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In the backside interferometric thermal mapping technique, an infrared (IR) laser beam probes the temperature-induced changes in the semiconductor refractive index inside a semiconductor device, which results in a change in the measured optical phase shift. In this paper, a theoretical analysis of the phase shift is reported. The focus is on nanosecond-to-microsecond time-scale thermal mapping during high current stress, as occurring e.g., during an electrostatic discharge (ESD) event or in some power applications. An analytical expression for phase shift is obtained from the analysis of the thermal diffusion equation. The phase shift is directly proportional to the two-dimensional (2-D) heat energy density in the semiconductor active region of the device. The phase shift is also expressed in terms of the local dissipated heat energy and the heat transferred to the device top and lateral sides. In addition, the space integral of the phase shift is expressed in terms of a total energy dissipated in the device and the total heat transferred from the semiconductor to the top device layers. The theory shows an excellent agreement with experimental data obtained for a p-n diode ESD protection structure working in the avalanche regime.
Date of Publication: Nov 2002