Frequency response of spin drift-diffusion in n-doped Ge, Si, and GaAs

The frequency dependent drift-diffusive spin transport of polarized electrons lying at the bottom of the conduction band of n -doped Ge, Si, and GaAs is numerically investigated at room temperature. First, we calculate the spin lifetime for such electron populations. Then, the temporal evolution of a spin population detected at a certain distance from the injection point is studied by employing a finite element method to solve the coupled spin drift-diffusion and continuity equations in a one-dimensional frame. In this way, we unveil the intricate dependence of the spin accumulation as a function of the distance between the injection and detection point, the doping level of the semiconductor, and the amplitude and frequency of the electric field. Notably, the spin signal features both a variation in phase with the electric field and a modulation at higher harmonics. The cut-off frequency of the spin signal increases with the electric field’s amplitude or by reducing the spin-diffusion length. With applied bias voltages compatible with those used in electronics, we obtain cut-off frequencies of about 35 GHz in Ge, 480 MHz in Si, and 15 THz in GaAs. Our results not only shed light on the fundamental mechanisms governing spin dynamics but also hold the promise for future applications in spin-dependent logic operations.