Multiscale approach to the electronic structure of doped semiconductor surfaces

Abstract

The electronic effects of semiconductor doping pose a unique challenge for first-principles simulations, because the typically low concentration of dopants would require intractably large system sizes in an explicit atomistic treatment. In systems which do not display longrange band bending, a satisfactory remedy is offered by the use of "pseudoatoms", with a fractional nuclear charge matching the bulk doping concentration. However, this alone is insufficient to account for charged semiconductor surfaces in the general case, where the associated space-charge region (SCR) may be very wide relative to tractable simulation dimensions. One generalization of the pseudoatom approach which overcomes this difficulty relies on the introduction of an artificially high doping level within a slab calculation, in conjunction with a multi-scale electrostatic energy correction. Here, we present an alternative technique that naturally extends the pseudoatom approach while bypassing the need for calculations with an unrealistically high doping level. It is based on the introduction of a two-dimensional sheet of charge within a slab-based surface calculation, which mimics the SCR-related field, along with free charge such that the system is neutral overall. The amount of charge involved is obtained from charge conservation and Fermi level equilibration between the bulk, treated semi-classically, and the electronic states of the slab/surface, which are treated quantum-mechanically. The method, which we call CREST -the Charge-Reservoir Electrostatic Sheet Technique -can be used with standard electronic structure codes. We validate the approach using a simple tight-binding model, which allows for comparison of its results with calculations encompassing the full SCR explicitly. Specifically, we show that CREST successfully predicts scenarios spanning the full range from no to full Fermi-level pinning. We then employ it with density functional theory, where it is used to obtain insights into the electronic structures of the "clean-cleaved" Si(111) surface and its buckled (2x1) reconstruction, at various doping densities.

Local aspects of hydrogen-induced metallization of theZnO(101¯0)surface

“…Since band-bending is entirely enclosed in our supercell, we did not employ the electrostatic schemes recently developed by some of us. 26,38,39 A region of 30Å vacuum was inserted between the ZnO slab Dependency of the work function of different ZnO(1010) samples on hydrogen dosage (blue curve) and integrated intensity of the CAL signature (red circles).…”

Controlling oxide surface dipole and reactivity with intrinsic nonstoichiometric epitaxial reconstructions

“…The value of ∆V bb is dependent on the interplay of surface and bulk states 52 . It is however possible to bound it by considering limiting cases.…”

Band Bending Engineering at Organic/Inorganic Interfaces Using Organic Self‐Assembled Monolayers

“…We therefore employ the CREST method. [33] In Figure 6d-f, the level alignment for all three systems is shown exemplarily for a doping concentration of 10 16 e cm − ³. The ZnO/Vio/TCNQ system does not exhibit any band bending, since the HOMO of Vio lies directly at the Fermi-energy already prior to adsorption, and hence, does not require any band bending to induce charge-transfer from the SAM to the adsorbate.…”

“…[51] In the present work, we use a modified version of the CREST method to account for doping. [33,34] CREST treats a part of the substrate (the surface) within DFT, while the long-range electrostatic behavior (i.e., in particular the band bending) is captured semi-classically using a charged plate at the bottom of the slab. Within the quantum-mechanically treated substrate, we employ the virtual crystal approximation to model the free charge carriers.…”

“…[32] Band bending and doping are treated using a simplified version of the charge reservoir electrostatic sheet technique (CREST). [33,34] In short, CREST simulates the space-charge region by a negatively charged sheet placed on the backside of the slab. The charge and position of the sheet is determined self-consistently, using only the substrates doping concentration N D and its dielectric constant as parameters.…”