Dec 7, 2015

Polytype control of spin qubits in silicon carbide

Crystal defects can confine isolated electronic spins and are promising candidates for solid-state quantum information. Alongside research focusing on nitrogen-vacancy centres in diamond, an alternative strategy seeks to identify new spin systems with an expanded set of technological capabilities, a materials-driven approach that could ultimately lead to ‘designer’ spins with tailored properties. Here we show that the 4H, 6H and 3C polytypes of SiC all host coherent and optically addressable defect spin states, including states in all three with room-temperature quantum coherence. The prevalence of this spin coherence shows that crystal polymorphism can be a degree of freedom for engineering spin qubits. Long spin coherence times allow us to use double electron–electron resonance to measure magnetic dipole interactions between spin ensembles in inequivalent lattice sites of the same crystal. Together with the distinct optical and spin transition energies of such inequivalent states, these interactions provide a route to dipole-coupled networks of separately addressable spins.
Figure 1Optical and spin transition spectra in the three most common SiC polytypes.
Optical and spin transition spectra in the three most common SiC polytypes.
(a) Optical spectrum of as-grown SI 4H-SiC, 12C-implanted SI 6H-SiC and 12C-implanted n-type 3C-SiC. (b) ODMR spectrum of SI 4H-SiC as a function of B parallel to the c axis (upper) and at B=0 (lower), showing six pairs of spin resonanc…
Figure 2Ensemble spin coherence at cryogenic temperatures.
Ensemble spin coherence at cryogenic temperatures.
(a) Hahn-echo measurement of spin coherence of the neutral divacancies in as-grown SI 4H-SiC at 20 K, showing T2 times of 140±5 μs (PL1), 144±3 μs (PL2), 360±20 μs (PL3) and 340±5 μs (PL4). Long Rabi pulses (150 kHz) were used to minimi…
Figure 3Ensemble spin coherence at room temperature.
Ensemble spin coherence at room temperature.
(a) ODMR in as-grown SI 4H-SiC as a function of B (upper) and at B=0 (lower). (b) ODMR as a function of B in n-type 6H-SiC (upper) and at B=0 (lower) for n-type (dark blue) and SI (grey) 6H-SiC, implanted at 1013 cm−2 dose of 12C. QL7–Q…
Figure 4Patterned SiC spins and illustration of dipole-coupled spins.
Patterned SiC spins and illustration of dipole-coupled spins.
(a) Implanted spin ensembles in n-type 4H-SiC through a PMMA mask with 50 nm holes, using 10 keV energy 12C ions at a 1013 cm−2 dose. Additional characteristics of these implanted spins are given in Supplementary Fig. S6. (b) Illustrati…
Figure 5Magnetic dipole-coupled spin ensembles in 6H-SiC.
Magnetic dipole-coupled spin ensembles in 6H-SiC.
(a) Pulse scheme for DEER measurements. As π pulses flip the orientation of the drive species spins, the sense species accumulates an extra phase (Δθfree) over a Hahn-echo sequence. (b) Varying the pulse duration of the drive spins (QL2…
The search for coherently addressable spin states1 in technologically important materials is a promising direction for solid-state quantum information science. Silicon carbide, a particularly suitable target234, is not a single material but a collection of about 250 known polytypes. Each polytype is a binary tetrahedral crystal built from the same two-dimensional layers of silicon and carbon atoms, but different stacking sequences give each its own crystal structure, set of physical properties and array of applications. 4H- and 6H-SiC, the most common hexagonal polytypes, are used for power and opto-electronics, and as growth substrates for graphene and gallium nitride. The cubic 3C-SiC can be grown epitaxially on silicon7 and is often used in micromechanics8. Driven by computational, electron paramagnetic resonance and optical studies, research into defect-based spins in SiC has also led to their increasing appreciation as candidate systems for quantum control.
Our results demonstrate that despite their varying optical, electronic and structural properties, the three most common SiC polytypes all exhibit optically addressable spin states with long coherence times. These spins are localized electronic states bound to neutral divacancies and related defects. Increasingly complex polytypes of SiC can host an increasing number of inequivalent defect sites–for instance, there are n inequivalent divacancy sites in nH-SiC.
We measure magnetic dipole–dipole interactions between ensembles of inequivalent spins and use these interactions to infer an estimate for the degree of optical spin polarization, 35–60%, depending on the defect species. These high polarization values are an important parameter for optically addressed spin control. Moreover, as these inequivalent defect sites are separately addressable through distinct optical and spin transition energies, extending our results to the single-spin limit could lead to quantum networks of dipole-coupled spins.

Optically detected spin states in SiC

To generate defect ensembles in SiC, we began with semi-insulating (SI), n-type and undoped SiC substrates. In substrates with a low intrinsic defect concentration, we then used carbon ion implantation followed by an annealing process designed to join vacancies into complexes (see Methods and Supplementary Note 1). The 3C-SiC samples consist of single and polycrystalline epitaxial films grown on silicon substrates, while the 4H- and 6H-SiC substrates are bulk single crystals.
Our optically detected magnetic resonance (ODMR) measurements show that all three measured polytypes host a number of optically addressable defect spins. These ODMR measurements rely on spin-dependent optical cycles both to polarize spins with laser illumination and to measure those spin states through changes in the photoluminescence (PL) intensity. We focus on defect optical transitions with zero-phonon lines in the 1.08–1.2 eV range. These can be observed as peaks in the PL spectrum when the samples are illuminated with higher energy laser excitation (Fig. 1a). In addition to these sharp peaks, much of the PL from these defects is emitted in broad phonon sidebands at lower energies, which we also collect.
Figure 1: Optical and spin transition spectra in the three most common SiC polytypes.
Optical and spin transition spectra in the three most common SiC polytypes.
(a) Optical spectrum of as-grown SI 4H-SiC, 12C-implanted SI 6H-SiC and 12C-implanted n-type 3C-SiC. (b) ODMR spectrum of SI 4H-SiC as a function of B parallel to the c axis (upper) and at B=0 (lower), showing six pairs of spin resonance lines. PL5 and PL6 appear faintly and are highlighted with dashed lines. (c) ODMR spectrum of SI 6H-SiC as a function of c axis B (upper) and at B=0 (lower), with a dashed lined highlighting the higher frequency QL5 resonance. (d) ODMR spectrum of 3C-SiC as a function of [100]-oriented B (upper) and at B=0 (lower). The 3C-SiC spins and the c-axis-oriented defects in the hexagonal polytypes (PL1, PL2, PL6, QL1, QL2 and QL6) have C3ν symmetry. The others (PL3, PL4, PL5, QL3, QL4 and QL5) are oriented along basal planes, resulting in the lower C1h symmetry and non-degenerate spin transitions at B=0.
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The ODMR spectra (Fig. 1b–d) are obtained by measuring the fractional change in PL intensity (ΔIPL/IPL) under continuous wave laser illumination as a function of both an applied out-of-plane DC magnetic field (B) and the frequency (f) of an applied radiofrequency (RF) magnetic field. Spin flips produce a ΔIPL/IPL signature and occur when f is resonant with one of the defect’s spin transitions, which can all be tuned by varying B. The large number of observed ODMR lines demonstrates the versatility of SiC as a host for optically addressable spin states.
In each polytype, wavelength-resolved ODMR measurements associate the various ODMR features with specific PL lines (see Koehl et al.3 and Carlos et al. for 4H-SiC and Supplementary Fig. S1for 6H- and 3C-SiC). Some of the defects in 4H-SiC (PL1-PL4) have been identified as spin-1 neutral divacancies9. The defects responsible for the other spin transitions observed (compiled in Supplementary Table S1) have similar spin and optical properties to the neutral divacancies but have not been conclusively identified.

Spin coherence at cryogenic and room temperatures

Long-lived spin coherence, an important prerequisite for quantum information and sensing technologies, is a general feature of spins in all three polytypes. Our coherence measurements are based on standard pulsed magnetic resonance techniques including Rabi, Ramsey, Hahn echo, Carl-Purcell-Meiboom-Gill (Fig. 2) and spin relaxation (Supplementary Fig. S2) sequences. At 20 K, the spin relaxation times range from 8 to 24 ms. The Hahn-echo coherence times (T2) range from 10 μs to 360 μs at 20 K, depending on the substrate, with significant dependence on implantation dose and substrate doping type. The longest T2 times we measured were in native neutral divacancies in 4H-SiC that were generated during crystal growth.
Figure 2: Ensemble spin coherence at cryogenic temperatures.
Ensemble spin coherence at cryogenic temperatures.
(a) Hahn-echo measurement of spin coherence of the neutral divacancies in as-grown SI 4H-SiC at 20 K, showing T2 times of 140±5 μs (PL1), 144±3 μs (PL2), 360±20 μs (PL3) and 340±5 μs (PL4). Long Rabi pulses (150 kHz) were used to minimize decoherence from instantaneous diffusion. (b) Hahn-echo measurement of the 3C-SiC spins at 6 K, implanted with 12C at doses of 1012 cm−2 and 1013 cm−2, with respective decoherence times of T2=24±4 μs and T2=12±1 μs. Inset: Ramsey measurement of 3C-SiC spin dephasing, showing T2*=52±3 ns. (c) Ramsey measurement at 20 K of QL4 in SI 6H-SiC implanted with 12C at a dose of 1012 cm−2. RF pulses were detuned from resonance by 10 MHz. The fit is to an exponentially decaying sinusoid with T2*=250 ns. (d) Hahn-echo measurement for QL1–QL6 in 1012 cm−2-implanted SI 6H-SiC at 20 K, except for QL5, whose overlap with other ODMR lines at B=0 inhibited zero-field measurements. Carl–Purcell–Meiboom–Gill (CPMG) dynamical decoupling for QL4 is also shown, with TCPMG=106±2 μs. The Rabi frequencies used (2.5 MHz) are less than the inhomogeneous linewidth, resulting in roughly half of the spins being driven. (e) Comparison of 20 K Hahn-echo coherence times in n-type 6H-SiC (grey) and SI 6H-SiC (coloured) for three different 12C implantation doses and spin densities. The error bars are 95% confidence intervals from exponential fits to the Hahn-echo data. B=0 for all the data in this figure.
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All three polytypes exhibit defects whose spin coherence persists up to room temperature (Fig. 3and Supplementary Figs S3–S5). In as-grown 4H-SiC, one neutral divacancy line (PL3) persists up to room temperature as well as three other ODMR lines (PL5–PL7) of unknown origin, all withT2=50±10 μs. Polycrystalline 3C-SiC also exhibits a state with room-temperature spin coherence, although similar states with the same zero-phonon line and ODMR transition in certain other 3C-SiC substrates that we measured did not. In 6H-SiC, the SI and n-type substrates have the same ODMR lines at 20 K, but their room-temperature ODMR signatures are substantially different from each other (Fig. 3b), with several additional ODMR lines in the n-type substrate that do not appear at 20 K or in the SI substrate. The presence of these coherent spin states at room temperature is a particularly promising result for spin-based sensing24 with SiC.
Figure 3: Ensemble spin coherence at room temperature.
Ensemble spin coherence at room temperature.
(a) ODMR in as-grown SI 4H-SiC as a function of B (upper) and at B=0 (lower). (b) ODMR as a function ofB in n-type 6H-SiC (upper) and at B=0 (lower) for n-type (dark blue) and SI (grey) 6H-SiC, implanted at 1013 cm−2 dose of 12C. QL7–QL9 have reduced ΔIPL contrast as the temperature is lowered, disappearing by 200 K. (c) Rabi driving at room temperature: PL5 in SI 4H-SiC, QL2 in SI 6H-SiC (multiplied by a factor of × 5), and the 3C-SiC spin species. (d) Hahn-echo measurements of room-temperature coherence for spin states in as-grown SI 4H-SiC. The fitted T2 times are 50±30 μs (PL3), 44±2 (PL5) and 50±15 μs (PL7). (e) Hahn-echo measurement of room-temperature coherence in n-type and SI 6H-SiC, implanted at the 1013 cm−2 dose. The fitted T2 times are 4.7±0.6 μs (purple, QL2, n-type), 5.6±1.8 μs (turquoise, QL2, SI), 4.4±1.5 μs (gray, QL3, n-type) and 4.9±0.9 μs (orange, QL7, n-type). The uncertainties are 95% confidence intervals from exponential fits to the Hahn-echo data.
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Coherent spin interactions

Ultimately, many spin-based quantum technologies will require not only separately addressable spins with long coherence times but also a means of coupling these spins together. Patterned ion implantation has generated individual and strongly coupled nitrogen-vacancy (NV) centres in diamond25. We have also patterned spin ensembles in SiC, using ion implantation through poly-(methyl-methacrylate) (PMMA) apertures (Fig. 4a; Supplementary Fig. S6). Though these are not individual spins, this patterning demonstration shows promise for spatially engineering SiC defects. As optical wavelengths significantly exceed the length scale required for strong magnetic coupling between single dipoles (<30 nm for diamond NV centres25), scaling up a dipole-coupled spin network is a significant challenge. Silicon carbide defects in inequivalent lattice sites have distinct RF and optical transition energies, giving complex polytypes of SiC with many inequivalent defect species the possibility of hosting many separately addressable spins in a single confocal volume (Fig. 4b).
Figure 4: Patterned SiC spins and illustration of dipole-coupled spins.
Patterned SiC spins and illustration of dipole-coupled spins.
(a) Implanted spin ensembles in n-type 4H-SiC through a PMMA mask with 50 nm holes, using 10 keV energy 12C ions at a 1013 cm−2 dose. Additional characteristics of these implanted spins are given in Supplementary Fig. S6. (b) Illustration of dipole-coupled spin network in 6H-SiC in which each spin has a unique orientation and optical/ODMR signature. The three spins shown here are the (hh) divacancy (turquoise), (k1k1) divacancy (purple) and (k2k2) divacancy (red).
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As a step towards independently addressable dipole-coupled spins, we measure dipole–dipole spin interactions between inequivalent defect ensembles. The study of these interactions also provides valuable information about the spin density and optical polarization in these defect states. Our measurements use double electron–electron resonance26 (DEER) to flip the spin of one spin ensemble (the ‘drive’ species), while the resulting change in the Larmor precession rate of another ensemble (the ‘sense’ species) is measured. We focused on 6H-SiC for these measurements, which when implanted, had higher spin densities than in our 4H-SiC substrates, and higher DEER-coupling strengths.
The change in precession rate (Δf), a measure of the average dipole-coupling strength, is experimentally observed as an additional phase (Δθfree) acquired by the sense species over the free precession segment of a Hahn-echo measurement (Fig. 5a). These parameters are related by , where tpulse is the delay of the drive pulses relative to the center of the Hahn-echo sequence. This pulse sequence is designed to refocus the sense spins due to all magnetic fields except those due to drive species spin flips. When we drive Rabi oscillations on the drive species, we simultaneously observe DEER oscillations in Δθfree of the sense spins (Fig. 5b).
Figure 5: Magnetic dipole-coupled spin ensembles in 6H-SiC.
Magnetic dipole-coupled spin ensembles in 6H-SiC.
(a) Pulse scheme for DEER measurements. As π pulses flip the orientation of the drive species spins, the sense species accumulates an extra phase (Δθfree) over a Hahn-echo sequence. (b) Varying the pulse duration of the drive spins (QL2) generates Rabi oscillations (right axis) and an oscillation in the DEER signal (left axis) corresponding to the sense spin species (QL1) acquiring Δθfree. The Rabi data are fitted according to an erfc-decaying sinusoid and Δθfree is fitted to a multiple of this function. (c) DEER signal, applying two π pulses to the drive species and varying θHahn and tpulse. The left data set is when the drive spins are polarized, and the right data set is for unpolarized spins, for which Δf vanishes. The data at different θHahn are not artificially offset. The solid lines are global fits to Equation 1. (d). Fitted Δf for the six spin orientations, when the drive-spin species is polarized (blue) and unpolarized (grey). The sense species is QL1 for all these data, except when QL1 is driven, in which case it is QL2. B=64 G andtfree=32 μs and T=20 K for all the data in Fig. 5.
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To measure both Δf and the decoherence rate of the sense spins due to drive-spin flips (τ), we vary both tpulse and the phase of the final π/2 pulse in the sense spin Hahn-echo sequence (θHahn). The resulting data (Fig. 5c, left) are well fit by:
For the data at θHahn=π/2, the coherent coupling term becomes  in equation (1), providing a sensitive measure of Δf, while the data at θHahn=0 and θHahn=π are dominated by the decoherence term, giving a more accurate measure of τ. The globally fitted values of Δf for various drive-spin ensemble species (Fig. 5d and Supplementary Fig. S7) show that the c-axis-oriented spins (QL1, QL2 and QL6) exhibit Δf values in the single kHz range. The lower symmetry of the basal-oriented spins (QL3–QL5) results in eigenstates with smaller magnetic moments, reducing Δf for these species (Supplementary Note 2).
We also repeated this experiment with the pulse sequence shown in Fig. 5a modified by the addition of a depolarizing π/2 pulse, which is applied to the drive spins before the sense spins’ Hahn-echo sequence. In this case, because the π pulses applied to the drive-spin population no longer cause a net change in magnetization, Δf vanishes (Fig. 5c, right). Additionally, when the drive spins are depolarized, τ increases slightly. When QL1 is the sense species and QL2 is the drive species, τchanges from 89±3 μs (polarized QL2) to 96±3 μs (unpolarized QL2).


The decoherence characterized by τ, known as instantaneous diffusion, arises from two effects. The first (and dominant) of these is microscopically inhomogeneous dipole-coupling strengths between randomly located individual spins, resulting in a distribution of coupling strengths, whose average is Δf. This distribution causes ensemble dephasing of the sense species when the drive species is flipped. The second effect is a macroscopically inhomogeneous magnetization field due to the spatial structure of the optically polarized volume of spins. The result of this effect is a slightly longer τ when the spin bath is depolarized, consistent with the data. The analysis of these data is complicated by the dynamics of discretely interacting spins in a polarized spin bath (Supplementary Note 3). Nevertheless, the standard quasi-static statistical model relating instantaneous diffusion to spin density provides a guide for analysing the DEER results.
On the basis of this model, we use τ for the unpolarized spin bath to infer that the spin densities of the three c-axis spin species (QL1, QL2 and QL6) range from 7–11 × 1015 spins cm−3. Because Δfis proportional to the magnetic field generated by the drive-spin ensemble, which in turn is proportional to the product of spin density and optical polarization, we can use the measured Δf and the calculated spin density to infer the degree of optical spin polarization. For the three c-axis spins, our DEER results lead to a high average optical spin polarization that ranges from 35% to 60%, depending on the defect species. Because of the inhomogeneous spatial profile of the optical illumination and collection areas in our measurements, the full optical polarization is likely to be even higher.
SiC spins are compelling analogues of diamond NV centres, with complementary properties and many unique prospects. Our demonstration that crystal polymorphism can be used to engineer new spin centres relies on SiC being a polymorphic material, a degree of freedom that is unavailable in diamond. In the future, established doping and epitaxial growth processes in SiC could lead to electronic interfaces with defect spins embedded in transistors and optoelectronic devices. Furthermore, due to its availability as a single-crystalline epitaxial film on silicon, the 3C polytype provides an excellent platform for hybrid quantum systems with photonic and mechanicaldegrees of freedom. Combining this sophisticated semiconductor technology with the versatility of coherent spin control in SiC stands to be an exciting route for solid-state quantum information.


Generation of defects

The 4H-SiC and 6H-SiC substrates used in this work include: a) n-type 4H-SiC, b) high-purity SI 4H-SiC, c) n-type 6H-SiC and d) SI 6H-SiC. Substrates a, b and c were purchased from Cree, Inc, while d was purchased from II-VI, Inc. The SI 4H-SiC contains a significant density of neutral divacancy spins as grown, and the data in Figs 1, 2a and 3 used that material without modification. Defects in the other substrates were generated by an ion implantation process consisting of 190 keV 12C ion implantations at doses of 1011, 1012 and 1013 cm−2, with a 7-degree tilt to minimize ion channelling effects.
After ion implantation, the samples were annealed at 900 °C for 30 min in Ar, a process designed to allow vacancies to diffuse and aggregate into pairs and vacancy complexes12. We estimate a 5% creation efficiency of fluorescent defects, defined as the number of created defects per implanted12C ion at 190 keV (Supplementary Note 1). For the n-type substrates, ion implantation with 12C can compensate the n-type doping. Throughout the text, our labelling of substrate doping types refers to the as-grown substrates, not to the semiconductor characteristic after implantation.
The 3C-SiC substrates used in this work consisted of [100] oriented epitaxial layers grown on [100]silicon substrates. The 3C-SiC substrates measured in Figs 1 and 2 were 3.85-μm-thick films and were obtained from Novasic. The substrates measured in Fig. 3 were grown at Case Western Reserve University and consisted of 1.5–2 μm thick polycrystalline films. Neither film was intentionally doped but both showed n-type behaviour. All samples were implanted with 190 keV 12C at doses of 1012 or 1013 cm−2 with a 7-degree tilt. The samples were then annealed at 750 °C for 30 min in Ar.
The patterned defects in Fig. 4a were generated by ion implantation at a lower energy (10 keV 12C ions at a dose of 1013 cm−2), which makes the 170-nm-thick PMMA a more effective ion mask. The PMMA mask used for the sample in Fig. 4b consisted of 50-nm apertures patterned by electron beam lithography.

Optically detected magnetic resonance

For our ODMR measurements, the laser excitation was higher energy than the defects’ zero-phonon lines, within their absorption sidebands. For the 4H- and 6H- substrates in Figs 1234, the laser energy was 1.45 eV (853 nm), with 16 mW of power reaching the sample. For the 3C-SiC data in Figs 1d and 2b, the laser energy was 1.33 eV (930 nm), and the power was 23 mW at the sample. For the double resonance data in Fig. 5, the laser energy was 1.27 eV (975 nm), with 60 mW reaching the sample. The laser excitation was gated with acousto-optical modulators and the fluorescence was collected using one of four detectors: a) a Thorlabs Femtowatt InGaAs photoreceiver (PDF10C), b) a Newport InGaAs photoreceiver (2011-FS), c) a Princeton instruments liquid-nitrogen cooled InGaAs camera attached to an Acton Spectrometer (2300i) and d) a Scontel superconducting detector (LTD 24/30-008).
The samples were mounted on top of 0.5- to 2-mm RF strip lines3. For the 3C-SiC, ring-shaped RF waveguides fabricated on chip were also used3. These sample/waveguide assemblies were then mounted in optical cryostats with RF access. The RF signals were generated by two signal generators (Agilent E8257C or Rohde & Schwarz SM300 vector source) whose outputs were gated using RF switches (MiniCircuits ZASWA-2-50DR+) for pulsed experiments. These signals were then combined, amplified to peak powers as high as 25 W (Amplifier Research 25S1G4A and Mini-Circuits ZHL-30W-252-S+), and sent to wiring in the cryostat connected to the waveguides and striplines. The RF and optical pulses were gated with pulse patterns generated by either a digital delay generator (Stanford Research Systems DG645), Pulse Pattern Generator (Agilent 81110A) or arbitrary waveform generator (Tektronix AWG520). The phase of the Rohde & Schwartz signal was also controlled by the AWG520.
The ODMR measurements in this paper were all taken using lock-in techniques, in which an RF pulse was alternatively gated on and off (Figs 1 and 3a–c) or the phase of one of the pulses was alternatively gated by 180° using IQ modulation (Figs 2, 3d, e and ). We used a 20-Hz software lock-in technique3 (Figs 1, 2, 3) and a hardware lock-in at frequencies up to 200 kHz (Fig. 5) to accommodate the bandwidths of the Thorlabs and Newport photoreceivers, respectively.
Because the PL spectra of the various divacancy orientations have overlapping phonon sidebands, these measurements collected IPL from all defect orientations at once. This procedure reduced the normalized ΔIPL/IPL signal but prevented defect PL from being rejected. The measured ΔIPL/IPLvalues are additionally reduced from their ideal values both by extra fluorescence from the SiCsamples (notably Vanadium impurities in the SI 6H-SiC) and by long fluorescence collection times. To achieve high optical spin polarization, we used long optical pulses (20–100 μs) in our measurement cycles. Because the timescale of optical polarization was faster than the bandwidth of most of our detectors, we did not gate the fluorescence collection. Therefore, much of the PL collected was from defect spins already polarized earlier in the pulse. Fast and gated fluorescence detection would lead to significantly higher ΔIPL/IPL values.
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Nov 26, 2015

From the Au nano-clusters to the nanoparticles on 4H-SiC (0001)

The control over the configuration, size, and density of Au nanoparticles (NPs) has offered a promising route to control the spatial confinement of electrons and photons, as a result, Au NPs with a various configuration, size and density are witnessed in numerous applications. In this work, we investigate the evolution of self-assembled Au nanostructures on 4H-SiC (0001) by the systematic variation of annealing temperature (AT) with several deposition amount (DA). With the relatively high DAs (8 and 15 nm), depending on the AT variation, the surface morphology drastically evolve in two distinctive phases, i.e. (I) irregular nano-mounds and (II) hexagonal nano-crystals. The thermal energy activates adatoms to aggregate resulting in the formation of self-assembled irregular Au nano-mounds based on diffusion limited agglomeration at comparatively low annealing temperature, which is also accompanied with the formations of hillocks and granules due to the dewetting of Au films and surface reordering. At high temperature, hexagonal Au nano-crystals form with facets along {111} and {100} likely due to anisotropic distribution of surface energy induced by the increased volume of NPs. With the small DA (3 nm), only dome shaped Au NPs are fabricated along with the variation of AT from low to elevated temperature.

Due to its wide band-gap, high current tolerance and high electron mobility, SiC is widely used in high power devices. α-SiC (3C-SiC) show zinc blende structure while β-SiC (4 H- and 6H-SiC) consists of wurtzite. Among the poly-types, the 4H-SiC possesses the highest band-gap of 3.26 eV and the 6H shows 3.02 eV while 3C shows much lower value at 2.39 eV. Recently, SiC are extensively applied for the fabrication of the high quality epitaxial graphene layers due to their thermal decomposition with a preferential sublimation of Si, and the C-terminated surface generally requires lower temperature than Si-terminated surface to grow a graphene film with an identical thickness as a result of a more rapid sublimation. On the other hand, owing to the localized surface plasmon resonance and large surface to volume ratio, Au NPs has received extensive research attentions for the optical, electric and biological applications. The variation of shape, size and density of Au NPs can provide an proficient way to optimize the performance of the corresponding devices such as enhanced light absorption in the solar cells, the performance of the localized surface plasmon resonance transducers by determining the surface plasmon decay and refractive index sensitivity, controlling the memory window of FETs. Also, the Au NPs with a remarkable catalytic capacity can serve as nucleation sites for NWs by absorbing the vaporized target materials based on the vapor-liquid-solid growth mechanism and the diameter and length, density, direction, and shape of the NWs can be inherently determined by that of the Au NPs. Recently, Au nanoparticles (NPs) have been applied to control the Schottky barrier height with a variation of its size on 4H-SiC. Au NPs have a potential of being applied in the various applications, however, the research on 4H-SiC is still relatively deficient and therefore, in this work we systematically investigate the controlled evolution of the various self-assembled Au nanostructures on 4H-SiC (0001) by the variation of annealing temperature (AT) with various deposition amounts (DAs). As shown in Fig. 1, depending on the DA, various nanostructures are fabricated, and evolve along with the increased AT. For example, with the 15 nm DA, Au nanostructures undergo drastic evolution in configurations with two distinctive phases: (I) irregular Au nano-mounds and (II) hexagonal Au nano-crystals. Phase I: With the thermal energy supplied, Au adatoms can gradually diffuse and aggregated at the pinholes perforated by the voids to form the irregular Au nano-mounds along with the formation of the hillocks and granules at relatively low annealing temperature which can be described with the diffusion limited agglomeration model, as shown in Fig. 1(a),and (a-2). Phase II: With the AT increase, all the Au structures gradually develop into the hexagonal nano-crystals owing to the enhanced surface diffusion, and the truncated facets formed to minimize the anisotropic surface energy, as shown with Fig. 1(b),(b-1). On the other hand, at relatively low DA (3 nm), the agglomeration process immediately proceed to the formation of dome-shaped Au NPs based on the Volmer-Weber growth model, and the Au NPs evolve with the increased size at the expense of the small Au NPs as a function of the AT.

Figure 1: Illustration of the fabrication of self-assembled Au nanostructures on 4H-SiC (0001) by the control of annealing temperature (AT) with various Au deposition amounts (DAs).
Figure 1
(a) Scanning electron microscopy (SEM) image (5 × 5 μm2) of a sample annealed at 600 °C with the 15 nm DA. (a-1)–(a-2) SEM images of a hillocks (1.6 × 1.6 μm2) and pinholes (1.3 × 1.3 μm2). (b) Atomic force microscope (AFM) side-view of hexagonal Au nano-crystals at 850 °C (5 × 5 μm2). (b-1) AFM top-view (1 × 1 μm2) of a hexagonal nano-crystal. (c,d) Dome-shaped Au nano-particles fabricated with a DA of 3 nm at 800 °C and 900 °C. (c,d) AFM top-views of 500 × 500 nm2.
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Figure 2: Evolution of the self-assembled Au nano-mounds on 4H-SiC (0001) at various annealing temperatures (AT) between 500 and 700 °C with 8 nm of Au deposition.
Figure 2
(a,d) AFM side-views of 1 × 1 and 3 × 3 μm2. (a-1)–(d-1) Cross sectional line-profiles. (a-2)–(d-2) Two dimensional (2-D) Fourier filter transform (FFT) power spectra.
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Results and Discussion
Figure 2 shows the fabrication of self-assembled Au nano-mounds on 4H-SiC (0001) by the variation of the annealing temperature (AT) between 500 and 700 °C. Corresponding SEM images are provided in Fig. S4. In general, with the AT variation, the heterogeneous dewetting of Au film gradually occurred as a function of surface energy, resulting in a drastic surface morphology evolution from a continuous Au thin film to isolated irregular Au nano-mounds, which can be described in conjunction with a diffusion limited agglomeration (DLA) model26. Initially, since the deposited Au thin film can generally possess a high vacancy concentration, being providing with the thermal energy, Au adatoms can spontaneously respond to diffuse, which can cause the nucleation of the vacancies, and in turn to form voids at random nucleation sites including highly strained sites and grain boundaries induced by the thermal expansion coefficient mismatch between Au and the SiC. Subsequently, the voids were kept forming with increased vacancy nucleation, and can perforated the Au film to form pinholes. Meanwhile, the agglomeration of Au can be initiated in the pinholes with a radius (Rp) bigger than the critical size (RC), which can be expressed as , where tAu is the thickness of Au layer. Also, the equilibrium contact angle of the Au nano-particle (Θ) can be described with the interfacial energy densities of γSiC/Vac (between SiC and vacuum), γAu/SiC (between Au and SiC), and γAu/Vac (between Au and vacuum) as . Namely, the pinholes with an Rpbigger than the RC can possess a stronger driving force for the agglomeration (dewetting), which can eventually result in the formation of the irregular nano-mounds. Meanwhile, based on the thermodynamic diffusion theory, the lD can be expressed as , where t is residence time of Au adatoms. And the Ds (diffusion coefficient) can be given by 31, where k is Boltzmann constant, D0 and EA (the diffusion barrier) are with certain values under an identical growth condition, therefore, the lD can be determined by the variation of the T(surface temperature). Consequently, an enhanced diffusion length can be expected with more thermal energy supplied, and as a result, when the AT was increased, more pinholes can be formed with a proper size (Rp>RC), which can correspondingly enhance the agglomeration initiation. On the other hand, with the increased lD, the connected irregular nano-mounds can have a tendency to expand and separate into isolated ones due to the Rayleigh instability as shown with AFM side- and top-views in , S3. In specific, the surface morphology with the 8 nm-thick Au deposition appeared quite smooth with only a few of nanometers of surface modulation, as shown in . After being annealed at 500 °C, partial formation of the connected nano-mounds occurred in the Au film due to the limited Au adatom diffusion as shown in . When the AT was increased to 600 and 700 °C, Au adatoms aggregated more compactly, resulting in the shape transition from the connected Au nano-mounds to the isolated ones with a drastic vertical size expansion as shown in. In addition, the morphology evolution can be clearly observed with the sharp increases in both the root-mean-squared roughness (RRMS) and surface area ratio (SAR), suggesting that the significant vertical size increase along with the AT increase, as shown in Fig. S3(e). As summarized in Table SI, the RRMS increased ×47.7 times from ~1 to ~47.7 nm, and the SAR increased from 0.09% to 8.27%, correspondingly. As a result, the drastic changes in the two dimensional (2-D) Fourier filter transform (FFT) power spectra along with the surface morphology evolution also can be similarly witnessed in Fig. 2. The symmetric bright spot indicating random distributed height drastically shrunk into a small spot caused by the reduction in the height distribution along with the vertical size increase. In brief, during the annealing between 500 and 700 °C the surface morphology underwent a drastic evolution from the flat Au thin film with only few nanometer modulation to the irregular Au nano-mounds with several hundred nanometers in height due to the enhanced surface diffusion as a function of temperature, which also can be equally observed with large-scale scanning electron microscopy (SEM) images in Fig S4. Similar evolution of the irregular Au nano-mounds can be observed on quartz substrate, various GaAs, sapphire and soft polymeric substrates.
Figure 3 shows the evolution of the self-assembled irregular Au nano-mounds with 15 nm DA on 4H-SiC (0001) controlled by the variation of the AT between 500 and 750 °C. The detailed surface morphology changes at the initial stage of the Au thin film agglomeration are presented in Fig. 4 and S5. Similar to the 8 nm Au deposition, Au adatoms gradually aggregated and developed into the isolated irregular nano-mounds with the incremental variation of AT. Meanwhile, the formation of pinholes and granules was simultaneously witnessed during the evolution of Au nano-mounds, as shown with SEM images in Fig. 3. More specifically, as shown in Fig. 3(a), hillocks were formed with diameters of several micrometers or even larger than 10 micrometers at 500 °C possibly because of the thermal expansion of Au films. The hillocks appeared to the prior process of the pinhole formation at increased thermal energy, and the hillocks would eventually evolve into the pinholes with the formation of nano-mounds subsequently, as mentioned. At 600 °C of annealing, with the increased thermal energy, the number of hillocks and pinholes were further increased, as clearly shown in Fig. 3(b). Also, the granules started forming on the hillocks due to the tendency of the Au film to release the compressive stress, which resulted from the higher thermal coefficient of the Au film than the substrate. The hillock formation was also observed with the Au films on Y2O3-doped ZrO2 (YSZ). Finally, when the AT was reached 750 °C, all the Au structures agglomerated into the isolated Au nano-mounds with a uniform distribution owing to the enhanced diffusion of Au adatoms as shown in Fig. 3(c). At the stage of the pinholes formation, with the temperature increase, the size of the pinholes noticeably extended because of the more drastic agglomeration, as shown with the AFM side-views, line-profiles and top-views and SEM images in Fig. 4 and S5.Figure 5 shows the elemental analysis of the irregularly connected Au nano-mounds by the energy-dispersive X-ray spectroscopy (EDS). As shown by the combined EDS phase map in Fig. 5(b), the Au (yellow color) and Si phases (red color) were clearly matched the surface morphology shown by the SEM image in Fig 5(a). The Si (green line) can be observed everywhere on the surface, whereas, Au counts (blue line) mainly distributed along the nano-mounds, suggesting the agglomeration occurred with the limited diffusion, as shown by line-profiles indicating by the yellow line in the enlarged image in Fig. 5(c). Similarly, more noticeable counts of Au existed at the area with nano-mounds, and rest area were full of the Si counts, as shown in Fig. 5(d–e).

Figure 3: Formation of hillocks, voids, granules and Au nano-mounds with 15 nm Au deposition by annealing between 500–750 °C on 4H-SiC (0001).
Figure 3
SEM images are of 100 (x) × 76.67 (y) μm2.
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Figure 4: Initial stages of the fabrication of Au nanostructure annealed at 500 and 600 °C with a DA of 15 nm.
Figure 4
(a,b) AFM side-views of 10 × 10 μm2. (a-1)–(b-1) Enlarged AFM side-views of 3 × 3 μm2. (a-2)–(b-2) Cross sectional line-profiles. (a-3)–(b-3) FFT power spectra. (c,d) SEM images (18.2 × 13.9 μm2) of the samples annealed at 500 °C and 600 °C.
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Figure 5: Elemental analysis of self-assembled Au nanostructures on 4H-SiC (0001) by the energy-dispersive X-ray spectroscopy (EDS).
Figure 5
(a) SEM image of the sample with the 8 nm DA annealed at 600 °C. (b) Combined EDS phase map of Au (yellow) and Si (red). (c) Line-profiles of element counts of Si (green) and Au (blue) denoted with the yellow line in the SEM image. (d,e) 3-D top-view phase maps of Si and Au.
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Figure 6 shows the transition phase between the Au nano-mounds and Au nano-crystals at a higher AT range between 750 and 950 °C with a DA of 15 nm on 4H-SiC (0001). The corresponding AFM top-views and SEM images are shown in Fig. 7, S6 and S7 respectively. Generally, Au nanostructure fabrication was quite sensitive to the AT, namely, above a certain AT, the hexagonal Au nano-crystals can be successfully synthesized. The equilibrium shape of NPs can be decided by the Wulff construction resulted from the orientation dependence of surface energy, and thus, with each fixed growth condition the shape of NPs tend to minimize the surface energy within a certain volume. The face-centered-cubic (fcc) materials, such as Au, have a tendency to truncate facets to reduce the surface energy and consequently, with the accumulation of Au adatoms, the anisotropy gradually appears more obviously. Thus, as soon as reaching the critical volume, the facet truncation can happen along each {111} and {100}, finally resulting in the formation of the hexagonal nano-crystals. In more detail, at 750 °C, the agglomeration (Au nano-mounds separation) was still dominant due to the insufficient diffusion, which can be evidenced with some elongated nano-mounds (phase I), as shown in . Being providing with a sufficient thermal energy at 850 °C, the nano-mounds gradually separated into Au nano-crystals with a noticeable size increase, as shown in Fig. 6(b),(b-1). As mentioned, owing to the anisotropic surface energy, the Au nano-crystals were turned into the hexagonal shape as shown in Fig. 6(phase II). When the AT reached 950 °C, the hexagonal nano-crystals can still be fabricated with a slight decrease in both the size and the density, as shown in . The size reduction at a higher surface temperature associated with the density decrease is against the general trend of surface diffusion, and this can be possibly due to the enhanced evaporation of nanoscale Au as a function of AT, which can similarly witnessed on Si, MgO, SrTiO3, and Al2O3. To specify the size and density evolution, the average height (AH), lateral diameter (LD) and average density (AD) are summarized in Fig. 7(a,b) and Table SII, which can be divided into two phases: phase I between 750 and 850 °C and phase II above 850 °C. The size and density evolution can also be clearly witnessed with SEM images in a larger scale, as shown in Fig. 7(c–e). Owing to the further enhanced diffusion energy, the AH kept increasing ×1.48 times and as a result of the compact aggregation of Au adatoms, the LD decreased by 17%, whereas, the AD increased ×1.39 times in phase I. The AD increase with an increase temperature from 750 to 850 °C can be due to the phase transition from the Au mounds to the hexagonal NPs. In phase II at 950 °C, the AD further decreased 47.4% due to the enhanced surface diffusion as expected, clearly shown in Fig. 7(b,e). However, both the AH and LD decreased 2.82% and 3.03% respectively at 950 °C likely due to the nanoscale Au evaporation as discussed. Accordingly, the RRMS and SAR initially increased with the growth of nano-crystals in vertical size, and went down due to the decreased size and density of the nano-crystals, as shown in. Similarly, the bright spot in the 2-D FFT power spectra radically shrunk into smaller ones with a hexagonal pattern, suggesting the formation of the Au nanocrystals in . The self-assembled nano-crystal formation can be also witnessed with the elementary analysis shown in Fig. 8. As clearly shown by phase map in Fig. 8(b), the Au (yellow) distributes among the NPs, which means the shape transition happened with the formation of the Au NPs. As a result, the Au can be only detected in the area with NPs, whereas, the Si evenly exists in the areas with/without NPs, as shown with line-profiles in Fig. 8(c). Similarly, the Si and C Kα peaks can be equally witnessed in the both locations, whereas, the Mα1 peak at 2.123 KeV only occurred in the area with NPs, as shown in . . The Au NPs are equally evidenced with the pillars indicating higher concentration in 3-D side-views of the Au map, which matched the holes in the Si map, as shown in.

Figure 6: Self-assembled Au nano-crystals fabricated at various ATs between 750 and 950 °C with a DA of 15 nm.
Figure 6
(ac) AFM side-views of 10 × 10 μm2. (a-1)–(c-1) 3 × 3 μm2. (a-2)–(c-2) Cross sectional line-profiles. (a-3)–(b-3) FFT power spectra.
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Figure 7: Summary of average height (AH), lateral diameter (LD) and average density (AD) of Au nano-crystals at various ATs between 750 and 950 °C with 15 nm DA.
Figure 7
(a) Average height (AH) and lateral diameter (LD) at each temperature. (b) Average density (AD) at each temperature. Error bars are ±5%. (ce) SEM images of 19.4 (x) × 14.6 (y) μm2 at each AT.
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Figure 8: EDS phase maps and spectra of the Au nano-crystals fabricated at 900 °C with the 15 nm DA on 4H-SiC (0001).
Figure 8
(a) SEM image of 40(x) × 30(y) μm2. (b) Combined phase map of Au (yellow) and Si (red). (c) Line-profiles of element counts of Si (green) and Au (blue). (d,e) Corresponding EDS spectra from the red box (d) and blue (e). (f,g) 3-D top-view phase maps of Si and Au.
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Figure 9 shows the evolution of the tiny dome-shaped Au NPs with a relatively low DA of 3 nm on 4H-SiC (0001) by the variation of AT between 300 and 900 °C. Figure S8 presents the corresponding samples with AFM top-views. Generally, with the increased AT, the tiny dome-shaped Au NPs were fabricated instantly after the annealing, and developed in size and density without the shape transition, which can be described with the Volmer-Weber growth model. As mentioned, Au adatoms can only freely aggregated with a limited lD in the pinholes perforated by the voids. Provided that the Au thin film with the DA of 3 nm is much thinner than 8 and 15 nm, the perforation can immediately happen at the initial stage with much less thermal energy. In addition, given that the bonding energy between Au atoms (EAu) was stronger than the bonding energy between Au adatoms and Si and C atoms (EI), namely, EAu > EI, with the sufficient thermal energy supplied, Au adatoms can spontaneously nucleate to form the three-dimensional (3-D) islands (NPs). On the other hand, as discussed, the equilibrium shape can be decided by the surface energy for each orientation, and with a small volume, the surface energy can still sustain isotropic, which can result in the spherical (dome) shaped Au NPs. As a result, the dome-shaped Au NPs were directly developed from the smooth Au thin film as soon as treated with sufficient thermal energy from 300 to 500 °C, as shown in. Accordingly, the surface modulation increased from ~1 nm to ~5 nm, as shown with line-profiles in . Meanwhile, being providing with EAu > EI, at elevated temperatures, the Au islands with larger boundaries tend to absorb more surrounding adatoms and merge smaller ones to form bigger in order to minimize the surface energy. Therefore, between 500 and 900 °C, with the enhanced lD, the dome-shaped Au NPs gradually increased in size at a expense of the Au NPs density, as shown in Fig. 9(c,d), which resulted in the slight increase of the surface modulation indicated by the line-profiles in Fig. 9(c-1),(d-1). As shown in Fig. S8(b)–S8(d), throughout the whole evolution, the tiny dome-shaped NPs were fabricated uniformly with a packed density at each AT, which results the symmetric bright spots instead of the irregular pattern in the 2-D FFT power spectra, as shown in Fig. 9(b-2)–(d-2). The evolved surface morphology can also be witnessed with the increase of the RRMS: Initially, the RRMS drastically increased from 0.7 to 2 nm owing to the Au NPs formation, and subsequently, the RRMSgradually increased as a function of the AT, as summarized in Fig. S8(e)and Table SIII. In short, the dome-shaped can be fabricated above 500 °C, and with the increased AT, the size of Au NPs increased with decreased density, which can be a conventional behavior for metallic NPs on various substrate, such as Ag NPs on the GaN and sapphire, Au and Ga NPs on the GaAs, and Au NPs on the Si. Figure S9 shows the EDS spectra of the sample with 3 and 15 nm DAs annealed at 800 °C. As shown in Fig. S9(a) and S9(b), the increased DA can be evidenced with nearly 5 times higher counts in the Mα1 (2.123 keV) peaks of Au than that of 3 nm DA, as similarly witnessed with the Lα1 (9.711 keV) peaks, shown in Fig. S9(a-2) and S9(b-2).

Figure 9: Evolution of the self-assembled Au nano-particles with a DA of 3 nm fabricated between 300 and 900 °C on 4H-SiC (0001).
Figure 9
(ad) AFM side-views 1 × 1 μm2. (a-1)–(d-1) Cross-sectional line-profiles acquired from the white lines in the corresponding AFM side-views. (a-2)–(d-2) 2-D FFT power spectra.
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In summary, the systematical investigation on the evolution of the self-assembled Au nanostructures on N-type 4H-SiC (0001) controlled by varying the annealing temperature (AT) between 300 and 950 °C was successfully demonstrate with various deposition amounts (DAs): 3, 8, 15 nm. At higher DAs (8 and 15 nm), with the increased AT, the drastic morphology evolution of Au nanostructures was observed into two phases: (I) Au nano-mounds, and (II) hexagonal Au nano-crystals. Below 700 °C, the Au nano-mounds gradually formed and developed in the pinholes perforated by the nucleated voids as a function of the AT, which was discussed as a dewetting process in conjunction with the DLA model. Meanwhile, the hillocks were fabricated at the lower AT range between 500 and 600 °C, caused by the thermal expansion of Au film. Above 750 °C, with a sufficient thermal energy, the hexagonal nano-crystals can be successfully fabricated on 4H-SiC (0001) as a result of anisotropic distribution of surface energy caused by the increased volume. Finally, the size of Au NPs started to decrease above 850 °C likely due to the nanoscale dependent evaporation of Au nanocrystals. For the samples with 3 nm DA, the tiny dome-shaped Au NPs were fabricated based on the Volmer-Weber growth model without the formation of the irregular nano-mounds. With a small volume, the distribution of surface energy of the Au NPs was still isotropic, which eventually resulted in the dome shape rather than the polyhedral shape

In this experiment, the annealing temperature (AT) effect was investigated with 3, 8 and 15 nm deposition amounts (DAs) by the variation of annealing temperature in the pulsed laser deposition (PLD) system. Epi-ready N-type 4H-SiC (0001) substrate was ~250 μm thick with an off-axis of ±0.1° from the Technology and Devices International (TDI, USA). Prior to the growth, samples were treated with a chemical cleaning in the hydrofluoric acid (49.0–51.0%) solution for 10 minutes and subsequently flushed with the deionization (DI) water for three times. For each growth, samples were mounted on an Inconel holder with indium solder for a good thermal conduction of samples and degassed at 700 °C for 30 min under a chamber vacuum below 1 × 10−4Torr. After degassing, the surface was quite flat without any contaminants as confirmed by the morphological and optical characterizations in. Subsequently, 3, 8 and 15 nm-thick Au thin films were deposited on the sample respectively in a plasma lion-coater at a growth rate of 0.05 nm/s with the ionization current of 3 mA below the vacuum of 1 × 10−1 Torr. To systematically investigate the AT effect, with the fixed DA and annealing duration, samples were systematically annealed at various ATs of 300, 500, 600, 700, 750, 800, 900, 950 °C with a ramping rate of 2 °C/s by a halogen lamp. After reaching each target substrate temperature, the samples were dwelled there for 450 s to ensure the uniformity of the Au nanostructures, and all the annealing process was strictly controlled with a computer-operated recipes in the PLD system under 1 × 10−4 Torr. To minimize the effect of the Ostwald ripening, the temperature was immediately quenched down to the ambient temperature after each growth. For the morphological characterization, an atomic force microscope (AFM) was utilized for smaller area scanning with the non-contact (tapping) mode. AFM tips (NSC16/AIBS, μmasch) employed were with a radius of less than 10 nm curvature, made of Si etching. The tips were 17–21 μm long with the spring constant of ~42 N/m and resonant frequency of ~330 kHz. The cantilevers of the tips were back-side coated with ~30 nm Al to enhance the laser reflection. The same batch of tips were hired in order to diminish the tip effect for the consistency of the analysis and characterization. A scanning electron microcopy (SEM) was employed for larger area scanning. The acquired original data was processed and analyzed with the XEI software (Park Systems) to generate the AFM images, cross-sectional line-profiles, Fourier filter transform (FFT) power spectra, root-mean-squared (RMS) roughness, size and density plots of the Au NPs. The FFT power spectrum was obtained by converting the height distribution from the spatial domain to the frequency domain by the Fourier filter transform. Additionally, the energy-dispersive X-ray spectroscopy (EDS) with the spectral mode (Thermo Fisher Noran System 7) was employed for the elemental analysis and phase mappings under vacuum. For the optical characterization, the Raman spectrum was excited by a CW diode-pumped solid-state (DPPS) laser of a wavelength of 532 ± 1 nm with an output power of 120 mW and was received with a TE cooled CCD detector.