Carrier mobility in a polar semiconductor measured by an optical pump-probe technique
Carrier mobility is one of the most important properties in semiconductor devices, such as high electron mobility transistor (HEMT) and field-effect transistor (FET), both of which are capable for realizing terahertz (1012 Hz) ultra-high-speed operation in telecommunication and optical memory. The carrier mobility is determined by µ = eτ/m*, where e denotes electron charge, τ is the carrier relaxation time introduced in the relaxation time approximation, and µ represents electron effective mass in n-type semiconductors. Here, the carrier relaxation time τ includes all scattering processes, such as electron-hole scattering, electron-phonon scattering (Frohlich and deformation potentials), and scattering by defects and disorders. In general, the time scale of τ is less than a few hundred femtoseconds. While the carrier mobility has recently been obtained by using THz time-domain spectroscopy with the fit by Drude function, the accessible range of the carrier density was limited to lower density than an order of 1016 cm-3, due to non-Drude behavior originating from nonthermal carrier distribution at the high carrier density region.

In doped semiconductors, such as n-type GaAs, it is well known that the plasmon and the longitudinal optical (LO) phonon form coupled modes through Coulomb interactions, and the frequencies of the LO phonon-plasmon coupled (LOPC) modes depend on the carrier density Ne through the relation of the plasma frequency. Using Raman spectroscopy Nakashima and Harima have developed characterization of carrier mobility in SiC. They observed plasmon-like LOPC modes in frequency domain and fit the spectra with the line profile determined by frequency-dependent amplitude and dielectric function. As the results of the fitting, they obtained bandwidth of the plasmon-like LOPC mode, and put it into the formula µ = e/m*γ, where γ is a damping rate of plasmon. The derived carrier mobility matched very well to that obtained by Hall measurements. Although Raman spectroscopy is a promising tool to estimate carrier mobility without any mechanical contact onto a sample, one need fitting of the line shape using a number of equations.

Here, the carrier (electron) mobility was determined from the dephasing time of the plasmon-like coherent LOPC mode (L+) in n-GaAs, which is obtained by mapping the time-frequency dynamics of the LOPC modes by the use of the wavelet analysis. The electron mobility extracted from the coherent phonon spectroscopy decreases with increasing the photo-doping levels, indicating the suppression of the mobility by enhanced electron-hole scattering. The availability of this technique will spread over the polar semiconductors, such as SiC, GaN, under the condition that the photo-doping level assure that the LOPC mode is plasmon-like.

EO signal in n-GaAs
Fig.1 Time derivatives of the transient reflectivity changes for n-GaAs obtained by electro-optic detection at 300 K. The inset shows their Fourier transformed spectra.
APL 94, 112111 (2009).

Fig. 2. Three-dimensional images of the electro-optic response obtained by the wavelet analysis. (a) Nexc=1.8x1018 cm-3 and (b) Nexc=8.9x1016 cm-3. The beating pattern observed at $\sim$8.7 THz is due to the two modes of the LO (8.75 THz) and the L- mode (7.9 THz).
APL 94, 112111 (2009).