Reduction of carrier mobility in semiconductors caused by charge-charge interactions

We investigate the effect of charge-charge interactions on carrier mobility in titanium dioxide $\left(\mathrm{Ti}{\mathrm{O}}_2\right)$ and silicon (Si) using terahertz spectroscopy. Charge scattering times and plasma frequencies are directly determined as a function of charge density. In Si, a linear increase in scattering rate for densities exceeding ${10}^{21}{\mathrm{m}}^{-3}$ is attributed to electron-hole scattering. In contrast, in $\mathrm{Ti}{\mathrm{O}}_2$, charge-charge interactions are suppressed due to dielectric screening, highlighting the vastly different dielectric properties for these two materials.

Figure 1

(Color online) THz transmission $E$ and modulation $\Delta E$ (scaled by a factor of 5) $10\mathrm{ps}$ after photoexcitation of (a) $\mathrm{Ti}{\mathrm{O}}_2$ and (b) Si with a $266\mathrm{nm}$ laser pulse. The red dashed and blue dotted lines are for high and low excitation fluences, respectively (values as stipulated in Fig. 2). Inset: $\Delta E$ at $t=2\mathrm{ps}$ measured as a function of $266\mathrm{nm}$ pump-THz probe delay for Si and $\mathrm{Ti}{\mathrm{O}}_2$, scaled for comparison.

Figure 2

Real (open symbols) and imaginary (filled symbols) of the complex conductivity for $\mathrm{Ti}{\mathrm{O}}_2$ (in the ⊥ direction, upper panels) and Si (lower panels), measured with different $266\mathrm{nm}$ excitation fluences at $30\mathrm{K}$: (a) $f_l\sim 0.18\mathrm{J}∕{\mathrm{m}}^2$, $2.4\times {10}^{17}\text{photons}∕{\mathrm{m}}^2$; (b) $6.40\mathrm{J}∕{\mathrm{m}}^2$, $8.6\times {10}^{18}\text{photons}∕{\mathrm{m}}^2$; (c) $0.02\mathrm{J}∕{\mathrm{m}}^2$, $2.5\times {10}^{16}\text{photons}∕{\mathrm{m}}^2$; and (d) $0.26\mathrm{J}∕{\mathrm{m}}^2$, $3.5\times {10}^{17}\text{photons}∕{\mathrm{m}}^2$. All conductivities are normalized by the incidence excitation fluence. Solid lines represent the Drude model.

Figure 3

(a) The plasma frequency ${\omega }_p$ as a function of excitation fluence $f_l$. The lines are straight line fits assuming ${\omega }_p^2=e^2{N}^{\mathit{av}}∕\left({\epsilon }_0{m}_{\mathit{con}}\right)$, with $N^{\mathit{av}}$ estimated from $f_l$ using Ref. 19. (b) Relaxation rate obtained from fitting the high-density conductivity after excitation with $266\mathrm{nm}$ pulses, plotted as a function of excitation fluence $f_l$. The lines are fits using Eq. (2). Note that for $\mathrm{Ti}{\mathrm{O}}_2$, the scattering time is almost density independent in the density range up to ${10}^{24}{\mathrm{m}}^{-3}$.

Figure 4

Relaxation rate of carriers in silicon after excitation with $400\mathrm{nm}$ pulses, plotted vs. charge density (Ref. 19). The line is a fit using Eq. (2).