Carrier-diffusion measurements in silicon with a Fourier-transient-grating method.

Abstract

Carrier-diffusion measurements in silicon using a newly developed Fourier-transient-grating technique is presented. The method uses a laser light pulse projected through a semitransparent grid pattern to excite a sinusoidal excess carrier grating within the sample. The interdiffusion of carriers is monitored by free-carrier absorption of a focused infrared probe beam. The grating is scanned across the probe beam and the spatial Fourier transform is calculated at each sampling time following the excitation pulse. The resulting Fourier spectrum shows a peak for a frequency corresponding to the grating period and the decay of the amplitude of this spatial-frequency component represents a characteristic grating erasure time, which is related to the carrier diffusivity. This Fourier-transient-grating method allows sensitive measurements of the carrier diffusivity over a broad range of injection levels, both in the minority carrier regime as well as for high-injection conditions including the transition between the two regimes. Here, measurement data are presented for silicon samples of various doping concentration and types for excess carrier injections in the range \ensuremath{\sim}${10}^{12}$--${10}^{17}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$. At low densities of injected carriers, our measurement data are in agreement with generally accepted low-injection lattice-scattering mobility values showing the transition to the high-injection range according to ambipolar theory. However, at excess carrier concentrations exceeding ${10}^{15}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$, the diffusion coefficient is clearly reduced with respect to the ambipolar diffusivity (using constant electron and hole diffusivities) due to carrier-carrier scattering effects. This reduction is stronger above an injected carrier density of ${10}^{16}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$ than that predicted by many-body quantum theory [J. F. Young and H. M. van Driel, Phys. Rev. B 26, 2147 (1982)]. The diffusivity data, converted to mobilities using Einstein's relation, have also been compared to recent semiempiric drift-mobility models used for semiconductor device simulation.