Fermi level pinning for zinc-blende semiconductors explained with interface bonds

Schottky barrier heights (SBHs) measured at polycrystalline metal-semiconductor (MS) interfaces have displayed an insensitivity to the work function (WF) of the metal, known as the “Fermi level pinning” (FLP) phenomenon. The obstacle presented by FLP in thwarting technological efforts to tune the SBH has been difficult to overcome because of a lack of understanding of the origin of the FLP effect. Presently, SBH explanation still largely relies on empirical models, and FLP remains a mystery. Here, the phenomenon of FLP for zinc-blende/diamond (ZBD) semiconductors is explicitly demonstrated to originate from interface metal-cation bonds, which are metallic in nature. Based on the analysis of two representative and electrically distinct types of interface, it is shown that screening by metallic bonds weakens the dependence of SBH on the metal and results in a SBH close to that found between the semiconductor and its own cation in elemental metal form. The latter SBH is shown to agree well with experimentally measured SBH from polycrystalline interface, i.e., the apparent pinning levels. A fundamental, self-consistent explanation of the FLP phenomenon thus emerges, and with it, strategies to avoid FLP for technological applications may also be suggested.

Figure 1

Models of the stacking sequence at epitaxial metal-zinc-blende (100) interface: small sphere = metal, medium sphere = anion, large sphere = cation. Neither the drawing on left for metal-anion (100) interface, nor that on right for metal-cation (100) interface necessarily corresponds to the actual atomic structure used in the calculations. Lines mark locations where the metal-semiconductor structure may be cut for determination of the range of interface dipole.

Figure 2

Macroscopically averaged potential energy profiles of various structures associated with the Rh/ZnS(100) interface with Rh-S bonds. All curves are averaged over the repeating distances in both the ZnS(100) and the strained Rh(100) crystals. The profile marked “supercell” is obtained from calculation of the entire structure. Locations of the atomic planes are marked on the bottom. Other calculations are based on the same (super) unit cell but with specified layers of atoms removed. “Rh + 1S” is calculated with all semiconductor planes, marked in black on bottom, removed. “ZnS + 1Rh” is calculated with all Rh planes marked in blue removed. “1Rh1S” is obtained with all planes removed, except the two interface planes marked in red. Lines marked “stitched” are the result of stitching two or more lines together, as illustrated symbolically in the legend box. Upper curves have been shifted vertically for clarity. See Fig. SM-1 in the Supplemental Material [23] for a magnified view of the difference curve between stitched and supercell calculations.

Figure 3

(a) Calculated $p$-type Schottky barrier height (SBH) of relaxed epitaxial metal-anion (100) interfaces, shown against the SBH stitched at the M + 1A location, which is the difference between the ionization potential (IP) of the semiconductor and the work function (WF) of the metal covered with a monolayer adsorbate of anion. (b) Calculated $p$-type SBHs of metal-cation (100) interfaces, plotted against the SBH stitched at the M + 1C1A location.

Figure 4

Work function (WF) of various metal (100) surfaces covered with one monolayer of adsorbate, plotted against the WF of the bare metal. (a) Group IV adsorbates, (b) group III and V adsorbates, and (c) group II and VI adsorbates. Horizontal lines mark the WFs of the metallic surface of elemental group II, III, and IV elements.

Figure 5

Plane-averaged charge density of interface states with energy in the band gap of the semiconductor at the epitaxial (100) interfaces of AlP and ZnS with (a) Ir, (b) Rh, and (c) Ca for metal-cation (solid lines) and metal-anion (dashed lines) interfaces. Zeros on the horizontal axis mark the locations midway between the last metal plane on the left and the first semiconductor plane on the right. The density tail at metal-cation interfaces extends further into the semiconductor than that at metal-anion interfaces.

Figure 6

Experimentally measured average $p$-type Schottky barrier height (SBH), shown against the $p$-type SBH calculated for each semiconductor with its own cation. See text for Si and Ge. Experimental results are adopted from the literature: InP [31, 32], GaAs [33, 34, 35], ZnSe [36, 37, 38], Si [39, 40, 41], Ge [42, 43], GaP [44], AlAs [45], and CdS [46, 47].