Investigation of Mechanical Properties, Thermal Properties and Their Correlations of Micro-scale Silicon Structures

Ming Gan, Purdue University

Abstract

Silicon micro-structures have been the essential parts of the microprocessors, sensors, microelectromechanical systems and metal-oxide-semiconductor field-effect transistors. For many of the electronic devices listed above, unwanted stress inside the device is almost inevitable. The stress could be generated from the attached materials with different thermal expansion rates, non-planar crystal growth or the packaging process. The unwanted stress reduces the reliability of the electronic devices. Besides the unwanted stress, there is another factor which eliminates the reliability and performance of the electronic devices – the generated heat. The temperature increase caused by the generated heat can reduce the operating frequency of the processor, and also reduce the channel mobility of silicon. At micro-scale, the mechanical stress and thermal properties are correlated to each other. The mechanical stress affects the thermal conductivity of silicon at micro-scale. The temperature gradient also generates thermal stress. Although the unwanted stress creates drawback to the performance and reliability of the semiconductor devices, the stress/strain can be utilized to enhance the performance as well. Similarly, the thermal conductivity of silicon can also be tuned to enhance the performance of the silicon devices. Therefore, the research of the mechanical properties, thermal properties and their correlations of silicon at micro-scale have attracted our research interest. There are multiple experimental methods available for measuring mechanical stress/strain and thermal conductivity at micro-scale, e.g. X-ray diffraction, transmission electron microscope, 3&ohgr; method, and Raman spectroscopy, etc. Compared with other experimental methods, Raman spectroscopy has the advantage of being non-contact, non-destructive and requiring minimal sample preparation. Most importantly, it can be integrated with the nano-loading system, which is necessary for investigation of the mechanical properties at micro-scale. In this research, an innovative test platform with corresponding measurement technique was developed, based on nano-loading system, temperature control module and Raman spectroscopy setup. The multi-functional platform was used to investigate the correlations of the global stress and nonlocal stress, the effect of mechanical stress on the thermal conductivity, and also the creep behavior of silicon at micro-scale and different temperatures. The Raman shift of silicon is affected by both stress and temperature. Separation of the stress-induced Raman shift and temperature-induced Raman shift is a prerequisite to perform the study of stress dependence of thermal conductivity. The separation process was based on the Stokes peak detection. The peak detection method is independent of the exposure time and the laser power, which makes this method more reliable than the one based on Stokes peak detection plus width observation. After separation of the Raman shift induced by the mechanical stress and temperature, the relationship between global stress and nonlocal stress, and the effect of mechanical stress on the thermal conductivity of the silicon cantilever were investigated. The result showed that the global stress overestimated the nonlocal stress in the silicon cantilever, due to the size effect. In the area of strain engineering, higher strain/stress leads to higher performance enhancement. This finding means that the upper bound limit of the stress/strain that can be applied to the silicon micro-structures could be higher than the value previously estimated using continuum theory. For the thermal conductivity dependence on stress, the experiments were performed with two different methods – the static method and the Raman spectroscopy method. The results from two different methods showed good agreement on the increase of the thermal conductivity caused by compressive stress. The increasing trend of the thermal conductivity also matches with values from literatures. The results showed that the compressive stress enhances the thermal conductivity mainly by increasing the group velocity of high-frequency phonons. The last part of this research is the creep behavior of the silicon micro-structures and the effect of creep on the Raman spectroscopy measurement. The silicon cantilever exhibited a unique creep behavior with much lower stress exponent value. It also showed that during the time interval of the Raman spectroscopy measurement, there was no obvious dependence of the Raman shift value on the creep of silicon, because the change of the strain was more than one magnitude smaller than the investigated strain level in this research. Overall, this research investigated the mechanical and thermal properties, and their interactions of silicon micro-structures at micro-scale and different temperatures. This research has both theoretical impact and experimental impact - it characterized the relationship between global and nonlocal stresses; it analyzed the effect of mechanical stress on thermal conductivity and found the physical interpretation of this phenomenon; also it presented a novel test platform for integrated thermal and mechanical measurements at micro-scale and different temperatures.

Degree

Ph.D.

Advisors

Tomar, Purdue University.

Subject Area

Mechanical engineering|Materials science

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