Evidence for “Unusual” Exchange–Correlation on Si(111) 7 × 7: Limitations of Density Functional Calculations for Charge Transfer Interactions on Semiconductor Surfaces

Abstract

Electron–electron interactions on the Si (111) surface associated with inaccuracies in treating exchange and correlation are shown to be consistent with discrepancies found between density functional calculations and experimental measurements of the 7 × 7 surface. Here, the measured filled and empty surface states of the 7 × 7 surface are shown to be shifted away from one another relative to those predicted by effective one electron calculations using density functional theory. This corresponds to the “energy gap problem” widely known to occur in most bulk semiconductors arising from the approximate treatment of electron exchange–correlation, X–C, within such theoretical constructs. Considering more realistic treatments of X–C to correct these energy shifts leads to a different interpretation of the surface states and a new interaction that stabilizes the 7 × 7. This provides a physical basis for its unusual properties some of which are also observed in related 2D systems. The effects of various electron–electron interactions from these new interactions are considered and their behavior is used to explain the metallic nature of the 7 × 7 at 300 K.

Reply to the “Comment on ‘Experimental Evidence for a New Two-Dimensional Honeycomb Phase of Silicon: A Missing Link in the Chemistry and Physics of Silicon Surfaces?’”

“…Such measurements of observable features represent physical information derived from experiment. As discussed by Demuth, − these suggest some aspects of DFT calculations are not correctly describing this system. In general, the total energy calculated within DFT usually reflects the relative energies of structures so as to define the lowest energy configuration and the most stable structure.…”

“…In general, the total energy calculated within DFT usually reflects the relative energies of structures so as to define the lowest energy configuration and the most stable structure. However, when charge transfer and/or electron localization occur, i.e., flat bands, these energies are no longer accurate . This is well illustrated in a historical review of DFT which notes that systems not accurately described by DFT are typically referred to as “highly correlated” electron systems …”

“…More specifically, self-interaction energy corrections in DFT calculations for bulk silicon are well established to be in error by ∼0.3 eV per atom for the electron states that form the valence band. , These errors have recently been shown to be evident for the 7 × 7 surface and can depend on the nature of the states involved . In addition, the half-filled band of a 7 × 7 or 5 × 5 DAS structure found by DFT fails to satisfy the requirements for DFT to be valid .…”

“…Yes, DFT calculations of the 7 × 7 indicate a low system energy for the DAS. However, these same DFT calculations fail to explain many other directly observed experimental quantitiesmost noticeably from angle resolved photoemission and tunneling measurements. − , These are significant failures of the DAS model which show the existence of an energy gap, an adatom charge density distortion in its ground state, the existence of a fourth surface state, − an incorrect description of the 7 × 7’s SBZ as well as the metallic nature of its Fermi surface at 300 K, and finally, a localization of the surface states arising in their ground state . The two simplest early paradoxes for the DAS structure are the absence of a bulk like stacking fault and, when DFT calculations became feasible, its failure to correctly predict the measured height of the adatoms on the 7 × 7 surface determined from a variety or experimental techniques…”

“…It is fair to say that these particular DFT calculations do not support a π-bonded DFA structure. However, there remain many experimental observables of the 7 × 7, and related structures, that tell us we do not yet understand the geometric and electronic structure of the Si(111) 7x7 surface.…”