Fundamental Mechanisms of Film Growth

Donald E. Savage; Feng Liu; Volkmar Zielasek; Max G. Lagally    University of wisconsin, Madison, Wisconsin

I Introduction

In this chapter, we review the fundamental mechanisms involved in the process of growing epitaxial films. We will begin with a general discussion of thermodynamic predictions of film morphology and continue with a discussion of equilibrium growth modes. We will then identify key kinetic processes occurring during growth that may limit the film’s ability to equilibrate.

Our initial discussion will be applicable to any growth system. We will then focus on the specific system of silicon on silicon, concentrating on recent work to extract atomic scale mechanisms of growth. We will finally describe Ge and SiGe alloy growth on Si, in which an understanding of both thermodynamics and kinetics is needed to explain and ultimately to control film structure and morphology.

1 EQUILIBRIUM GROWTH MODES

A natural starting point for learning about film growth is a discussion of the so- called equilibrium growth modes (Bauer, 1958), which represent limiting cases of how a film can grow on a substrate. While no growth can occur at equilibrium and most film growth is performed far from equilibrium, it is useful to consider thermodynamic limits.

Thin crystalline films grown near equilibrium exhibit one of three growth modes, depicted schematically in Fig. 1, the Frank-van der Merwe (layer-by-layer), Stranski-Krastanov (layer-cluster), and Volmer-Weber (cluster) modes (Bauer, 1958). The mode in which a particular materials combination will grow depends on the relative bond strengths of atoms in the deposited layer and between these atoms and the substrate atoms, as well as the degree of lattice match between the two materials. A film will initially wet the substrate if the adlayer-substrate bond is sufficiently stronger than the adlayer-adlayer bond to overcome any strain energy generated to grow the adlayer in registry with the substrate. In this simple description of growth, reaction or interdiffusion is not allowed.

A more formal way to predict growth mode involves the relationship between surface and interfacial free energies. Surface free energy is defined as the free energy to create a unit area of surface on an infinite bulk solid. Given specific (per area) surface energies for the substrate and film as γs, γf, respectively (where these are the values for the semi-infinite crystals), and an interfacial energy γin, where the subscript i stands for interface and n stands for the number of monolayers of film deposited, monolayer-by- monolayer growth occurs only when

γn=γfn+γin−γs≤0

for all values of n (Bauer and van der Merwe, 1986). The term γfn differs from γf to allow for an n-dependent surface strain. The term γin includes the excess free energy needed to create the initial interface between two different materials γi0, plus the additional free energy arising from strain due to lattice mismatch between the overlayer film and the substrate.

In the opposite extreme, one obtains cluster growth when, for all values of n,

γn=γfn+γin−γs>0

In this case the overlayer does not wet the substrate. In the intermediate case, the ad-layer initially wets the substrate, but because of lattice mismatch, as n increases, strain energy contributes to γin the point at which the film no longer wets. Typically, at this point, misfit dislocations are incorporated to relieve strain and, given sufficient mobility of adatoms, preferential growth will occur in the relaxed region, leading to the nucleation of 3-D clusters. Alternatively, roughening of the growth front can relieve strain at the expense of additional surface energy. For example, for pure Ge deposited on Si(001) nondislocated 3-D structures form to relieve strain energy (this will be discussed in detail in Section III). The film thickness at which Eq. (1) no longer holds is one of the definitions of the critical thickness, below which the overlayer film grows in registry with the substrate. The concept of critical thickness will be discussed in more detail in Section III, with specific application to strain relaxation in the absence of dislocation formation, for which strain is relieved by growth-front roughening or islanding. The concept of critical thickness, applicable in the limit in which dislocation formation relieves strain, is covered in detail by Hull in Chapter 3.

In principle, layer-by-layer growth occurs only for a material deposited on itself. In that special case γfn = γs and γin = 0. For species deposited on an unlike substrate there is generally some lattice mismatch and layer-by-layer growth will occur only up to some finite thickness. Thus for a system of B deposited on A one expects either the layer-cluster or the cluster-growth mode. There are exceptions in more complicated growth systems, such as ternary and quaternary III-V alloys, in which it is possible to have essentially lattice-matched growth by choosing the appropriate alloy composition.

Equations (1) and (2) show that it would be quite difficult to grow a coherent strained-layer superlattice of two unlike materials A and B. If A wets B, then B will not wet A. The fact that binary strained-layer superlattices can be grown shows that more is involved than thermodynamics, that is, kinetics also plays a role. To grow a binary strained-layer superlattice, one would like γA ≈ γB and γin≈ 0. Interdiffusion, chemical reaction, or surface segregation also can change surface wetting and the growth mode. We will return to superlattices towards the end of the chapter.

So far, we have discussed thermodynamic predictions only and these in a very simplistic way. While thermodynamics cannot be violated, it is clear that additional terms can be folded into interfacial energy. For example, where surface segregation of the more weakly bonded material occurs to reduce surface free energy, the resulting natural wetting layer, sometimes called a surfactant, can alter growth dramatically. Materials that form strongly bonded compounds at the interface or strongly interdiffuse will also change the interfacial energy. All the terms needed to describe fully the thermodynamics of growth are therefore not a priori obvious.

2 KINETIC PROCESSES DURING VAPOR DEPOSITION

Film growth cannot occur, by definition, under equilibrium conditions. In most cases growth occurs under conditions of supersaturaliun far from equilibrium. Therefore, kinetics will play an important role in determining film morphology. One can obtain a great range of growth morphologies when one considers the kinetics (Zhang and Lagally, 1997). Kinetic processes can be partly controlled by varying substrate temperature and deposition rate. In an evaporative growth process, such molecular-beam epitaxy (MBE), in which one can independently control sample temperature and deposition rate, one can influence which of the kinetic processes is rate limiting, allowing some control over film morphology.

During vapor deposition, a clean substrate in an ultrahigh-vacuum environment is exposed to the vapor of the growth materials. As adatoms are continuously deposited onto the substrate, the system is driven into supersaturation, that is, the 2-D vapor pressure is higher than at equilibrium. A condensed phase, either a 2-D island or 3-D cluster, will then form to relax the system back toward equilibrium. Two major processes form a condensed phase from a 2-D vapor: nucleation and growth (see, for example, Matthews, 1975; and Lewis and Anderson, 1978). Arriving atoms make a random walk on the surface and, when meeting each other, form islands. The rate limiting step is the formation of a critical nucleus, which is defined as an island that is more likely to grow than decay (Venables, 1973). The nucleated islands grow by further addition of adatoms, and the lateral accommodation kinetics determine the growth shape of the islands. Growth continues until deposition is interrupted. Thereafter, coarsening, in which islands evaporate laterally and the adatoms diffuse to larger islands, controls the dynamics of further ordering. The driving force is the difference between the local equilibrium vapor pressures around the large and small islands.

An adatom, in addition to meeting another to form a nucleus, meeting an existing island (growth), or traveling between existing islands along a concentration gradient (coarsening), may also meet one of these fates: walking into a...