Laser-induced oxidation kinetics of bismuth surface microdroplets on GaAsBi studied in situ by Raman microprobe analysis

J. A. Steele; R. A. Lewis

doi:10.1364/OE.22.032261

1. Introduction

GaAsBi is an emerging III–V semiconductor alloy containing semiconductor and semimetal components. At mass number 208, Bi is the heaviest non-radioactive element in the periodic table and roughly 25% larger than Ga or As. Current methods of coherent GaAsBi crystal growth are greatly hindered by the strong tendency of Bi to segregate and form surface droplets [1–3]. Nonetheless, due to the exceptional Bi-induced changes observed in the host matrix [4–8], GaAsBi alloys are receiving considerable attention for scientific and technological interests. Notably, the dilute introduction of Bi into GaAs causes a dramatic reduction in the bandgap [8]. Until recently there existed no materials lattice matched to GaAs with a bandgap of 1 to 1.1 eV, for realizing high-efficiency sequential optical gap solar cells [9]. To date, the inclusion of GaAsBi alloys in high-performance electronic devices is stalled by the challenges faced by growers to simultaneously incorporate Bi and maintain smooth, droplet free surfaces. While much of the current work on molecular-beam-epitaxy (MBE) growth of GaAsBi has done well to identify growth conditions which lead to Bi surface segregation [2], the exact composition of the droplets remains unknown.

On the other hand, the inclusion of surface metallic nanostructures in GaAs-based solar cells was recently shown to enhance efficiency and function [10], and the droplet epitaxy of semimetal bismuth nanodroplets on a GaAs surface recently realized group-V based MBE nanoscale droplet formation for low-dimensional photovoltaic applications [11]. Further oxidizing the nanodroplets [12] forms bismuth trioxide (Bi₂O₃), a fascinating optical material subject to increasing interest for potential applications in energy generation due to its high refractive index, large photoconductive response, wide optical bandgap, and high ionic conductivity [13–15]. The intrinsic polarizability of paired 6s² lone electrons in trivalent bismuth favors the separation of photo-excited electron-hole pairs and the transfer of these carriers [16]. Consequently, the integration of Bi₂O₃ nanoislands was recently shown to be suitable for thin-film solar cells [17].

The optical response and functionality of polymorphic bismuth oxides (the four main polymorphs [18–21] of Bi₂O₃ being α, β, γ, and δ) are inherently dependent on the phase utilized. Recently, we [22] revealed that following bismuth oxidation the ensuing oxide phase is critically dependent on the final oxide volume and adheres to a fixed kinetic transformation sequence:

\frac{3}{2} O_{2} (g) + 2 Bi (l) \to β - {Bi}_{2} O_{3} (s) \to α - {Bi}_{2} O_{3} (s) .

Moreover, it was demonstrated that the often desirable β-Bi₂O₃ – with high oxygen ion conductivity and strong visible-light-driven photocatalytic activity – acquires room-temperature metastability below a critical oxide microisland volume.

While thermal oxidation of bismuth is inexpensive and easily controlled [23, 24], a recent investigation of high-temperature oxidation of bismuth nanodroplets on a GaAs substrate highlighted the indiscriminate nature of bulk thermal treatments [12]. High-temperature annealing of GaAsBi alloys ultimately changes the opto-electronic properties of the as-grown semiconductor [25–29] and offers limited options for real-time in situ diagnostics [22, 30–33]. In the interest of controlled surface engineering of such arrangements, alternative techniques ought to be explored.

In this paper, we perform micro-Raman studies of GaAsBi metallic Bi surface droplets and investigate the possibility of inducing a local and permanent Bi → β-Bi₂O₃ transformation by cw-laser (HeNe; 632.8 nm, 437.8 THz) irradiation. By utilizing the transformation dynamics imposed by Eq. (1), and oxidizing isolated micron-sized Bi surface droplets, a high level of control is introduced over the transformation, which ensures a final pure β-Bi₂O₃ is always achieved. The ability to locally modify the electrical conductivity and optical properties of a wide range of materials is the focus of much current research and laser irradiation-induced oxides tend to be compact with good adherent properties with a well-defined metal/oxide interface [34]. Within this context, local laser irradiation for surface engineering of structure, composition, and physical properties, bypassing conventional bulk thermal treatments, is important.

2. Experimental details

2.1. Sample details

Our GaAs_1−xBi_x sample was grown by MBE with Bi concentration x = 0.048 and with a nominal epilayer thickness of 0.3 μm. The sample was grown at a substrate temperature of 330°C and with relatively large Bi flux. The concentration of bismuth in our GaAsBi film was determined through a combination of x-ray diffraction (XRD) [35] and photoluminescence [36] measurements, and found to be in a saturation regime which formed Bi droplets on the surface during growth.

Figure 1 shows representative scanning electron microscope (SEM) and corresponding energy-dispersive x-ray spectroscopy (EDS) images obtained from the GaAsBi expilayer surface. The appearance of pure Bi droplet formation (no Ga/Bi dual composites) on the (100) GaAsBi surface is indicative of bismuth-rich growth (Bi saturation) and attributed to Bi segregation [2]. SEM micrographs revealed the droplets ranged in diameter from 0.1 to 2 μm, with a mean of roughly 1.5 μm over the entire sample surface. While the observed surface droplet size and density can fluctuate over different regions, the Raman scattering measurements indicated that the GaAsBi epilayer was highly homogeneous with respect to phonon frequencies and the general Raman lineshape (see Fig. 2(b)).

Fig. 1 (a) SEM image of GaAsBi sample surface showing droplet formation, with (b) the corresponding EDS image. The insets show an enlargement of a typical surface droplet. The EDS data of the droplet reveals a pure bimsuth structure which is free from any dual (Ga/Bi) metallic segregation [2].

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Fig. 2 (a) Optical micrograph of GaAs_0.952Bi_0.048 sample surface and relative laser spot size. Micro-Raman spectra obtained using a relatively low [22] laser power density (I_R < 5×10² W/cm²) from (b) a droplet-free GaAsBi surface exhibiting characteristic two-mode and free-carrier (hole) plasmon behavior and (c) the Bi droplet indicated in the optical image above. Here * denotes substrate features emerging from scattered probe light. Left inset: spectra expanded and resolved over the second-order bismuth harmonics. Right inset: trigonal two-atom unit cell of bismuth with arrows showing the direction of atomic displacement for non-degenerate A_1g and doubly degenerate E_g phonon modes.

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2.2. Raman scattering experiments

Room-temperature Raman spectra were acquired in a quasi-backscattering configuration on the (100) sample surface using a Jobin-Yvon HR800 integrated micro-Raman system with confocal microscope, 20 mW HeNe 632.8 nm (473.8 THz) laser, and air-cooled CCD detector. Rayleigh backscatter was filtered using an appropriate notch filter and a focused laser spot diameter of 1.7 μm was defined by employing an Olympus ×100 objective with laser power densities controlled by a neutral variable density filter positioned before the microscope optics. Optical dispersion was achieved with a 1800 g/mm diffraction grating resulting in a spectral resolution of 0.2 cm⁻¹. Instrument calibration was verified with the Si band at −520.7 cm⁻¹ (15.6 THz) prior to recording Stokes Raman scattering spectra.

3. Results

3.1. Raman spectroscopic characterization of GaAsBi metallic surface droplets

Elemental bismuth can readily be identified in metallic surface droplets using methods such as EDS (see Fig. 1(b)), however the bismuth form (i.e. pure metal, defected/polycrystalline or oxidized) must be determined using phase-specific techniques such as Raman spectroscopy or XRD. Figure 2(a) shows an optical micrograph of the GaAsBi sample surface with corresponding micro-Raman spectra measured from a smooth, droplet-free region (Fig. 2(b)) and from a metallic surface droplet (Fig. 2(c)). The spectral features and two-mode behavior exhibited in Fig. 2(b) are characteristic of GaAs_1−xBi_x for x = 0.048 [35, 37]. Figure 2(c) displays two strong modes at 73 cm⁻¹ (2.1 THz) and 98 cm⁻² (2.9 THz), which are consistent with the two first-order optical bands of rhombohedral bismuth corresponding to E_g and A_1g phonon modes, respectively [38]. Contrary to the amorphous state suggested by Ciatto et al. [39], the frequency, linewidths, and second-order harmonics measured here indicate a good crystalline Bi structure. From the inset of Fig. 2(b), bismuth is shown to crystallize in a trigonally distorted cubic lattice (A7 structure) with two atoms per primitive cell. Thus, for center point scattering (q = 0), there are three optical modes: totally symmetric A_1g singlet and the doubly degenerate E_g. Our GaAsBi sample was typically stored under ambient conditions and Raman measurements indicated a negligible presence of naturally-forming bismuth oxide [40].

Enlarged in the inset of Fig. 2(c) are the resolved weak bismuth second-order harmonics near ∼188 cm⁻¹ (∼5.64 THz) consisting of three overtones of similar frequencies which do not originate from GaBi-like modes scattered from the GaAsBi epilayer. The large central peak (II) is primarily composed of the A_1g symmetry component [41]. Since the laser spot is comparable in size to the Bi island, the relatively weak bands between 270 to 290 cm⁻¹ (indicated in Fig. 2(c) by *) do originate from the GaAsBi epilayer surface due to light scattering off the droplet and correspond to the GaAs-like TO(Γ), LO(Γ), and LO-phonon-hole-plasmon coupled (LOPC) modes [37].

3.2. Power dependence and laser-induced oxidation of bismuth surface droplets

It is well known that the high power densities used in micro-Raman experiments can often increase local temperatures due to the intense optical focus. The temperature increase can be hundreds of degrees and may cause wavenumber shifts in Raman modes and potentially induce chemical/structural alterations of the probed surface. Due to its low thermal conductance and very low (with respect to other group V semimetals) melting point (545 K), several micro-optical studies of bismuth have demonstrated its tendency to oxidize while under intense illumination [22, 40, 42–44].

Figure 3(a) shows Raman spectra obtained for increasing laser power densities incident on the Bi droplet studied in Fig. 2(c). For laser power densities in excess of 7.4×10⁴ W/cm², three additional modes at 125, 315, and 460 cm⁻¹ are introduced into the Raman spectra which correspond to unique Bi-O vibrations and are attributed to β-phase Bi₂O₃ [22,45]. Low-laser-power Raman measurements obtained after oxidation indicated the β-Bi₂O₃ possessed phase stability over time at room-temperature, in agreement with our previous study [22]. The laser-induced oxidation of Bi irradiated with 632.8 nm (473.8 THz) laser light has insignificant photolytic contributions and is thermally driven. Only once temperatures in the laser-heated volume (a detailed discussion on spectral temperature estimations is given in Sec. 3.3.1) surpass the bismuth melting point will an oxidation reaction occur; $\frac{3}{2} O_{2} (g) + 2 Bi (l) \to β - {Bi}_{2} O_{3} (s)$ . The isolation and small size of the Bi microdroplets impose constraints on the transformation sequence presented in Eq. (1), permitting the formation of only a purely β-phase Bi₂O₃ [22].

Fig. 3 Raman spectra of droplet studied in Fig. 2(c) for (a) increasing laser power, and (b) decreasing laser power. Here * denotes GaAsBi substrate features due to scattered probe light and the insets expand these data over the first-order bismuth optical phonon range. For decreasing power, time was spent between measurements to allow for cooling. The three solid vertical lines at 125, 315, and 460 cm⁻¹ represent the three β-Bi₂O₃ vibrational signatures. Spectra have been scaled and shifted vertically for clarity.

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The insets of Fig. 3(a) and 3(b) demonstrate the migration of phonon peak frequencies with rising and falling local temperatures, respectively [46, 47]. The shifts essentially emerge from the changing atomic bond lengths as a result of the thermal expansion of the bismuth matrix. That modes ultimately return to their original frequencies (see inset of Fig. 3(b)) verifies purely thermal mechanisms.

Zayed et al. [48] highlighted the variability of the Bi melting point in low dimensions and that the temperature is significantly lower for sub 0.1 μm structures. Given the shallow penetration depth of laser light, the small probe beam size, and the unique morphology of different metallic surfaces, this effect should not be overlooked. However, we only consider the laser-induced oxidation of isolated and smooth micron-sized Bi droplets, studies of which yielded findings consistent with bulk Bi properties.

3.3. Temporal Raman study of bismuth laser-induced oxidation

In this section the power and versatility of micro-Raman direct laser processing is demonstrated. Oxidation reactions were investigated for an isolated ∼ 1.5 μm GaAsBi surface droplet (similar to that studied Fig. 2(c)) using a constant laser power density and recording spectra at fixed time intervals. A laser power density of 5.73×10⁴ W/cm² was selected as it allowed an oxidation reaction to occur on a resolvable timescale.

Figure 4 shows chosen Raman spectra obtained in situ at different times during the laser-induced oxidation. The low-frequency bands of the spectra (associated with the Bi vibrations) strongly redshift during laser heating, reaching a minimum frequency at ∼3 min 20 s. A visibly larger shift is observed for the A_1g mode than for the E_g. Typically, higher frequency Raman modes are prone to larger shifts, however the difference here is attributed to the anisotropy in bismuth thermal expansion [49] and the fact that nuclear displacements of A_1g and E_g are perpendicular and parallel to the basal plane, respectively. Oxidation coincides with maximum phonon redshifts and is indicated by the introduction of three new β-Bi₂O₃ signatures, identified in Fig. 4 as A_β, B_β, and C_β. For longer exposure times, the β-Bi₂O₃ bands intensify before temporal changes in the Raman spectra effectively cease. The weak features in Fig. 4 identified by * originate from stray light Raman scattered from the GaAsBi epilayer surface and appear unchanging during the reaction.

Fig. 4 Mirco-Raman spectra of an isolated ∼ 1.5 μm bismuth surface droplet acquired in situ at different times of an oxidation reaction using a laser power density of 5.73×10⁴ W/cm². The spectra have been offset and the lower frequency portion rescaled for clarity. Here * denotes GaAsBi substrate features due to scattered probe light. The vertical lines act as an aid for the eye in identifying the three Raman modes of β-Bi₂O₃ labeled A_β, B_β, and C_β, which are assigned to 125, 315, and 460 cm⁻¹ vibrations, respectively.

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3.3.1. In situ spectral determination of bismuth temperature

Spectroscopic real-time temperature estimates of bismuth requires an accurate knowledge of the properties of the metal both in solid and liquid phase. Surprisingly, there are very few reports on the properties of molten Bi and traditional anti-Stokes/Stokes ratio (I_AS/I_S) techniques for determining local temperatures do not lend themselves to our attempts to time-resolve or use of a micro-Raman system [50]. Alternatively, the phonon shifting for bismuth under laser irradiation can be approximated as a purely thermal occurrence (assumed to be non-destructive) and a relatively simple semi-empirical model can be developed [30, 47].

By attributing the change in frequency to the change in the interatomic distance d within the bismuth matrix, and assuming the bismuth is excited in equilibrium conditions (meaning the temperature of heated lattice and electrons are the same), the redshift can be understood by considering the binding energy ε_b. Rising temperatures see d increase and the binding energy decrease. Thus the phonon frequency scales with the binding energy and inter-atomic distance by

ω^{2} = ε_{b} / (M_{Bi} d^{2}) \Rightarrow ω = ω (T_{0}) + Δ ω (Δ d, Δ ε_{b}),

where M_Bi is the mass of Bi atom, ω(T₀) is the phonon frequency under ambient conditions, and Δω represents a shifting term caused by changes in d and ε_b. Since the restoring force is non-linear in the displacement, the phonon frequencies are heavily dependent on d, and thus the resulting molar volume V_m. The desired temperature T is related the molar volume through

V_{m} (T) \equiv V_{m 0} \times exp (- 3 \int_{T_{0}}^{T} α (T^{'}) \partial T^{'}),

where V_m0 is the molar volume of bismuth under ambient conditions and α(T′) = 1/3[2α_⊥(T′) + α_‖(T′)] is the thermal expansion coefficient [51]. We can examine the thermal dependence of phonon shifts by only considering changes in V_m. Neglecting phonon-phonon interactions, the frequency of the phonon is approximated through the isothermic Grüneisen parameter [52]

γ_{therm}^{E, A} = - \frac{\partial [ln ω_{E, A}]}{\partial [ln V_{m}]} .

The superscript here indicates the two different Grüneisen parameters,

γ_{therm}^{E}

and

γ_{therm}^{A}

, for the two first-order bismuth optical modes E_g and A_1g, respectively. By integrating Eq. (4) for only the center scattering phonons (q = 0) we arrive at an expression relating the experimentally observed phonon frequency and local temperature T by

ω_{E, A} (T) = ω_{E, A} (T_{0}) \times exp (- 3 γ_{therm}^{E, A} \int_{T_{0}}^{T} α (T^{'}) \partial T^{'}) .

For T₀ and T ≫ 100 K, this can be approximated by the linear equation

ω_{E, A} (T) ≃ ω_{E, A} (T_{0}) + Δ ω_{E, A} \times Δ T .

Here Δω_E,A is the coefficient of temperature change and ΔT = T − T₀. Höhne et al. [47] accurately determined the isothermal Grüneisen parameters for the two first-order optical modes of bismuth to be

γ_{therm}^{E} = 4.9

and

γ_{therm}^{A} = 2.9

. Inserting these values into Eq. (5) we calculate the coefficients to be Δω_E = −0.0134 cm⁻¹/K and Δω_A = −0.0195 cm⁻¹/K. This suggests upon melting the bismuth E_g and A_1g first-order modes should experience a total redshift of approximately −3.7 cm⁻¹ and −4.8 cm⁻¹, respectively.

Figure 5 displays the temporal analysis from fits made to all spectra measured in the droplet oxidation shown in Fig. 4 and is separated into three time intervals, as interpreted by the Raman data. Figure 6 displays the estimated Bi droplet temperature using the measured two first-order Bi optical phonon peak frequency shifts and Eq. (6). Early in the reaction the two temperature determinations are very different and extrapolating backward in time to t = 0 s for the A_1g phonon yields a temperature of approximately 350 K, which is larger than the expected 300 K. A small initial redshift offset in the A_1g phonon can be attributed to the altered dynamics of bismuth in response to a relatively high incident fluence [53]. In general, the analysis of the A_1g phonon peak frequency using Eq. (6) yields a reasonable account of the changes in temperature leading up to oxidation; increasing from just above room temperature to the melting point of bismuth.

Fig. 5 Temporal results from fitting all spectra measured during the laser-induced oxidation reaction shown in Fig. 4. Values of Raman peak frequency shifts are shown for (a) bismuth modes, and (b) β-Bi₂O₃ modes. Measured Raman peak intensities are shown for (c) bismuth modes, and (d) β-Bi₂O₃ modes. Data is broken into three time intervals which are indicated across the top time axis. The broken vertical line at ∼200 s separates time intervals t₁ and t₂ and indicates observation of β-Bi₂O₃ Raman modes, t_oxi.

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Fig. 6 (a) Local bismuth temperature determined using Eq. (6) for both E_g and A_1g wavenumber shifts. The broken vertical line represents time of bismuth oxidation, t_oxi, while the dashed horizontal line indicates the bismuth melting temperature. Inset presents A_1g peak intensity as a function of temperature with a linear fit made to data acquired prior to thermal runaway. (b) Ratio $I_{A}^{(2)} / I_{A}^{(1)}$ of second- to first-order scattering intensities. Inset shows $I_{A}^{(2)} / I_{A}^{(1)}$ as a function of temperature for t <t_oxi with a linear fit acting as an aid for the eye. The temperature basis used in both insets was calculated using Eq. (6) and A_1g phonon shifts.

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On the other hand, a practical application of Eq. (6) in micro-Raman experiments must take into account the degeneracy of the E_g band. Initial laser heating sets up large local temperature differentials and strain-induced symmetry changes lift the double degeneracy of E_g. The E_g linewidth was measured to be approximately 9 cm⁻¹ during the whole reaction, changing very little throughout. This value is much larger than that reported by Höhne et al. [47], even at elevated temperatures (∼4–6 cm⁻¹), reflecting the large splitting in the two degenerate E_g phonons. Moreover, while the E_g band is redshifted to lower frequencies it becomes partially truncated by the Rayleigh filter. Thus the temporal analysis of the E_g modes in Fig. 5 is included only for completeness and we therefore use the temperature estimates determined from shifts in the A_1g phonon (before oxidation) as a basis to the data plotted in the insets of Fig. 6(a) and 6(b).

3.3.2. Laser-induced bismuth microdroplet oxidation kinetics

Time interval t₁

Linear (or non-linear) mechanisms of photon absorption occur on the Bi droplet surface which raises local temperatures. In relation to Fig. 5, the initial rate of energy absorption and subsequent temperature increase is linear, causing bismuth first-order (and second-order) Raman peaks to intensify and redshift. At approximately t = 160 s the laser heating is accelerated to melting point through a thermal runaway effect. The small bandgap of bismuth gives rise to a relatively large population of intrinsic carriers which will, by their very nature and composition, exhibit free-carrier absorption. The tipping point is defined by the rate of phonon redshifting; it changes from linear to nonlinear and occurs at ω_A = 95.3 cm⁻¹ (2.86 THz), corresponding to approximately T = 440K using Eq. (6). This value appears fairly constant when compared to results obtained from laser-induced oxidations of different sized droplets (data not shown), and regardless of laser intensity. Examining the varied Bi oxidation studies in the literature we make the observation that a thermal runaway study of bismuth is yet to be reported, preventing comparison.

The rise in Raman scattering intensity can be evaluated through the rate of Stokes scattering R_S = A_S[n(ω) + 1], where n(ω) is the population of frequency ω phonons at lattice temperature T and given by the Plank distribution n(ω) = 1/(e^ħω/k_BT − 1). Thus we have

R_{S} = \frac{A_{S}}{1 - e^{- ℏ ω / k_{B} T}},

where k_B is Boltzmann’s constant. The rate of Stokes scattering R_S is proportional to A_S, which includes optical parameters such as Raman susceptibility, which depend on wavelength and temperature. If we simply consider A_S to be independent of T, the value of dA_S/dT should be roughly constant for temperatures well above 0 K. This suggests deviations from linearity arise due to temperature dependencies in A_S when exciting with constant 632.81 nm (473.8 THz) laser light.

Renucci et al. [54] have closely examined the bismuth Raman scattering cross-section for E_g and A_1g phonons as a function of excitation frequency and determined that for 632.81 nm (HeNe; 1.96 eV, 473.8 THz) excitation the scattering cross-section is off resonance and resides low on the high-energy shoulder of the E₂ transition peak (∼1.6 eV). An increase in temperature would only lower the energy of E₂, rather than increase it, and thus reduce the Raman cross-section when using 632.81 nm (473.8 THz) excitation. From the inset of Fig. 6(a), however, we observe the A_1g scattering intensity increases away from a linear relationship with higher temperatures. The departure from linearity coincides with the beginning of the thermal runaway effect (at ∼ T = 440K), accelerating the energy transfer. A pronounced shift in the concentration of free electrons at this temperature can account for both observations. Increases in laser heating reflect an enhancement of photon absorption and their conversion into heat energy, through free-carrier absorption. Likewise, the electron-phonon contribution of A_S in Eq. (7) for A_1g modes is large; the A_1g phonon corresponds to a vibration of different crystal planes with respect to each other and produces a strong coupling between phonons and electrons [47, 54].

For contrast, we examine the measured ratio of second- to the first-order scattering intensities $I_{A}^{(2)} / I_{A}^{(1)}$ for bismuth in Fig. 6(b) as a function of exposure time and spectrally derived temperature (Fig. 6(b) inset). The initial value measured near room temperature is similar to that reported by Lannin et al. [41] for a comparable excitation frequency (647.1 nm, 463.3 THz). The value of $I_{A}^{(2)} / I_{A}^{(1)}$ is seen to steadily increase over time with rising temperatures. These observations of higher-harmonic behavior discount the notion of dramatic changes in system anharmonicity having any influence over the observed thermal runaway, leading into laser-induced oxidation.

Time interval t₂

The time of initial oxidation is represented in Fig. 5 by t_oxi and the broken vertical line at t = 204 s. In the liquid phase, the bismuth droplet reacts with ambient oxygen forming Bi₂O₃ molecules that dissociate and adhere to the droplet surface. They then establish nucleation sites and form weak Bi-O stretches in the Raman spectra. The temporal frequency of the new oxide modes appear to harden strongly during the oxidation reaction (see Fig. 5(b)). Just after nucleation the newly-formed β-Bi₂O₃ is relatively free from the pressures of a large oxide network. As the oxide grows, it builds internal pressure which reduces bond lengths and manifests as mode hardening. The speed at which the vibrations stiffen is related to the rate of growth for the oxide layer. A purely empirical interpretation of metal-oxide stretching frequencies is related to the Bi-O bond length d (in units of Å) by

ω_{Bi - O} = L \times exp (- N d),

where L and N are fitting parameters. Using experimental results of Raman stretching frequencies and crystallographic bond length, Hardcastle et al. [45] determined L and N to respectively be 92 760 cm⁻¹ and 2.511 Å⁻¹. A calculation reveals a relative change in the bond lengths over the hardening period of 0.22% and 0.27% for A_β and B_β mode frequencies, respectively. This agrees, at least qualitatively, with a non-linear bonding potential. As the oxidation progresses the increase in Raman signal from β-Bi₂O₃ slows whereby further oxidation reactions can only proceed by solid-state diffusion of reactants through the oxide. The scale thickness determines the absorption which leads to a temperature decrease in the bismuth – inferred from Bi optical phonon blueshifting – and further reduces the chemical reaction rate. Our measurements of A_1g intensity appear to grow continually through t_oxi. This is simply due to an overlap of the β-Bi₂O₃ and Bi Raman spectra, with Bi-Bi vibrations within the oxide contributing to a similar frequency which is difficult to resolve.

Time interval t₃

The rate of new oxide formation dramatically slows and, towards 1800 s, effectively ceases. The frequency and intensity of the bismuth modes in Fig. 5 flatten out and stabilize, though small temperature fluctuations manifest as small variations in the quantities; the process settles into an approximately equilibrium state.

3.3.3. Modeling of bismuth microdroplet oxidation reaction

The purpose of oxidation experiments is generally to assess the reaction kinetics and the mechanisms of oxidation of the metal (or alloy) under a particular set of exposure variables. We perform here analysis for a single oxidation reaction under ambient conditions (reaction displayed in Fig. 4), although this could readily be extended to include changes in environmental conditions. Because the Raman scattering cross-section is proportional to the total scattering volume, the evolving Raman peaks allow a direct measure of oxidation in real-time and can be used to analyze the reaction. Therefore we replot the measured temporal intensity of B_β band in Fig. 7 for detailed treatment.

Fig. 7 Degree of Bi droplet oxidation obtained from normalized B_β Raman intensity vs time t. The inset shows the Avrami plot ln[−ln(1−X(t))] vs ln(t) of the data plotted with corresponding Avrami exponent as derived from the gradient value. Two separate regimes of the Avrami plot are fitted using n₁=4 and n₂=1 (dashed horizontal lines).

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Parabolic oxidation equations are often used for metallic surfaces exposed to high temperatures and free oxygen, with solid-state migration across the scale being the rate-controlling process. However, a parabolic oxidation rate does not describe our data (see Fig. 7; the data does not trend parabolically) because of two system factors: (i) While laser heating propels the Bi droplet toward melting point, the surface rapidly cools soon after and forms a protective scale which effectively blocks the radiation required to sustain the oxidation reaction. (ii) Bismuth microislands provide limited Bi reactants which, in turn, also controls rate.

Our data exhibits an initially rapid reaction rate which quickly slows and looks typical of metal surface oxidizing under exposure to relatively low temperatures. This behavior is reflective of the factor (i) and is usually found to conform to rate laws described by logarithmic functions. The interpretation of the logarithmic laws are based on the adsorption of oxygen reactants on the metal surface and the forming of an extremely well-defined metal/oxide interface [55]. Beyond 800 s, however, the reaction is no longer logarithmic as it asymptotically approaches its maximum final volume. This behavior is indicative of the phase transformation kinetics of solids (crystallization), as both are strongly limited by the availability of reactants. The universal method to describe nucleation to coalescence of thin films is the Johnson-Mehl-Avrami-Kolmogorov (JMAK) theory [56–58], which has been successfully applied to describe the oxidation kinetics of metallic systems [59]. The JMAK theory presumes that the transformed volume fraction X(t) will follow an exponential dependency on time

X (t) = 1 - exp [- k {(t - t_{oxi})}^{n}] .

Here t is time, and k and n are fit parameters that depend on the surface mechanisms of transport, nucleation, and growth. By theoretical considerations, the Avrami exponent n acquires an integer or half integer value in the range 0.5 to 4, depending on the dimensionality of the transformation and is defined as the local slope in a double logarithmic Avrami plot ln[−ln(1−X(t))] vs ln(t). A nonconstant Avrami exponent as a function of time can be considered as a deviation from normal JMAK behavior.

In relation to our data, we assume that the integrated Raman intensity of mode B_β – chosen for its relatively strong Raman signal – is proportional to the volume of transformed β-Bi₂O₃ material within the Raman microprobe. The intensity of B_β has been normalized in Fig. 7 with corresponding Avrami plot and exponent data presented in the inset. The Avrami plot reveals a time-dependent Avrami exponent with two clear regimes, transitioning from n = 4 to n = 1, which is used for two separate linear fits of the data. An initial Avrami exponent of n₁ = 4 suggests, based on nucleation theory, the transformation is tri-dimensional and interface controlled with a decreasing number of nucleation sites. After a well-defined critical time, the Avrami exponent transitions to n₂ = 1, describing a bi-dimensional reaction with nucleation site saturation which is diffusion controlled. Interpreting the oxidation reaction using JMKA theory here appears to yield a reasonable reconstruction of the evolving surface dynamics, suggesting it could prove useful under more elaborate environmental conditions.

4. Conclusion

In conclusion, we have performed real-time in situ studies of laser-induced oxidation of GaAsBi bismuth surface droplets by means of Raman microprobe analysis. The synthesized oxide microisland is β-Bi₂O₃, which exhibits phase stability at room temperature. Spectra acquired at fixed time intervals during the oxidation yield insights into laser-induced bismuth oxidation kinetics and permit the meaningful interpretation of oxidation dynamics within JMKA theory. In terms of engineering practical Bi₂O₃ elements, the level of control over local β-Bi₂O₃ synthesis demonstrated here is favorable to the exacting preparation of functional materials at the micron scale.

Acknowledgments

The authors would like to thank Prof. Shui-Qing Yu and Prof. Greg Salamo from the University of Arkansas for providing the sample used in this study. We are also grateful to Prof. M. Henini for assistance in furthering this work. We thank the Australian Research Council and the University of Wollongong for support.

References and links

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Laser-induced oxidation kinetics of bismuth surface microdroplets on GaAsBi studied in situ by Raman microprobe analysis

Abstract

1. Introduction