Two-State Double-Continuum Fano Resonance at the Si(100) Surface

Fano resonances are well-known manifestations of the interference between a direct and an indirect ionization process. Here we report on a more complicated interference pattern observed in two-photon photoemission at the Si(100) surface. This two-dimensional Fano profile involves two discrete surface resonances which couple as initial and intermediate states to the silicon valence and conduction band, respectively. Tuning the photon energy across the surface resonance reveals asymmetric line profiles with pronounced destructive interference in the two-photon photoelectron intensities of both initial and intermediate states. The interference pattern is explained by an analytic extension of Fano’s model to describe the coupling of two discrete states with two continua. This coupling strongly modifies the photoabsorption and is of general importance for light conversion in nanostructures and light-harvesting devices.

Figure 1

In the 2PPE experiment the ultraviolet laser pulse $h{\nu }_{\mathrm{UV}}$ excites electrons along the different quantum paths $q_1$, $q_2$, $q_3$, which are normalized to the bulk absorption $q_b=1$. ${\delta }_D$ and ${\delta }_n$ describe the detuning when varying the UV photon energy across the resonance between $D_{\mathrm{up}}$ dangling-bond and $n=1$ image-potential-surface states. Both discrete states are degenerate with the valence and conduction bands (VB and CB) and the couplings $V_D$ and $V_n$ describe their hybridization. In the second step, electrons are photoemitted by a visible laser pulse with constant photon energy $h{\nu }_{\mathrm{vis}}$ and recorded in normal emission with a kinetic energy $E_{\mathrm{kin}}$.

Figure 2

(a) 2PPE energy-distribution curves recorded in normal emission at room temperature for various UV photon energies. Triangles indicate the position of the initial $D_{\mathrm{up}}$ anticipated for $E_{\mathrm{kin}}\propto h{\nu }_{\mathrm{UV}}$, while circles and squares mark the expected constant kinetic energy of the $n=1$ and 2 intermediate states. (b) Data of (a) shown in a color plot. Expected positions of $D_{\mathrm{up}}$, $n=1$ and 2 are indicated by the solid lines. The contour plot is the fit result of the analytic two-state double-continuum Fano model.

Figure 3

(a) Surface plot illustrating the 2D Fano interference pattern of Eq. (4). ${\epsilon }_D$ and ${\epsilon }_n$ describe the reduced detunings with respect to the initial and intermediate states $D_{\mathrm{up}}$ and $n=1$. The $q$ values have been fitted to the experimental data in Fig. 2. (b) 2PPE intensity of the $D_{\mathrm{up}}$ and $n=1$ states as a function of UV photon energy. Solid and dashed lines are extracted from the analytic fit at ${\epsilon }_n=0$ and ${\epsilon }_D=0$. They reproduce the regular Fano line shapes of the initial and intermediate states.