Written by Z. Kancleris from the Semiconductor Physics Institute, Vilnius, Lithuania.
The integration method used for the analysis of the transients is based on the algorithm proposed by Tittelbach-Helmrich [1]. The number of exponents (M) (discrete components) is not known beforehand, thus the calculations are performed by increasing M beginning with M=0. As a criterion for finding the “right” solution a few empirically determined rules are used. These are: (i) an increase of the number of exponents that are extracted from the transient must improve the fit between the calculated and initial signal; (ii) any calculated emission rate has to be positive; (iii) any amplitude of the component must be bigger than the noise. If the new solution calculated for M+1 exponent meets all the above-mentioned requirements it is accepted otherwise it is rejected. If this is the case the parameters calculated one step before are accepted as the final result of transient analysis.
Numerical tests showed that the efficiency of the algorithm is different for a different number of components and noise-to-signal ratios (NSR). If the transient has only one exponential component this component is properly revealed even from very noisy signals (NSR can approach 0.3), however, to get reliable parameters for three exponential components one needs NSR to be smaller than 10-3. Numerical tests showed that although the criterion for NSR seems to be rather rigid, the improvement in the resolution offered by our method in comparison with standard DLTS is substantial. For satisfactory NSR the Tittelbach-Helmrich algorithm can, for example, distinguish two equal amplitudes when the difference in the emission rates is only 25%.
Reference
[1] K. Tittelbach-Helmrich, Meas. Sci. Technol., 4, 1323 (1993)