HAMILTONIAN PLASMA-HARMONIC OSCILLATOR THEORY - GENERALIZED DEPTH PROFILOMETRY OF ELECTRONICALLY CONTINUOUSLY INHOMOGENEOUS SEMICONDUCTORS AND THE INVERSE PROBLEM

The Hamilton-Jacobi formalism of the propagation of an electron-hole p hotoexcited plasma in continuously inhomogeneous semiconductors with a rbitrary depth profiles in carrier diffusivity and/or minority-carrier lifetime is presented. The theoretical model is based on the variatio nal formulation of the canonical Hamiltonian for the evolution of carr ier plasmas and shows that propagating plasma waves can be formally de scribed by a plasma-harmonic oscillator, thus generalizing existing th eoretical treatments of photoexcited carrier diffusion in electronic s olids. Simple analytical expressions for the free-carrier diffusion ma gnitude and phase frequency dependencies in the case of exponential ca rrier diffusivity and minority carrier lifetime profiles are obtained. The effect of continuously varying electronic properties on the surfa ce plasma density magnitude and phase frequency behavior is demonstrat ed through computer simulations and very good quantitative agreement i s obtained with photothermal radiometric data from an ion-implanted Si wafer allowing the reconstruction of the lifetime depth profile. (C) 1996 American Institute of Physics.