Pramana - J. Phys., Vol. 38, No. 6, June 1992, pp. 545-639. © Printed in India. Electronic structure of epitaxial interfaces G P DAS Solid State Physics Division, Bhabha Atomic Research Centre, Bombay 400085, India MS received I0 October 1991; revised 2 April 1992 Abstract. Metal-semiconductor (Schottky barrier) and semiconductor-semiconductor (hetero- junction) interfaces show rectifying barrier heights and band offsets, which are two key quantities required to optimize the performance of a device. A large number of models and empirical theories have been put forward by various workers in the field during the last 50 years. But a proper understanding of the microscopic origin of these quantities is still missing. In this article, our focus is mainly to present a unified framework for first principles investigation of the electronic structure of epitaxial interfaces, in which one of the constituents is a semiconductor. LMTO method is now a well established tool for self-consistent electronic structure calculations of solids within LDA. Such calculations, when performed on supercell geometries, are quite successful in predicting a wide range of interface specific electronic properties accurately and elBciently. We describe here the basic formalism of this LMTO- supercell approach in its various levels of sophistication and apply it to investigate the electronic structure of A- and B-type NiSi2/Si(lll) interface as a prototype metal- semiconductor system, and CaF2/Si(I I 1) interface as a prototype insulator-semiconductor system. These are a few of the most ideal lattice matched epitaxial interfaces whose atomic and electronic structures have been extensively studied using a wide range of experimental probes. We give here a glimpse of these experimental results and discuss the success as well as limitations of LDA calculations to achieve accuracies useful for the device physicists. Keywords. Epitaxial interfaces; Schottky barrier; LMTO method; supercell approach; electronic structure. PACS Nos 73.20; 68.35 Table of contents 1. Introduction 1.1 Overview of the problem 1.2 Experimental considerations 1.3 A band structure primer 2. Schottky barrier height and band offset 2.1 Model theories 2.2 First principles calculations 3. Theoretical treatment 3.1 Supercell approach 3.2 Basic formalism of LMTO method 3.3 The envelope function 3.4 LMTO orbitals and ~p- tb augmentation 3.5 Hamiltonian and overlap 3.6 Practical scheme for self-consistency 3.7 From ASA to full potential 546 G P Das 4. Bulk electronic structures 4.1 Si: a benchmark for covalent semiconductors 4.2 NiSi2: a unique metallic silicide 5. NiSi2/Si(l 11) interface 5.1 Atomic structure of the interface 5.2 Details of calculation 5.3 Results on electronic structure 5.4 LDA calculation of SBH 5.5 Different methods of extracting SBH 5.6 Results on SBH 5.7 SBH discrepancy: possible corrections 5.8 Discussion and summary 6. CaF2/Si(111) interface 6.1 Experimental studies 6.2 Theoretical calculations 7. Concluding remarks I. Introductory survey 1.1 Overview of the problem When two different solids are joined together, the junction or interface formed quite often shows novel properties different from either of the bulk constituents. For example, Braun (1874) realized more than 100 years ago that the contact between a thin metal wire and a crystal shows a resistance dependent on the polarity of the applied voltage. This rectification behaviour in a metal-semiconductor interface, as we all know, plays a crucial role in semiconductor devices. Similarly when two semiconductors having different band gaps form a heterojunction, there is a band discontinuity (or offset) which dictates the transport properties of the interface. In general, in any 'bicrystal' formed by joining two solids A and B, the electronic structure is perturbed locally near the interface, while it reduces to that of the individual solids a few layers away from the interface. One of the aims of this article is to present a unified approach for microscopic understanding of the interface electronic structure (Das 1989). The bulk electronic structure of solids is now well understood. Surfaces are relatively more difficult to handle, as it is nontrivial to produce an atomically clean surface and to characterize it properly. Nevertheless, with the advent of advanced ultra-high vacuum facilities and a number of experimental techniques for probing the atomic and electronic structure of surfaces, we are now more or less well equipped to do surface research. The crystalline periodicity being lost in the direction normal to the surface, special theoretical methods, like cluster method, slab method, matching method, superlattice method etc. have been developed (Applebaum and Hamann 1976; Schliiter 1978; Pollman 1980). Interface is rather distinct from both bulk and surface. It is a solid state discontinuity that provides the matching of crystailographically and/or compositionally different materials. It is a spatially extended phenomenon in a two dimensional plane, unlike point defects, dislocations or grain boundaries. The distinction between a surface and Electronic structure of epitaxial interfaces 547 an interface is somewhat subtle. Qualitatively, an interface may be looked upon as an 'internal surface', i.e. a surface forming common boundary between two regions, just as a surface can also be looked upon as an interface between a solid and vacuum. In this new 'sandwitch' structure, the top overlayer may be as thick as the substrate or as thin as only a few monolayers. Being 'buried', it cannot be 'seen' by the normal bulk or surface sensitive probes, resulting in some inherent experimental difficulties. A clean Si(111) surface, for example, shows certain unique features (Prutton 1983) like say 7 x 7 reconstruction, which can be seen by a low energy electron diffraction (LEED) experiment. The surface unit cell is actually quite complicated and is thought to be best described by the dimer adatom stacking-fault (DAS) model developed by Takayanagi et al (1985). As soon as a native oxide (SiO2 in this case) overlayer is formed on the top, there is a drastic change in the atomic as well as electronic structure. The Si/SiO2 interface formed shows unique interface state distribution, crucial for metal-oxide-semiconductor (MOS) technology (Schulz 1983). SiO2 being an insulator is used to isolate the gate electrode from the semiconductor in a MOS device. Even though considerable experimental effort has gone to understand the physics of Si/SiO2 interface, there is no real base for interpretation, because on the atomic scale the interfacial layer is non-uniform, rough and full of defects and disorder. By oriental growth of an insulating material like say CaF2 (having nearly same dielectric properties as SiO2) on the surface of a Si(111) single crystal, an atomically smooth epitaxial interface (see section 6) can be formed, with well controlled and superior properties (Schowalter and Fathauer 1989). The term epitaxy (i.e. 'arrangement on'), coined by Royer (1928), means that one particular crystallographic direction in the contact plane of the guest crystal is parallel to some crystallographic direction in the contact plane of the host crystal. Such well controlled (on nearly atomic scale) layer-by-layer growth has been made possible with the advent of techniques like molecular beam epitaxy, MBE (Parker 1985; Chang and Giessen 1985; Cho 1989; Ploog 1990; Joyce 1991) and metal-organic chemical vapour deposition, MOCVD (Miller and Coleman 1988) during the last decade. MBE or MOCVD grown interfaces have some unique features, like they are single crystalline, so that host and guest crystal together can be described by a single space group; they are clean, uniform, atomically abrupt and form intimate contact with highly controlled thickness and composition; the atomic structure and coordination number at the interface can be well specified and in some cases, even the relative orientation of the two half crystals can be controlled. An important, but not essential, factor relevant to epitaxial growth is the 'lattice matching', which means a periodic translation symmetry of interface being compatible with the crystal structures on both sides of that interface (Zur et al 1985). With Si, for example, there are some metals, semiconductors and insulators which are lattice matched (see table 1) and in fact, high quality epitaxial growth of all these materials on Si have been achieved. Multiple epitaxial interfaces with alternate thin layers of two solids give rise to artificially modulated structures like superlattices and quantum wells. The idea of semiconductor superlattices first came from Esaki and Tsu (1970) and its practical realization was achieved only after the advent of MBE (Ploog and Dohler 1983). The ability to exercise independent and spatial control over both the semiconductor band gap and the level of doping has made it possible to grow a whole new range of 548 G P Das Table 1. Metals,semiconductors and insulators, closelylattice matched with silicon. The exact magnitude of the small lattice mismatch (with respect to silicon) is given within brackets. si Metal Semiconductor Insulator NiSi2( - 0-4%) GaP( + 0.4%) a = 5.431 ,~ CaF2(+ 0.6%) CoSi2( - 1.2%) ZnS(- 0.5%) artificially tailored quantum well structures, which in turn gives rise to novel physical properties (Kelly and Nicholas 1985). The flexibility of electronic properties of these novel materials has given birth to a fashionable field today, known as band structure engineering (Abram and Jaros 1989). A lot of empirical and first principles investigations of the electronic structure of semiconductor superlattices have been attempted (Smith and Mailhiot 1990). Lattice mismatched heterostructures can also be grown epitaxially with essentially no misfit defect generation, provided the layers are sufficiently thin so that the mismatch is accommodated by coherent strain in the individual layers. The fact that strain need not be a nuisance, but can indeed offer new functionality, has given rise to a relatively new field called strained layer superlattices (Pearsall 1991; Mailhiot and Smith 1990).