Contributions of the escape depth to the photoelectron intensity of a well-defined initial state

Using the adsorbate-induced two-dimensional electron system on InAs(110) as an initial state, which provides rather small energy and $k$-space distribution, we measure the photoelectron intensity as a function of photoelectron energy. It oscillates twice between $3\mathrm{eV}$ and $23\mathrm{eV}$ having maxima at $5.5\mathrm{eV}$ and $19\mathrm{eV}$. Comparison with calculations performed within the one-step model shows that the maximum at low energy is due to an overlap of a maximum in the photoelectron escape depth and a maximum of the matrix elements corresponding to the atomic wave functions. In contrast, the maximum at high energy is caused by final states crossing the $\Gamma$ point exactly at this energy. The comparison confirms the theoretical prediction that the escape depth at low excitation energies can be significantly modified by band-structure effects.

Figure 1

(a) Energy scan of 2DES peak and fit (see text) at $h\nu =10\mathrm{eV}$, $\theta =0°$, $E_{\text{pass}}=4\mathrm{eV}$; $E1$, $E2$: subband energies. (b) Angular scans of 2DES peak at different $E-E_F$, $h\nu =10\mathrm{eV}$, $E_{\text{pass}}=4\mathrm{eV}$. (C) Fit curves to (b) with same fit parameters as in (a); same symbols are used in (b) and (c) as marked in between.

Figure 2

(a) and (b) Energy scans of 2DES peak at different $h\nu$ as indicated, $E_{\text{pass}}=20\mathrm{eV}$, $\theta =0°$; data are scaled to photon fluence and offset as marked by horizontal lines. (c) Angular scans of 2DES peak at different $h\nu$ as indicated, $E_{\text{pass}}=4\mathrm{eV}$, $E-E_F=-50\mathrm{meV}$; data are scaled to the same height at $\theta =0°$; the horizontal line [full width at half maximum (FWHM)] is at half maximum.

Figure 3

(a) 2DES peak intensity normalized to the photon fluence and to the angular collection efficiency of the analyzer; different $E_{\text{pass}}$ are indicated. (b) Calculated photoelectron intensity in normal emission using the initial states at the bottom of the conduction band of InAs(110); calculation performed according to Ref. 15.

Figure 4

(a) Calculated escape depth $\lambda$ as a function of energy. (b) Matrix elements corresponding to the As $s$ orbitals of the initial states displayed for different layers from the surface as indicated. (c) Complex band structure of InAs(110) perpendicular to the surface; thin lines are real states of the infinite crystal, thick lines are complex states of the semi-infinite crystal; vertical bars mark the strength of the coupling of complex states to vacuum states; only states with significant coupling are plotted; $E_{\text{final}}$ at the lower bar is given with respect to the valence-band maximum.