Theory of Non-linear Heat Conduction

大温度梯度下的热输运是当前研究的热点问题。为了开发消除离子注入材料中注入损伤的方法，以及生产亚稳态化合物和过饱和合金，实现半导体材料的快速熔化和随后的再结晶是重要的。当热量在固相中流动时，温度分布变化高达每厘米10度并不罕见。在足够大的温度梯度下，热传导变得异常，特别是在固液界面附近。这一现象尚未完全被理解，但已知的是，半导体中高温下的热传导涉及几个过程，包括一些高度非线性的过程，这可能会导致这种反常情况。在这项研究项目中，杰拉尔德·马汉教授与智利天主教大学的弗朗西斯科·克拉罗教授合作，计划研究硅和锗固体熔融界面附近的热诱导间隙缩小对载流子的捕获。能带变窄产生了一种限制势，这应该有助于发展电子和电子-空穴对热传输的理论。此外，研究人员感兴趣的是温度梯度抑制热传导的阈值，以及在固体-熔体界面附近稳定热流下的空间分布。马汉教授在半导体和非线性传输理论方面的专业知识与Claro教授在热传输技术方面的互补背景相结合，创建了一支高度合格的团队来解决这一复杂而重要的研究。这种合作的互惠互利符合发展中国家科学计划的一个重要标准。

Heat transport under a large temperature gradient is a topic of much current interest. In order to develop methods for removing implantation damage in ion-implanted materials and, also, to produce metastable compounds and supersaturated alloys, it is important to achieve rapid melting and subsequent recrystallization of semiconductor materials. As heat flows in the solid phase, temperature profiles varying as much as 10 degrees per centimeter are not unusual. Under a large enough temperature gradient, heat conduction becomes anomalous, particularly near solid-liquid interfaces. The phenomenon is not yet fully understood but it is known that thermal conduction at high temperatures in semiconductors involves several processes, including some highly non-linear ones, that may contribute to the anomalous case. In this research project, Professor Gerald Mahan, in collaboration with Professor Francisco Claro of the Catholic University of Chile plans to investigate the trapping of carriers by a thermally induced gap-narrowing near the solid-melt interface in silicon and germanium. The band narrowing produces a confining potential that should be helpful in developing a theory of heat transport by electrons and electron-hole pairs. Additionally, the investigators are interested in the threshold for suppression of thermal conduction by temperature gradients, and in obtaining the space profile under steady heat flow near solid-melt interfaces. The combination of Professor Mahan's expertise with semiconductors and with nonlinear transport theory, with Professor Claro's complementary background in thermal transport techniques, creates a highly qualified team for addressing this complex and significant research. The mutual benefits of this collaboration fulfill an important criterion of the Science in Developing Countries Program.