Fully nonlinear photocarrier radiometry / modulated photoluminescence dynamics in semiconductors: Theory and applications to quantitative deconvolution of multiplexed photocarrier density wave interference and recombination processes

Abstract Semiconductor characterization techniques based on modulated photoluminescence (PL) combine the general advantages of PL metrology with the superior quality benefits of modulated signal generation and lock-in detection. The exciting field of camera-based PL imaging has recently emerged and is proving to be very promising for in-line spatially resolved and globally integrated monitoring of dynamic electronic properties of semiconductor materials and devices during various fabrication and manufacturing stages. Yet, the multiple nonlinearities involved in dynamic PL and their behavior under modulated excitation have neither been adequately addressed theoretically nor quantitatively analyzed, resulting in either misleading interpretations of experimental data or leading to the popular compromise of using the physically ambiguous concept — effective lifetime — as the target measurement parameter, which lumps all the excess carrier de-excitation events together and creates persistent confusion in the comparison among different lifetime measurement techniques. By taking three dominant nonlinearities into account that contribute to dynamic PL responses in Si, the present investigation provides a fully nonlinear frequency-domain model of carrier recombination dynamics under harmonically modulated excitation, based on which six intrinsic electronic parameters of a Si wafer can be resolved and measured simultaneously, i.e. the doping density, the two Shockley-Read-Hall time constants, the radiative recombination coefficient, and the two Auger recombination coefficients. The combined theoretical and experimental technique represents a time demultiplexing methodology which allows the deconvolution of temporally superposed excess carrier de-excitation processes which might otherwise remain unresolved — hidden in superposition — as is typically the case with conventional effective lifetime metrologies. This all-optical and non-contacting electronic quality control approach links substrate property optimization and key device-fabrication processing steps to optimized device performance through elucidating the relationship between the global behavior of the system/device/material and the specific controlling/limiting dynamic (opto)electronic process(es) behind it.