Surface States at Si(001)

M. Weinelt, M. Kutschera, C. Kentsch, Ch. Orth, and Th. Fauster

in Proc. Symposium on Surface Science 2002

The template of most semiconductor devices is the Si(100) surface which has been studied by a variety of surface science techniques [1]. The atoms of the bulk truncated surface rebond in asymmetric dimers. A filled dangling bond band Dup as well as an empty band Ddown located at the up and down atoms of the dimer are formed. Depending on surface temperature the dimerization leads to (2 x 1) and c(4 x 2) arrangements of the dimers [1].

The occupied and unoccupied dangling bond bands have been studied by photoemission [2], inverse photoemission [3], and various ab initio approaches [4]. In the experiment the Fermi level is usually determined on a metal surface in contact to the semiconductor. Theoretical calculations are referred to the silicon valence band maximum (VBM). Moreover, on Si(001) the Fermi level is pinned at the surface at different positions depending on doping, temperature and surface defect density [5, 6]. Missing a common, reproducible reference level the overall agreement between individual experiments and theory is moderate [7].

Two-photon photoemission (2PPE) allows to probe both occupied and unoccupied surface states. In our experiment we used infrared (IR) and frequency-tripled ultraviolet (UV) pulses of a tunable Ti:sapphire oscillator. Time duration of pump and probe pulses was about 100~fs. Photoelectrons are detected normal to the surface by means of a hemispherical analyzer. We thus probe states at k || = 0, i.e. the surface Brillouin zone center. Experimental setup and Si(001) sample preparation are described in Ref. 7.

Figure~1 depicts spectra measured at a IR photon energy of 1.69 eV for zero pump-probe delay Td and for a situation where the UV pulse follows the IR pulse at Td = 2.7~ps. The two peaks observed at $Td = 0 are assigned to transitions involving the Dup and Ddown states, respectively. The schematics illustrates the pump-probe scheme. Details of the excitation process were studied by varying the IR photon energy between 1.47 eV and 1.70 eV (this implies a 3 x IR variation of the UV pulse). At photon energies below 1.59 eV the kinetic energy of the Dup state shows a 4 x IR -dependence, while above a 1 x -dependence. Thus depending on the photon energy the Dup state is either excited off-resonantly by direct absorption of two photons, or excitation is mediated by an intermediate state close to Evac. The Ddown state is observed at photon energies > 1.61 eV and exhibits a 3 x IR -dependence. It is thus populated by the IR pulse and probed by the UV pulse. From these measurements we determine the splitting between Dup and Ddown states at to 0.81 +- 0.05 eV.
Fig 1: 2PPE spectra for Si(001) and energy diagram for a p-type Si sample. Under laser
illumination flat-band condition is reached. The reference level is the bulk Fermi level EF(bulk).

Due to the low density of states at the Fermi level EF the spectra in Fig. 1 do not exhibit a signature related to EF. However, the vacuum level Evac shows up as a sharp cut-off at kinetic energy zero \DeltaE with respect to the sample (analyzer). Using the known work function of the analyzer \Phi_A the vacuum energy of the sample can be referenced to the Fermi level of the analyzer and thus the silicon bulk Fermi level EF(bulk) (see schematics in Fig.~1). EF(bulk) - EVBM can be calculated for known doping and temperature. We thus obtain under flat-band condition the ionization energy Evac - EVBM = (\Delta E + \Phi_A + EF(bulk)) - EVBM. The intensity of the laser pulses was varied by more than two orders of magnitude to assure that the experiments are done under saturation, i.e. flat-band condition. For p-type samples we obtain an ionization energy of 5.40 +- 0.03 eV and a surface band bending Vs < 50 meV [7]. As already discussed, to ionize the occupied Dup or afore populated Ddown dangling bond states photon energies of UV+IR or UV are required. Combining all results the energy of the Ddown and Dup bands at the surface Brillouin center are determined to 0.66 +- 0.05 eV and -0.15 +- 0.05 eV with respect to VBM, respectively.

Since the Dup band is probed by off-resonant excitation the corresponding photoemission peak is solely seen when pump and probe pulses overlap. As a consequence the spectrum recorded at 2.7 ps delay shows emission from the Ddown band only. Its intensity is significantly enhanced when compared to delay zero. At 2.7 ps the IR pump pulse is for a long time over. Thus main population of the Ddown state has to occur indirectly. Time-resolved measurements reveal that the band bottom is filled by interband scattering processes within the Ddown band and overall population of the Ddown band is dominated by electron-phonon scattering which couples bulk and surface states. The decay rate of the Ddown population is strongly influenced by surface defects which give rise to deep impurity levels and cause sizeable one-photon photoemission intensity close to the low energy cut-off.

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