Defect concentration analysis: Combining Laplace deep-level transient spectroscopy with constrained curve fitting

Abstract

Deep-level transient spectroscopy is the standard technique for characterizing electrically active defects in semiconductors. The conventional double-boxcar evaluation fails when multiple defect emissions overlap, causing peak broadening or merging. Two established routes overcome this resolution limitation: The numerical inverse Laplace transform resolves closely spaced emission rates but inherits regularization-dependent peak shapes that bias the recovered amplitudes, particularly for imbalanced peaks, while direct multi-exponential time-domain fitting avoids regularization yet is sensitive to noise and prone to overfitting when rates and amplitudes are determined simultaneously as free parameters. This work presents a two-step evaluation routine that combines Laplace transform analysis with constrained multi-exponential curve fitting of the capacitance transient. The inverse Laplace transform first identifies the emission rates, which are then held fixed in a constrained least-squares fit that recovers the individual amplitudes from the time-domain transient, thereby combining the rate resolution of Laplace DLTS with a noise-robust, regularization-free amplitude determination. The method requires no material-specific assumptions and is applicable wherever Laplace DLTS can resolve multiple defect emission rates, providing a practical tool for quantitative defect concentration analysis in semiconductor development. Validation with synthetic data demonstrates accurate recovery of defect concentrations. Application to n-type GaAs, where the well-known EL2 defect overlaps with the ELO level, reveals ELO at a concentration 20 times lower than that of EL2. Despite this difference, the order-of-magnitude higher capture cross section of ELO renders both defects comparably important for carrier recombination, highlighting the importance of accurate concentration determination via the presented method.