Joule heating in nanowires
Joule heating in nanowires
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DOI：
10.1103/physrevb.84.054437
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发表时间：
2011-08-11
影响因子：
3.7
通讯作者：
Meier, Guido
中科院分区：
文献类型：
--
作者：
Fangohr, Hans;Chernyshenko, Dmitri S.;Meier, Guido
我们研究了流经铁磁纳米线的电流产生的焦耳加热对纳米线的温度和生长纳米线的衬底温度的影响。模拟了纳米线和衬底中电流密度的空间分布、相关热的产生和热的扩散。我们研究了几种不同的纳米线和约束几何以及不同的衬底：(薄的)氮化硅薄膜、(厚的)硅晶片和(厚的)金刚石晶片。计算了作为时间函数的空间分辨温度升高。对于有效的三维衬底(其中衬底厚度大大超过纳米线长度)，我们确定了三种不同的通过衬底的热传播区域：区域(I)，其中纳米线温度随时间以近似对数的方式增加。在这种情况下，You等人很好地解析地描述了纳米线温度。[APPL.太棒了。让我们来吧。，222513(2006年)]。我们给出了时间t(C)的解析表达式，它标志着You模型的适用上限。在TC之后，热流进入区域(II)，在该区域中，纳米线的温度保持恒定，而半球形的热锋将热量从线上带走并进入衬底。当热锋到达衬底边界时，进入区域(III)，此时纳米线和衬底温度开始快速增加。对于有效的二维衬底(纳米线长度远远超过衬底厚度)，在热锋到达衬底边界之前，只存在一个温度随时间对数增加的区域。我们提供了一个对所有脉冲持续时间都有效的解析表达式，它允许人们准确地计算薄衬底上纳米线的温度升高。
We study the effect of Joule heating from electric currents flowing through ferromagnetic nanowires on the temperature of the nanowires and on the temperature of the substrate on which the nanowires are grown. The spatial current density distribution, the associated heat generation, and diffusion of heat are simulated within the nanowire and the substrate. We study several different nanowire and constriction geometries as well as different substrates: (thin) silicon nitride membranes, (thick) silicon wafers, and (thick) diamond wafers. The spatially resolved increase in temperature as a function of time is computed. For effectively three-dimensional substrates (where the substrate thickness greatly exceeds the nanowire length), we identify three different regimes of heat propagation through the substrate: regime (i), where the nanowire temperature increases approximately logarithmically as a function of time. In this regime, the nanowire temperature is well described analytically by You et al. [Appl. Phys. Lett. 89, 222513 (2006)]. We provide an analytical expression for the time t(c) that marks the upper applicability limit of the You model. After tc, the heat flow enters regime (ii), where the nanowire temperature stays constant while a hemispherical heat front carries the heat away from the wire and into the substrate. As the heat front reaches the boundary of the substrate, regime (iii) is entered, where the nanowire and substrate temperature start to increase rapidly. For effectively two-dimensional substrates (where the nanowire length greatly exceeds the substrate thickness), there is only one regime in which the temperature increases logarithmically with time for large times, before the heat front reaches the substrate boundary. We provide an analytical expression, valid for all pulse durations, that allows one to accurately compute this temperature increase in the nanowire on thin substrates.