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Ultrafast electron diffraction at surfaces after laser excitation
Surface Science 600 (2006) 4094–4098 www.elsevier.com/locate/susc
Ultrafast electron diffraction at surfaces after laser excitation A. Janzen, B. Krenzer *, P. Zhou, D. von der Linde, M. Horn-von Hoegen Fachbereich Physik, Universita¨t Duisburg-Essen, Lotharstraße 1, 47048 Duisburg, Germany Available online 8 May 2006
Abstract Ultrafast electron diffraction in a RHEED setup is used to determine the dynamics of surface temperature of an epitaxial thin Bismuth-film on a Si(0 0 1) substrate upon fs-laser excitation. A transient temperature rise by 120 K is followed by a slow exponential cooling with time constant 640 ps. The surface cooling rate deviates from simple heat diffusion and is dominated by total internal reflection of ballistic phonons at the Bi/Si-interface which determines the thermal properties of the hetero-system. 2006 Elsevier B.V. All rights reserved. Keywords: RHEED; Time-resolved diffraction; Energy dissipation; Silicon; Bismuth; Heteroepitaxy; Thermal boundary conductance
The study of ultrafast dynamics subsequent to fslaser pulse excitation reveals insight into the fundamental processes of electron–electron, electron–phonon and phonon–phonon scattering. Up to now the main effort was focused on the ultrafast dynamics of the electron system and its coupling to the phonon system [1–4]. These processes occur on a timescale of a few fs to ps which is accessible by means of time-resolved photoelectron emission spectroscopy in an optical pump–probe setup. The response of the crystal lattice upon the excitation of the electron system, however, requires probes sensitive to structural changes such as X-ray or electron diffraction. The recent progress in time-resolved diffraction techniques allowed the observation of lattice dynamics even on the fs-timescale. Instead of using an optical probe pulse, short X-ray or electron pulses are used as probes subsequent to a laser pump pulse. This allowed a straightforward observation of the excitation of coherent lattice vibrations [5,6] or the dynamics of non-thermal melting [7,8]. Application of time-resolved diffraction studies to surfaces, however, requires a probe with large scattering cross section to ensure high surface sensitivity which leaves
*
Corresponding author. E-mail address: [email protected] (B. Krenzer).
0039-6028/$ - see front matter 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.susc.2006.02.070
electrons as ideal candidates. Electron pulses are scattered at the surface, and the resulting diffraction pattern reflects the surface morphology [9] and structure of the surface unit cell [10]. Changes of the diffraction pattern upon systematic variation of the time delay between the laser excitation (pump) and the subsequent electron pulse (probe) yields insight into the temporal evolution of the surface structure [11–15]. Due to their vacuum dispersion and inherent electrostatic repulsive interaction the use of fast, i.e., high energy electrons, is indispensable for this experiment which makes a setup in a RHEED scattering geometry necessary to ensure surface-sensitivity. In addition the intensity of the diffraction spots is directly related to the atoms’ motion and therefore to the lattice temperature via the Debye–Waller-factor ! ~2 IðT Þ h2 jKj ¼ exp ðT T 0 Þ ð1Þ IðT 0 Þ mk B h2D ~ the Planck and Boltzmann with the momentum transfer K, constant h and kB, and the mass m of the surface atoms. The Debye-temperature hD is characteristic for a particular solid and is related to its maximum phonon frequency. It is evident from Eq. (1) that the Debye–Waller-effect, i.e., the drop of intensity, is more pronounced for large momentum transfers and small Debye-temperatures.
A. Janzen et al. / Surface Science 600 (2006) 4094–4098
Recording the intensity of the RHEED spots and utilizing Eq. (1) the transient surface temperature could be determined in a surface-sensitive time-resolved experiment [15]. Due to the direct connection of diffraction spot intensity with atomic motion (which is directly linked to the temperature) electron diffraction is in advantage to timeresolved thermoreflectance where the surface temperature is assumed to be linearly related to the reflectivity [16]. In addition, electron diffraction is not restricted to a small temperature interval but can usually be applied over a large temperature range. In this paper we present results on the transient surface temperature of a thin Bi-film upon excitation by fs-laser pulses studied by means of time-resolved electron diffraction. For the first experiments with our new ultrafast-electron diffraction apparatus (UED) [17] a Bi-surface was chosen which exhibits one of the lowest Debye-temperatures with hD = 119 K for the bulk crystal [18]. Thus we expect significant intensity drops due to the small Debye– Waller-factor even for small temperature jumps. The setup of the UED experiment is sketched in Fig. 1. To excite the surface we use near-IR 800 nm fs-heating pulses at a repetition rate of 1000 Hz with an energy of 0.45 mJ and a spot diameter of 4 mm on the sample. Electron pulses are generated by photoemission from a Auphotocathode on a sapphire substrate by back-illumination with a frequency-tripled fs-laser pulse with a photon energy of 4.65 eV [17]. The electrons are accelerated by an extraction field of 2.5–5 kV/mm to an energy of 5–10 keV and focused by an electrostatic Einzel-lens onto the detector. The sample was mounted on a liquid He cryostat on a goniometer with three degrees of freedom in translation and two axes of rotation. A grazing incidence of 4–7 ensures surface sensitivity with a vertical momentum transfer of
Fig. 1. Setup of the ultrafast electron diffraction experiment.
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˚ 1 for the specular spot. The time delay between 5–12 A laser and electron pulse was varied by an optical delay line from 500 ps to 3000 ps. The diffraction patterns were recorded by a cooled CCD camera after image intensification by a microchannel plate. The experiments were performed under ultra-high vacuum conditions. Clean Si(0 0 1) samples were prepared in situ by a short flash to 1200 C to remove the native oxide. This results in a well ordered surface with a (2 · 1)-reconstruction (Fig. 2(a)). Epitaxial Bi(0 0 0 1) films have been grown in situ by deposition at room temperature from a Knudsen-cell and slightly annealed to 400 K to improve the film quality. The thickness of the Bi-film was determined by a calibrated quartz crystal microbalance. The resulting LEED-pattern of a 5.5 nm Bi-film, shown in Fig. 2(b), exhibits a 12-fold symmetry. All occurring spots are explained by the superposition of two hexagonal domains rotated by 90 (unit cells are indicated in the image). The appearance of the two orientations is caused by
Fig. 2. (a) LEED-pattern at 100 eV of the bare Si(0 0 1)-(2 · 1) surface after flashing to 1200 C (linear scale). (b) LEED-pattern at 100 eV after Bi-deposition at room temperature followed by a slight anneal to 400 K (logarithmic scale). The 12-fold symmetry is explained by the superposition of two hexagonal domains rotated by 90. It is evident that Bi grows in (0 0 0 1)-orientation. (c) RHEED pattern of the sample taken at 5.5 keV electron energy (logarithmic scale). (d) Temperature dependence of the (0 0)-spot intensity at 5.5 keV. The exponential fit according to the Debye– Waller-effect yields a surface Debye-temperature of 47 ± 5 K. (e) Dependence of the surface Debye-temperature on electron energy.
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the presence of the (2 · 1) and (1 · 2) dimer reconstructions ˚ is of the Si(0 0 1)-surface. A lattice constant of a0 = 4.43 A derived for the Bi-surface. This and the hexagonal symmetry is evident for Bi-growth in a (0 0 0 1)-orientation with an in plane lattice compression by 2.6% compared to bulk values [19]. Similar results have been previously observed for thin Bi-films grown on the Si(1 1 1)-surface [20]. The corresponding RHEED pattern of the sample exhibits sharp diffraction spots as shown in Fig. 2(c). The electron energy was 5.5 keV at an incident angle of 5 resulting in a perpen˚ 1 for the specular dicular momentum transfer K? = 6.63 A spot. In order to provide an unambiguous calibration the temperature dependence of the spot intensity was measured between 80 and 300 K in a stationary experiment where the sample holder was set to the desired temperature. After a couple of minutes the diffraction pattern was recorded allowing the sample to thermally equilibrate. The temperature was monitored by a thermocouple attached to the sample holder. The peak intensity of the (0 0)-spot is displayed in Fig. 2(d). Every data point was background subtracted and normalized to the value at 80 K. The intensity drops by 70% upon a temperature rise from 80 to 300 K and follows nicely the exponential decay expected from the Debye–Waller-effect. The solid line in Fig. 2(d) is a fit of Eq. (1) to the data points with hD as the only free parameter. We observed a Debye-temperature of hD = 47 ± 5 K, which is significantly lower than the bulk value, owing to the reduced coordination of the surface atoms. This result is in good agreement with previously reported values for single crystal Bi(0 0 0 1)-surfaces [14,21], which indicates that the finite thickness of the thin film has negligible or no influence on the Debye-temperature. According to Eq. (1), variation of the momentum trans~ leads to a tuning of the Debye–Waller-effect. Howfer K ever, this effect is partly lifted as can be seen in Fig. 2(e) where the dependence of the measured Debye-temperature on the electron energy for a constant scattering angle is plotted. The Debye-temperature increases almost linearly with increasing electron energy from 4 to 7 keV. This effect clearly shows the decreasing surface sensitivity for increasing electron energies due to the higher penetration depth of fast electrons. For large penetration depths the observed Debye-temperature approaches the bulk [21]. We will use the curve from Fig. 2(d) to convert time-dependent intensity drops subsequent to laser pulse excitation into the transient surface temperature of the Bi-film. Fig. 3(a) shows the normalized (0 0)-spot intensity as function of the pump pulse travel time for two data sets taken at different electron energies with a pump fluence of 1.3 mJ/cm2 at a base temperature of 80 K. For long pump pulse travel times the spot intensity remains constant (negative time delays). At 6250 ps for the 5.5 keV electrons and around 5750 ps for the 7 keV electrons a sharp intensity drop by about 40% is observed. The decrease in the intensity is associated with the temporal overlap of pump and probe pulse. The shift between both curves by 500 ps
Fig. 3. (a) Time-dependent normalized (0 0)-spot intensity for 5.5 and 7 keV electrons. The observed minimum shifts by 500 ps to shorter pump pulse travel times due to the increased electron kinetic energy. (b) Using the stationary Debye–Waller-factor from Fig. 2 the intensity drops for both curves are converted to a transient temperature rise. The delay t = 0 was set to the leading edge of the temperature rise. The surface temperature decrease is well described by an exponential decay with a time constant t = 640 ± 30 ps for both data sets.
is explained by the shorter travel time of the 7 keV electrons compared to the 5.5 keV electrons on the 200 mm distance between photocathode and sample. For longer time delays (shorter travel times) the (0 0)spot intensity recovers asymptotically in both data sets. Due to the long timescale the observed intensity behavior is attributed to the heating and cooling of the Bi-film rather than to a change in the structure factor as recently observed by X-ray diffraction on a fs-timescale [5]. From the measurement of the diffraction spot intensity with and without pump pulse at negative time delays we can conclude that any steady state heating by the intense laser pump pulse is below 10 K. Fig. 3(b) shows the surface temperature after conversion using the calibration curve from Fig. 2(d) and (e). For better comparability the time scale for both curves was set to t = 0 ps at the leading edge of the intensity drop. Within the statistical error both sets result in an equal transient
A. Janzen et al. / Surface Science 600 (2006) 4094–4098
temperature evolution for delays smaller than 1500 ps. The deviation for longer time delays may be due to a reduction of the electron intensity. However, the following discussion is based on the temperature decay which is given by the behavior at short delays and the deviation at long delays has a negligible influence in the determination of the decay time constant. Negative delays denote that the electron probe pulse arrives at the sample prior to the excitation with the laser pump pulse: the surface is not excited yet. At t = 0 ps a linear increase of the surface temperature by 120 K is observed. The rise time of 90 ps is due to the finite temporal resolution of the experiment which is dominated by the velocity mismatch and grazing incidence of electrons onto the sample as sketched in Fig. 4. In our experiment the pump pulse impinges at normal incidence resulting in the temporally simultaneous excitation of the entire width of the sample. Due to the grazing incidence, however, the electron pulses probe the sample at different time delays along the width of the sample. The diffracted electrons thus contain information of the surface temperature and structure, which is averaged over this probing time Dt which is determined by the electron velocity and incident angle. For a sample width of 4 mm as used in our experiment Dt = 90 ps and Dt = 80 ps is calculated for 5.5 keV and 7 keV electrons, respectively, which is in excellent agreement with the observed rise time of 90 ps. After reaching the maximum, the surface temperature decreases exponentially with a time constant of s = 640 ± 30 ps. Previous studies on bulk-single crystals of Bismuth have observed a surface cooling that was in accordance with thermal heat diffusion [14]. As the hyperbolic temperature decay expected for one dimensional heat diffusion [22] significantly differs from the observed exponential decay we have to conclude that the phonon transport from the thin Bi-film towards the Si-substrate is strongly altered compared to the bulk and is dominated by the Bi/Si-interface: the heat is trapped in the Bi-film and only leaks out slowly into the Si-substrate. It is well known that liquid–solid and solid–solid interfaces act as a barrier to thermal diffusion. The net heat flow Q_ per unit area across such an interface is given by
Fig. 4. Grazing incidence and velocity mismatch between pump and probe pulse. The electron and laser pulses travel at velocities ve and c, respectively. During the travel time Dt the electron pulse probes the surface.
Q_ ¼ rK DT ;
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ð2Þ
where the thermal boundary conductance rK relates the heat flow across the interface with the temperature discontinuity DT at the interface [16,23]. The solution of Eq. (2) for the film temperature is an exponential decay with time constant [16] s¼
Cqd : rK
ð3Þ
In Eq. (3) C and q are the specific heat and mass density of Bismuth and d the film thickness. In deriving Eq. (3) it was assumed that the temperature of the Si-substrate remains constant [24]. It is additionally assumed that the surface temperature represents the film temperature. From the observed time constant we extracted a thermal boundary conductance of rK = 1025 ± 193 W/(cm2 K). The thermal boundary conductance rK is fundamentally related to the transmission probability of phonons and electrons across the interface. The two simplest models for the calculation of rK are the acoustic mismatch model (AMM) and the diffusive mismatch model (DMM) [16,24]. Both models consider only phonons for the heat transport across the interface which can safely be assumed for the semimetal Bi. The AMM treats phonons as elastic waves that are reflected and refracted at a smooth interface without scattering. Calculation of the energy transfer of the transmitted waves is achieved by using the acoustic equivalent of the Fresnel equations in optics [25]. Because the velocity of sound in Si is 4–5 times larger than in Bi the vast majority of phonons in the Bi-film undergoes internal total reflection at the interface and is therefore trapped in the Bifilm. A thorough calculation yields a transmission probability CAMM = 0.13 which results in the thermal boundary conductance rAMM ¼ 1400 50 W=ðcm2 KÞ [27]. In conK trast, in the framework of DMM the phonons are considered to be strongly scattered at a rough or disordered interface. The transmission probability then only depends on the phonon density of states in the two media. This model yields CDMM = 0.14 and rDMM ¼ 1500 60 W= K ðcm2 KÞ [27]. Previously observed thermal boundary conductances were up to an order of magnitude larger than theoretically predicted which lead to the conclusion that a poor interface quality and inelastic effects have a major influence on rK. The AMM and DMM were therefore extended to describe the experimental findings [16,26]. Due to the preparation under UHV conditions the high quality of our epitaxial Bi-films together with an abrupt Bi/Si-interface leads to a much lower thermal boundary conductance in good agreement with the theoretical predictions. In conclusion, ultrafast electron diffraction in a RHEED setup has been applied for the determination of the transient surface temperature of a thin Bi-film deposited onto a Si(0 0 1)-surface upon fs-laser excitation. The cooling of the surface cannot be described by simple thermal diffusion but is well understood in terms of the thermal boundary
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conductance of the Bi/Si-interface. The high film and interface quality made it possible for the first time to test the models describing the thermal boundary conductance. In the near future ultrafast electron diffraction will be extended to study the transient structural properties of surfaces yielding new insights into the ultrafast processes subsequent to laser excitation. Acknowledgements The authors like to thank B. Rethfeld and M. Aeschlimann for fruitful discussions. This work was supported by the DFG through SFB 616 ‘‘Energy dissipation at surfaces’’. References [1] H.E. Elsayed-Ali, T.B. Norris, M.A. Pessot, G.A. Mourou, Phys. Rev. Lett. 58 (1987) 1212. [2] W.S. Fann, R. Storz, H.W.K. Tom, J. Bokor, Phys. Rev. Lett. 68 (1992) 2834. [3] M. Bonn, D.N. Denzler, S. Funk, M. Wolf, S.S. Wellershoff, J. Hohlfeld, Phys. Rev. B 61 (2000) 1101. [4] M. Weinelt, M. Kutschera, T. Fauster, M. Rohlfing, Phys. Rev. Lett. 92 (2004) 126801. [5] K. Sokolowski-Tinten et al., Nature 422 (2003) 287.
[6] A.M. Lindenberg et al., Phys. Rev. Lett. 84 (2000) 111. [7] B.J. Siwick, J.R. Dwyer, R.E. Jordan, R.J.D. Miller, Science 302 (2003) 1382. [8] A.M. Lindenberg et al., Science 308 (2005) 392. [9] M. Horn-von Hoegen, Z. Kristallogr. 214 (1999) 591. [10] K. Heinz, L. Hammer, Z. Kristallogr. 213 (1998) 615. [11] M. Aeschlimann et al., Rev. Sci. Instrum. 66 (1995) 1000. [12] Ch.-Y. Ruan, V.A. Lobastov, F. Vigliotti, S. Chen, A.H. Zewail, Science 304 (2004) 80. [13] X. Zeng, H.E. Elsayed-Ali, Phys. Rev. B 64 (2001) 085410. [14] E.A. Murphy, H.E. Elsayed-Ali, J.W. Herman, Phys. Rev. B 48 (1993) 4921. [15] H.E. Elsayed-Ali, J.W. Herman, Appl. Phys. Lett. 57 (1990) 1508. [16] R.J. Stoner, H.J. Maris, Phys. Rev. B 48 (1993) 16373. [17] A. Janzen, B. Krenzer, M. Horn von Hoegen, Rev. Sci. Instrum., submitted for publication. [18] Ch. Kittel, Einfu¨hrung in die Festko¨rperphysik, 12. ed. (R. Oldenburg, Mu¨nchen, 1999), 138. [19] F. Jona, Surf. Sci. 8 (1967) 57. [20] M. Kammler, M. Horn-von Hoegen, Surf. Sci. 576 (2005) 56. [21] R.M. Goodman, G.A. Somorjai, J. Chem. Phys. 52 (1970) 6325. [22] J.H. Bechtel, J. Appl. Phys. 46 (1975) 1585. [23] E.T. Swartz, R.O. Pohl, Rev. Mod. Phys. 61 (1989) 605. [24] B. Krenzer, A. Janzen, P. Zhou, D. von der Linde, M. Horn-von Hoegen, Phys. Rev. Lett., submitted for publication. [25] J. Miklowitz, The Theory of Elastic Waves and Waveguides, NorthHolland, Amsterdam, 1978. [26] R.J. Stevens, A.N. Smith, P.M. Norris, J. Heat Trans. 127 (2005) 315. [27] B. Krenzer, M. Horn-von Hoegen, in preparation.
Ultrafast electron diffraction at surfaces after laser excitation A. Janzen, B. Krenzer *, P. Zhou, D. von der Linde, M. Horn-von Hoegen Fachbereich Physik, Universita¨t Duisburg-Essen, Lotharstraße 1, 47048 Duisburg, Germany Available online 8 May 2006
Abstract Ultrafast electron diffraction in a RHEED setup is used to determine the dynamics of surface temperature of an epitaxial thin Bismuth-film on a Si(0 0 1) substrate upon fs-laser excitation. A transient temperature rise by 120 K is followed by a slow exponential cooling with time constant 640 ps. The surface cooling rate deviates from simple heat diffusion and is dominated by total internal reflection of ballistic phonons at the Bi/Si-interface which determines the thermal properties of the hetero-system. 2006 Elsevier B.V. All rights reserved. Keywords: RHEED; Time-resolved diffraction; Energy dissipation; Silicon; Bismuth; Heteroepitaxy; Thermal boundary conductance
The study of ultrafast dynamics subsequent to fslaser pulse excitation reveals insight into the fundamental processes of electron–electron, electron–phonon and phonon–phonon scattering. Up to now the main effort was focused on the ultrafast dynamics of the electron system and its coupling to the phonon system [1–4]. These processes occur on a timescale of a few fs to ps which is accessible by means of time-resolved photoelectron emission spectroscopy in an optical pump–probe setup. The response of the crystal lattice upon the excitation of the electron system, however, requires probes sensitive to structural changes such as X-ray or electron diffraction. The recent progress in time-resolved diffraction techniques allowed the observation of lattice dynamics even on the fs-timescale. Instead of using an optical probe pulse, short X-ray or electron pulses are used as probes subsequent to a laser pump pulse. This allowed a straightforward observation of the excitation of coherent lattice vibrations [5,6] or the dynamics of non-thermal melting [7,8]. Application of time-resolved diffraction studies to surfaces, however, requires a probe with large scattering cross section to ensure high surface sensitivity which leaves
*
Corresponding author. E-mail address: [email protected] (B. Krenzer).
0039-6028/$ - see front matter 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.susc.2006.02.070
electrons as ideal candidates. Electron pulses are scattered at the surface, and the resulting diffraction pattern reflects the surface morphology [9] and structure of the surface unit cell [10]. Changes of the diffraction pattern upon systematic variation of the time delay between the laser excitation (pump) and the subsequent electron pulse (probe) yields insight into the temporal evolution of the surface structure [11–15]. Due to their vacuum dispersion and inherent electrostatic repulsive interaction the use of fast, i.e., high energy electrons, is indispensable for this experiment which makes a setup in a RHEED scattering geometry necessary to ensure surface-sensitivity. In addition the intensity of the diffraction spots is directly related to the atoms’ motion and therefore to the lattice temperature via the Debye–Waller-factor ! ~2 IðT Þ h2 jKj ¼ exp ðT T 0 Þ ð1Þ IðT 0 Þ mk B h2D ~ the Planck and Boltzmann with the momentum transfer K, constant h and kB, and the mass m of the surface atoms. The Debye-temperature hD is characteristic for a particular solid and is related to its maximum phonon frequency. It is evident from Eq. (1) that the Debye–Waller-effect, i.e., the drop of intensity, is more pronounced for large momentum transfers and small Debye-temperatures.
A. Janzen et al. / Surface Science 600 (2006) 4094–4098
Recording the intensity of the RHEED spots and utilizing Eq. (1) the transient surface temperature could be determined in a surface-sensitive time-resolved experiment [15]. Due to the direct connection of diffraction spot intensity with atomic motion (which is directly linked to the temperature) electron diffraction is in advantage to timeresolved thermoreflectance where the surface temperature is assumed to be linearly related to the reflectivity [16]. In addition, electron diffraction is not restricted to a small temperature interval but can usually be applied over a large temperature range. In this paper we present results on the transient surface temperature of a thin Bi-film upon excitation by fs-laser pulses studied by means of time-resolved electron diffraction. For the first experiments with our new ultrafast-electron diffraction apparatus (UED) [17] a Bi-surface was chosen which exhibits one of the lowest Debye-temperatures with hD = 119 K for the bulk crystal [18]. Thus we expect significant intensity drops due to the small Debye– Waller-factor even for small temperature jumps. The setup of the UED experiment is sketched in Fig. 1. To excite the surface we use near-IR 800 nm fs-heating pulses at a repetition rate of 1000 Hz with an energy of 0.45 mJ and a spot diameter of 4 mm on the sample. Electron pulses are generated by photoemission from a Auphotocathode on a sapphire substrate by back-illumination with a frequency-tripled fs-laser pulse with a photon energy of 4.65 eV [17]. The electrons are accelerated by an extraction field of 2.5–5 kV/mm to an energy of 5–10 keV and focused by an electrostatic Einzel-lens onto the detector. The sample was mounted on a liquid He cryostat on a goniometer with three degrees of freedom in translation and two axes of rotation. A grazing incidence of 4–7 ensures surface sensitivity with a vertical momentum transfer of
Fig. 1. Setup of the ultrafast electron diffraction experiment.
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˚ 1 for the specular spot. The time delay between 5–12 A laser and electron pulse was varied by an optical delay line from 500 ps to 3000 ps. The diffraction patterns were recorded by a cooled CCD camera after image intensification by a microchannel plate. The experiments were performed under ultra-high vacuum conditions. Clean Si(0 0 1) samples were prepared in situ by a short flash to 1200 C to remove the native oxide. This results in a well ordered surface with a (2 · 1)-reconstruction (Fig. 2(a)). Epitaxial Bi(0 0 0 1) films have been grown in situ by deposition at room temperature from a Knudsen-cell and slightly annealed to 400 K to improve the film quality. The thickness of the Bi-film was determined by a calibrated quartz crystal microbalance. The resulting LEED-pattern of a 5.5 nm Bi-film, shown in Fig. 2(b), exhibits a 12-fold symmetry. All occurring spots are explained by the superposition of two hexagonal domains rotated by 90 (unit cells are indicated in the image). The appearance of the two orientations is caused by
Fig. 2. (a) LEED-pattern at 100 eV of the bare Si(0 0 1)-(2 · 1) surface after flashing to 1200 C (linear scale). (b) LEED-pattern at 100 eV after Bi-deposition at room temperature followed by a slight anneal to 400 K (logarithmic scale). The 12-fold symmetry is explained by the superposition of two hexagonal domains rotated by 90. It is evident that Bi grows in (0 0 0 1)-orientation. (c) RHEED pattern of the sample taken at 5.5 keV electron energy (logarithmic scale). (d) Temperature dependence of the (0 0)-spot intensity at 5.5 keV. The exponential fit according to the Debye– Waller-effect yields a surface Debye-temperature of 47 ± 5 K. (e) Dependence of the surface Debye-temperature on electron energy.
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the presence of the (2 · 1) and (1 · 2) dimer reconstructions ˚ is of the Si(0 0 1)-surface. A lattice constant of a0 = 4.43 A derived for the Bi-surface. This and the hexagonal symmetry is evident for Bi-growth in a (0 0 0 1)-orientation with an in plane lattice compression by 2.6% compared to bulk values [19]. Similar results have been previously observed for thin Bi-films grown on the Si(1 1 1)-surface [20]. The corresponding RHEED pattern of the sample exhibits sharp diffraction spots as shown in Fig. 2(c). The electron energy was 5.5 keV at an incident angle of 5 resulting in a perpen˚ 1 for the specular dicular momentum transfer K? = 6.63 A spot. In order to provide an unambiguous calibration the temperature dependence of the spot intensity was measured between 80 and 300 K in a stationary experiment where the sample holder was set to the desired temperature. After a couple of minutes the diffraction pattern was recorded allowing the sample to thermally equilibrate. The temperature was monitored by a thermocouple attached to the sample holder. The peak intensity of the (0 0)-spot is displayed in Fig. 2(d). Every data point was background subtracted and normalized to the value at 80 K. The intensity drops by 70% upon a temperature rise from 80 to 300 K and follows nicely the exponential decay expected from the Debye–Waller-effect. The solid line in Fig. 2(d) is a fit of Eq. (1) to the data points with hD as the only free parameter. We observed a Debye-temperature of hD = 47 ± 5 K, which is significantly lower than the bulk value, owing to the reduced coordination of the surface atoms. This result is in good agreement with previously reported values for single crystal Bi(0 0 0 1)-surfaces [14,21], which indicates that the finite thickness of the thin film has negligible or no influence on the Debye-temperature. According to Eq. (1), variation of the momentum trans~ leads to a tuning of the Debye–Waller-effect. Howfer K ever, this effect is partly lifted as can be seen in Fig. 2(e) where the dependence of the measured Debye-temperature on the electron energy for a constant scattering angle is plotted. The Debye-temperature increases almost linearly with increasing electron energy from 4 to 7 keV. This effect clearly shows the decreasing surface sensitivity for increasing electron energies due to the higher penetration depth of fast electrons. For large penetration depths the observed Debye-temperature approaches the bulk [21]. We will use the curve from Fig. 2(d) to convert time-dependent intensity drops subsequent to laser pulse excitation into the transient surface temperature of the Bi-film. Fig. 3(a) shows the normalized (0 0)-spot intensity as function of the pump pulse travel time for two data sets taken at different electron energies with a pump fluence of 1.3 mJ/cm2 at a base temperature of 80 K. For long pump pulse travel times the spot intensity remains constant (negative time delays). At 6250 ps for the 5.5 keV electrons and around 5750 ps for the 7 keV electrons a sharp intensity drop by about 40% is observed. The decrease in the intensity is associated with the temporal overlap of pump and probe pulse. The shift between both curves by 500 ps
Fig. 3. (a) Time-dependent normalized (0 0)-spot intensity for 5.5 and 7 keV electrons. The observed minimum shifts by 500 ps to shorter pump pulse travel times due to the increased electron kinetic energy. (b) Using the stationary Debye–Waller-factor from Fig. 2 the intensity drops for both curves are converted to a transient temperature rise. The delay t = 0 was set to the leading edge of the temperature rise. The surface temperature decrease is well described by an exponential decay with a time constant t = 640 ± 30 ps for both data sets.
is explained by the shorter travel time of the 7 keV electrons compared to the 5.5 keV electrons on the 200 mm distance between photocathode and sample. For longer time delays (shorter travel times) the (0 0)spot intensity recovers asymptotically in both data sets. Due to the long timescale the observed intensity behavior is attributed to the heating and cooling of the Bi-film rather than to a change in the structure factor as recently observed by X-ray diffraction on a fs-timescale [5]. From the measurement of the diffraction spot intensity with and without pump pulse at negative time delays we can conclude that any steady state heating by the intense laser pump pulse is below 10 K. Fig. 3(b) shows the surface temperature after conversion using the calibration curve from Fig. 2(d) and (e). For better comparability the time scale for both curves was set to t = 0 ps at the leading edge of the intensity drop. Within the statistical error both sets result in an equal transient
A. Janzen et al. / Surface Science 600 (2006) 4094–4098
temperature evolution for delays smaller than 1500 ps. The deviation for longer time delays may be due to a reduction of the electron intensity. However, the following discussion is based on the temperature decay which is given by the behavior at short delays and the deviation at long delays has a negligible influence in the determination of the decay time constant. Negative delays denote that the electron probe pulse arrives at the sample prior to the excitation with the laser pump pulse: the surface is not excited yet. At t = 0 ps a linear increase of the surface temperature by 120 K is observed. The rise time of 90 ps is due to the finite temporal resolution of the experiment which is dominated by the velocity mismatch and grazing incidence of electrons onto the sample as sketched in Fig. 4. In our experiment the pump pulse impinges at normal incidence resulting in the temporally simultaneous excitation of the entire width of the sample. Due to the grazing incidence, however, the electron pulses probe the sample at different time delays along the width of the sample. The diffracted electrons thus contain information of the surface temperature and structure, which is averaged over this probing time Dt which is determined by the electron velocity and incident angle. For a sample width of 4 mm as used in our experiment Dt = 90 ps and Dt = 80 ps is calculated for 5.5 keV and 7 keV electrons, respectively, which is in excellent agreement with the observed rise time of 90 ps. After reaching the maximum, the surface temperature decreases exponentially with a time constant of s = 640 ± 30 ps. Previous studies on bulk-single crystals of Bismuth have observed a surface cooling that was in accordance with thermal heat diffusion [14]. As the hyperbolic temperature decay expected for one dimensional heat diffusion [22] significantly differs from the observed exponential decay we have to conclude that the phonon transport from the thin Bi-film towards the Si-substrate is strongly altered compared to the bulk and is dominated by the Bi/Si-interface: the heat is trapped in the Bi-film and only leaks out slowly into the Si-substrate. It is well known that liquid–solid and solid–solid interfaces act as a barrier to thermal diffusion. The net heat flow Q_ per unit area across such an interface is given by
Fig. 4. Grazing incidence and velocity mismatch between pump and probe pulse. The electron and laser pulses travel at velocities ve and c, respectively. During the travel time Dt the electron pulse probes the surface.
Q_ ¼ rK DT ;
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ð2Þ
where the thermal boundary conductance rK relates the heat flow across the interface with the temperature discontinuity DT at the interface [16,23]. The solution of Eq. (2) for the film temperature is an exponential decay with time constant [16] s¼
Cqd : rK
ð3Þ
In Eq. (3) C and q are the specific heat and mass density of Bismuth and d the film thickness. In deriving Eq. (3) it was assumed that the temperature of the Si-substrate remains constant [24]. It is additionally assumed that the surface temperature represents the film temperature. From the observed time constant we extracted a thermal boundary conductance of rK = 1025 ± 193 W/(cm2 K). The thermal boundary conductance rK is fundamentally related to the transmission probability of phonons and electrons across the interface. The two simplest models for the calculation of rK are the acoustic mismatch model (AMM) and the diffusive mismatch model (DMM) [16,24]. Both models consider only phonons for the heat transport across the interface which can safely be assumed for the semimetal Bi. The AMM treats phonons as elastic waves that are reflected and refracted at a smooth interface without scattering. Calculation of the energy transfer of the transmitted waves is achieved by using the acoustic equivalent of the Fresnel equations in optics [25]. Because the velocity of sound in Si is 4–5 times larger than in Bi the vast majority of phonons in the Bi-film undergoes internal total reflection at the interface and is therefore trapped in the Bifilm. A thorough calculation yields a transmission probability CAMM = 0.13 which results in the thermal boundary conductance rAMM ¼ 1400 50 W=ðcm2 KÞ [27]. In conK trast, in the framework of DMM the phonons are considered to be strongly scattered at a rough or disordered interface. The transmission probability then only depends on the phonon density of states in the two media. This model yields CDMM = 0.14 and rDMM ¼ 1500 60 W= K ðcm2 KÞ [27]. Previously observed thermal boundary conductances were up to an order of magnitude larger than theoretically predicted which lead to the conclusion that a poor interface quality and inelastic effects have a major influence on rK. The AMM and DMM were therefore extended to describe the experimental findings [16,26]. Due to the preparation under UHV conditions the high quality of our epitaxial Bi-films together with an abrupt Bi/Si-interface leads to a much lower thermal boundary conductance in good agreement with the theoretical predictions. In conclusion, ultrafast electron diffraction in a RHEED setup has been applied for the determination of the transient surface temperature of a thin Bi-film deposited onto a Si(0 0 1)-surface upon fs-laser excitation. The cooling of the surface cannot be described by simple thermal diffusion but is well understood in terms of the thermal boundary
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conductance of the Bi/Si-interface. The high film and interface quality made it possible for the first time to test the models describing the thermal boundary conductance. In the near future ultrafast electron diffraction will be extended to study the transient structural properties of surfaces yielding new insights into the ultrafast processes subsequent to laser excitation. Acknowledgements The authors like to thank B. Rethfeld and M. Aeschlimann for fruitful discussions. This work was supported by the DFG through SFB 616 ‘‘Energy dissipation at surfaces’’. References [1] H.E. Elsayed-Ali, T.B. Norris, M.A. Pessot, G.A. Mourou, Phys. Rev. Lett. 58 (1987) 1212. [2] W.S. Fann, R. Storz, H.W.K. Tom, J. Bokor, Phys. Rev. Lett. 68 (1992) 2834. [3] M. Bonn, D.N. Denzler, S. Funk, M. Wolf, S.S. Wellershoff, J. Hohlfeld, Phys. Rev. B 61 (2000) 1101. [4] M. Weinelt, M. Kutschera, T. Fauster, M. Rohlfing, Phys. Rev. Lett. 92 (2004) 126801. [5] K. Sokolowski-Tinten et al., Nature 422 (2003) 287.
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