Linking density functional and density-matrix theory: Picosecond electron relaxation at the Si(100) surface

We describe an approach that links the density-matrix theory for electron transport and relaxation with the density-functional theory for electronic structure. Our analysis of the electron dynamics at Si(100) reveals an unanticipated phonon bottleneck between bulklike and surface states. The fastest relaxation process observed in recent two-photon photoemission experiments is in good agreement with the calculated phonon-mediated intrasurface-band scattering.

Figure 1

(a) Band structure of a 30 layer Si(100) slab ($\overline{X}=\left(\sqrt{2}\pi /a,0\right)$, $\overline{M}=\left(\sqrt{2}\pi /a,\sqrt{2}\pi /a\right)$, ${\overline{X}}^{\prime }=\left(0,\sqrt{2}\pi /a\right)$. The lowest band is the surface band (thick); the higher bands are bulklike. (b) The initial occupation (solid), the total density of states (dashed), and the partial density of states for the surface band (dotted) are depicted. The density of states is smeared with a Gaussian function of width 0.05 eV. The zero of the energy scale is set the surface band state at $\overline{\Gamma }$.

Figure 2

Population as a function of energy for 0, 100 fs, 2 ps, and 190 ps after optical excitation. At $t=2\text{ps}$, it is observed that part of the population still remains in bulklike electronic states above 0.2 eV (relaxation bottleneck).

Figure 3

Temporal evolution of the population of the surface band minimum (solid line) and exponential fits assuming two time scales for relaxation (dotted lines). For $t<0.5\text{ps}$, the population increase is governed by the fast time scale. The population saturates after $t=190\text{ps}$.