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(369g) Fluid Instabilities, Density Stratification, and Lee Waves That Result in Growth Limitations and Morphological Instability of Liquid-Crystal Interfaces

Authors: 
Peterson, J. H., University of Minnesota
Derby, J. J., University of Minnesota
It has long been known that bulk crystal growth processes are strongly affected by fluid flows arising from radial temperature and density gradients. In this presentation, we present new insight to flows that arise from the interactions of a destabilizing radial temperature profile and a stabilizing vertical gradient. This interaction explains a decades-long issue that has plagued the growth of the II-VI semiconductor, cadmium telluride, from a liquid solvent in a system known as the traveling heater method (THM).

Historically, the THM has suffered from growth rates that are an order of magnitude slower than other directional solidification techniques. We demonstrate that the growth rate limit in the THM system is intrinsically tied to a phenomenon known as lee waves, most typically observed in atmospheric flows. On the downwind side of a mountain, the denser air at low altitude acts as a spring to resist the downward flow of air coming over the mountain. The spring-like effect causes the flow to enter into an oscillation that can extend hundreds of miles downwind of the mountain itself. These standing waves are then called lee waves due to their downwind position and can often be observed in the formation of wave clouds that appear to hover motionless at regular intervals.

In our analysis of flows in the THM, we examine the role of buoyancy, not only as the primary driving force for flow in the system but also through its stabilizing influence that results in the creation of lee waves. First, we present results from a finite-element model of the THM that demonstrate the strong coupling between mass, momentum, and heat transport. Model predictions provide quantitative evidence for the formation of lee waves in the liquid zone of the THM.

Furthermore, we show how these lee waves lead to anomalous mass transfer in the melt zone, promoting excess solvent underneath the peak of the standing wave at the phase change interface. These regions of high solvent concentration depress the local melting temperature via conitutional effects, leading to undercooling of the liquid. We then discuss how the linear stability analysis of Mullins and Sekerka [1] predicts that this undercooling will cause the normally stable, planar phase-change interface to become unstable and develop a cellular structure. Thus, the outcome of the lee-wave structure is that stable growth is limited to rates far less than expected. Additionally, we will discuss possible process improvements that could either eliminate or help manage the undercooling in front of the solidification interface.

[1] W. W. Mullins and R. F. Sekerka, “Stability of a planar interface during solidification of a dilute binary alloy”, Journal of Applied Physics 35(2), pp. 444–451 (1964).

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This work has been supported in part by the National Science Foundation, under DMR-1007885, and no official endorsement should be inferred.

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