Defect concentration and Delta n change in light- and elevated temperature-induced degradation

The wide variety of silicon materials used by various groups to investigate LeTID make it difficult to directly compare the defect concentrations (N (t)) using the typical normalised defect density (NDD) metric. Here, we propose a new formulation for a relative defect concentration (beta) as a correction for NDD that allows flexibility to perform lifetime analysis at arbitrary injection levels (Delta n), away from the required ratio between Delta n and the background doping density (N (dop)) for NDD of Delta n/N (dop) = 0.1. As such, beta allows for a meaningful comparison of the maximum degradation extent between different samples in different studies and also gives a more accurate representative value to estimate the defect concentration. It also allows an extraction at the cross-over point in the undesirable presence of iron or flexibility to reduce the impact of modulation in surface passivation. Although the accurate determination of beta at a given Delta n requires knowledge of the capture cross-section ratio (k), the injection-independent property of the beta formulation allows a self-consistent determination of k. Experimental verification is also demonstrated for boron-oxygen related defects and LeTID defects, yielding k-values of 10.6 +/- 3.2 and 30.7 +/- 4.0, respectively, which are within the ranges reported in the literature. With this, when extracting the defect density at different Delta n ranging between 10(14) cm(-3) to 10(15) cm(-3) with N (dop) = 9.1 x 10(15) cm(-3), the error is less than 12% using beta, allowing for a greatly improved understanding of the defect concentration in a material.