Numerical Analysis of Thermal Stress in a Voltage Standard Chip

The thermal stress of the voltage standard chip soldered on a copper or sapphire substrate was numerically analyzed by a finite element method. It was confirmed that the thermal stress in the chip soldered on the sapphire substrate is much smaller than that in the chip soldered on the copper substrate. Since the magnitude of the thermal stress applied to the chip depended on the thickness of the substrate, the thickness of the substrate should be properly chosen, e.g., the 0.5-mm thick sapphire minimized the thermal stress for the 0.4-mm thick silicon chip. It was also found that the copper substrate with a few slits did not decrease the risk of the damage due to the thermal stress.