考虑通孔效应和边缘传热效应的纳米级互连线温度分布模型

提出了同时考虑通孔效应和边缘传热效应的互连线温度分布模型,获得了适用于单层互连线和多层互连线温度分布的解析模型,并基于65 nm互补金属氧化物半导体（CMOS）工艺参数计算了不同长度单层互连线和多层互连线的温度分布.对于单层互连线,考虑通孔效应后中低层互连线的温升非常低,而全局互连线几乎不受通孔效应的影响,温升仍然很高.对于多层互连线,最上层互连线的温升最高,温升和互连介质层厚度近似成正比,而且互连介质材料热导率越低,温升越高.所提出的互连线温度分布模型,能应用于纳米级CMOS计算机辅助设计. 关键词： 通孔效应 边缘传热效应 纳米级互连线 温度分布模型     

An RLC interconnect analyzable crosstalk model considering self-heating effect

According to the thermal profile of actual multilevel interconnects, in this paper we propose a temperature distribution model of multilevel interconnects and derive an analytical crosstalk model for the distributed resistance-inductance-capacitance (RLC) interconnect considering effect of thermal profile. According to the 65-nm complementary metal-oxide semiconductor (CMOS) process, we compare the proposed RLC analytical crosstalk model with the Hspice simulation results for different interconnect coupling conditions and the absolute error is within 6.5%. The computed results of the proposed analytical crosstalk model show that RCL crosstalk decreases with the increase of current density and increases with the increase of insulator thickness. This analytical crosstalk model can be applied to the electronic design automation (EDA) and the design optimization for nanometer CMOS integrated circuits.     

A multilevel nano-scale interconnection RLC delay model

Based on the multilevel interconnections temperature distribution model and the RLC interconnection delay model of the integrate circuit,this paper proposes a multilevel nano-scale interconnection RLC delay model with the method of numerical analysis,the proposed analytical model has summed up the influence of the configuration of multilevel interconnections,the via heat transfer and self-heating effect on the interconnection delay,which is closer to the actual situation.Delay simulation results show that the proposed model has high precision within 5% errors for global interconnections based on the 65 nm CMOS interconnection and material parameter,which can be applied in nanometer CMOS system chip computer-aided design.     

考虑通孔和边缘效应的互连网络热电分析

考虑互连通孔和边缘效应,建立互连层间、层内、通孔热阻模型,利用热电二元性,提出一种考虑温度效应对热流影响的热电耦合仿真方法,利用热电之间的反馈关系,修正建模后的温度分布对节点网络热流的影响.并对以聚合物和硅氧化物为介质的多层互连进行分析,以有限元建模结果为参照,与已有模型相比,互连热分布结果的相对标准差分别降低了71.2%、12.9%.考虑通孔效应和边缘效应后,该方法在不同纳米级工艺中所得峰值温升,较已有模型均有一定程度的降低.     

Investigating the thermal conductivity of materials by analyzing the temperature distribution in diamond anvils cell under high pressure

Investigating the thermal transport properties of materials is of great importance in the field of earth science and for the development of materials under extremely high temperatures and pressures. However, it is an enormous challenge to characterize the thermal and physical properties of materials using the diamond anvil cell (DAC) platform. In the present study, a steady-state method is used with a DAC and a combination of thermocouple temperature measurement and numerical analysis is performed to calculate the thermal conductivity of the material. To this end, temperature distributions in the DAC under high pressure are analyzed. We propose a three-dimensional radiative-conductive coupled heat transfer model to simulate the temperature field in the main components of the DAC and calculate in situ thermal conductivity under high-temperature and high-pressure conditions. The proposed model is based on the finite volume method. The obtained results show that heat radiation has a great impact on the temperature field of the DAC, so that ignoring the radiation effect leads to large errors in calculating the heat transport properties of materials. Furthermore, the feasibility of studying the thermal conductivity of different materials is discussed through a numerical model combined with locally measured temperature in the DAC. This article is expected to become a reference for accurate measurement of in situ thermal conductivity in DACs at high-temperature and high-pressure conditions.     

一种基于多目标约束的互连线宽和线间距优化模型

优化线宽和线间距已经成为改善系统芯片性能的关键技术.本文基于互连线线宽和线间距对互连延时、功耗、面积和带宽的影响,提出了基于多目标优化方法实现优化线宽和线间距的思路,并利用曲线拟合方法得到了多目标约束的解析模型.Hspice验证结果显示,该解析模型精度较高,平均误差不超过5%,算法简单,能有效弥补应用品质因数方法的缺陷,可以应用于纳米级互补金属氧化物半导体系统芯片的计算机辅助设计.     

Study of thermal conductivity and thermal rectification in exponential mass graded lattices

Concept of exponential mass variation of oscillators along the chain length of N oscillators is proposed in the present Letter. The temperature profile and thermal conductivity of one-dimensional (1D) exponential mass graded harmonic and anharmonic lattices are studied on the basis of Fermi-Pasta-Ulam (FPU) β model. Present findings conclude that the exponential mass graded chain provide higher conductivity than that of linear mass graded chain. The exponential mass graded anharmonic chain generates the thermal rectification of 70-75% which is better than linear mass graded materials, so far. Thus instead of using linear mass graded material, the use of exponential mass graded material will be a better and genuine choice for controlling the heat flow at nano-scale.     

氮化硅纳米薄膜非平衡热导率实验研究

3ω实验方法是一种可以对薄膜热导率进行瞬时测量的方法。根据3ω方法测试原理,搭建了薄膜导热系数测试平台,并且分别测试低频率段和高频段薄膜与基底的温升以及薄膜热导率。测试结果表明:Si3N4薄膜的热导率随温度的升高而增大;高频段下,热导率受频率影响大,误差大;在低频段下薄膜热导率与频率变化基本无关;基于电子与声子的局部热平衡运输方程假设,S i3N4薄膜的热导率具有极度非平衡性;通过比较电阻、热导率与温度的关系可以看出加热器的尺寸大小会影响薄膜的热导率,最佳加热器的宽度选用20μm左右。     

Model for heat conduction in nanofluids

A comprehensive model has been proposed to account for the large enhancement of thermal conductivity in nanofluids and its strong temperature dependence, which the classical Maxwellian theory has been unable to explain. The dependence of thermal conductivity on particle size, concentration, and temperature has been taken care of simultaneously in our treatment. While the geometrical effect of an increase in surface area with a decrease in particle size, rationalized using a stationary particle model, accounts for the conductivity enhancement, a moving particle model developed from the Stokes-Einstein formula explains the temperature effect. Predictions from the combined model agree with the experimentally observed values of conductivity enhancement of nanofluids.     

GaN薄膜的热导率模型研究

准确预测GaN半导体材料的热导率对GaN基功率电子器件的热设计具有重要意义.本文基于第一性原理计算和经典Debye-Callaway模型,通过分析和完善Debye-Callaway模型中关于声子散射率的子模型,建立了用于预测温度、同位素、点缺陷、位错、薄膜厚度、应力等因素影响的GaN薄膜热导率的理论模型.具体来说,对声子间散射项和同位素散射项基于第一性原理计算数据进行了系数拟合,讨论了两种典型的处理点缺陷和位错散射的散射率模型,引入了应用抑制函数描述的各向异性边界散射模型,并对应力的影响进行了建模.热导率模型预测值和文献中典型实验数据的对比表明,基于第一性原理计算数据拟合的热导率模型和实验测量值总体符合较好,300 K温度附近热导率数值及其随温度变化的趋势存在20%左右的偏差.结合实验数据和热导率模型进一步确认了第一性原理计算会高估同位素散射的影响,给出了薄膜热导率随薄膜厚度、位错面密度、点缺陷浓度的具体变化关系,同位素和缺陷散射会减弱薄膜热导率的尺寸效应,主要体现在100 nm附近及更小的厚度范围.     

使用条件生成对抗网络生成预定导热率多孔介质

多孔介质在工程领域中的应用非常广泛,其中有效导热率和孔隙率为多孔介质材料非常重要的性质,得到一个符合需要的有效导热率和孔隙率的多孔介质材料具有重要意义.本文使用四参数随机生成方法制作了训练数据集,搭建了一个条件生成对抗网络(CGAN),使用预定的有效导热率和孔隙率作为输入,生成一个满足输入条件的多孔介质结构.特别地,由于多孔介质的孔隙结构分布对材料的有效导热率影响巨大,提出局部结构损失函数参与网络训练,使得网络更好地学习到孔隙分布与导热率之前的关系.通过使用格子Boltzmann方法验证神经网络生成的多孔介质结构的有效导热率,结果表明该方法能够快速且准确地生成预定参数的多孔介质结构.     

板状激光振荡介质温度场和应力场的数值模拟

以非均匀内热源模型为基础,并考虑材料的导热系数和热膨胀系数的温度相关性,利用有限元方法,对板状激光振荡介质在不同功率和冷却强度下的温度和热应力分布进行了数值模拟及分析。根据计算结果提出了最大有效换热系数的概念,指出换热系数超过最大有效换热系数后,继续强化传热对减小高功率激光器的热效应已无明显效果。以此得出采用常规冷却技术所允许的最大泵浦加热功率。     

聚乙烯单链量子热输运的同位素效应

高分子导热材料的有效调控受到了日益广泛的关注.应用密度泛函理论(DFT)、中央插入延展(central insertion scheme,CIS)方法及非平衡格林函数(NEGF)理论,对包含432个原子、长18.533 nm的聚乙烯单链量子热输运的同位素效应进行了研究.计算结果表明,室温下长100 nm的纯12C聚乙烯单链的热导率理论上限高达314.1 W·m~(-1)·K~(-1);对于~(12)C聚乙烯单链,其他条件一定时,~(14)C掺杂引起的热导同位素效应比~(13)C更为显著;室温下纯~(12)C聚乙烯单链中~(14)C掺杂原子百分数为50%时同位素效应最显著,此时平均热导比未掺杂时下降了51%.这对探索聚乙烯材料热输运的同位素影响机理具有十分积极的意义.     

Electronic thermal Hall effect in silicene

We theoretically investigate the electronic thermal Hall effect in silicene via a discrete four-band model. Based on the linear response theory, a formalism to address the transverse thermal conductivity is developed. In the absence of an exchange field, the transverse thermal conductivity vanishes due to the time-reversal symmetry. The transverse conductivity becomes finite in the presence of an exchange field and exhibits several peaks with opposite signs. The peak values increase as the field becomes strong. However, as the temperature becomes high, the peak values begin to decay. The results may be helpful in exploring spin caloritronics based on silicene.     

Nonlocal heat conduction in suspended graphene

In order to investigate the mechanism of the extremely high thermal conductivity of the suspended graphene, a nonlocal heat conduction model of heat conduction in two-dimensional materials under a temperature gradient along the length direction is proposed. This model shows that the heat transport of the suspended graphene along the length direction under the nonlocal effect in the width and thickness directions demonstrates a similarity with the viscous Poiseuille flow between two parallel plates. Based on this model, the dimensional crossover of heat conduction in few-layer graphene is demonstrated and the impact of temperature variation on the thermal conductivity of graphene is investigated. The obtained results show a good agreement with the experimental ones. The proposed model indicates that the combination of the Poiseuille phonon transport and boundary conditions on the upper and lower surfaces of the suspended graphene plays a decisive role on the ultra-high heat conductivity of graphene.     

集成电路微互连结构中的热迁移

高工作电流在集成电路微互连结构中产生大量焦耳热,引起局部区域的温升、形成高温度梯度,金属原子沿着温度梯度反向运动发生热迁移.热迁移是集成电路微互连失效的主要原因之一.阐述了热迁移原理、失效模式及原子迁移方程.综述和分析了在单纯温度场、电场和温度场耦合等不同载荷条件下金属引线和合金焊料的热迁移研究.归纳并提出了集成电路微互连结构热迁移研究亟待解决的问题. 关键词： 集成电路 微互连 热迁移     

An interconnect width and spacing optimization model considering scattering effect

As the feature size of the CMOS integrated circuit continues to shrink, the more and more serious scattering effect has a serious impact on interconnection performance, such as delay and bandwidth. Based on the impact of the scattering effect on latency and bandwidth, this paper first presents the quality-factor model which optimises latency and bandwidth effectively with the consideration of the scattering effect. Then we obtain the analytical model of line width and spacing with application of curve-fitting method. The proposed model has been verified and compared based on the nano-scale CMOS technology. This optimisation model algorithm is simple and can be applied to the interconnection system optimal design of nano-scale integrated circuits.     

A thermal conductivity model for nanofluids including effect of the temperature-dependent interfacial layer

The interfacial layer of nanoparticles has been recently shown to have an effect on the thermal conductivity of nanofluids. There is, however, still no thermal conductivity model that includes the effects of temperature and nanoparticle size variations on the thickness and consequently on the thermal conductivity of the interfacial layer. In the present work, the stationary model developed by Leong et al. (J Nanopart Res 8:245–254, 2006) is initially modified to include the thermal dispersion effect due to the Brownian motion of nanoparticles. This model is called the ‘Leong et al.’s dynamic model’. However, the Leong et al.’s dynamic model over-predicts the thermal conductivity of nanofluids in the case of the flowing fluid. This suggests that the enhancement in the thermal conductivity of the flowing nanofluids due to the increase in temperature does not come from the thermal dispersion effect. It is more likely that the enhancement in heat transfer of the flowing nanofluids comes from the temperature-dependent interfacial layer effect. Therefore, the Leong et al.’s stationary model is again modified to include the effect of temperature variation on the thermal conductivity of the interfacial layer for different sizes of nanoparticles. This present model is then evaluated and compared with the other thermal conductivity models for the turbulent convective heat transfer in nanofluids along a uniformly heated tube. The results show that the present model is more general than the other models in the sense that it can predict both the temperature and the volume fraction dependence of the thermal conductivity of nanofluids for both non-flowing and flowing fluids. Also, it is found to be more accurate than the other models due to the inclusion of the effect of the temperature-dependent interfacial layer. In conclusion, the present model can accurately predict the changes in thermal conductivity of nanofluids due to the changes in volume fraction and temperature for various nanoparticle sizes.     

Nanoscale thermal cloaking by in-situ annealing silicon membrane

With the advent of thermal metamaterials, many new thermal functionalities have been proposed, like thermal cloaking, concentrating, etc. However, these thermal functionalities are based on the transformation thermotics or scattering cancellation technique, which, derived from Fourier's law, cannot apply to the micro-/nanoscale counterparts. In this paper, we design a nanoscale thermal cloak based on a crystalline silicon (Si) membrane and investigate the in-plane phonon transport via non-equilibrium molecular dynamics (NEMD) simulation by in-situ tuning the thermal conductivity of the thermal cloak from crystalline Si to amorphous Si. The two-dimensional temperature profile is obtained, and the thermal cloaking effect is evaluated by the ratio of heat flux. By analyzing the phonon density of state (PDOS) and the mode participation ratio (MPR), the mechanism can be attributed to the phonon localization in the annealed cloaking region. The proposed nanoscale thermal cloak by in-situ tuned thermal conductivity, may trigger the development of nanoscale thermal functionalities and open avenues for and thermal management for nano-photonics and nano-electronics.     

Efficient thermal analysis method for large scale compound semiconductor integrated circuits based on heterojunction bipolar transistor

In this paper, an efficient thermal analysis method is presented for large scale compound semiconductor integrated circuits based on a heterojunction bipolar transistor with considering the change of thermal conductivity with temperature.The influence caused by the thermal conductivity can be equivalent to the increment of the local temperature surrounding the individual device. The junction temperature for each device can be efficiently calculated by the combination of the semianalytic temperature distribution function and the iteration of local temperature with high accuracy, providing a temperature distribution for a full chip. Applying this method to the InP frequency divider chip and the GaAs analog to digital converter chip, the computational results well agree with the results from the simulator COMSOL and the infrared thermal imager respectively. The proposed method can also be applied to thermal analysis in various kinds of semiconductor integrated circuits.