Solidification kinetics of pulsed laser melted silicon based on thermodynamic considerations

Abstract

The measured solidification velocities in silicon after pulsed laser melting are analyzed in terms of thermodynamic and kinetic considerations. Both interface and thermal transport limited growth regimes are observed. From the observed kinetics in the 1–6-m/s regime, the undercooling at the liquid-solid interface can be calculated. At velocities ≤6 m/s the undercooling increases with interface velocity at the rate of 15±5 deg/m/s.

Experimental constraints on nonequilibrium interface kinetic models

“…[29] for solute trapping of Bi in Si (001), we may first assume that the value of the fundamental time-step of the Monte Carlo simulation can be assigned such that the solidification velocity in the simulation matches Baeri's reported solidification velocity of v = 1.8 m/s. If this is indeed the case then the reported simulation is very far from matching the measured velocity-undercooling relation for pure Si (001) within the range of experimental uncertainty [10][11][12][13][14][15][16] The authors compared their simulations to Baeri et al's original experiment in which there is considerable uncertainty about the actual solidification velocity. In the early solute trapping studies [29,30] the velocity was estimated using a numerical solution of the heat equation.…”

“…(c) The velocity-undercooling function for pure Si (001) has been measured [10][11][12][13][14][15][16]. Although some of the measurements are more direct than others, in all cases the reported "interface sluggishness" [17], d(∆T ) / d v or, for the cases under consideration, ∆T/v, near the melting point falls in the range 3-18 K/(m/s).…”

“…Typically, for Isingbased models to produce solute trapping in the past, an atomic mobility has had to be reduced so drastically that other unintentional departures from reality are manifested. For example, with the parameters in a Monte Carlo simulation adjusted to permit more trapping on (111) than (001) interfaces [25], the interfacial undercoolings were much greater than indicated by experiment [10][11][12][13][14][15][16]. In another example, an analytical model based on similar principles to those of the kinetic Ising model [26,27], with the parameters adjusted to permit trapping of dilute A in B, did not permit trapping of dilute B in A at any speed [5], in conflict with experiments on the SiGe system [5,9].…”

Modeling and Analysis of Novel Horizontal Ribbon Growth of Silicon Crystal

“…Additionally, we also found that the extent at which undercooling varies is dependent on the initial thickness value; this is because latent heat extraction decreases as the thickness is decreased, and the amount of surface heat extraction decreases as a result of reduced latent heat released through the surface. Galvin [19] reported that undercooling is dependent on the solidification velocity. Additionally, it has been previously reported that the solidification velocity increases as the undercooling temperature is increased, and that a high nucleation rate is helpful to generate smaller grains, whereas quasi-crystal and non-crystal silicon are generated when the undercooling temperature exceeds 225 K [20].…”

Faceted dendrite growth of silicon from undercooled melt of Si–Ni alloy

“…As described above the growth velocity of a /1 0 0S dendrite is smaller than that of a /2 1 1S dendrite and the results are is in agreement with experiments. The values of linear kinetic coefficient for /1 0 0S and /1 1 1S faces of silicon have been obtained by numerical simulations [35,36] or experiments [37][38][39], and most of the data for a (1 0 0) face of silicon are in the range from 0.2 to 0.05 m/s K. The value of linear kinetic coefficient for silicon alloys is not reported but it is supposed to be smaller than that of silicon because the driving force for solute partition at interface would be additionally necessary. Therefore the value of linear kinetic coefficient used in the simulation is acceptable, and the agreement between simulations and experiment show that the conditions in the simulations have been appropriately assumed.…”