The role of quantum confinement in the formation of Schottky barriers in Pb–Si interfaces

Abstract

a b s t r a c tSchottky barriers form when semiconductors are in contact with metal overlayers establishing a common Fermi level. Few theoretical studies of these materials exist as electronic structure calculations are computationally intensive for mismatched interfaces. We explicitly model a Pb(111) film on a Si (111) substrate. For thick Pb overlayers, we find a bulk regime where the Fermi level is pinned. For thin film regimes (less than five overlayers), structural relaxations dominate the interfacial energy as charge transfer is suppressed by quantum confinement. In this case, the Schottky barrier height follows the trend of the metal work function.One of the first models to predict the formation of a Schottky barrier is from Schottky [1,2] and Mott [3] some 70 years ago. The Schottky-Mott theory assumes that the metal and the semiconductor are not strongly interacting at the interface. Under such an assumption the vacuum levels are aligned, and the size of an ntype Schottky barrier Φ B;n ¼ ϕ M Àχ, which is the difference between the work function of the metal, ϕ M , and the electron affinity of the semiconductor, χ. If the Schottky-Mott picture was to be correct, then one might consider altering the barrier by changing the work function of the metal, e.g., by using different metals or by physically changing the thickness of the metal to alter the work function by quantum confinement. For some semiconductors, such as those with a wide band gap, Φ B;n exhibits an increasing trend with larger ϕ M ; however, the Fermi level E Fermi is often pinned within a small range for a given semiconductor regardless of the work function of the metal, especially for small gap semiconductors or elemental semiconductors like Si or Ge [4][5][6]. The Schottky-Mott model was rapidly abandoned for some semiconductor systems because of experimental evidence for a pinned Fermi level [7]. E Fermi when pinned is essentially independent of the metal contact. Bardeen [8] considered the role of surface states, whose theory had been previously developed by Matt [9] and Shockley [10], and argued that these states would control the formation of a dipole at the metal-semiconductor interface and pin E Fermi .Later, Heine [11] and Louie et al. [12,13] refined the ideas of Bardeen by noting that intrinsic surface states could not exist in the presence of an intimate contact with metallic states. They argued that the role played by the surface states pinning E Fermi in the Bardeen model could be played by the tails of intrinsic metallic states, which were capable of penetrating several layers into the semiconductor side. These metal induced gap states (MIGS) have been widely studied theoretically since the mid-1970s. For example, Louie and coworkers [12][13][14][15] used a jellium model for the metal films, replacing the nuclear charges by a uniform electronic charge density.The jellium model removes structural details of a metal overlayer and avoids the complexity of any lattice mismatch between the metal and semiconductor crystal structure...