Transient lattice dynamics in fs-laser-excited semiconductors probed by ultrafast x-ray diffraction

Transcription

1 Transient lattice dynamics in fs-laser-excited semiconductors probed by ultrafast x-ray diffraction K. Sokolowski-Tinten, M. Horn von Hoegen, D. von der Linde Inst. for Laser- and Plasmaphysics, University of Essen, Essen, Germany, Phone: , Fax: , A. Cavalleri 1, C.W. Siders 1,5, F.L.H. Brown 1, D.M. Leitner 1, Cs. Toth 2, J.A. Squier 3, C.P.J. Barty 4, K.R. Wilson 1 1 Dep. of Chemistry and Biochemistry, 2 Inst. for Nonlinear Science, 3 Dep. of Electrical Engineering, 4 Dep. of Applied Mechanics and Engineering Sciences, University of California San Diego, La Jolla, CA , U.S.A. 5 School of Optics/CREOL, University of Central Florida, Orlando, FL , U.S.A. M. Kammler Inst. for Solid State Physics, University of Hannover, Hannover, Germany

2 K. Sokolowski-Tinten, M. Horn von Hoegen, D. von der Linde, A. Cavalleri, C.W. Siders, F.L.H. Brown, D.M. Leitner, Cs. Toth, C.P.G. Barty, J.A. Squier, K.R. Wilson, M. Kammler Abstract. Using time-resolved x-ray diffraction ultafast lattice dynamics in fs-laser-excited crystalline bulk Ge and Ge/Si-heterostructures has been studied. This experimental technique uniquely allows us to observe fast energy transport deep into the bulk of the material, coherent acoustic phonon dynamics, lattice anharmonicity, and vibrational transport across a buried interface. Short pulse optical excitation of semiconductors creates highly non-equilibrium states of the irradiated material. To re-establish equilibrium a complex sequence of relaxation processes is necessary, starting with intra-band thermalization of the hot carriers, carrier relaxation via diffusion, phonon-emission and recombination, vibrational acoustic transport into the bulk, and eventual complete thermalization within the phonon-subsystem. The processes involving the electronic degrees of freedom and Raman-active optical phonons have been characterized in the past with time-resolved optical techniques. On the other hand, access to the ultrafast acoustic phonon dynamics has been indirectly achieved only at surfaces. By combining the temporal resolution of ultrafast laser spectroscopy with the structural sensitivity of x-ray scattering, direct quantitative studies of ultrafast atomic motion deep inside the bulk of matter have recently become possible [1-7]. In this contribution, we report on time-resolved x-ray measurements of ultrafast strain dynamics in fs-laser-excited, impulsively heated Ge crystals. The experiments give clear evidence that the heating dynamics in Ge is mainly determined by the interplay of delayed Auger-heating [8] and fast ambipolar electron-hole diffusion [9]. Moreover, we observed excitation-dependent anharmonic damping of coherent lattice vibrations and acoustic transport across a buried interface [7]. (111)-oriented bulk Ge crystals and single crystalline Ge thin films, grown on Si- substrates by surfactant-mediated heteroepitaxy [10], have been optically excited with 30fs laser pulses at 800nm. Evolution of the impulsively generated transient lattice strain is then observed by diffraction, in a symmetric Bragg-configuration, of short bursts of Cu K α line radiation at 8 kev from a laser-produced microplasma. Experimental results obtained on a bulk Ge sample are shown in the left part of Fig. 1. It displays in a two-dimensional gray-scale representation (time-resolved diffractogram) the diffraction pattern of the laser-excited material as a function of diffraction angle (horizontal axis) and delay time between the optical pump and the x-ray probe (vertical axis). At negative time delays the diffraction pattern of the unperturbed material consists of two lines due to spin-orbit splitting of the Cu K α line. At positive time delays the original K α -lines become broadened and shifted slightly to larger angles. At the same time two new lines appear, broader and weaker than the original lines and deviated by approximately -1arcmin relative to the original Bragg angle, indicating expansion of the lattice. At later times ( 400 ps), these new lines decreased in width and merged asymptotically with the broadened and shifted main lines.

3 Figure 1. Left: measured time-resolved diffractogram of a bulk (111) Ge-crystal after excitation with a 100mJ/cm 2, 30fs laser pulse at 800nm. Right: diffractogram obtained from model calculations (effective heating depth 1µm). Similar behavior has been recently reported on GaAs [4], and interpreted as follows: After absorption of the laser pulse, thermalization between the hot carriers and the lattice occurs faster than thermal expansion of the solid, leading to quasi-isochoric heating. Relaxation of the impulsively generated inhomogeneous thermal stress occurs by surface expansion and propagation of an acoustic pulse into the bulk. Importantly, the shape of this pulse is uniquely determined by the initial stress profile, which can be retrieved over a depth of several microns from the diffraction data. Therefore, we compared the experimental data shown in Fig. 1 to model calculations, in which we started with stress distributions (exponential) of variable scale lengths. The one-dimensional elastic equation was then used to calculate the time-dependent strain, and dynamic diffraction theory yields the transient x-ray diffraction patterns. The result which gave the best approximation to the measured data is shown in the right part of Fig. 1, and was obtained with an effective heating depth of approximately 1µm. This is much larger than the 200nm linear absorption depth in Ge at 800nm wavelength. In order to explain this behavior we performed additional simulations by numerically solving the coupled transport equations for the laserexcited e-h-plasma and the lattice, taking into account Auger recombination and carrier diffusion. It turns out that the effective heating depth in Ge is not determined by the initial absorption depth or the electronphonon scattering rates, but strongly influenced by very fast ambipolar electron-hole diffusion [9] and a delayed electron-lattice equilibration due to Auger-heating [8]. The dominant role of fast carrier diffusion in Ge has been confirmed by additional diffraction experiments on Ge/Si-heterostructures with different thickness of the Ge-overlayer (160nm, 400nm, 900nm). In all the thin film samples we observed not a splitting of the diffraction lines, as in the bulk crystal, but a pure shift of the essentially unbroadened lines towards smaller diffraction angles, indicating homogenous heating over the entire film thickness (up to 900nm!). Moreover, on the Ge/Si-samples we were able to simultaneously measure the strain dynamics in both components of the heterostructure (overlayer and the substrate). As an example, Fig. 2 shows the shifts of the centroid of the rocking curve of a 400nm Ge-film (left) and of the Si-substrate (right), averaged over the K α1 and K α2 -lines, as a function of pump-probe delay for four different pump fluences. From maximum negative shifts of the Bragg-angle in the Ge-film between 25-50arcsec, values for the peak strain of %, corresponding to an increase in the 111-lattice plane spacing of about fm, are obtained. Maximum expansion is reached approximately ps after excitation, followed by damped oscillations at later time delays, indicating periodic expansion and compression of the film. Damping of these oscillations is apparently fluence dependent, becoming stronger for higher excitation. In the Si substrate mainly positive line shifts, indicating compression of the material, are observed. The peak of the

4 measured compression, representing a spatial average over the 2-3µm probing depth of the Cu-K α radiation, corresponds to a 20-40fm change in lattice spacing (a few nuclear diameters!). Figure 2. Time dependent shift of the centroid of the measured rocking curves in the Ge-overlayer (left) and in the Si-substrate (right) for different fluences. The solid lines are obtained from a pure harmonic model of the film vibration. The dashed lines (only plotted for Ge) represent phenomenological fits to the measured data to include lattice anharmonicity. Interpretation of the experimental data shown in Fig. 2 proceeds along the following lines. Irradiation of the sample leads to the generation of a dense e-h-plasma (peak densities cm -3 ) in the Geoverlayer, but negligible photo-excitation of the Si-substrate. As explained above, fast carrier diffusion distributes the energy over the entire thickness of the Ge-film, before complete energy relaxation between the electrons and the lattice can take place. On the other hand, electronic energy transport into the Sisubstrate is inhibited due to the 0.43eV difference of the energy gap in both materials. Impulsive heating produces an initially highly stressed state of the Ge-film. Acoustic relaxation of the stress leads then to vibrations of the film with a period of 2d/c L 140ps (d=400nm±20nm: film thickness; c L =5560m/s: sound velocity). In harmonic approximation and assuming perfect crystal lattices, the observed damping of the film vibrations and the compression of the Si-substrate can be attributed to acoustic transmission across the Ge/Si-interface. However, in a real crystal other processes, like defect-, surface- and phonon-phonon-scattering, lead to additional contributions to the decay of the oscillations. While damping due to acoustic transmission and defect- and surface-mediated scattering should be independent of the degree of excitation, the anharmonic phonon-phonon interaction scales with the population of the individual modes and thus with temperature. Our data allow us to distinguish between these mechanisms: the observed fluence dependent damping is strong indication of lattice anharmonicity. For a quantitative estimate of the relative importance of the different processes we first compare the data to a fully harmonic description. For the two-layer system we solved again the coupled transport equations and the one-dimensional elastic equation (in conjunction with dynamic diffraction theory). The solid curves in Fig. 2 represent the results of these calculations. As expected, the model predicts a fluence-independent damping, originating solely from the acoustic transmission of the Ge/Si-interface. For the lowest fluence the calculated curves follow the measured data very closely, demonstrating that defect-mediated processes play only a minor role. For increasing fluences the harmonic calculations progressively deviate from the measurement, as would be expected for an anharmonic, temperature dependent damping process. To describe lattice anharmonicity we fit the measured Ge data to a phenomenological response function (dashed curves in the left part of Fig. 2: damped oscillation

5 superimposed on a thermal background), which includes the fluence-independent damping due to acoustic transmission and an additional fluence-dependent contribution. The obtained anharmonic damping rates are shown in Figure 3 as a function of (calculated) temperature. They range from a few times 10-3 ps -1 at low fluences/tempearatures up to 2x10-2 ps -1 for high fluences/temperatures. Theoretical estimates of the inelastic lifetime (T 1 ) of 7GHz phonons in a thermal bath of lattice vibrations give values of 10-5 ps -1 [11], about three orders of magnitude smaller than what is measured. On the other hand, as has been discussed in more detail in reference 7, the experimental values are consistent with estimated elastic dephasing times (T 2 ) for 7-GHz LA-phonons in Ge. Figure 3. Anharmonic damping rates as a function of the calculated temperature in Germanium, as obtained from a fit of the measured time dependencies shown in Fig. 2 with a phenomenological response function. In conclusion, we have investigated impulsively stimulated lattice dynamics in fs-laser-excited crystalline bulk Ge and Ge/Si-heterostructures, using time-resolved x-ray diffraction. Measuring atomic displacements with 10fm resolution on an ultrafast time-scale, we are able to study fast energy transport deep into the bulk of the material, coherent acoustic phonon dynamics, lattice anharmonicity, and vibrational transport across a buried interface. Acknowledgements K.S.T. gratefully acknowledges support by the Deutsche Forschungsgemeinschaft and by the Stiftung Flughafen Frankfurt/Main. References [1] Rischel C. et al., Nature 390 (1997) [2] Larsson J. et al., Appl. Phys. A 66 (1998) [3] Rose-Petruck C. et al., Nature 398 (1999) [4] Chin A.H. et al., Phys. Rev. Lett. 83 (1999) [5] Siders C.W. et al., Science 286 (1999) [6] Lindenberg A.M. et al., Phys. Rev. Lett. 84 (2000) [7] Cavalleri A. et al., Phys. Rev. Lett. 85 (2000) [8] Young J.F. et al., Phys. Rev. B 26 (1982) [9] Downer M. C. et al., Phys. Rev. Lett. 56 (1986) [10] Horn-von-Hoegen M., Appl. Phys. A 59 (1994) [11] Tamura S. et al., Phys. Rev. B 51 (1995)