The interaction of short laser pulses with semiconductors has been studied by a variety of techniques, including time- resolved reflectivity,(1-5) transmission,(1-5) photoluminescence,(1-5) surface ellipsometry,(6) and surface second-harmonic generations. In the present work, we describe an imaging technique used to obtain the first reported time-resolved photographs of a silicon surface at fixed time delays ranging from 100 fsec to 600 psec following excitation with an intense ultrashort optical pulse. When the fluence E of the excitation pulse exceeds a threshold value ETH (approximately 0. I J/cm^2 under our experimental conditions), a rapid increase in surface reflectivity occurs that has been widely interpreted as thermal melting. (14) The photographs depict the evolution of the surface reflectivity during and following melting with a time resolution of 100 fsee and a spatial resolution of 5m m. Using a movie camera and elementary synchronization electronics, we have also made a motion picture that shows the continuous sequence of melting, boiling, and material ejection over a 600-psec period slowed in time by as much as a factor of 10^13. The still photographs presented here depict the major events in this sequence.

    Our photographs provide a detailed study of the physics of a highly excited semiconductor surface as a function of time, position on the silicon surface, and reflected light frequency. The optical pump pulse initially excites an electron-hole plasma, which alters the real part of the dielectric constant and therefore the reflectivity and transmission. Within a few hundred femtoseconds following excitation, much of the energy of the excited carriers is transferred to the lattice by longitudinal-optical phonon emission. This results in melting for E > ETH. This process is evident in the present photo- graphs as a rapid rise in surface reflectivity up to the known value (R @-- 70% at optical frequencies) for molten silicon. Material ejected from the hottest parts of the molten surface further alters the observed reflectivity at time delays of ten to several hundred picoseconds by scattering and absorbing the illuminating light. We have obtained strong evidence that this material is ejected in the form of liquid droplets several hundred angstroms in diameter that atomize in less than a nanosecond by using selective imaging and spectral analysis of the light reflected from these hot regions. The time-resolved images were obtained using a variation of the pump-and-probe technique. A 10-Hz train of 80-fsec, 0.2-mJ pulses at 620 nm was produced by a colliding-pulse mode-locked dye laser (10) followed by a four-stage optical am- plifier. (11) A 50 % beam splitter divided this output into a pump beam, which was focused at normal incidence onto a silicon [111] surface (spot diameter - 150 m m), and a second beam, which was focused into a I-cm path-length cell containing water to produce a white-light continuum pulse, (12) which then served as a probe. The continuum beam was focused at near-normal incidence to a spot of approximately 400-m m diameter overlapping and illuminating the area excited by the pump pulse. The silicon wafer was translated 300 m m after each laser shot by an electronically controlled stage that moved the wafer in a raster pattern. Consequently, each laser shot interrogated a fresh region of the sample.

    A magnified image of the excited surface region was obtained at a given pump-probe time delay by collecting the specularly reflected continuum light with an objective lens at f/5 and then imaging the collected light with a second lens onto a screen or photographic film, as shown in Fig. 1. Typical magnifications were IOOX. To obtain still photographs, the camera shutter was opened for slightly less than the time between successive laser pulses (-O.l sec) to prevent double exposures. For motion pictures, the rotation of the camera reel shaft was used to producer an electronic signal that fired the ND:YAG laser in the optical amplifier (11) at a 12-Hz repetition rate in synchronization with the opening of the camera shutter. The time delay between pump and probe was then varied during filming by a stepper-motor-controlled optical delay. The stepper-motor increments were I m m, corresponding to an optical delay of 6.66 fsec.

    The images of the excited silicon surface at time delays ranging from D t = -0.5 to D t = +600 psec are shown in Figs. 2a)-2h). Here the pump fluence was approximately 5ETH. The images appear green because of a red-absorbing filter in front of the camera used to block scattered pump light. Before arrival of the excitation pulse, only a uniformly illuminated region of the surface is seen [see Fig. 2a)]. After arrival of the excitation pulse, the reflectivity of the excited region is selectively increased because significant melting has occurred in this region [see Figs. 2b)-2d)]. At D t = +0.1 psec, this region is faint [see Fig. 2b)] for two reasons. First, melting is not complete by this time, (7,9) and second, there is a frequency sweep on the probe pulse because of dispersive optics in the path of the probe beam. Thus only the trailing blue frequencies see the molten silicon at the earliest pump-probe delays. In Figs. 2c) and 2d), where D t = 0.5 and 1.0 psec, respectively, the excited region becomes brighter and whiter as melting is completed and all frequencies in the continuum pulse are reflected by the molten layer.

    The appearance of the highly reflective molten spot at later times (D t > 1.0 psec) depends dramatically on the pump fluence. For fluences between ETH and about 2.5 ETH, it remains essentially unchanged from D t = 1.0 to D t = 600 psec. This is consistent with earlier results (9) showing that for these fluence levels the reflectivity levels off after about 1.0 psec (Ref. 9) and remains unchanged until later than a nanosecond, (13) when resolidification begins.

    At higher fluence levels, a dark region begins to appear in the center of the molten spot at D t = 5-10 psec, as shown in Fig. 2e). This central region continues to darken, becoming darkest between D t = 50 and D t = 100 psec, although the edge remains bright [see Fig. 2f)]. At still later times, the center of the dark spot begins to become transparent again [Fig. 2g)], and, by D t = 600 psec, it has substantially dissipated [Fig. 2h)], except for a narrow dark ring at the outer edge of the original dark spot.

    We believe that this dark region originates from an optically dense cloud of material ejected from the molten-silicon surface following photoexcitation. This hypothesis is consistent with simple thermodynamic arguments that show that a pulse of 0.5 J/CM2 can melt and vaporize silicon to a maximum depth of 3600 A. Detailed calculations presented below show that this quantity of silicon can cause the observed optical attenuation, provided that the silicon is injected initially in the form of liquid droplets. Maximum ejection is expected in the hot central portion of the molten silicon, where the excitation intensity is highest, while the edge remains cool enough that a substantial absorptive cloud never develops. This explains the bright outer ring of unobscured molten silicon that persists throughout the time of observation. Earlier studies have demonstrated substantial emission of both charged particies (14) and neutral silicon atoms (15,16) above melting threshold.

    In order to elucidate the absorptive and/or scattering, mechanism responsible for the strong probe attenuation through the silicon cloud, we analyzed the spectrum of the light reflected from the dark central region as a function of D t by selectively imaging this region of the molten spot onto the entrance slit of an optical multichannel analyzer. The re- flectance spectrum was recorded from 500 to 1040 nm at several time delays ranging from D t = 2 to D t = 550 psec. Differential spectra that related the reflectivity for D t > 10 psec to the reflectivity of the unobscured molten surface at D t = 2 psee were then computed electronically.

    In Fig. 3, the measured fraction of light transmitted through the cloud is plotted versus frequency for D t = 50, 300, and 550 psec. For these and all intermediate time delays, transmission was least in the blue and increased monotonically toward the red. Significantly, no discrete absorption lines or bands appeared in any of the spectra, as expected if absorption by isolated ground- or excited-state silicon atoms and ions were primarily responsible for the probe attenuation. The weak oscillator strength of atomic silicon lines at optical frequencies is further evidence that absorption by individual silicon atoms cannot explain the observed attenuation.

    The magnitude of the probe attenuation, as well as its frequency, position, and time dependence, can be explained by postulating that the ejected material emerges from the surface in the form of multiatomic droplets of hot, molten silicon, which later atomize into smaller, less-absorptive particles of atomic dimensions. For simplicity in constructing a model, we assume that these droplets are spherical and uniform in size at any given time. The degree of absorption can then be calculated by applying Mie scattering theory to the case of conductive, absorbing spheres. (17)

The light intensity transmitted through the cloud is given by

where I(0) is the intensity reflected from the unobscured molten-silicon surface at D t = 2 psec (nearly constant across the frequency range investigated), N is the density of particles, and L is the thickness of the absorbing/scattering region. The factor of 2 enters because the reflected light makes two passes through the cloud. For particle radii a < 0.05l , the extinction cross section s (ext) is (17)

where the first term represents the cross section for absorption and the second term the cross section for scattering. Here m = n + ik is the wavelength-dependent complex index of re- fraction for liquid silicon.

    If we neglect expansion of the cloud in the lateral direction on the time scale of interest (D t < 500 psec), which is a reasonable assumption as long as the lateral component of the average particle velocity is less than about 10^6 cm/sec, then the product NL is equal to 3d(c)l/4*pi*a^3*d(l) where d(c) is the density of crystalline (liquid) silicon, I is the depth of material removed from the silicon surface (assumed constant across the excited region), and a is the radius of the emerging particles. The optical density of the cloud of silicon droplets then becomes

where the small difference between d(c) and d(l) has been neglected. For a < 0.05l and physically reasonable m, the optical density contributed by scattering [second term in Eq. (3)] is at least an order of magnitude smaller than that contributed by absorption [first term in Eq. (3)]. The optical density thus depends on particle size only in the limits of very small particles (atomic dimensions), where the optical constants no longer approximate those of liquid silicon, and very large particles (a > 0.05l ), where scattering becomes important compared with absorption.

    The wavelength-dependent index of refraction m for liquid silicon has not, to the authors' knowledge, been measured. Its value can be approximated by using a Drude model. (18) In this approximation, the quantity Im(m^2 - 1)/(m^2 + 2) varies monotonically from -0.12 at l = 500 nm to about -0.05 at l = 1000 nm. If we assume that the ejected particles are small (a < 0.05l ), the required depth I to which material must be removed from the surface in order to explain the maximum observed probe attenuation at D t = 50 psec is then about 3500 A. This is approximately equal to the maximum depth (3600 A) of silicon that, according to the law of energy conservation, could be melted and vaporized by a pulse of 0.5 J/CM2.

    We believe, however, that the actual depth I of material removed from the surface is substantially less than 3500 A, since a highly reflective molten layer is still evident after dissipation of the cloud, proving that some of the pulse energy has been deposited in melted, but unvaporized, silicon. In order to explain the data for D t = 50 psec with I < 3500 A, we must assume particle radii a > 0.05 l and a significant con- tribution from scattering. The dotted curve in Fig. 3 was obtained using Eq. (3) with I = 1400 A and a = 700 A. In obtaining this curve, Eq. (3) has been extended somewhat beyond its range of validity (a < 0.05l ). Nevertheless, the qualitative point that scattering becomes comparable with, or greater than, absorption with larger particle sizes remains valid in a more rigorous treatments of the extinction cross section.

    The decrease in optical density of the cloud at later times (D t > 50 psec) can be explained as a decrease in droplet size caused by evaporation or fragmentation. Since the ejected liquid is probably superheated, the evaporation may occur in an extremely rapid, explosive fashion. We have fitted the data for D t = 300 psec in Fig. 3 (dashed curve), using the same depth l = 1400 A in Eq. (3), for particle sizes small enough (a < 250 A) that the scattering contribution has become negli- gible. Absorption remains unaffected by the decrease in particle size because the decreased absorption cross section per particle is exactly compensated for by the increased number of particles. The fit to the D t = 300-psec data is poorer if significant scattering is introduced.

    The continuing decrease in optical density at later times can be interpreted as the atomization of the liquid droplets into single atoms or small aggregates of atoms, which have negligible absorption and scattering cross sections at optical wavelengths. This change is equivalent to the removal of effectively absorbing particles from the cloud or, in the terms of Eq. (3), to a reduction in 1. In Fig. 3, we fitted the data for At = 550 psee (dashed upper curve) by using I = 400 A and neglecting scattering. The wavelength dependence of the probe light transmitted through the cloud is thus explained for all time delays by using a model of conducting liquid droplets.

    The spatial variations in the optical density at the later time delays are also explained in a natural way by this model. Because of the approximately Gaussian intensity profile of the excitation pulse, the absorbing cloud is hottest in the center. Consequently, the liquid droplets atomize most rapidly in the center, while near the cooler edges of the cloud the droplets remain large for a longer time. This explains why the cloud becomes transparent first in the center, while a dark ring remains at the edge (inside the bright ring of unobscured molten silicon) even at the latest time delays studied.

    A propensity for initial droplet formation following ultrafast nonadiabatic heating could be the result of high surface ten- sion, which is typical of liquid metals. Total surface energy is therefore minimized initially by minimizing total surface area through the formation of large droplets. As atomization progresses, -the number n of droplets increases, and total surfaceenergyincreasesasnII3. lfweassumeatypicalliq- uid-metal surface tension (-500 dyn/cm), it is a straightfor- ward matter to calculate that an energy of approximately 0.025 J per square centimeter of photoexcited area, or one fourth of the melting fluence, is required to atomize the ejected liquid silicon completely. This energy barrier may serve to slow the atomization time to several hundred picoseconds.

    We have demonstrated a simple technique for filming the progress of an ultrafast melting and material-ejection process, with a time resolution of 100 fsec. The results suggest that, for excitation fluences several times the melting threshold, silicon is ejected from the melted surface in the form of droplets with radii of several hundred angstroms, which at- omize in several hundred picoseconds. Applications of this femtosecond imaging technique to the study of other ultrafast processes, such as carrier transport in semiconductors, should be possible. Infrared illumination frequencies would be particularly sensitive to the presence of photoexcited carriers. With optically thin samples, transmitted as well as reflected light could be imaged.
 

ACKNOWLEDGMENTS

We are grateful to A. Ashkin and P. L. Liu for helpful dis- cussions, to D. W. Taylor for the computer interface, and to F. Beisser for technical support.
 

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