A COMPOSITION-DEPENDENT MODEL FOR THE COMPLEX DIELECTRIC FUNCTION OF IN1-XGAXASYP1-Y LATTICE-MATCHED TO INP

Accurate and numerically efficient models for the complex dielectric f unction vs wavelength and material characteristics are essential for t he use of nondestructive optical techniques such as spectroscopic elli psometry or reflectometry. These optical techniques are commonly used for real-time and run-to-run monitoring and control of growth and etch processes to determine a material's composition and thickness. In thi s work, we discuss an improved composition-dependent model for the com plex dielectric function for lattice-matched In1-xGaxAsyP1-y/InP syste ms valid over the entire composition range 0 less than or equal to y l ess than or equal to 1. We describe our model, which is an extension o f the critical point parabolic band method and is based on the model p roposed by Charles Kim et al. for the AlxGa1-xAs/GaAs system. We demon strate the quality of the model in fitting optical data for individual compositions and compare our results to other established models incl uding the harmonic oscillator approximation and the model of Adachi. U sing results obtained from the individual fits, we generate a composit ion-dependent model that is valid for the entire range of lattice-matc hed compositions. Also, we show how this model can be used to accurate ly determine the composition (+/- 0.01) of an unknown material whose d ielectric response has been obtained using spectroscopic ellipsometry or a similar technique.