Nanooptics and photonics

Using Kramers-Kronig compatibility for analysis of photoconductivity kinetics in InSe layered crystals 
Fliunt O. Ye.
Faculty of Electronics and Computer Technologies, Ivan Franko National University of Lviv. Dragomanov str., 50, Lviv-79005, Ukraine. 
E-mail: Orest.Fliunt@lnu.edu.ua

Photoconductivity decay in semiconductors may be presented in the form of time dependence characteristic or frequency dependence spectra. In the first case photoconductivity kinetics is measured after abrupt termination of light illumination of the sample as time dependence. In the second case the sample under study is illuminated by light beam ac component of intensity of which is changed according to sinusoidal law with time. Measuring at different frequencies allow to get frequency dependencies of in-phase (real) and quadrature (imaginary) components of photoconductivity. Both time and frequency characteristics describe kinetic of the same process been interconnected via integral Fourier transforms. Frequency spectra have the same advantages in comparison with time-domain response, e.g. allow to observe kinetics on wider frequency range, a few orders on magnitude, what is difficult to realize in time-domain because of fast decreasing of photoconductivity with increasing time especially by orders of magnitude and presence of static term. 
Frequency dependence of real and imaginary components of intensity modulated photoconductivity are not independent functions. They have to be interconnected via integral Kramers-Kronig transform in the case of linear response. This property give one more advantage of photoconductivity kinetics measurement in the frequency domain that gives possibility to check the reliability of experimental spectra, that is impossible in the case of time-domain measurement. 
The Kramers-Kronig compatibility of intensity modulated photoconductivity of InSe layered crystals has been checked using double integral Fourier transform. The numerical calculation has been carried out using cubic spline interpolation of experimental spectra. High-precision arbitrary arithmetic library ZKCM C++ has been used to avoid error caused by the lack of number width during operation with drastically different order terms. Effect of different type dispersion on accuracy of forward and reverse Fourier transform has been discussed. Time-domain kinetics of photoconductivity of InSe crystals has been obtained on wider range by order of time, than it is possible by usual time-domain measurement.