Effect of Inhomogeneous Temperature in Chip-Scale Infrared Thermal Sources: A Revisited Blackbody Radiation Formula with Experimental Validation

Abstract

Miniature and low-cost light sources are highly desirable for numerous optical microsystems. Among these, devices based on blackbody radiation of a filament heated at a few hundred degrees, perfectly fit with the requirements of producing a broad spectral range falling in the infrared range, owing to Planck's law. These light sources are of primary interest for Fourier transform infrared (FTIR) spectroscopy. Although thermal light production is simple, achieving precise light intensity is not a trivial task. Herein, the impact of the inhomogeneous temperature on the emitted radiation is studied. Blackbody radiation formulae are revisited for miniature sources, taking into account the temperature distribution and using the principle of superposition of non-coherent sources. A theoretical model is formulated by dividing the source into multiple annular elementary sources of different temperature. This results in effective, corrected blackbody emission. Analytical formulae are derived in the case of a quadratic temperature distribution. For the experimental validation, a silicon-based source, made of a platinum resistive micro-heater on top of heavily doped silicon, is fabricated and experimentally characterized at temperatures ranging from 300 to 520 K. The experimental results show good agreement with the model predictions in the explored wavelength range of (λ = 2.5–4.8 µm).