Dense-plasma Dynamics during Pulsed Laser Annealing

The flow of energy from the laser to the lattice during pulsed laser annealing of Si is examined, with particular attention paid to the influence of the dense'plasma of hot, photoexcited carriers on-the manner in which this energy transfer occurs. Consideration of carrier thermalization and recombination at high carrier densities suggests that under certain conditions carrier diffusion may increase the spatial extent to which the lattice is heated and consequently decrease the rate of temperature rise near the surface. Because it has recently been argued that simple-melting or strictly-thermal models for pulsed laser annealing of ionimplanted and amorphous Si cannot provide consistent explanations for a large body of experimental evidence, /1-3/ an important subject to be addressed is the manner in which the energy is transferred from the laser to the semiconductor lattice. Considerable theoretical and experimental investigation of hot carrier relaxation on picosecond to nanosecond time scales in Ge /4 ,5 / and GaAs /6-10/ has indicated that as carrier densities increase, the effects of carriercarrier interactions grow in importance. In this paper, the influence of the dense plasma of photoexcited carriers on the laser-tolattice energy tranfer will be examined. previous calculations have been performed which assume that the laser energy is deposited in the lattice in the same region in which it is initially absorbed /11-15/. However, consideration of carrier thermalization and recombination at high carrier densities suggests that under certain conditions, carrier diffusion may increase the spatial extent to which the lattice is heated and consequently decrease the rate of temperature rise near the surface. Most of the laser energy is ultimately deposited into the semiconductor Aattice in the form of heat. However, the laser energy does not couple directly to the lattice but is instead initially absorbed by the carriers, where it resides for a short time interval. During this intermediate step, h his work was supported in part by the Air Force Office of Scientific Research under several mechanisms redistribute the carriers both energetically and spatially, thereby altering the original, absorbed distribution of energy before its final delivery to the lattice. The photoexcited carriers then thermalize and recombine by means of rapid Coulomb collisions. At the same time, they diffuse from the surface as a result of the large carrier gradients generated by the laser. An important point which shall be demonstrated is that these processes take place primarily within the system of carriers, thereby conserving the total carrier energy. It is then only through phonon emission by the carriers within the plasma that a significant amount of energy can be transf erred. The spatial distribution of this plasma consequently directly influences the spatial distribution of lattice heating. Carrier redistribution in both space and energy occurs as the plasma responds to the driving forces set up by the laserinduced generation of carriers. The characteristic absorption profile causes large carrier density gradients resulting in diffusion of the carriers--and the energy they contain--inward from the surface. At the same time, because the carriers are originally excited into nonequilibrium energy distributions, collisions among them lead to rapid thermalization and establishment of individual electron and hole distributions characterized by a common,temperature which is much higher than the lattice temperature. In addition, the high density of Contract No: F 49620-77-C-0005. Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1980402 C4-8 JOURNAL DE PHYSIQUE excess electron-hole pairs leads to recombination, which occurs primarily by Auger processes for high laser excitation rates. An electron and hole can recombine, giving their energy to a third carrier. The driving force for this recombination is the concentration of carriers in excess of equilibrium (at the carrier temperature) which results from the optically-induced splitting of the electron and hole quasi-fermi levels. Finally, owing to the large difference between the carrier and lattice temperatures, the plasma energy can leave the carriers altogether by emission of phonons. In general, therefore, it is necessary to examine the rates at which the several intercarrier processes occur in order to determine the spatial and energetic distributions of these excited carriers when they interact with the lattice. It is important to recognize thatthe magnitude of the photon absorption rate, g, plays a crucial role in determining the physics of the ensuing interactions For g 2 l ~ ~ ~ c m ~ s ~ , carrier densities N (N = 2Ne) attained during the laser pulse /16/ will in general exceed 10'~cm-~. As an example, a typical /17/ 10 nsr0.53pm laser annealing pulse of 1~/cm~ (i.e. 108w/cm2), corresponds to a surface absorption rate of g~1~31cm-3s-1, and therefore leads to ~>10'~cm-~. Because higher generation rates result in higher carrier densities, a number of important differences exist between the cases of low and high excitation. For high carrier densities (~>10' , /18/ the carrier-phonon scattering rate, which is proportional to N, is dominated by the rate of intercarrier collis~ons, which is proportional to iV2 and is found to exceed 1014 collisions/s. Additionally, a hot carrier may lose a considerable fraction of its energy (-lev) due to collisions with other carriers, whereas only a small fraction of an eV is lost by phonon emission. /19/ Therefore, carriers thermalize among themselves long before they thermalize with the lattice. Also at high carrier concentrations, recombination is comprised primarily of nonradiative Auger processes /20/ (with rates proportional to N ~ ) as opposed to the radiative recombination (with rates proportional to lower powers of N) that occurs at lower generation rates. Finally, higher values of g result in larger excited carrier gradients, thereby increasing the extent of carrier diffusion. Because typical pulsed laser annealing experiments involve generation rates inexcess of 10~~cm-'s-', this paper will focus on the high excitation regime. Thelaser energy is absorbedby thecarriers via both electron-hole pairexcitation and free-carrier absorption. At the startof the laser pulse, the former process dominates, but as the free carrier density rises, its contribution to the absorption grows. Because both mechanisms have characteristic N -dependent absorption lengths, the degree of excitation determines the details of the generated carrier profile. Both processes are phonon-assisted, but the amount of energy lost through phonon emission during absorption is negligible compared to the total energy absorbed per photon. The primary consequence of absorption, then, is the creation of a non-equilibrium distribution of very hot carriers which initially contains nearly all of the original laser energy. Theelectrons' and holes will thenrapidly begin to relax to thermal distributions characterized by distinct quasi-fermilevels but a common temperature Te = Th which greatly exceeds the lattice temperature. plasmons are emitted during this carrier thermalization process, /18,21/ most of which rapidly decay. Because plasmon energies exceed available phonon energies, the plasmons decay primarily by carrier reexcitation rather than by phonon emission. (During a short period near the start of the laser pulse,theplasmafrequency passes through resonance with the phonons, but only a small amount of energy will be transferred in this manner /1'6/). In addition, it will be shown that some of the excess carrier energy is used to thermally populate plasmon modes. The entire carrier thermalization process, as a consequence of the rapid carrier-carrier collisions at high carrier densities, occurs within 10-l4 s of excitation and does not involve appreciable transfer of energy from the carriers to the lattice. At these high densities, Auger processes will dominate the carrier recombination /20/. Except at extremely large N, the recombination time falls as /22/ 1/iV2. Auger reduces the laser generation-induced separation between the electron and hole quasifermi levels. However, the most important aspect of these processes is that the pair recombination energy is given to a third carrier, which then rapidly thermalizes with the remaining carriers through the means discussed above. As was the case for the phonon-assisted absorption processes, energy transferred to the lattice by any phonon emission accompanying the recombination is a negligible fraction of the total energy gained by the hot carrier. Consequently, althhugh the carrier number density changes, the carrier energy density does not. Because essentially all, of the energy is retained in the carrier system during absorption, carrier thermalization, and recombination, an interdependence is established between that energy and the carrier temperature and number density. The rela,tive amounts of pair creation and free carrier absorption, for example, are therefore unimportant, as are the details of the thermalization and recombination processes. The crucial aspect of these events is that they respond to the driving forces which tend to restore quasiequilibrium by redistributing the absorbed laser energy within the carrier system. The carrier energy is partitioned into three primary reservoirs : energy of excitation across the gap, kinetic energy, and thermally-excited collective carrier oscillations. Assuming dispersionless plasmons, the third contribution is given by with E the bulk dielectric constant /24/and m* the appropriate reduced effective mass. r /25/ The importance of this term is clear from figure 1, where the carrier temperature is plotted as a function of the average energy per carrier in excess of the gap excitation energy. The temperature falls below that value calculated by neglecting the plasmons. This reflects the fact that some of the carrier energy is tied up in the form of plasma oscillations rather than in kinetic energy. In other words, the heat capacity of the carrier system is increased as a consequence of the partitioning of energy into the additional degrees of freedom provided by the plasmons, so that an energy increment is less effective in raising the carrier temperature. where kc is the plasmon cutoff wavevector /18,23/ (roughly equal to the Debye wavevector) and w is the plasma frequency P Fig. 1 : k~ as a function of ( E -7%' E )/A'. Ed2--tot e G i s the con&ibution to the average energy per carr ier from excitation across the gap. C 4 1 0 JOURNAL DE PHYSIQUE This result is shown in figure 2, which depicts the fraction of the total carrier energy contained in the plasmons. For semiconductors under normal conditions the plasma frequency is sufficiently small that although many plasmons are thermally excited, their contribution to the total energy is negligible. For metals, on the other hand, the energy of the plasmons is so large that few are thermally excited and the fraction of the total energy that they contain is similarly small. However, for just those values of carrier temperature and density (km ~0.l—1 eV and tf~io — 10cm) relee vant to the pulsed laser generation rates referred to earlier, this fraction may be as large as 10 per cent.