利用热反射和电学测量实验评估金属薄膜中的维德曼-弗朗兹定律
Experimental assessment of the Wiedemann-Franz law in thin metal films using thermoreflectance and electrical measurements
- School of Energy and Power Engineering, Huazhong University of Science and Technology（华中科技大学能源与动力工程学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本研究通过SPS热反射和范德堡测量评估Al、Ti、Ta薄膜的WF定律，发现高电阻Ta薄膜偏差达40%，表明块体L_0不适用，为热建模提供指导。
AI中文摘要：
金属薄膜的准确热学性质对于微电子热建模以及当信号对薄膜热输运敏感时解释热反射测量至关重要。在实践中，薄膜热导率通常通过维德曼-弗朗兹（WF）定律从电阻率推断，使用索末菲-洛伦兹数L_0，忽略了声子贡献和依赖于微结构的散射。在此，我们将方波脉冲源（SPS）热反射技术与范德堡测量相结合，以表征通过热蒸发、电子束蒸发和磁控溅射制备的Al、Ti和Ta薄膜的热和电输运。从80到300 K的SPS测量得到薄膜热导率k_m和体积热容C_m，其中C_m与块体值在±8%内一致。与使用L_0和模拟电阻率\r{ho}_model (T)=\r{ho}_bulk (T)+\r{ho}_0的基于WF的估计相比，在300 K时，Al和Ti的k_m偏差为5-20%，而溅射Ta的偏差高达40%。虽然较小的偏差与实验不确定性相当，但Ta的大失配表明了将块体L_0应用于高电阻金属薄膜的局限性。从150到300 K的表观洛伦兹数L_app=k_m \r{ho}_meas/T进一步揭示，沉积诱导的无序、晶界散射和可能的相相关效应可以改变金属薄膜中热和电荷输运之间的关联。这些结果阐明了WF定律对沉积金属薄膜的适用性，并为热建模和热反射分析提供了实用指导。
英文摘要：
Accurate thermal properties of metal thin films are essential for microelectronic thermal modeling and for interpreting thermoreflectance measurements when signals are sensitive to film thermal transport. In practice, film thermal conductivity is commonly inferred from electrical resistivity via the Wiedemann-Franz (WF) law with the Sommerfeld-Lorenz number L_0, neglecting phonon contributions and microstructure-dependent scattering. Here, we combine square-pulsed source (SPS) thermoreflectance with van der Pauw measurements to characterize thermal and electrical transport in Al, Ti, and Ta thin films prepared by thermal evaporation, e-beam evaporation, and magnetron sputtering. SPS measurements from 80 to 300 K yield the film thermal conductivity k_m and volumetric heat capacity C_m, with C_m agreeing with bulk values within +/-8%. Compared with WF-based estimates using L_0 and a modeled resistivity, \r{ho}_model (T)=\r{ho}_bulk (T)+\r{ho}_0, k_m deviates by 5-20% for Al and Ti and up to 40% for sputtered Ta at 300 K. While the smaller deviations are comparable to experimental uncertainty, the large mismatch for Ta demonstrates the limitation of applying the bulk L_0 to highly resistive metal films. Apparent Lorenz numbers L_app=k_m \r{ho}_meas/T from 150 to 300 K further reveal that deposition-induced disorder, grain-boundary scattering, and possible phase-related effects can modify the correlation between heat and charge transport in thin metal films. These results clarify the applicability of the WF law to deposited metal thin films and offer practical guidance for thermal modeling and thermoreflectance analysis.
