Determination of lifetime and diffusion constant of minority carriers by a phase-shift technique using an electron-beam-induced current

The lifetime and diffusion constant of minority carriers in Si have been determined by a phase-shift technique using an electron-beam-induced current (EBIC). The phase of an EBIC is shifted because of the recombination of minority carriers in a material when the intensity-modulated electron beam is used in the line scan method of EBIC. The phase shift between the electron beam and the EBIC is clarified theoretically by solving the three-dimensional time-dependent diffusion equation. The phase shift increases linearly with the scanning distance. The relation between the phase shift and lifetime τ was found to be expressed using the approximated solutions of the one-dimensional diffusion equation with empirical correction factors. The normalized phase shift (i.e., the amount of the phase shift when the beam scans over one diffusion length) becomes a function of only ωτ (ω = 2πf, where f is modulation frequency). With the aid of a curve of the normalized phase shift vs ωτ, the lifetime and diffusion constant can be determined without any restriction for modulation frequency. Experimental results in Si showed good agreement with the theory.