 14 nm. The formed type-II nanoclusters reveal typical lateral sizes of 50–80 nm, like does STM image in Fig. 2. The nanocluster heights are of 12–15 nm. The density of cluster numbers on the surface seen in Fig. 3(a) is somewhat larger than that on the surface seen in Fig. 2(a). In testing the structure documented in Fig. 3 we purposefully remove the on-surface type-II Au nanoclusters by mechanical brushing off them by the AFM tip. The result is illustrated in Fig. 3(a) by the onsample harrowed square area, whose surface profile is shown in Fig. 3(b). The square area is bounded by the gold walls heaped up after the mechanical brushing the film, and the depth of the hollow is comparable with the thickness of initial Au film. To anticipate, registered with the same AFM tip are the image of surface and its profile at the square area of Au film on nitridized GaAs surface. Also, the profile reveals the fragments of Au clusters of type I which appear after longterm (30 min) annealing and coexist with on-surface clusters of type II. Of principal interest is Fig. 4 which demonstrates the scanning electron microscopy (SEM) image of the in-situ obtained cleavage face of Au/GaAs structure whose typical AFM image is presented in Fig. 3. To emphasize, this SEM image observed with the microscope JSM 7001F (JEOL, Japan) represents directly the Au nanoclusters formed at a nitridized Au/GaAs surface. Fig. 4, likewise Fig. 3, argue definitely for coexistence on nitridized GaAs surface of Au nanoclusters of types II and I, the latter being embedded into GaAs bulk. Bearing in mind the above results of diagnostics, we arrive to a general conclusion that Au nanoclusters of two dissimilar types can be created on GaAs(0 0 1) surfaces depending on the preparation

4. Plasmonic reflectance spectroscopy 4.1. Spectroscopy experiments Plasmons of our Au/GaAs nanostructures at different stages of annealing are investigated by the method of optical reflectance spectroscopy. Using the spectrophotometer Cary 5000, the reflectance spectra at normal light incidence are measured in the range of photon energies 1.4–5.5 eV. It should be noted that the observed spectra of GaAs(0 0 1) substrates with no Au coverage reveal the peaks characteristic of optical transitions E1 and E1 + Δ1 (2.9–3.2 eV) and E0′ (4.4 eV) in GaAs bulk. In the range 1.5–3.5 eV of our main interest, a part of the reflectivity spectrum measured for a nitridized GaAs(0 0 1) surface before gold deposition is presented in Fig. 5(a) by curve 1. Curve 2 in Fig. 5(a) shows the related reflectivity spectrum just after deposition of 10 nm thick Au film onto the nitridized GaAs(0 0 1) surface. As compared to spectrum 1, reflectivity 2 increases significantly below 2.5 eV due to the electron plasma of Au, but it changes slightly at energies above 2.5 eV. On postheating the Au/GaAs structure at 350 °C for 15 min, the reflectivity spectrum 2 transforms to spectrum 3, as Fig. 5(a) shows. The reflectivity is seen to arise appreciably in the range below 2.5 eV, where two spectral features appear near 1.6 eV and 2.15 eV. Presumably, we attribute these resonant features to the localized plasmons of Au nanoclusters formed after annealing the Au/GaAs sample whose surface morphology is illustrated in Fig. 2. In the range above 2.5 eV, 3

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film contributing to spectrum 4 is eliminated essentially in contrast to nearly unchanged Au film contributing to spectrum 3. It should be emphasized that experimentally the reflectance peak at 2.15 eV does appear only for surface-nitridized GaAs substrates, in which case a material contact between Au and GaAs is impeded by the nitride monolayer. In turn, the peak at 1.6 eV dominates in reflectance spectra of Au/GaAs structures prepared on oxidized GaAs surfaces, when Au and GaAs contact takes place ensuring chemical reaction (1) in annealing. The indicated dependence of the reflectivity peaks on the chemical state of the GaAs surface is firmly asserted in Fig. 6. Actually, Fig. 6 shows the reflectivity spectra measured after identical annealing the Au/GaAs structures formed, respectively, on nitridized (curve 1) and on oxidized (curve 2) surfaces. As stated above, the observed reflectivity peaks 1.6 and 2.15 eV belong to the dissimilar plasmons of type-I and type-II gold nanoclusters, accordingly. To conclude, the appearance of these plasmonic peaks is conditioned, respectively, by Au clusterization mode I (through chemical reaction (1) between Au and GaAs) and mode II (through Au film recrystallization in the absence of material contact between Au and GaAs). 4.2. Theoretical analysis Next we discuss thoroughly the above optical data and substantiate theoretically the existence of Au nanoclusters of two types on the related GaAs surfaces. For this purpose, we consider normal reflection of light in a three-layer model “air / Au film / GaAs” (Fig. 7) with Au nanoclusters adjoining Au film from the side of either GaAs (ν = I) or air (ν = II). To describe the spectrum of plasmons, we consider the nanoclusters in a model of identical spheroids (ellipsoids of revolution) whose rotation axes are perpendicular to GaAs surface. For a single spheroid, the polarizability of dipole plasmons has the in-plane components [30]

Fig. 3. (a) Surface-topography image and (b) the related surface profile measured by AFM for 1.5 μm × 1.5 μm area selected on surface of Au/GaAs structure prepared on nitridized substrate and annealed at 350 °C during 30 min. The thickness of initially deposited Au film is 14 nm, the square area on the sample is brushed off from type-II nanocluster layer by the AFM tip. In Fig. (b) the large-height features correspond to on-surface Au nanoclusters of type II, and the small-height features are associated with under-surface Au nanoclusters of type I.

ην a ν3 ε − εν . 3 (ε − ε ν ) Nν + ε ν

χ (ν) =

(2)

Here, ε is the spheroid material (gold) permittivity and ε ν (ν = I, II ) stands for the permittivity of the medium surrounding the ν -type Au spheroid (εI = εGaAs for ν=I and εII = εAir=1 for ν=II according to Fig. 7). The in-plane depolarizing factor Nν of for ν -type spheroid depends on the ratio ην = bν a ν of its normal bν to tangential a ν semi-axis lengths [30]. Following the theory [31,32], we derive the normal-incidence reflectivity 2

R (ω) =

r (0) +

∑

θν Δr (ν)

ν =I, II

(3)

for Au/GaAs structure with Au spheroids monolayer of type ν=I or/and II (Fig. 7). In Eq. (3),

Fig. 4. SEM image of a cleavage face for Au/GaAs structure formed on nitridized GaAs surface and annealed at temperature of 350 °C during 40 min. The numbers with arrows indicate the under-surface Au nanoclusters of type I embedded into GaAs crystal and the on-surface Au nanoclusters (grains) of type II, respectively.

r (0) =

1 (r12 + r23 e 2i k2 L), Δ = 1 + r12 r23 e 2i k2 L Δ

(4)

is the reflection coefficient calculated for the three-layer model without Au clusters. In Eq. (4), rnn′ = (kn − k n′) (kn + k n′) , kn = εn k 0 , k 0 = ω c , and εn (n=1, 2, 3) stands for the permittivity of n -th medium of the three-layer in the direction of light incidence in Fig. 7. The contribution Δ r (ν) is due to a monolayer of idential ν -type spheroids having the efχ (ν) and occupying a square lattice of the period fective polarizability ∼ A ν < < 1 k 0 . The contribution Δ r (ν) in Eq. (3) is taken into account, if θν = 1, or neglected, if θν = 0 . Within a self-consistent approach [31,32], the terms Δ r (ν) entering Eq. (3) are expressed in the forms

spectra 2 and 3 in Fig. 5(a) are close to each other, and their inessential negative difference can be explained by the effective shrinking of Au film thickness that leads to decreasing the reflectivity of the film. The all-range difference between spectra 3 and 2 from Fig. 5(a) due to appearance of Au clusters is presented by curve 1 in Fig. 5(b). Spectrum 1 exhibits a strong peak at 1.6 eV and a weak one at 2.15 eV. Further annealing of the sample during about 50 min makes the 1.6 eV peak more pronounced and the 2.15 eV peak slightly decreased, as spectrum 4 in Fig. 5(a) demonstrates. As well, spectrum 4 as a whole shifts downward, so that at energies higher than 2.7 eV it almost coincides with spectrum 1 of bare GaAs surface. This fact implies that Au

Δ r (I) =

4

χ (I) t12 t23 2 2i ( k2 L + k3 h I ) 2πi k 0∼ ⎛ ⎞e , ε1 AI2 ⎝ Δ ⎠

(5)

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Fig. 5. (a) Reflectivity spectra measured at normal incidence of light onto nitridized surface GaAs(0 0 1) before (1) and after (2) deposition of 10 nm Au film followed by annealing the film at 350 °C for 15 min (3) and for 50 min (4). (b) Difference 1 between the experimental reflectivity spectra (3) and (2) taken from Fig. 5(a) is fitted by curve 2 (multiplied by 0.7, for convenience) which is decomposed then into Lorentzians 3 and 4. The latter two spectra are attributed to plasmons of Au nanoclusters of types I and II, respectively.

64

−1

1 1 ⎡ ε −ε h ∼ χ (ν) = ⎧ (ν) − S + ν Si ⎛ ν ⎞ ⎤ ⎫ . 3⎢ d ⎥ ⎨χ ε + ε A ε A ν ν⎠ ⎦ ⎬ ν ν ⎝ ⎣ ⎭ ⎩ ⎜

1.6 eV

⎟

(7)

Reflectivity, %

In this equation, the contribution additional to (2) contains the dimensionless dipolar lattice sums

60

Sd =

2

l1, l2

1

2.15 eV

1,6

2,0

5 2

≈ 4.51,

2l12 − l22 − 4ζ 2 (l12 + l22 + 4ζ 2)5 2

(8)

over the sites l1 e x + l2 e y numbered by the integers l1 and l2 in a square lattice. The sums (8) express the local-field effect in a layer of induced near-surface dipoles, the details being available in Refs. [31,32]. For a layer of spheroids under study (Fig. 7), the sums Sd and Si determine the corrections to the field acting on a given dipole plasmon in the layer, respectively, from the other plasmons of the same layer and from their “images” caused by the nearest surface of Au film. To proceed to numerical results, the reflectivity R(0)= r (0) 2 is calculated first for the three-layer model with a gold film of thickness L (Fig. 7). The results of calculation with known permittivities of Au [33] and GaAs [34] and different L are presented in Fig. 8(a), where the spectra R(0) (ω) for L = 0 and L > > c ω correspond to light reflection from bulk GaAs and Au, respectively. The nanometer-L reflectivities R(0) are seen to grow essentially relative to that of GaAs (L = 0 ) owing to the optical mirror effect caused by the high-density electron gas of Au film. Above the energy of “plasma edge” about 2.5 eV, the reflectivity R(0) changes rather slightly with L, as in Fig. 5(a) do the spectra 1 and 2 measured before sample annealing. Given the ratio ην for a single ν -type Au nanospheroid, the frequencies ω η ν of its high-quality plasmons with in-surface polarization are given by equation Re[(ε − ε ν ) Nν + ε ν] = 0 derived from Eq. (2), ω η ν increases with increasing ην and decreasing ε ν . For the frequency ω η ν to be in the visible range, Au spheroids of type I in GaAs should be prolate (η I > 1) and spheroids of type II in air should be oblate (η II < 1). This conclusion is illustrated in Fig. 8(b) by the spectra of normalized plasmonic polarizabilities 3 χ (ν) (ω) (ην a ν3) calculated from Eq. (2) for different η ν . Two series of spectral peaks are seen in Fig. 8(b) corresponding to Au spheroids of type I in GaAs and of type II in air. The peaks of one series (ν = I ) appear in the range from 1.5 eV for Au spheres (η I = 1) up to 1.8 eV for very prolate (η I ≫1) Au spheroids. The peaks of another series (ν = II ) correspond to oblate Au spheroids, the peak maxima decreasing essentially in the transition from very oblate spheroids (η II ≪1) near 2.1 eV to spheres near 2.3 eV. A few reflectivities R(I) (ω) obtained from Eqs. (2)–(8) with θ I = 1 are shown in Fig. 8(c) in comparison with R(0) (ω) , a weaker

2,4

Photon energy, eV Fig. 6. Reflectivity spectra obtained after annealing at 350 °C for 15 min of type-II Au/GaAs structure prepared on the surface-nitridized substrate (1), and of type-I structure formed on the surface-oxidized substrate (2). The thickness of Au film is 10 nm in both structures.

Fig. 7. Geometry of the problem. Gold film and Au nanoclusters of types I and II are shown in red.

χ (II) −i k1 h II 2πi k 0∼ (e + r (0) ei k1 h II )2 . ε1 AII2

2l12 − l22

2 2 l1, l2 (≠ 0) (l1 + l2 )

Si (ζ ) = ∑

56

Δ r (II) =

∑

(6)

Here, tnn′ = 1 + rnn′, h I and h II are the distances from one or another surface of Au film to the mid-plane of nearest layer of ν -type Au spheroids as is depicted in Fig. 7. For the spheroids with intra-layer plasmonic interaction, the in-plane components of effective plasmon polarizability are [31,32]

5

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Fig. 8. (a) Reflectivity spectra R(0) calculated for three-layers “air-Au film-GaAs” and marked by the thickness L of Au film. (b) Spectra of the dimensionless polarizability 3 χ (ν) (ην a ν3) of prolate (ν=I) Au spheroids with η I = 1 (1), 2 (2), 5 (3) in GaAs and of oblate (ν=II) Au spheroids with η II = 0.2 (1′), 0.5 (2′), 0.8 (3′) in air. (c) Reflectivities R(I) of three-layers including a monolayer of Au spheroids in GaAs (ν=I) with b I = 3 nm, a I = b I η I , where η I = 0.8 (1), 1 (2), 2 (3) and 5 (4). Dashed is the reflectivity spectrum R(0) for the three-layer. Calculated from Eqs. (2)–(4) with permittivities of Au33 and GaAs34, the thickness of Au film is L=10 nm.

localized plasmons approximates well the experimental reflectivity 1 without spectral contribution of residual Au film.

contribution of type-II Au spheroids is omitted (θ II = 0). Each spectrum R(I) (ω) is evaluated for a model of three-layer including a periodic monolayer of η I -fixed Au spheroids located in GaAs near its surface. Given η ν , the calculated plasmonic peaks displayed in Fig. 8(b) and (c) are homogeneously broadened owing to electron relaxation. The widths of peaks in the theoretical spectra R(I) in Fig. 8(c) are narrower noticeably than the widths of peaks in their experimental counterparts (Fig. 5) observed for the non-regular arrays of Au nanoclusters discussed above. Thus, the measured reflectivity peaks are inhomogeneously broadened in addition, and to fit them the theoretical spectra should be averaged with a still unknown distribution of Au spheroids (nanoclusters) over η I or ω η I . Such a procedure implies constructing the superposition of spectra like shown in Fig. 8(c) with the proper statistical weights. From this viewpoint, the observed reflectivity spectrum can be thought of as a collective effect of resonant plasmons supported by ην -conditioned sub-ensembles of nanoclusters which are treated suitably within the above lattice model of induced dipoles. To summarize, in Fig. 5(b) the measured reflectivity difference 1 is fitted by curve 2 which is decomposed then into spectra 3 and 4. We ascribe the latter two peaks to Au nanoclusters of types I and II, respectively. To note, the sum of spectra 3 and 4 assigned to the related

5. Discussion The presented results allow us to put forward a general concept how the discovered dissimilar Au nanoclusters of two kinds are formed at GaAs surfaces under heating. In increasing temperature, a film of gold deposited on GaAs surface pre-covered with a monolayer of GaN is found to undergo recrystallization followed by increasing the sizes of as-deposited Au grains. These grains are partially transformed into separate nanoislands (type-II clusters seen in Figs. 2 and 3), the process being accompanied by disintegration of the gold film. Under further annealing of Au/GaAs structure at 350 °C the intermediate nitride layer apparently begins to lose its continuousness. This should activate the chemical reaction (1) of Au with GaAs substrate through the breaking places of GaN coverage. The reaction leads to dissolution of Ga atoms in gold whose atoms occupy afterwards the vacant places occurring near the surface of GaAs crystal after evaporation of As molecules. Under prolonged annealing, the gold atoms migrate into GaAs crystal away of its surface and form Au-based columns (type-I nanoclusters) buried in the near-surface region of GaAs. In conformity with this concept, the 6

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review & editing. V.P. Ulin: Investigation. F.Yu. Soldatenkov: Metodology. I.V. Makarenko: Visualization. V.S. Levitskii: Data curation. A.V. Nashchekin: Visualization. P.A. Alekseev: Formal analysis.

plasmon peak at 2.15 eV belonging to type-II nanoclusters is observed only for Au/GaAs structures prepared on nitridized GaAs surfaces. To make the picture complete, the peak at 1.6 eV due to type-I Au clusters can occur also for Au/GaAs structures with broken GaN interlayer. In contrast to the situation with GaN overlayer, the oxide layer on GaAs surface does not hinders chemical contact between Au and GaAs in annealing even at 250 °C [15]. Then, the dominant formation of typeI nanoclusters at 350 °C results in the only strong spectral peak at 1.6 eV. The suggested ideas are embodied in a hypothetical model which is schematically presented in Fig. 7 to include Au nanoclusters of types I and II in consistency with experimental (Figs. 1–6) and theoretical, Fig. 8(b), data. Keeping in mind reaction (1), one could surmise the buried type-I clusters to consist of Au-Ga alloy and estimate the concentration f of Ga from a phase diagram for binary gold alloys [35]. The diagram asserts that expectable in long-term annealing at 350 °C is socalled γ-phase with f about 0.3, i.e. 30%. However, being of some academic interest, this circumstance is unessential for the above conclusions made up in Sect. 4 for the optics of Au-based nanoclusters. The matter is that the effective permittivity of Au-Ga alloy, e.g. < ε > = εAu + (εGa − εAu) f , seems to be close to the permittivity of gold εAu owing to smallness of f stated above and/or nearness of εGa to εAu . A few facts speak in favor of the latter statement, too. First, the observation [36] confirms that the energies of localized plasmons of Ga nanoparticles are in the same interval 1.9–2.2 eV of energies as is found above for Au nanoclusters of type II and are measured for Au clusters deposited on Si photovoltaic cell [37]. Second, comparing the permittivities εAu of Au [33] and εGa of Ga [38], one concludes that the frequency-dependent real parts Re εGa and Re εAu are close to each other quantitatively, and so should do the frequencies of plasmons in clusters of Ga and Au. At that, relatively strong damping could be expected for Ga plasmons since |Im εGa| ≫ |Im εAu| [38]. The existence of type-I Au nanoclusters embedded in GaAs substrate is confirmed by our direct SEM observation (Fig. 4) and by the related reflectance spectrum, Fig. 5(a). Fig. 4 demonstrates clearly the presence of prolate Au clusters which are in essence the nanowires buried in the near-surface area of GaAs crystal normally to it, the tops of similar typeI Au nanoclusters being visible in Fig. 3, too. The arrays of such Au nanowires formed after annealing at 350 °C could be supposed to provide a transformation of the Schottky barrier initially formed by Au film on GaAs surface into Ohmic contact [15]. Then, one might guess that Ohmic contact between Au film and GaAs substrate is resulted from the tunnel breakdowns caused by the applied electric field strongly enhanced at the ends of buried Au nanowires.

Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgments One of the authors (A.V.N.) acknowledges the Federal Joint Research Center “Material science and characterization in advanced technology” financially supported by the Ministry of Education and Science of the Russian Federation for providing the equipment for SEM characterization. References [1] U. Kreibig, M. Vollmer, Optical Properties of Metal Clusters, Springer series in material science, Springer, Berlin, 1995. [2] A.A. Toropov, T.V. Shubina, Plasmonic Effects in Metal-Semiconductor Nanostructures, Series on Semiconductor Science and Technology, Oxford University Press, 2015. [3] C.D. Geddes (Ed.), Reviews in Plasmonics 2015, Springer Internat. Publishing, Switzerland, 2016. [4] V.L. Berkovits, V.A. Kosobukin, V.P. Ulin, A.B. Gordeeva, V.N. Petrov, Plasmonic anisotropy of In nanocluster arrays on InAs(001) surface observed by differential reflectance spectroscopy, Surf. Sci. 632 (2015) L9–L12. [5] V. Amendola, R. Pilot, M. Frasconi, O.M. Marago, M.A. Iati, Surface plasmon resonance in gold nanoparticles:a review, J. Phys.: Condens. Matter 29 (2017) 203002 (1–48). [6] M. Moskovits, Surface-enhanced Raman spectroscopy: a brief retrospective, J. Raman Spectrosc. 36 (2005) 485–496. [7] A. Maiti, B. Satpati, A. Patsha, S. Dhara, A. Maity, T.K. Chini, Probing localized surface plasmons of trisoctahedral gold nanocrystals for surface enhanced Raman scattering, J. Phys. Chem. C 120 (2016) 27003–27012. [8] J. Homola, Surface plasmon resonance sensors for detection of chemical and biological species, Chem. Rev. 108 (2008) 462–493. [9] M. Losurdo, M.M. Giangregorio, G.V. Bianco, A. Sacchetti, P. Capezzuto, G. Bruno, Enhanced absorption in Au nanoparticles/a-Si:H/c-Si heterojunction solar cells exploiting Au surface plasmon resonance, Sol. Energy Mater. Sol. Cells 93 (2009) 1749–1754. [10] V.M. Shalaev, S. Kawata (Eds.), Nanophotonics with Surface Plasmons, Elsevier, 2007. [11] C. Louis, O. Pluchery, Gold nanoclusters for physics, chemistry and biology, 2nd ed., World Sci. Publ. Europe Ltd., 2017. [12] J.S. Wu, S. Dhara, C.T. Wu, K.H. Chen, Y.F. Chen, L.C. Chen, Growth and optical properties of self-organized Au2Si nanospheres pea-podded in a silicon oxide nanowire, Adv. Mater. 14 (2002) 1847–1850. [13] G. Lin, Q. Zhang, X. Lin, D. Zhao, R. Jia, N. Gao, Z. Zuo, X. Xu, D. Liu, Enhanced photoluminescence of gallium phosphide by surface plasmon resonances of metallic nanoparticles, Roy. Soc. Chem. Adv. 5 (2015) 48275–48280. [14] V.L. Berkovits, V.A. Kosobukin, V.P. Ulin, F.Yu. Soldatenkov, I.V. Makarenko, V.S. Levitskii, Gold Nanoclusters at the Interface Au/GaAs(001): Preparation, Characterization, and Plasmonic Spectroscopy, Semiconductors 52 (2018) 1849–1852. [15] R.M. Charatan, R.S. Williams, Initial stages of the formation of the Au/GaAs(001) interface: a low-energy ion scattering study, J. Appl. Phys. 72 (1992) 5226–5231. [16] J.C. Harmand, M. Tchernycheva, G. Patriarche, L. Travers, F. Glas, G. Cirlin, GaAs nanowires formed by Au-assisted molecular beam epitaxy: effect of growth temperature, J. Cryst. Growth 301–302 (2007) 853–856. [17] A.M. Whiticar, E.K. Mårtensson, J. Nygård, K.A. Dick, J. Bolinsson, Annealing of Au, Ag and Au–Ag alloy nanoparticle arrays on GaAs (100) and (111)B, Nanotechnology 28 (2017) 205702 (1–12). [18] E. Hilner, A. Mikkelsen, J. Eriksson, J.N. Andersen, E. Lundgren, A. Zakharov, H. Yi, P. Kratzer, Au wetting and nanoparticle stability on GaAs (111)B, Appl. Phys. Lett. 89 (2006) 251912 (1–3). [19] A.A. Zakharov, E. Marsell, E. Hilner, R. Timm, J.N. Andersen, E. Lundgren, A. Mikkelsen, Manipulating the dynamics of self-propelled gallium droplets by gold nanoparticles and nanoscale surface morphology, ACS Nano 5422 (2015) 1–30. [20] M.M. Giangregorio, B. Dastmalchi, A. Suvorova, G.V. Bianco, K. Hingerl, G. Bruno, M. Losurdo, Effect of interface energy and electron transfer on shape, plasmon resonance and SERS activity of supported surfactant-free gold nanoparticles, Roy. Soc. Chem. Adv. 4 (2014) 29660–29667. [21] M. Sami, M.S. El-Shall, Laser vaporization for the synthesis of nanoparticles and polymers containing metal particulates, Appl. Surf. Sci. 106 (1996) 347–355.

6. Conclusions To summarize, annealing of a thin Au film deposited on GaAs(0 0 1) substrate is found to result in formation of Au nanoclusters. Those appear either on the surface of Au film or in GaAs bulk beneath the film, the two situations depending on the chemical state of GaAs surface. For plasmons of Au nanoclusters formed on oxidized and nitridized GaAs surfaces, the optical reflectivity peaks are observed at the energies of about 1.6 eV and 2.15 eV, respectively. The peak at 1.6 eV is ascribed to localized plasmons of prolate Au nanoclusters penetrating into GaAs bulk as a result of a chemical reaction of Au with GaAs. Another peak at 2.15 eV is associated with localized plasmons of oblate-shaped Au islands set at the Au film-air interface. Hopefully, the Au nanoclusters buried in GaAs play a significant role both in formation of Ohmic contact at Au/GaAs interfaces and in the interface conductivity of Au/ GaAs nanostructures. As to type-II Au clusters reported in this paper, those could be of interest for the physics of metal surfaces. CRediT authorship contribution statement V.L. Berkovits: Writing - original draft. V.A. Kosobukin: Writing 7

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