Simulation of photoacoustic imaging of microcracks in silicon wafers using a structure-changeable multilayered thermal diffusion model

The detection characteristics for photoacoustic imaging of microcracks in silicon wafers were theoretically and quantitatively investigated using a numerical simulation. The simulation is based on a one-dimensional multilayered thermal diffusion model coupled with the thermal-wave impedance of each layer, the layer structures of which are constructed along the wafer surface and are variable according to the scanning position of the point heat source. As the modulation frequency was reduced, the spatial resolution of the temperature amplitude profile at the cracks decreased, showing good agreement with the experimentally obtained photoacoustic amplitude images. At a modulation frequency of 200 kHz, for cracks with narrow air gaps of up to 20 nm, which is much smaller than both the beam spot size of 1.5 microm and the thermal diffusion length of 12 microm, the temperature amplitude is twice that of regions without cracks, and the temperature contrast increased with an increase in the modulation frequency. These calculation results suggest the effectiveness of using a high modulation frequency, making it possible to detect microcracks of the order of 10 nm.