Electron Diffraction Studies of Structural Dynamics of Bismuth

Article pubs.acs.org/JPCC

Electron Diffraction Studies of Structural Dynamics of Bismuth Nanoparticles Ahmed R. Esmail,† Aleksey Bugayev, and Hani E. Elsayed-Ali* Department of Electrical and Computer Engineering and the Applied Research Center, Old Dominion University, Norfolk, Virginia 23529, United States ABSTRACT: The lattice response of bismuth nanoparticles to femtosecond laser excitation is probed by ultrafast electron diffraction. The transient decay time after laser excitation is observed to be longer for diffraction from the (012) lattice planes compared to that from (110). From the position of the (012) diffraction peak, a transient lattice contraction due to hot electron blast force is observed over several picoseconds followed by expansion while the position of the (110) peak shows only expansion. The diffraction peak width indicates partial disorder of the nanoparticles consistent with formation of a liquid shell as the lattice is heated.

1. INTRODUCTION Advances in ultrafast X-ray and electron diffraction have made it possible to probe the structure of matter as it undergoes excitation and phase transitions initiated by ultrafast laser pulses.1−7 In semiconductors, the excitation of valence electrons into the antibonding conduction band weakens its covalent bonding, causing expansion due to increased repulsive interactions among atoms.8 For free electron metals such as aluminum, excitation of hot electrons does not appear to affect the lattice stability.9 The lattice is only affected by electron− phonon collisions. For crystals that are stabilized by the Peierls−Jones mechanism, such as for Bismuth, femtosecond laser excitation shifts the minimum of the potential energy surface toward a non-Pierls distorted state and causes displacive excitation of coherent phonons of the symmetric A1g mode.2 Softening of the lattice is detected as a downward shift in the frequency of the A1g oscillations.10 Here, we report on ultrafast electron diffraction (UED) studies of the lattice response of Bi nanoparticles to femtosecond laser excitation. By measuring the Bragg angle, a transient lattice contraction along the ⟨012⟩ direction is observed over several picoseconds followed by expansion, while along the ⟨110⟩ direction only expansion is detected. This lattice dynamics are thought to be due to hot electron kinetic pressure. The anisotropy in the transient decay time after laser excitation, which is observed to be longer for diffraction from the (012) lattice planes compared to the (110), could be related to sensitivity of the (012) diffraction order to the optically induced distortion of the structure factor due to the Peierls interaction and subsequent lattice relaxation or could indicate a different directional-dependent mechanism for energy transfer. Bismuth (Bi) crystallizes in the α-arsenic, A7, structure.11 Its lattice can be derived from face-centered-cubic structure with a weak rhombohedral distortion. That unit cell has two atoms: one on a lattice site, while the other is slightly displaced from the center along the trigonal axis. This configuration is © 2013 American Chemical Society

stabilized by the Peierls mechanism, which introduces a narrow bandgap over the Brillouin zone and renders Bi as a semimetal.12 When Bi is excited by an ultrashort laser pulse, the equilibrium distance of the two basis atoms is perturbed, initiating damped oscillations of the Bi atoms.1,2,10,13−16 The induced coherent atomic motions along the trigonal axis result in the widely observed, totally symmetric A1g coherent optical phonons. Bi has a very small electron effective mass, large mean-free path (∼100 nm at 300 K), highly anisotropic Fermi surface, and small energy overlap between the L-point conduction band and the T-point valence band of ∼38 meV, making bulk Bi a semimetal.17 When the electrons are confined in nanowires or nanoparticles, the electronic energy states split into sub-bands due to the transverse momenta of the electrons becoming discrete and a small indirect bandgap develops.17 A semimetalto-semiconductor transition was observed for Bi nanowires when the diameter is reduced to ∼50 nm.18 Excitation of Bi by ultrashort laser pulses changes the equilibrium atomic positions within the unit cell by displacive excitation of coherent phonons of the A1g mode. The photoexcited carriers generate nonequilibrium electron distribution that changes the lattice bonding. The Bi crystal begins to oscillate around a new lattice position. The main mechanism for the relaxation of the A1g coherent phonons in Bi is damped by phonon−phonon interaction.19 The carrier relaxation time and the damping time of the A1g phonons were found to depend on size and defect level. For a polycrystalline Bi film, these times were both ∼4.1 ps. The carrier relaxation time was shorter at 2.8 ps in the Bi single crystal, while the A1g phonons’ damping time was about the same as for the polycrystalline sample.19 Received: February 23, 2013 Revised: April 6, 2013 Published: April 9, 2013 9035

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2. EXPERIMENT We used UED to probe the lattice response of Bi nanoparticles to femtosecond laser excitation. In UED, an ultrashort laser pulse is split into two; one interacts with the sample, while the other laser pulse generates a synchronized electron pulse that is diffracted from the sample. An electron gun20,21 was used to produce electron pulses by photoemission from silver thin film photocathode excited by frequency-tripled femtosecond (110 fs duration, 800 nm wavelength, at 1 kHz repetition rate) laser pulses. The gun was operated at an acceleration voltage of 35 keV. The electron bunches were collimated and directed toward the sample by a set of electromagnets located outside the vacuum chamber. The measured full width at halfmaximum (fwhm) of the excitation laser beam at the sample was 2.0 ± 0.1 mm while that of the electron beam is 0.75 ± 0.05 mm. The Bi nanoparticles were exposed to the fundamental 800 nm wavelength at a fluence up to ∼3.8 mJ/ cm2. The laser pulses exciting Bi (pump) were p-polarized and incident on the sample at 45°. The time delay between the laser pump and the electron probe was introduced by an optical delay stage located in the path of the probe to control the arrival time of the probe electron pulse to the sample with respect to the pump laser pulse. The temporal resolution of the UED setup is better than 2 ps at the photocathode excitation level used. This was confirmed by performing the time-resolved experiment on 20 nm free-standing Al film in which the lattice thermalization time was measured and showed good agreement with that reported previously.22 A microchannel plate proximity focused to a phosphorus screen is used for diffraction pattern detection, while a computer-controlled charge-coupled device camera is used to capture the diffraction pattern for analysis. The UED system is operated in an ultrahigh vacuum (low 10−9 Torr). Bi film of 5 nm average thickness was grown by thermal evaporation on 3 mm copper transmission electron microscopy (TEM) grids coated with

phonon energy exchange time. To take into account the electron blast force, the initial conditions for the differential equation have to satisfy the conditions X(0) = a ≥ 0 and X′(0) = b ≥ 0. These conditions imply that at the maximum amplitude of the exciting laser pulse (τ = 0) the atom can stay close to or leave the initial equilibrium position (X(0) = a ≥ 0) and possesses a certain speed X′(0) ≥ 0, which is caused by the compressing hot-electron blast force. Figure 3 shows the

0⎞ ⎟ 0⎠

where A and B are the fitting parameters and gives τ = 9.2 ± 1.1 and 7.5 ± 1.0 ps, respectively. The data in Figure 2 were obtained for a pump laser fluence of ∼2.9 mJ/cm2. When the pump laser fluence was reduced to ∼2.1 mJ/cm2, the decay time τ was 10.5 ± 1.1 and 7.9 ± 1.0 ps for the (012) and (110) diffraction orders, respectively. The error reported accounts for measurements taken over four different runs conducted on three different samples which were all fabricated using the same procedure. The differences in the absolute value of the decay time from one run to another are mainly related to the sample size and size distribution since the deposited film coverage is 5 ± 1 nm, which is then processed to produce the nanoparticles. For each experimental run, τ was always longer for the (012) diffraction order compared to the (110). Also, the observation that the decay time τ is larger for the (012) diffraction order compared to the (110) was consistent at all laser fluencies studied (∼2.0−2.9 mJ/cm2), and this observation was also made for Bi 5 nm thin film in the form of flat islands.21 This could be a result of anisotropy in energy transfer from excited carriers and coherent phonons to the lattice. The decay time τ is affected by the different relaxation processes following femtosecond laser photoexcitation.36 Lattice excitation occurs through carrier thermalization by electron−phonon and phonon−phonon interactions. Electron−hole recombination causes charge carrier removal. Electron−phonon interaction in metals is usually considered isotropic. However, Bi has a highly anisotropic Fermi surface, and its electron−phonon coupling cannot be described by the isotropic Eliashberg spectral function α2F(ω), which includes the energy of the phonon modes and their coupling strength.37 For Bi, the Eliashberg spectral function is isotropic. Moreover, for femtosecond laser excitation, it is also time-dependent due to lattice distortion by electronic excitation. The longer τ observed for the (012) peak is probably due to the directiondependent nature of the structure factor, F(h,k,l), which is given by2 F(h,k,l) = 2f Bi cos[π(h + k + l)x] and x = 0.5 ± δ, where f Bi is the Bi atomic scattering factor, x is the normalized equilibrium coordinate in the hexagonal unit cell length c, and δ is a measure of the Peierls distortion. The intensity of the diffracted electron beam is directly related to the structure factor through I(h,k,l) ∝ |F(h,k,l)2|; therefore, the generation of coherent optical phonons and their subsequent decay into acoustic phonons can affect the equilibrium coordinate x and consequently the structure factor. The (110) planes are parallel to the trigonal axis, and therefore, diffraction from these planes is not sensitive to A1g oscillations or their decay into coherent acoustic phonons oscillating along the trigonal axis. However, the (012) peak is sensitive to oscillations along the trigonal axis. The decay of A1g oscillations into coherent acoustic phonons and the subsequent relaxation of these coherent phonons into the phonon bath could also contribute to the anisotropy in decay time. The unperturbed phonon energy ∼ 1.17 × 10−3 eV,38 and the acoustic phonon generation resulting from the decay of A1g was previously studied.7,39 The observed τ is longer than those for Bi thin films,7,21 which is consistent with reduced electron−phonon coupling in Bi nanoparticles due to their semiconducting nature. To estimate the final lattice temperature, we used the normalized diffraction intensity level near the end of the

Figure 3. Numerical fit of the hot electron blast model (solid line) to the experimental data (closed circles) of the relative change in diffraction ring radius Δr(t)/r0 of the (012) order after FFT filtering.

numerical fit of the solution of the equation of driven harmonic oscillator to the experimental data of the relative change in diffraction ring radius Δr(t)/r0 of the (012) order after FFT filtering. From this fit, τe−ph = 7.4 ps, while the ratio of Grüneisen parameters γe/γl = 0.6. Because of the spread of nanoparticle sizes, shown in Figure 1, the observed oscillations result from summation of a large number of modes, which its frequencies are inversely proportional to nanoparticles radius:34 ∑RCR cos[ω0,0(R)t − φ], where ω0,0(R) is the breathing mode frequency and R is mode number. Increasing the number of modes leads to decreasing time in which coherent oscillation can be observed. The general features of lattice compression followed by expansion are well described by the electron blast force model. The time-resolved, normalized diffraction intensity of the (012) and (110) Bragg peaks is shown in Figure 2. The decay time of the normalized intensity τ depends on the laser fluence and the diffraction order. The use of the Debye−Waller treatment to obtain transient lattice temperature was proposed many years ago.35 The Debye−Waller treatment is generally considered valid in UED experiments as a measure of the mean vibrational amplitude;3−5 however, defining a temperature is valid only when the phonon distribution has reached equilibrium. UED measurements of the decay of coherent acoustic phonons in Bi film show a decay time of 40−50 ps,5 which is 4 times longer than for optical phonons.19 Therefore, the time required for the phonons to reach equilibrium in the Bi film is longer than ∼50 ps for the experimental conditions used. From Figure 2, the decay time τ is observed to be longer for diffraction from (012) lattice planes compared to (110). The decay time τ is obtained from a single exponential fit to the normalized diffraction intensity I(t)/I0 based on 9039

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compression is followed by expansion and oscillations in the Bragg peak position indicative of lattice motion in the nanoparticles with some coherence limited mainly by the naoparticle size distribution. The transient decay time after laser excitation is longer for diffraction from the (012) lattice planes compared to that from (110) which results from anisotropy in laser energy coupling in Bi. The increase in diffraction peak width with time indicates partial disorder of the nanoparticles consistent with formation of a liquid shell with lattice heating. These results show that melting of Bi nanoparticles with ultrafast lasers involves surface effects, at least for the lower excitation fluencies.

pump−probe scans in Figure 2 and the dependence of the normalized Bragg intensity of the (110) peak with temperature measured on a similar ensemble of Bi nanoparticles that we studied under continuous heating on a thermally heated stage.40 The lattice temperature established at the end of the scan for the 2.9 mJ/cm2 femtosecond laser fluence is ∼515 K. Surface melting of the Bi nanoparticles occurs at this temperature.40 Figure 4 shows the normalized full width at half-maximum (fwhm) of the (012) diffraction order at time delay of 27 ps.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Present Address †

A.R.E.: Also with Physics Department, Cairo University, Cairo, Egypt. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This material is based upon work supported by the US Department of Energy, Division of Material Science, under Grant DE-FG02-97ER45625 and the National Science Foundation under Grants MRI-0821180, and NIRT-0507036. TEM images were obtained by Dr. Wei Cao.

Figure 4. Normalized diffraction width change (fwhm) of the (012) diffraction order measured at time delay of 27 ps for different laser fluences. Inset: change in (012) Bragg peak diffraction width as a function of delay time for a laser fluence of 2.0 ± 0.1 and 2.9 ± 0.15 mJ/cm2. The increased fwhm is consistent with developing a liquid shell around the nanoparticles.

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REFERENCES

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The behavior of the (110) order was similar in shape. The increase in fwhm indicates a reduction in size of the probed nanoparticles. We have previously observed increased diffraction width in Bi nanoparticles under continuous heating, and this was attributed to formation of a liquid shell around the nanoparticles.40 The results in Figure 4 show that some disorder, probably the formation of a liquid shell, is occurring at a fluence of ∼2 mJ/cm2 and increases with the laser fluence. The inset in Figure 4 shows the temporal development of the fwhm, which shows that the diffraction width reaches a plateau at a time that is reduced with the laser fluence and is ∼15 ps after the laser pulse for a fluence of 2.9 ± 0.15 mJ/cm2. The fwhm remains constant up to the maximum probed time, ∼90 ps. This observation is consistent with the formation of a stable liquid shell that persists in time due to the slow heat diffusion out of the Bi nanoparticles that are deposited on the carboncoated grid. Stress-induced effects on the diffraction width are not expected to behave that way since the stress decays in a few tens of picoseconds,24 whereas the data in Figure 4 (inset) show the persistence of the increase in diffraction width for more than 90 ps. For time < 0, the standard deviation for the diffraction widths of the (012) order is 0.0341 and 0.0242 for the laser fluences of 2.9 ± 0.15 and 2.0 ± 0.1 mJ/cm2, respectively.

4. CONCLUSION Ultrafast electron diffraction studies of femtosecond laser excited Bi nanoparticles show a transient lattice contraction over several picoseconds due to hot electron blast force in nanoparticles with sizes larger than the laser skin depth. This 9040

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