Impact of Surface Charge Depletion on the Free Electron Nonlinear Response of Heavily Doped Semiconductors

We propose surface modulation of the equilibrium charge density as a technique to control and enhance, via an external static potential, the free electron nonlinear response of heavily doped semiconductors. Within a hydrodynamic perturbative approach, we predict a 2 order of magnitude boost of free electron third-harmonic generation.

Figure 1

Effects of surface charge depletion on the FE THG efficiency $\eta$ of a doped InP slab: (a) a TM plane wave impinging on a semi-infinite geometry is considered; (b) equilibrium charge density $n_0(\mathbf{r})$ as a function of the distance $d$ from the surface of the slab for different levels of modulation (in $\mathrm{V}/\mu \mathrm{m}$); (c) related $\eta$, normalized to the squared input intensity $I_0^2$, as a function of the angle of incidence $\theta$; (d) enhancement factors $\zeta$ as a function of the depletion factor $\delta$ in correspondence of the peak efficiencies at $\theta =60$.

Figure 2

Effects of surface charge depletion on the FE THG efficiency $\eta$ of a doped InP semi-infinite grating: (a) the structure and its reflectance $R$ at normal incidence for $n_b={10}^{19}{\mathrm{cm}}^{-3}$, $d=1\mu \mathrm{m}$, $a=150\mathrm{nm}$, $h=500\mathrm{nm}$. The orange and the light blue shadows evidence the considered range of variation of ${\lambda }_{\mathrm{FF}}$ and that of the corresponding ${\lambda }_{\mathrm{TH}}$, respectively. (b) $n_0(\mathbf{r})$ along the grooves contour in the case of maximum depletion of Fig. 1; (c) normalized efficiencies of THG as a function of ${\lambda }_{\mathrm{FF}}$ in the proximity of the resonance, at normal incidence, in the case of zero and maximum modulation (in $\mathrm{V}/\mu \mathrm{m}$); (d) related enhancement factors $\zeta$ as a function of the depletion factor $\delta$ in correspondence of the peak efficiencies at ${\lambda }_{\mathrm{FF}}=12.2\mu \mathrm{m}$.