Modeling of luminescence phase delay for nondestructive characterization of Si wafers

Abstract

We have modeled the generation, diffusion, and recombination of photoexcited electrons and holes for the case of Czochralski Si wafers having a defect-free-zone (DFZ) device layer of thickness d above a highly precipitated wafer core and having a finite surface recombination velocity, S. The incident photoexcitation source has a Gaussian power distribution and is focused to a small spot on the sample surface. When the source is sinusoidally modulated at frequency ν, the intrinsic band-edge photoluminescence (PL) emission displays modulations at the fundamental and first overtone of the modulation frequency. The PL signals at frequencies ν and 2ν are delayed in phase, with respect to the source modulation by angles φ2(ν) and φ2(2ν). We relate these phase angles to material properties such as d, S, the optical absorption coefficient α at the incident wavelength, and to the effective carrier lifetimes τ1 and τ2 in the DFZ and precipitated wafer core, respectively. We show that when τ1 and τ2 are independently measured and S≲100 cm/s, as is common for a Si surface passivated with a thermally grown oxide layer, it is possible to deduce d from a measurement of φ2(ν) or φ2(2ν).