Theoretical Investigations of Solid Interfaces: 1. The Position of the Fermi Level at a Metal-Semiconductor Interface. 2. Geometric Lattice Match and Its Application to Heteroepitaxy. 3. Ab-Initio Calculation of the Elastic Properties of Silicon, Using Small Clusters

Citation

Zur, Amikam (1984) Theoretical Investigations of Solid Interfaces: 1. The Position of the Fermi Level at a Metal-Semiconductor Interface. 2. Geometric Lattice Match and Its Application to Heteroepitaxy. 3. Ab-Initio Calculation of the Elastic Properties of Silicon, Using Small Clusters. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/w8vp-2g07. https://resolver.caltech.edu/CaltechETD:etd-01222007-152908

Abstract

The work presented in this thesis is concerned with theoretical investigations of the electronic, geometric, and elastic properties of solid interfaces. The interfacial electronic property studied was the effect of doping on the Fermi-level position at a metal-semiconductor interface. Geometric lattice match in heteroepitaxy was studied using a novel method of systematically determining every possible orientation of the two crystals which would result in lattice match at the interface between the two crystals. Finally, the parameters of several elastic models that can be used in calculating the elastic properties of silicon interfaces were computed, using ab-initio quantum-chemistry methods. The predictions of these models to bulk elastic properties were compared to experimental results to test the models.

(1) Chapter 1 presents the effect of semiconductor doping on the Fermi-level position at a metal-semiconductor interface. A model based on the concept of a dipole layer was used. The number of chargeable defects at the interface required to pin the Fermi level was determined in the limits of thin and thick metallic coverages. The calculations included the metal response to large charge transfer at the interface, using a jellium model for the metal.

The major findings of this chapter are:

• It takes about 10¹⁴defects • cm^-2 to pin the Fermi level in a bulk metal-semiconductor interface, but only about 10¹²defects • cm^-2 during the initial stages of metallization.

• The Fermi-level position at the metal-semiconductor interface may be very different for n- and p- type semiconductors during the initial steps of metallization. These Fermi-level positions seem to stabilize after the creation of about 10¹²defects • cm^-2 (which usually corresponds to less than a monolayer of metallic coverage). However, as the metallization proceeds, the two Fermi-level positions on n- and p-type semiconductors should merge to within 0.05 eV at the interface (for doping not exceeding 10¹⁷ cm^-3).

• During the initial steps of metallization most of the carriers required to charge the defects come from the semiconductor. When the metallic overlayer is fully grown, it is the metal that contributes most of the charge.

• The potential difference between the metal surface and bulk, in the jellium model, changes quadratically with charge removed or added to the surface. For a charge density of 10¹⁴ electrons/cm² removed from the surface, the slope of the potential vs. charge removed is of the order of 1V per 10¹⁴e • cm^-2 or less.

(2) In Chapter 2 the relevance of lattice mismatch to heteroepitaxiall growth was investigated. A novel method to determine all the possible lattice matches between any two given materials, with any given crystal structure, has been developed. This method allows for an arbitrary periodic reconstruction of the interface. Such reconstruction results in two-dimensional superlattices on both sides of the interface, that have to be similar to each other. The input parameters to these calculations, besides the crystal structure of both materials, are the upper bound on the superlattice unit cell areas, and the maximum allowed mismatch in unit cell dimensions. This method was applied to study known heteroepitaxial interfaces of CdTe on GaAs, CdTe on sapphire, silicon on sapphire, and transition-metal silicides on silicon, to determine the relevance of lattice match in heteroepitaxy. For the last class of materials, namely, silicides on silicon, we list many possible lattice matches, including many that have not been grown so far.

The principal results described in Chapter 2 are:

• A good lattice match is not necessary for epitaxial growth of a single crystal on another.

• In those cases checked in which the epitaxial layer is metallic (silicide on silicon) and a single crystal, there is a good lattice match (bulk mismatch of 2.5% or less).

• Even a polycrystalline epitaxial layer may have some epitaxial relations, that is, some preferred orientations of the crystallites with respect to the substrate. In this case mismatches of up to 15% may be present; this means that the lattice match requirement is probably irrelevant.

(3) In Chapter 3 the elastic properties of silicon are calculated using four models. The parameters of these models were calculated from the elastic constants of a small silicon cluster (Si₅H₁₂) using ab-initio quantum-chemistry methods. The calculated elastic properties were compared to experimental results to assess the quality of the models.

The main findings are:

• All four different models yield a phonon-band structure which is qualitatively correct but not very accurate numerically.

• The deviations of the model predictions from experimental results were attributed to the models and not to the quantum-chemistry methods used to obtain their parameters.

• The LA branch of the phonon-band structure agreed very well with experiment in all the different models used.

• The TA branch of the phonon-band structure was in poor agreement with experiment in all the four models; in particular, the slopes of the TA branch near the Γ point (which determine the elastic constants c₁₂ and c₄₄) were inaccurate.

• The accuracy of the calculated optical phonons varied among the four models.

• Elastic properties associated with bond stretching were calculated much more accurately than elastic properties associated with bond bending.

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