Free carrier recombination lifetime calculation from photoconductivity decay measurement in non-passivated silicon
In indirect band gap semiconductors, for example, in silicon, the free carrier recombination lifetime is determined by recombination through deep level centers and inversely proportional to their concentration. This parameter is of the utmost importance for characterizing the quality of the material. Contactless methods of free carrier recombination lifetime measurements by protoconductivity decay analysis are most widely used. The measurement results are largely affected by surface recombination. The calculation of the lifetime in the bulk of a sample from the characteristic time of photoconductivity decay remains relevant since there is no ambiguous analytical solution of the continuity equation for this case. In this paper, an analysis of the relaxation of photoconductivity in single-crystal silicon wafers with non-passivated surfaces was carried out with numerical methods. The applicability of the well-known formulas for estimating the contribution of surface recombination to the effective photoconductivity decay time was discussed. We show that the time in which the «fast» exponents disappear depends on the relative thickness of the sample. It is only this part of the relaxation curve that the effective decay time is determined by the maximum value of the surface component of the relaxation time and is described by the well-known formulas. The saturation of the effective relaxation time at the point when the signal intensity reaches 45 % of the peak one (the onset point of effective decay time counting pursuant to the SEMI MF 1535 standard recommendation) only occurs in samples with thicknesses less than 3-5 diffusion lengths. For thick samples the contribution of the «fast» exponentials to the effective photoconductivity relaxation time is observed up to 5 % of the peak signal (i.e., until the noise level of the measured signal is reached). Use of the recommended formulas, including for the «infinite recombination rate» case at which the maximum surface lifetime is d<sup>2</sup>/p<sup>2</sup>D, leads to a sufficiently large (up to 20 %) error in free carrier recombination lifetime calculation.