ANÁLISIS DINÁMICO NO LINEAL TIEMPO HISTORIA

Silicon carbide (SiC) is a binary compound consisting of two group-IV elements, silicon and carbon (it is in fact the only naturally stable group-IV compound [175]). It was first synthesised in 1891 by Eugene G. Acheson following the work of Jons Jakob Berzelius on the possibility of a silicon-carbon bond [176]. Soon after its formation the phenomenon of polytypism (which will be discussed later) was discovered along with semiconducting electrical characteristics. However the Acheson method of preparation did not lend itself to industrial scale applications and so the use of silicon carbide as an industrial material was delayed until 1955 when Jan Antony Lely at Phillips perfected a new class of high tem perature crystal furnace [177, 178]. Recently the development of such materials pro­ cessing technologies as molecular beam epitaxy (MBE) and chemical vapour deposition (CVD) have enabled the fabrication of high quality device structures and increased re­ search activity on the material (of which this thesis is one example). However we (as a species) should not feel pride in our ability to synthesise SiC crystals as microcrystals of the material have been found in meteorites which have been dated to before the formation of our Solar System.

The wide bandgap, high thermal conductivity, robust mechanical properties and re­ sistance to radiation damage have made SiC an attractive material for such applications as high tem perature, high power devices and nuclear power applications. SiC may also be a useful material for various optical applications such as blue and ultraviolet light emitting devices and detectors [178] (although GaN devices are more successful in this area). As a ceramic SiC has a very high hardness surpassed only by diamond and boron nitride. Finally SiC is one of the best bio-compatible materials, especially in regard to compatibility with human blood [109].

SiC is a tetrahedral compound with each silicon atom bonding to four surrounding carbon atoms (and vice versa, see Figure 4.1). Depending on the stacking of atoms in one

109.47

Figure 4.1: The bonding scheme of cubic silicon carbide. Each carbon atom (black) is bonded to four silicon atoms (yellow) in a tetrahedral arrangement. The bond angle is 109.47°.

direction SiC can possess more than one type of crystal structure (this polytypism is the one-dimensional variant of polymorphism [118]), ranging from purely cubic (zinc-blende) to the purely hexagonal (wurtzite) with more than two hundred polytypes in between [173].

We shall use the Ramsdell notation [179] to denote different types of crystal structure, using 3C for purely cubic crystals and 2H for purely hexagonal. The number refers to the number of atomic bilayers one has to stack perpendicular to the trigonal axis before recovering the original atomic position (so for cubic crystals the number of atomic layers is

three in the (111) direction and for purely hexagonal crystals the number of atomic layers

is two in the (0001) direction). This polytypism is due to the fact that successive planes along a trigonal axis can be displaced, and that there are three equivalent possibilities [118] (see Figure 4.2). These possibilities can be combined in any order, which results in the wide range of different polytypes that are available. Except for the cubic structure, all other polytypes represent hexagonal (H) or rhombohedral (R) combinations of these

stacking sequences with n Si-C bilayers in the primitive cell. Examples would include 4H

and 6H with four (six) double layers and eight (twelve) atoms in the primitive unit cell. It is possible to change the crystal structure from one polytype to another [180], but in our simulations we use one polytype only.

The three polytypes that have received the most attention are 6H-SiC, 3C-SiC and

4H-SiC. The first polytype to be manufactured at the industrial scale was 6H-SiC. 3C-SiC

can be fabricated in bulk but is usually replete with defects. To minimise the number of defects in 3C-SiC it is a common practice to grow 3C-SiC epitaxially on a Si substrate.

K

3C-SiC (cubic) 2H -SiC (hexagonal)

Figure 4.2: Illustration of polytypism based upon close packing of spheres (the spheres must be all of the same type: for silicon carbide they must all be silicon or carbon atoms only). Displaced initial layer contains spheres in A-type positions surrounded by six voids (top). Spheres of the next layer are situated either in the voids 1, 3 and 5 (B type) or in voids 2, 4 and 6 (C type positions). Spheres of any polytype have their centres located in parallel vertical planes whose interactions with the ground plane are represented by par­ allel lines (dashed lines). Taken from Defects and Defect Processes in Nonmetallic Solids, by W. Hayes and A. M. Stoneham, (1985). Other diagram shows bond orientation of the cubic (stacking sequence ABCA) and hexagonal (stacking sequence ABA) polytypes.

All polytypes of silicon carbide are wide bandgap semiconductors, with the gap indi­ rect. However the bandgap is not the same for each poly type, rather there is a strong variation of bandgap with respect to polytype (in contrast to other semiconductors which possess polytypism, such as ZnS). The bandgap varies from 2.4 eV for 3C-SiC to 3.3 eV for 4H-SiC, with the increase in bandgap depending in a linear manner on the degree of ‘hexagonality’ involved (although this is only true up to a factor of 50% after which the variation with hexagonality is much less strong [181]). The degree of hexagonality is defined as the proportion of the unit cell which does not have a cubic stacking sequence [181].

In this thesis we are only interested in the specific polytype 3C-SiC, as the surface we want to study exists for this polytype. Experimentally the lattice parameter of the unit cell is found to be 4.36 Â with a surface lattice parameter of 3.08 Â [178]. The Young’s modulus in the literature is found to be in the region of 392-448 GPa [176]. The length of the silicon-carbon bond is 1.89 Â. The lattice parameter of 3C-SiC possesses a lattice

mismatch of ~20% when compared with the lattice parameters of silicon or diamond

(the carbon-silicon bond is ~20% longer than a carbon-carbon bond and ~20% shorter 95

than a silicon-silicon bond). This has several consequences: firstly th a t when 3C-SiC is grown as a film on a Si substrate, the interface between the two materials possesses an associated strain field. This strain is relieved by the formation of anti-phase boundaries th at typically extend throughout a silicon carbide film for a /xm [182]. Secondly, an unreconstructed Si or C-terminated SiC surface is under compressive or tensile stress. This stress is a driving force for significant reconstructions on both surfaces.

In the next section we detail one possible result of this stress on the silicon-rich surface of 3C-SiC, the formation of the ( n x2) series of reconstructions. (A note on notation: throughout the following three chapters we will use the terms silicon carbide and SiC interchangeably, as well as /3, 3C and cubic.)

4.1.2

T h e (n x 2 ) series o f recon stru ction s (silicon a to m ic lines):