Theoretical Analysis of Ahermal Conductivity in Amorphous Inter-layer Dielectrics
- PDF / 735,372 Bytes
- 7 Pages / 612 x 792 pts (letter) Page_size
- 78 Downloads / 175 Views
0914-F03-01
Theoretical Analysis of Ahermal Conductivity in Amorphous Inter-layer Dielectrics Manu Shamsa1, Patrick Morrow2, and Shriram Ramanathan2 1 Electrical Engineering, UC Riverside, Riverside, CA, 92521 2 Components Research, Intel, Hillsboro, OR, 97124
ABSTRACT Understanding thermal conduction in interlayer dielectrics (ILDs) is important for the optimal design of interconnect layers in backend semiconductor processing for future highperformance nano-scale devices. Reduced thermal conductivity of porous ILDs for example can adversely affect the temperature rise in the embedded metal lines leading to un-desirable reliability issues and design constraints. In this paper, we report results of our theoretical and experimental investigation of thermal transport in amorphous and porous dielectrics. A phononhopping model has been adapted to calculate the thermal conductivity in disordered materials. The value of hopping integral has been calculated by comparing the modeling results with experimental data for various amorphous and porous materials. The model shows reasonable agreement with experimental data for various amorphous materials including SiO2 and other glasses over a wide temperature range from 50K – 300K. The model suggests that the hopping of localized high frequency phonons is a dominant thermal transport mechanism in such material systems. INTRODUCTION Low-dielectric constant dielectrics are presently being intensively researched for integration into interconnect architectures in high-performance microprocessors [1]. The thermal conductivity of such dielectrics tend to be lower than that of amorphous silicon dioxide thereby leading to higher temperatures in the embedded metal interconnect lines for the same current density [2]. Such a temperature rise can lead to reduced performance as well as reliability issues in interconnects [3-7]. Thus, an understanding of thermal transport in such materials is crucial in the selection of suitable dielectrics and also in the design of interconnect layers. Prior models for thermal conductivity of amorphous materials include the Cahill-Pohl model [8] which was a modification of the Einstein expression [9] to calculate minimum thermal conductivity of solids. Empirical models have been proposed for the thermal conductivity of porous dielectrics [10], however these are based on rule of heterogeneous mixtures and do not necessarily consider the heat conduction at the atomic scale. It is therefore of fundamental scientific interest as well to develop models for thermal conduction that take into account the microstructure effects as well. In this paper, we report our theoretical examination of thermal transport in amorphous and porous dielectrics and calculate thermal conductivity as a function of temperature. The modeling results have been compared with reported experimental data for various amorphous materials.
We have evaluated the thermal conductivity of amorphous materials by suitable modification of the phonon-hopping model originally developed for polycrystall
Data Loading...
