Using noise to stochastically enhance the resolution of charge coupled device based thermoreflectance imaging

Abstract

Charge coupled device (CCD) based, frequency-domain thermoreflectance imaging can be used to characterize the thermophysical properties of solid-state materials, as well as electronic and optoelectronic devices. A four-bucket algorithm is used to obtain the amplitude and phase of the thermoreflectance signal, i.e. the relative change in reflectance of a sample in response to an induced thermal modulation. Prior experiments have shown that thermoreflectance signals smaller than the bit depth of the camera can be accurately measured; this enhanced resolution is posited to be due to stochastic resonance, in which measurement noise dithers the signal over multiple bit levels. Here, we develop an experimentally validated analytical and computational model of the quantization error imposed on the thermoreflectance measurement by the analog-to-digital conversion at the CCD camera and of stochastic resonance in this imaging system, examining how measurement noise, combined with averaging required by the imaging algorithm, can be used to maximize the thermal resolution. We demonstrate analytically and experimentally that noise is required to obtain accurate thermoreflectance measurements; in the absence of noise, the analog-to-digital conversion can lead to large errors in the measured thermoreflectance signal for experimentally reasonable signal levels. Using the model, we derive a close upper bound for the optimal noise amplitude of the thermoreflectance measurement system. Furthermore, we show that, by tuning the experimental parameters, stochastic resonance enhancement can be achieved for any noise level, enabling an order of magnitude or greater improvement in the thermal resolution of this key technique for thermophysical characterization of materials and devices.