The present research work describes the compositional analysis of silicon, germanium and their alloys using calibration free laser induced breakdown spectroscopy (CF-LIBS) technique. In the initial experimental work, the fundamental plasma parameters of silicon have been studied as a function of laser irradiance, ambient pressure, and distance along the plume length using the fundamental (1064 nm) and second harmonic (532 nm) of Q-switched Nd: YAG laser were investigated. Electron temperature was determined using Boltzmann plot method and electron number density by the Stark broadening in the line profile. In the next series of experiments, calibration free laser induced breakdown spectroscopy (CFLIBS) technique has been applied for the quantitative analysis of silicon and germanium alloys and polycrystalline solar cells. The emission spectrum of a standard Al-Si alloy was captured using single pulse LIBS and the analysis confirmed the presence of Mg, Al, Si, Ti, Mn, Fe, Ni, Cu, Zn, Sn, and Pb in the alloy. After background subtraction and incorporating self-absorption corrections, the corrected emission intensities and accurate evaluation of plasma temperature (10100 K) yield the reliable quantitative results up to a maximum 2.2% deviation from the standard values. Furthermore, the double-pulse LIBS in collinear configuration was used to record the emission spectra of two unknown alloys (Ge-Cu/Si, Ge-Ba/Si), a standard alloy (GdGe-Si) and three polycrystalline solar cell samples. The experimental parameters such as interpulse delay, gate delay and energy ratio between the two laser pulses were optimized to improve the signal to background and signal to noise ratio in the LIBS spectra. The concentration of the species was determined with and without using Boltzmann plots. The later approach was used for the trace elements with emission lines not enough to draw Boltzmann plot of it. The results of this approach show maximum deviation of 4% from the reference data. Furthermore, the analysis of unknown polycrystalline silicon solar cells extracted the concentration of trace impurities C, Ca, Sb, In, Sn, Ti, Al, and K in parts per million (ppm). These impurities in crystalline structure reduce the conversion efficiency of solar cells and therefore their detection and quantification is important for efficient photovoltaic applications