8.2.3.1 Crystallographic Notation

In cases other than graphoepitaxy involving dissimilar materials, the relative orientations between the film and substrate are generally coupled. To understand the epitaxial relationship and the nature of the interfacial structure it is necessary to identify the crystallographic orientations between the film and substrate. Unlike the notation used to describe the two-dimensional surface crystallography in Section 7.2.3.2, the traditional (3-D) Miller indices are employed assuming there is no reconstructed substrate surface. For this purpose the indices of the overgrowth plane are written as (HKL) while those of the parallel substrate plane at the common interface are taken as (hkl). The corresponding parallel directions in the overgrowth and substrate planes, denoted by [UVW] and [uvw], respectively, must also be specified. This tetrad of indices, written by convention as (HKL)//(hkl); [UVW]//[uvw], serves to define the epitaxial geometry. As an example, for parallel epitaxy of Ni on Cu, the notation would read (001)Ni//(001)Cu; [100]Ni//[100]Cu. In this case both planes and directions coincide. For (111)PbTe//(111)MgAl₂O₄; [211]PbTe//[101]MgAl₂O₄ the interfacial plane is common but the directions are not. Sometimes, the epitaxial relationships can be predicted on the basis of lattice fitting arguments. Those planes and directions which give the best lattice fit often, but certainly not always, determine the film–substrate orientation.

An important quantity which characterizes epitaxy is the lattice misfit f, which was defined in Section 7.3.4.1 as

     (8-1)

where a₀(f) and a₀(s) refer to the unstrained lattice parameters of film and substrate, respectively. Epitaxy is often a matter of accommodation where elimination of defects requires some bond stretching at the interface by both film and substrate atoms. A compromise is struck, creating a common interfacial lattice parameter. Thus, a positive f implies that the initial layers of the epitaxial film will be stretched in tension while the substrate is compressed. Similarly, a negative f means film compression and an extended substrate.

8.2.3.2 Geometrical Features of Metal/Semiconductor Heteroepitaxy

Metal/semiconductor structures are used for contact applications in all solid-state devices, and although epitaxial films may be desirable they are generally not essential. However, as device and contact dimensions continue to shrink the issue of metal/semiconductor heteroepitaxy assumes a greater urgency; not only does epitaxy affect electrical transport across the junction, but through heteroepitaxy the potential to fabricate three-dimensional silicon circuits is facilitated. Examples of metal- (and metal-silicide–) semiconductor heteroepitaxy are briefly treated in turn.

8.2.3.2.2 β-FeSi₂/Silicon

Other metal silicide films do not exhibit the same epitaxial quality described above. The much-studied β-FeSi₂ is nevertheless interesting because it is a semiconductor and not a metal like other silicides (11). Imposing its low-symmetry orthorhombic structure (a = 9.86 Å, b = 7.79 Å, c = 7.88 Å) on the threefold symmetric (111) Si substrate causes oriented domains of epitaxial βFeSi₂ films to form. As shown in Fig. 8-4a the domains are rotated relative to one another. For the indicated overgrowth the epitaxial notation for β-FeSi₂ grown on (111) Si is (101)β FeSi₂//(111)Si:[010]β-FeSi₂//[10]Si. Similarly, when β-FeSi₂ films form on (100) Si substrates, the epitaxial orientation shown in Fig. 8-4b is (100)β-FeSi₂//(100)Si:[010]β-FeSi₂//[110]Si. If there is no surface reconstruction in these diagrams, calculation of the misfit is relatively straightforward. For example, in the case of the latter, assuming the tetragonal structure approximates the orthorhombic lattice,

Figure 8-4 Epitaxial relationships between β-FeSi₂ and Si. (a) β-FeSi₂ (shaded) grown on (111) Si. (b) β-FeSi₂ grown on (100) Si.

(From Ref. 11. Reprinted with the permission of the authors.)

8.2.3.2.3 Metal–GaAs Heteroepitaxy

Similar epitaxial relationships between assorted metals and compounds deposited on GaAs and other compound-semiconductor surfaces have also been investigated (Ref. 12). Based on simple geometric matching we can distinguish three different epitaxial arrangements in Fig. 8-5, where the cubic (zinc blende) GaAs substrate (a₀(s) = 5.653 Å) is covered by films of materials that also have a cubic crystal structure (e.g., FCC, BCC, CsCl, NaCl).

Figure 8-5 Simple epitaxial alignments for cubic films (f) on a cubic substrate (s). (a) a₀(f) = a₀(s); (b) 2a₀(f) = a₀(s); (c) 2^1/2a₀(f) = a₀(s).

(From Ref. 12. Reprinted with the permission of the author.)

The simplest epitaxial alignment is the cube-on-cube (Fig. 8-5a) where the lattice parameters are equal (a₀(s) = a₀(f)). For (100) GaAs only the impractical elements Ca (FCC) and Rb (BCC) provide the closest lattice matches. However, rare-earth arsenide (RE-V) films, e.g., ErAs, YbAs, and Er_xSc_1-x As films, exhibit reasonably good epitaxy. These compounds have the NaCl structure so that the As sublattice is continuous across the (100) interface, thus promoting chemical stability.

There are cases where a₀(s) is almost twice a₀(f), and such metals are expected to grow epitaxially (Fig. 8-5b). For example, consider the growth of an (110) Fe (BCC) film on (110) GaAs. Because the lattice parameter for Fe is 2.866 Å it appears that two Fe unit cells could be accommodated by one of GaAs. The resulting epitaxial geometry is denoted by

In this system the misfit in the [001] direction is

High-quality epitaxial Fe films have been deposited on GaAs, enabling fundamental studies of ferromagnetism (Ref. 13).

If a₀(s) is close to a₀(f) in magnitude, epitaxial deposits are expected to grow in 45° rotated alignment based on lattice-matching arguments (Fig. 8-5c). Candidate metals for such epitaxy include Al and Ag. Epitaxy does occur, but since other film orientations are also observed the situation is more complex. A few monolayers of intervening metal, e.g., Ga for Al, Fe for Ag, sometimes fosters the predicted epitaxy, perhaps by altering surface energies or by providing a growth template.

It is clear that a more complete understanding of dissimilar materials epitaxy must consider issues of interfacial bonding, stress, and thermodynamic stability in addition to simple geometric matching.

8.3.3.1 Defect Propagation from Substrate

A classic example of this is the propagation of an emergent screw dislocation spiral from the substrate surface into the growing film. Depositing atoms preferentially seek the accommodating ledge sites of the dislocation spiral staircase. Layers of defect-free film then radiate laterally to cover the substrate. Except for the screw dislocation, an epitaxial layer of otherwise good fit is possible. Occasional substrate dislocations which are present are apparently sources of such dislocations observed in homoepitaxial layers. Gross defects such as grain boundaries and twins are, however, rarely present.

8.3.3.2 Stacking Faults

Stacking faults are crystallographic defects in which the proper order of stacking planes is interrupted. For example, consider the first three atomic planes or layers of a (111) silicon film. Each of these planes may be imagined to be a close-packed array of atomic spheres (Fig. 1-2a), and each successive layer fits into the interstices of the previous layer. Atoms in the second layer (B) have no choice but to nest in one set of interstices of the first (A) layer. It now makes a difference which set of B layer interstices atoms of the third layer choose to lie in. If they lie above neither the A nor the layer atoms, the stacking sequence is ABC, and in a perfect epitaxial film the ABCABCABC, etc, order is preserved. If, however, a plane of atoms is missing from the normal sequence, e.g., ACABCABC, or a plane of atoms has been inserted, e.g., ABCBABCABC, then stacking fault defects are produced. It is established that they propagate from dislocations and oxide precipitates at the substrate interface. Misoriented clusters or nuclei containing stacking faults coalesce with normal nuclei and grow into the film in the manner of an inverted pyramid. Continuing growth causes the characteristic closed triangle shown in Fig. 8-10 to become progressively larger. For (100) growth the stacking faults form squares which can be revealed by appropriate etches. Although stacking faults are a vanishing breed in homoepitaxial Si films their density increases with decreasing growth temperature. In mismatched heteroepitaxial films, e.g., GaAs on Si, stacking faults are common.

Related to stacking faults are the ubiquitous "oval defects" observed during MBE growth (Section 8.6.2) of compound semiconductors. These defects, shown schematically in Fig. 8-10, are faceted growth hillocks which nucleate at the film–substrate interface and nest within the epitaxial layer. They usually contain a polycrystalline core bounded by four {111} stacking-fault planes. With densities of ∼ 10–100 cm⁻² and sizes ranging from 1 μm² to ∼ 30 μm², these defects are a source of considerable concern. There are a number of possible sources for oval defects in GaAs including carbon contamination from CVD precursors, incomplete desorption of oxides prior to growth, and spitting of Ga and Ga₂O from melts.

8.3.3.3 Dislocation Loops from Precipitates, Impurities, or Dopants

This category is self-explanatory. The precipitates and dislocations usually form during cooling and are the result of solid-state reactions subsequent to growth. Films containing high intentional or accidental dopants or impurity levels are susceptible to such defects.

8.3.3.4 Low-Angle Grain Boundaries and Twins

These defects arise from misoriented islands which meet and coalesce. When this happens small-angle grain boundaries or crystallographic twins result. The lattice stacking is effectively mirrored across a twin plane C, i.e.,… BCABCBACB…. Both types of defects may anneal out by dislocation motion if the temperature is high enough. During heteroepitaxial growth Matthews (Ref. 17) has suggested that there is some ambiguity in the exact orientation of small nuclei. He has formulated a rule of thumb that the relaxation of elastic misfit strain causes a variation in the orientation of crystal planes (in radians) roughly equal to the magnitude of the lattice misfit f. Such an effect would naturally give rise to a network of small-angle grain boundaries.

8.4.2.1 Properties

Materials employed for epitaxial electronic and optoelectronic devices are largely drawn from a collection of direct-bandgap III–V semiconductor compounds. Although II–VI and IV–VI semiconductors are used to a much lesser extent, the discussion applies to them as well. Table 8-1 contains a list of important semiconductors together with some of their physical properties. Those that are pertinent to the possibility and quality of epitaxy are semiconductor nature, i.e., direct or indirect bandgap; bandgap energy; lattice constant; and thermal expansion coefficient. The implications of some of these properties on epitaxy/devices are detailed below.

Table 8-1 Semiconductor Properties

8.4.2.1.1 Direct and Indirect Energy Bandgaps

When light is emitted from or absorbed in a semiconductor, energy as well as momentum must be conserved. In a direct-bandgap semiconductor the carrier transitions between the valence and conduction bands occur without change in momentum of the two states involved. In the energymomentum or equivalent energy-wave vector, parabola-like (E vs k) representation of semiconductor bands (Fig. 8-13), emission of light occurs by a vertical electron descent from the minimum conduction band energy level to the maximum vacant level in the valence band. This is what occurs in the direct energy gap materials GaAs and InP. However, in indirect-bandgap semiconductors such as Ge and Si the transition occurs with a change in momentum that is essentially accommodated by excitation of lattice vibrations and heating of the lattice. This makes direct hole–electron recombination with photon emission unlikely. But in direct-bandgap semiconductors such processes are more probable, making them far more efficient (by orders of magnitude) light emitters.

Figure 8-13 Depiction of electron transitions between conduction and valence bands in (a) direct- and (b) indirect-gap semiconductor materials.

8.4.2.1.2 Bandgap Energy

This important semiconductor property can be understood by considering the variation of the absorption coefficient (α) as a function of photon energy as shown in Fig. 8-14. If light of intensity I₀ is incident on a semiconductor surface, the photon intensity at a depth x below the surface is attenuated to I(x), such that

Figure 8-14 Optical absorption coefficients for various semiconductor materials.

(Reprinted with permission from J. Wiley & Sons, S. M. Sze, Semiconductor Devices – Physics and Technology. McGraw-Hill, New York, 1985.)

     (8-7)

In all semiconductors α becomes negligible once the wavelength exceeds the cutoff value. This critical wavelength, λ_c, is related to the bandgap energy E_g by a variant of the well-known relation E = hv or E_g = hc/λ_c, where h, c, and ν are Planck’s constant and speed and frequency of light, respectively. Alternatively,

     (8-8)

For direct-bandgap semiconductors the value of α becomes large on the short-wavelength side of λ_c, signifying that light is absorbed very close to the surface. For this reason even thin-film layers of GaAs are adequate, for example, in solar cell applications. In Si, on the other hand, α varies more gradually with wavelength less than λ_c because of the necessity for phonon participation in light absorption/generation processes. Therefore, efficient solar-cell action necessitates thicker layers if indirect-energy-gap semiconductors are employed. In addition to a direct-bandgap semiconductor, photonic device operation generally requires a specific wavelength or value of E_g for light emission or absorption processes.

8.4.2.1.3 Lattice Parameter

To ensure defect-free interfaces in semiconductor film/substrate heterostructures, it is essential that the lattice parameters (a₀) of both be closely matched. For optical devices, lattice mismatches of less than 0.1% are sought. As an example consider GaAs and AlAs with respective a₀ values of 5.6532 and 5.6611Å. The lattice mismatch between these compounds is Δa₀/a₀ or 0.16%. No hint of structural defects at the interface between epitaxial films of these compounds is observed in the lattice image of Fig. 8-15.

Figure 8-15 Electron microscope lattice image of GaAs/AlAs heterojunction taken with [100] illumination.

(From H. Ichinose, Y. Ishida, and H. Sakaki, JOEL News 26E(1), 8, 1988.)

8.4.2.2 Designing Epitaxial Film–Substrate Combinations

The first three of the semiconductor properties just mentioned converge in the extremely handy graphical representations of E_g vs a₀ shown in Figs. 8-16a and 8-16b. These apply, respectively, to the common III–V compound semiconductors (Fig. 8-16a) where E_g < 2 eV, and to the III–V and II–VI materials where E_g >2 eV (Fig. 8-16b), together with their corresponding alloys. Through the use of these figures, the design and selection of complex semiconductor alloys with the desired properties may be visualized. Elements and binary compounds are represented simply as points. Ternary alloys are denoted by lines between constituent binary compounds. When one of the elements is common to both compounds, a continuous range of solid-solution ternary alloys generally forms upon alloying binaries. Thus the line between InP and InAs in Fig. 8-16a represents the collection of InP_x As_1–x, ternary solution alloys, with x dependent on the proportions mixed. Within the areas outlined by four binary compounds are quaternary alloys. Therefore, the Ga_1–x In_xAS_1–yP_y system may be thought of as arising from suitable combinations of GaAs, GaP, InAs, and InP. However, there is no need to start with these four binary compounds when synthesizing a quaternary; it is usually only necessary to control the vapor pressures of the Ga-, In-, As-, and P-bearing species. Furthermore, solid lines represent direct-bandgap ternary compounds while the dashed lines refer to materials with an indirect bandgap.

Figure 8-16 Energy gaps and corresponding lattice constants for (a) various III–V compound semiconductors with E_g 2 eV; (b) various II–VI and III–V compound semiconductors with E_g 2 eV. Only data for the hexagonal αAlN, GaN, and InN phases are plotted.

(a) (courtesy of P. K. Tien, AT&T Bell Laboratories); (b) (From T. Matsuoka, A. Ohki, T. Ohno, and Y. Kawaguchi, J. Cryst. Growth 138, 727, 1994. Reprinted with the permission of Dr. T. Matsuoka.)

A few examples will illustrate the use of these important diagrams. Suppose it is desired to create semiconductor materials for optoelectronic devices that have an energy gap of 1.0 eV. What are the compositions of some candidate materials and what are their lattice parameters? Extending a horizontal line across Fig. 8-16a at E_g = 1.0 eV (or λ = 1.24 μm) we see that the alloys of the following pairs are crossed: GaAs–InAs; GaAs–GaSb; InP–InAs; AlAs–InAs; AlSb–GaSb; and AlSb–InSb. Although these all appear to be potentially useful, AlSb–GaSb has an indirect bandgap and is disqualified. Even though AlAs and AlSb are also indirect semiconductors, the indicated ternary compositions at 1 eV appear to be direct. Upon alloying these binary compounds we may assume, in the simplest approximation, that the resultant lattice constants and energy gaps of the ternaries are weighted averages of the binary values. As an example, let us determine the composition of the desired InGaAs alloy for which a₀ must equal 5.76Å, the value at 1.0 eV. For a linear law of lattice-constant mixtures, i.e., Vegard’s law, a₀(In_xGa_1–xAs) = (x)a₀(InAs) + (1 – x)a₀(GaAs). Since 5.76 = 6.07x + 5.65(1 – x), x = 0.26, and the predicted alloy has the composition In_0.26Ga_0.74As. Alternatively, linear averaging of energy gaps gives E_g(In_xGa_1–xAs) = (x)E_g(InAs) + (1 – x)E_g(GaAs). Thus, 1.0 = 0.36x + 1.43(1 – x) or x = 0.40. To resolve this discrepancy in x, let us consult Table 8-2 for experimental values of direct energy gaps in selected III–V ternary solid solutions. On this basis x is calculated to be 0.40, so the preferred ternary composition is In_0.40Ga_0.60As.

Table 8-2 Composition Dependence of Direct Energy Gaps in Selected III - V Alloys^a

a From J. W. Mayer and S. S. Lau, Electronic Materials Science: For Integrated Circuits in Si and GaAs. Macmillan, New York, 1990.

Next, consider the practical problem of fabricating lasers emitting coherent light at 1.0 eV. In these devices, semiconductor films must be deposited on a readily available substrate, e.g., GaAs or InP, and, importantly, be lattice matched to it. Our ternary alloy is lattice-matched to neither GaAs nor InP, and none of the prospective 1 eV materials is lattice-matched to GaAs. A new semiconductor must therefore be found. Calculation using Vegard’s law shows that Ga_0.47In_0.53As, which is commercially produced for optoelectronic devices, has the same lattice constant as InP; unfortunately, E_g for this ternary alloy is not 1 eV but rather 0.70 eV (from Fig. 8-16a). All is not lost, however, because by alloying Ga_0.47In_0.53As with InP E_g for the new quaternary GaInAsP alloy can be raised to a value of 1.0 eV, all the while simultaneously maintaining a₀ = 5.87Å. To estimate the required stoichiometry we assume E_g(GaInAsP) = (1– x)E_g(Ga_0.47In_0.53As) + xE_g(InP), where x is the fraction of P added. Substituting, 1.0 = (1 – x)0.70 + x1.27 and x = 0.53; therefore, the desired semiconductor film composition is Ga_0.22In_0.78As_0.47P_0.53. Growing such a lattice-matched film may not be easy but is certainly not insurmountable.

Other ternary semiconductor properties are similarly altered upon blending binary compounds. For example, the index of refraction n, required for light-guiding properties in lasers, varies as (Ref. 31)

     (8-9)

in the AlAs–GaAs system. Thus it is possible to design ternary alloys with a larger E_g and smaller n relative to GaAs, while maintaining an acceptable lattice match for high-quality heterojunctions. These unique combinations of properties have led to the development of a family of injection lasers, light-emitting diodes, and photodiodes in the GaAs–AlAs system and other III–V semiconductors as well.

8.4.4.1 Optical Communications

Optical communication systems transmit information optically through fibers. This is done by converting the initial electronic signals into light pulses employing laser or light-emitting diode light sources. The light launched at one end of an optical fiber is confined to the fiber core and propagates along it over long distances. At the other end of the system the light pulses are detected by photodiodes and converted back into electronic signals, which, in telephone applications, finally generate sound. In such a system it is crucial to transmit the light with minimum attenuation or low optical loss. Great efforts have been made to use the lowest-loss fiber possible and minimize loss at both the source and detector ends. If optical losses are high, it means that the optical signals must be reamplified with additional, costly repeater stations. The magnitude of the problem can be appreciated when transoceanic communications systems are involved. In silica-based fibers it has been found that minimum transmission losses occur at a wavelength in the range 1.3–1.55 μm The necessity to operate within this IR-wavelength window bears directly on the choice of suitable semiconductors and epitaxial deposition technology required to fabricate the required sources and detectors.

Reference to Table 8-1 shows that InP is transparent to 1.3–1.55 μm light. This means that InP wafers can serve both as a substrate on which epitaxial films can be grown and as a mechanical support facilitating the coupling of fibers to devices (Fig. 8-17). As we have seen earlier a very close lattice match to InP (a0 = 5.869Å) can be effected by alloying Ga_0.47In_0.53As and InP. In this way high-performance lasers based on the lattice-matched GaInAsP/InP system have emerged for optical communications use.

8.4.4.2 Light-Emitting Semiconductor Devices

Bright visible-light-emitting devices with λ > 0.5 μm have been available for well over 30 years. The ubiquitous red lasers and light-emitting diodes are based on epitaxial AlGaAs on GaAs, while orange, yellow, and green LEDs are fabricated from indirect bandgap materials, e.g., GaAsP doped with nitrogen. However, practical sources for the violet-blue-green end of the spectrum, i.e., 0.4–0.5 μm have been notably slow in appearing. They require semiconductors with wide energy bandgaps ranging from somewhat below 2.5 to 3 eV and greater. Table 8-1 reveals that all compound semiconductor classes have potential candidate materials in this E_g range, e.g., (II–VI) ZnS, ZnSe, and ZnTe; (III–V or III–N) GaN, AlN, and InN; and (IV–VI) SiC, an indirect semiconductor. Despite much research and development over the years, particularly in II–VI materials (Ref. 34), devices derived from them were not commercialized even though sizable wafers of ZnS, ZnSe, ZnTe, and SiC have been available for some time (Ref. 35). Two major obstacles to the fabrication of II–VI and III–N diode devices have been the difficulty in doping these materials p-type, and the unacceptably large dislocation and stacking fault densities at heteroepitaxial interfaces. The former has limited junction formation while the latter has led to short-lived devices. With advances in p-doping (˜ 10¹⁸/cm³ in ZnSe) coupled with a reduction in defect density (to ∼ 10⁵/cm²) due to epitaxial growth first on GaAs (where f = 0.25%) and then on ZnSe wafers, device performance improved (laser lifetimes of ∼ 1000 h); however, it still fell short of what was demanded. Blue-light device prospects for the wurtzite or hexagonal III–N materials appeared to be even more dim. For example, in the case of GaN the substrate of choice is sapphire (Al₂O₃) but the lattice mismatch of 14% has led to dislocation densities of ∼ 10¹⁰/cm². In comparison, defect densities of less than ∼ 10³/cm² are typical in lattice-matched III–V devices grown on GaAs and InP.

8.4.4.3 GaN Light-Emitting Semiconductor Devices

The situation just described prevailed until 1993 when Nichia Chemical Industries, a small family-owned business in Japan, astonished the world by demonstrating a very bright blue GaN LED (Ref. 36). This revolutionary advance as well as subsequent ones based on it were spearheaded by S. Nakamura and enabled Nichia to leap ahead of Western efforts in this area (Refs. 37-40). Two key discoveries contributed to this progress. First, satisfactory p-type doping was achieved using Mg. Secondly, a compliant, recrystallized amorphous buffer film of GaN on top of the sapphire substrate reduced the harmful effects of dislocations and lattice and thermal expansion coefficient mismatches. This enabled device-quality epitaxial GaN layers to be grown by MOCVD methods, despite initially high dislocation densities (Ref. 2).

Today, highly efficient UV, blue, and green InGaN LEDs have been fabricated with (external) quantum efficiencies of 7.5% at 0.371 μm (UV), 11.2% at 0.468 μm (blue), and 11.6% at 0.520 μm (green). Some of these blue-light sources have brightnesses of more than 1000 mcd and are comparable to superbright red LEDs; they are more than a hundred times brighter than SiC blue LEDs. There are many actual as well as potential applications for this new generation of light sources. The largest LEDdisplay sky screen in the world, located in Tianjin, China, measures 40 meters in length and 14 meters in height and contains some 680,000 blue and 1,700,000 green LEDs. Traffic lights composed of blue LED sources have already appeared.

An important recent advance has been the development of long-lived InGaN blue-light lasers (Ref. 40) such as that shown in Fig. 8-20. Laser lifetimes critically depend on the dislocation density in the active diode region, and this has been dramatically reduced by fabricating devices on epitaxial layers that are seeded and grown over a buffer layer (see Section 8.5.2.2). Upon commercialization of blue lasers, an important application promises to be optical storage for memories. Since information storage densities vary as the inverse square of the wavelength of light used, increases by a factor of about 4 may be anticipated relative to the present red AlInGaP lasers. A big prize would be an LED or laser-based replacement for the incandescent lamp. For more detailed information the reader should consult the now extensive literature on this subject.

Figure 8-20 Structure of the first InGaN multiquantum-well laser diode.

(From Ref. 40. Reprinted with the permission of the author.)

8.5.2.1 Liquid-Phase Epitaxy

In liquid-phase epitaxy (LPE) melts rather than vapors are in contact with the growing films and substrates. Introduced in the early 1960s LPE is still widely used to produce compound-semiconductor devices. For example, of commercially produced devices presently over 40% are light-emitting diodes, and of these almost 50% are LPE-grown GaP devices; another 20% are LPE-grown AlGaAs/GaAs LEDs (Ref. 41). However, for greater layer uniformity and atomic abruptness, LPE has been supplanted by various vapor-phase epitaxy methods, notably MOCVD. LPE involves the precipitation of a crystalline film from a supersaturated melt onto a substrate that serves as both the template for epitaxy and the physical support for the heterostructure. The process can be understood by referring to the GaAs binary phase diagram (Fig. 1-15). Consider a Ga-rich melt containing 10 at.% As. When heated above ∼ 920°C all of the As dissolves. If the melt is cooled below the liquidus temperature into the two-phase field, it becomes supersaturated with respect to As. Only a melt of lower than the original As content can now be in equilibrium with GaAs. The excess As is, therefore, rejected from solution in the form of GaAs which grows epitaxially on a suitably placed substrate. Readers will appreciate that the crystals they grew as children from supersaturated aqueous solutions essentially formed by this mechanism.

Through control of cooling rates, different kinetics of layer growth apply. For example, the melt temperature can either be lowered continuously together with the substrate (equilibrium cooling) or separately reduced some 5–20°C and then brought into contact with the substrate at the lower temperature (step cooling). Theory backed by experiment has demonstrated that the epitaxial layer thickness increases with time as t^3/2 for equilibrium cooling and as t^1/2 for step cooling (Ref. 29). Correspondingly, the growth rates or time derivatives vary as t^1/2 and t^−1/2, respectively. These diffusion-controlled kinetics respectively indicate either an increasing or decreasing film growth rate with time depending on mechanism. Typical growth rates range from ∼ 0.1 to 1 μm per minute. A detailed analysis of LPE is extremely complicated in ternary systems because it requires knowledge of thermodynamic equilibria between solids and solutions, nucleation and interface attachment kinetics, solute partitioning, diffusion, and heat transfer. LPE offers several advantages over other epitaxial deposition methods, including low-cost apparatus capable of yielding films of controlled composition and thickness, with lower dislocation densities than the parent substrates.

To grow multiple GaAs/AlGaAs heterostructures, the seed substrate is sequentially translated past a series of crucibles holding melts containing various amounts of Ga and As together with such dopants as Zn, Ge, Sn, and Se as shown in Fig. 8-21. Each film grown requires a separate melt. Growth is typically carried out at temperatures of ∼ 800°C with maximum cooling rates of a few degrees Celsius per minute. Limitations of LPE growth include poor thickness uniformity and rough surface morphology, particularly in thin layers. The CVD and MBE techniques are distinctly superior to LPE in these regards.

Figure 8-21 Schematic of LPE reactor.

(Courtesy of M. B. Panish, AT&T Bell Laboratories.)

Although semiconductor LPE applications have been stressed here, the technique is also widely practiced to prepare epitaxial films of niobates and garnets.

8.5.2.2 Seeded Lateral Epitaxial Film Growth over Insulators

The methods we describe here briefly have been successfully implemented in Si but not in GaAs or other compound semiconductors. Inclusion of this subject here is suggested by the use of melts. Technological needs for three-dimensional integrated circuits and isolation of high-voltage devices have spurred the development of techniques to grow epitaxial Si layers over such insulators as SiO₂ or sapphire. The LEGO (Lateral Epitaxial Growth over Oxide) process (Ref. 42) is one such technique whose intent is to form isolated surface tubs of high-quality Si surrounded on all sides by a moat of SiO₂. Because of this excellent insulation, devices fabricated within the tubs are also radiation hardened or immune from radiation-induced charge effects originating in the underlying bulk substrate. The process, shown schematically in Fig. 8-22, starts with patterning and masking a Si wafer to define the tub regions followed by etching of deep slanted wall troughs. A thick SiO₂ film is grown, and seed windows are opened down to the substrate by etching away the SiO 2. Then a thick polycrystalline Si layer (100 μm thick) is deposited by CVD methods. This surface layer is then melted by the unidirectional radiant heat flux from incoherent light emitted by tungsten halogen-arc lamps (lamp furnace). The underlying wafer protected by the thermally insulating SiO₂ film does not melt except in the seed windows. Crystalline Si nucleates at each seed and grows vertically and then laterally across the SiO₂, leaving a single-crystal layer in its wake upon solidification. Lastly, mechanical grinding and lapping of the solidified layer prepares the structure for further microdevice processing. Conventional dielectric isolation processing also employs a thick CVD Si layer. But the latter merely serves as the mechanical handle that enables the bulk of the Si wafer to be ground away.

Figure 8-22 Process sequence employed to isolate single-crystal Si tubs. (Left) Conventional dielectric isolation process. (Right) LEGO process.

(Courtesy of G. K. Celler, AT&T Bell Laboratories.)

An alternate process for broad-area lateral epitaxial growth over SiO₂ (i.e., Si on SiO₂ or SOI) employs a strip heat source in the form of a hot graphite or tungsten wire, scanned laser, or electron beam. After patterning the polycrystalline or amorphous Si on the oxide, the strip sweeps laterally across the wafer surface. Local zones of the surface then successively melt and recrystallize yielding, under ideal conditions, one large epitaxial Si film layer.

Lateral-overgrowth epitaxy is not only limited to silicon technology. An interesting example occurs in the processing of blue GaN lasers. As shown in Fig. 8-23, the buffer layer of GaN deposited on (0001) Al₂O₃ (sapphire), although smooth, contains too high a dislocation density for the fabrication of reliable devices. However, by utilizing a SiO₂ mask containing an array of windows, subsequently deposited GaN films seed or nucleate within them as single crystals. These grow into relatively thick crystalline overgrowths that laterally coalesce to yield a continuous layer. Importantly, a relatively defect-free epitaxial layer is created since the propagation of threading dislocations is effectively curtailed at the constricted seed windows. Diode lasers (Fig. 8-20) fabricated on this top layer have displayed 10,000 h lifetimes during continuous operation at room temperature (Ref. 2).

Figure 8-23 Cross-sectional TEM micrograph of laterally overgrown GaN film on a SiO₂ mask and window areas.

(From Ref. 2. Reprinted with the permission of the author.)

8.5.3.1 Metalorganic CVD Processes for Semiconductor Epitaxy

We have already discussed various MOCVD processes in connection with the deposition of metal and oxide films (Section 6.6.4); whereas the former invariably deposit in polycrystalline form, oxide films assume structures ranging from amorphous to polycrystalline. However, MOCVD was invented to deposit III–V and II–VI compound semiconductor films where it is always the intent to grow high-quality single-crystal or epitaxial films (Refs. 43-45). For this reason the acronyms MOVPE (metalorganic) or OMVPE (organometal) vapor-phase epitaxy are equivalently used when speaking of processes to deposit epitaxial films. In overcoming the shortcomings of the earlier chloride and hydride CVD methods, MOCVD has been particularly effective in preparing films for a variety of visible and long-wavelength lasers as well as quantum-well devices.

8.5.3.1.1 Precursors

Availability of suitable precursors is critical to the success of MOCVD processes (Ref. 46). Over the years a workable number have been synthesized and some of these are entered in Table 8-3. Among the attributes precursors must possess are adequate volatility, a sufficiently large temperature window between evaporation and decomposition, clean decomposition at relatively low temperatures, good shelf life, manufacturability (yield, cost), and, importantly, low toxicity. Chemically, precursors largely consist of metal alkyl compounds with methyl (M) and ethyl (E) groups present in twofold (di, D) or threefold (tri, T) coordination. Vapor pressures for some precursors are also entered together with typical semiconductor deposition-temperatures.

Table 8-3 Metalorganic Precursors and Semiconductors Grown by MOCVD^a

8.5.3.1.3 Reactors

The design of MOCVD reactors means confronting issues frequently absent in other CVD systems. These include the efficient delivery of expensive precursors, the generally hazardous nature of the gases, the often severe temperature gradients in the system, and precise pressure control and valving necessary to deposit multilayer films. The latter capabilities are critical in order to maintain atomically abrupt interfaces in high-performance optoelectronic devices, e.g., quantum-well lasers. To ensure film growth uniformity, substrates usually face upward and lie horizontally on a rotating platform where they are exposed to showerheads or gas nozzles that supply the Group III and V precursors from above as shown in Fig. 8-24. Under such conditions (Refs. 47, 48) the boundary-layer thickness (δ) varies as δ(cm) ∼ [Pω]^−1/2;, where P is the reactor pressure and ω is the substrate angular velocity. Certain critical gas-flow parameters are also dependent on ω. For example, the Reynolds number, Re r_d ρω/η, where r_d is the substrate disk radius, ρ is the density, and η is the viscosity. In addition, a mixed convection parameter (MCP) has been defined (Ref. 48) as MCP = g{(T_d/T_∞–1)/(ω^3/2η^1/2)}, where g is the gravitational constant, and Td and T_∞ are the temperatures of disks with radii rd and infinity, respectively. Increasing ω causes Re to rise and MCP to decline. Avoidance of unstable flows, therefore, requires a trade-off between these two dimensionless numbers, e.g., Re < 2000, MCP < 2. It is found that rotational speeds of several hundred to a thousand rpm are optimum in order to reduce δ in a controlled way while avoiding turbulent gas flow. Utilizing computer-controlled gas exchange and supply systems, high-quality, epitaxial multilayer semiconductor structures have been grown in reactors containing a 42-cm diameter rotating disk that accommodates thirty-eight 2.5 cm or nine 10 cm diameter wafers. In addition to GaAs, other III–Vas well as II–VI and IV–VI semiconductor compound films have been synthesized this way.

Figure 8-24 Simplified schematic of a III–V MOCVD system showing the gas delivery system and vertical rotating disk reactor.

(From A. G. Thompson, Materials Letters 30, 255 (1997). Reprinted with the permission of the author.)

The deposition of GaN-based films for blue-green-violet photonic devices (Section 8.4.4.3) represents an important triumph for MOCVD methods. Because of the very high equilibrium nitrogen vapor pressures for GaN and InN, growth of InGaN films poses a great challenge. Unusually high nitrogen/Group III (e.g., TMGa) partial pressure ratios of 1000 or more are required, and the nitrogen source gases (N₂, NH₃) must be efficiently delivered to substrates typically maintained at ∼ 550°C for InN and ∼ 900°C for GaN (Ref. 49). Special reactors with high gas flow capabilities have been built for this purpose.

8.5.3.2 Atomic Layer Epitaxy (ALE)

This CVD-based technique enables the growth of epitaxial compound-semiconductor films an atom layer at a time (Refs. 51, 52). For this reason ALE has also been called digital epitaxy. To see how it works let us consider Fig. 8-25, where the binary compound AB is being deposited on an AB substrate surface that is terminated by a layer of A–and B–atoms (–denotes a bond). We assume that the precursors for atoms A and B, molecular AC and BD, respectively, have high vapor pressures. Furthermore, the chemical bonding between A and B is assumed to be stronger than that between A–A and B–B pairs. Upon introducing the AC precursor (1) the reaction with B atoms on the substrate effectively create a surface layer of B– A –together with weakly held C. If the growth temperature is sufficiently high, excess AC merely reevaporates and film growth is self-limiting (2). To add another monolayer the reactor is purged of AC, and BD precursor is introduced (3).

Figure 8-25 Schematic of the atomic layer epitaxy process. The process steps are described in the text.

(From T. F. Kuech, Proc. IEEE 80, 1609, 1992. Reprinted with the permission of the author.)

The B atoms will now combine with the A–atoms to form the B–A–B–structure, and as before, excess BD evaporates. But in addition, C and D react and the CD molecular by-product desorbs leaving an AB film layer behind (4). Through successive cycles of stepwise deposition, films of the desired thickness can be deposited without precise control of process variables.

In the II–VI compounds ZnS, ZnTe, and ZnSe epitaxial film growth by ALE is even simpler than described above; the precursors can simply be the individual atomic species, e.g., Zn and S₂. But for the III–V semiconductors, ALE growth is more difficult because the group III elements, e.g., Ga and In, have much lower vapor pressures than corresponding elements from group V. Raising the temperature to promote group III atom volatility results in group V atom loss and film degradation. Therefore, instead of elemental sources, atomic layer epitaxy in III–V semiconductors is accomplished using molecular precursors as in Fig. 8-25, particularly metalorganics for the group III metal (e.g., Ga(CH₃)₃) and a hydride, e.g., PH₃, AsH₃, for the group V element. In the case of GaAs growth the first step involves thermal cracking of hydrides which generates AsH_x (with x = 1, 2) and As₄ products; the As (i.e., A) then directly reacts with the substrate-surface terminated Ga- (i.e., B). Reaction of remaining hydrogen with the metalorganic precursor gas liberates Ga, which bonds to the monolayer of As-, as well as the volatile by-product CH₄ (i.e., DC). It is clear that narrow processing temperature windows for condensation, reaction, precursor decomposition, and reevaporation must be optimized. The adsorption–desorption kinetics presented earlier (Section 7.2.5), extended to include surface chemical reactions, can help to model such ALE processes.

In addition to compound semiconductors, other materials have been grown by ALE methods, including elements (e.g., Si, Ge); oxides (e.g., Al₂O₃, SnO₂, In₂O₃); nitrides (e.g., TiN, TaN); and superconductors (e.g., δ-NbN, YBa₂Cu₃O₇). Employing ALE-grown materials, devices such as monolayer (delta) doped field-effect and heterojunction transistors, as well as quantum-well lasers and superlattice structures, have been demonstrated. Selective epitaxy, side-wall coverage, and monolayer etching are some of the unique features of ALE. On the other hand, low overall film-deposition rates and the complexity of purging and sequencing precursors are decided disadvantages.

8.5.3.3 Additional CVD Epitaxy Processes

In closing, a couple of novel concepts to produce epitaxial films will be briefly addressed. The first, known as vapor-levitation epitaxy, or VLE, is schematically shown in Fig. 8-26. In this process a heated substrate is levitated above a nitrogen track close to a porous frit through which the hot gaseous reactants pass. Upon impingement on the substrate, chemical reactions and film deposition occur while product gases escape into the effluent stream. The gas velocity increases while the gas-concentration profile exhibits depletion as a function of radial distance from the center of the circular substrate. These effects cancel one another and uniform films are deposited. The VLE process was designed for the growth of epitaxial III–V semiconductor films and has certain advantages worth noting:

Figure 8-26 (Top) Illustration of VLE process. (Bottom) Schematic of RTCVD process.

(Courtesy of M. L. Green, AT&T Bell Laboratories.)

The second method, known as rapid-thermal CVD processing (RTCVD), enables epitaxial deposition through rapid, controlled variations of substrate temperature. Source gases (e.g., halides, hydrides, metalorganics) react on low thermal-mass substrates heated by radiation from external high-intensity lamps (Fig. 8-26). The latter undergo rapid temperature excursions, and heating rates of hundreds of degrees Celsius per second are possible. In the case of III–V semiconductors, high-quality epitaxial films have been deposited by first desorbing substrate impurities at elevated temperatures followed by immediate lower temperature growth (Ref. 53).

Lattice-matched, atomically sharp heterojunction interfaces can be grown by RTCVD methods, particularly with metalorganic precursors. Only molecular beam epitaxy, considered next, can match or exceed these capabilities.

8.6.2.1 Gas Source MBE

Although MBE, which uses solid sources for both group III and V elements, has been extremely successful for the growth of arsenides and antimonides, it has been less useful for phosphides (Ref. 54). The very high vapor pressure of phosphorus has meant excessive desorption relative to incorporation in growing films. To offset this desorption, the V/III flux ratio is an order of magnitude higher than for arsenides. The large quantities of P employed means physically big sources which stretch the capacity of pumping systems. It was primarily as a response to difficulties with phosphorus that gas-source MBE was introduced into compound semiconductor technology (Ref. 56). Because the process shown in Fig. 8-28b incorporates a gas source to supply group V elements, terms such as gas-source molecular beam epitaxy (GSMBE) or, less commonly, chemical beam epitaxy (CBE) have been coined. Organometallics, often used for this purpose, are thermally cracked, releasing the group V element as a molecular beam into the system. Hydride gas sources, e.g., AsH₃, PH₃, have also been similarly employed for this purpose. Excellent epitaxial-film quality has been obtained in these hybrid MBE–MOVPE processes. A final process known by the acronym MOMBE employs metalorganics for the group V elements and solid group III elements.

MBE systems have been employed in manufacturing environments since 1984 to fabricate GaAs laser diodes (Ref. 57) and since 1986 to make monolithic microwave integrated circuits and high-power heterojunction bipolar transistors (Ref. 58). Surface defect densities less than 10 cm^{− 2} have been attained by optimizing the function of the group III Knudsen cell. More recently, GSMBE systems using an AsH cracker source have been built to continuously deposit 1.7 thick metal–semiconductor field-effect transistor (MESFET) structures with growth occurring at 540°C and 10⁻⁵ torr. Multiwafer throughput of four 10 cm diameter or seven 3 cm diameter wafers per 2.5 h, using a vacuum load-locked capability of recharging 500 cm3 Knudsen cells of Ga, Al, and In, gives an idea of the operation scale. Electrical (sheet) resistance variations of less than 2% (over a 27 cm diameter area), GaAs electron mobilities as high as 124,000 cm²/V-s (77 K), and an oval defect density of ∼ 40 cm⁻² are indicative of the excellent quality of the epitaxy.

8.6.2.2 MBE vs OMVPE: Advantages and Disadvantages

These two epitaxy techniques have emerged as the ones of choice in high-performance applications (Ref. 54). Relative to LPE and VPE they both readily enable near-atomic film/substrate interface abruptness, high levels of doping uniformity, and growth of multilayered structures having different compositions and doping levels. When compared to OMVPE, MBE’s former advantage in interface abruptness no longer exists. However, MBE growth is further removed from thermodynamic equilibrium so that films are produced at lower substrate temperatures. Perhaps the greatest advantage of MBE is the vacuum environment that makes possible the in situ diagnostic capabilities of reflection high-energy electron diffraction (RHEED) and mass spectrometry. Discussed later in Section 8.7.4.2, the former technique yields precise monolayer growth rates and provides a measure of film smoothness; the latter is used to monitor desorption of species from chamber wall or depositing film surfaces. Relative safety is another advantage of MBE as the metalorganic sources are often toxic and or pyrophoric. Advantages of OMVPE include two to three times greater film growth rates, less maintenance downtime, and little difficulty in depositing phosphorus. Although the situation has occasionally flip-flopped, transistor and laser diode device characteristics from MBE-grown III–V materials have generally exceeded those of devices prepared by OMVPE.

8.6.3.1 Wafer Bonding

Direct wafer bonding refers to the phenomenon of making mirror-polished, flat and clean wafers of almost any materials adhere to each other by bringing their surfaces into contact; van der Waals forces are the source of the bonding. Special treatments are required to make the surfaces hydrophilic (with one or two monolayers of oxygen or water) or hydrophobic (hydrogen-covered due to a HF dip); such surfaces facilitate subsequent bonding, e.g., by hydrogen bridge bonds. Assorted combinations such as Si–Si, Si–SiO₂–Si for silicon-on-insulator (SOI) technology (Section 8.5.2.2), and Si-based heteroepitaxial structures with large substrate mismatches have been fabricated by these methods (Ref. 59).

In wafer bonding the epi-film layer (X) is first deposited on a lattice-matched substrate (Y). Then a clean, atomically flat Si wafer is bonded, usually with applied heat and pressure, to the similarly flat Y–X–combination so as to produce a Y–X–Si sandwich. After substrate Y is chemically etched off, the desired X–Si pair remains. By these means wafer-bonded, III–V semiconductor/Si heteroepitaxial structures of large lattice mismatch have been fabricated containing misfit dislocations but apparently no threading dislocations.

Despite the exciting possibilities of wafer bonding, Ge_xSi_1–x/Si strained-layer epitaxy appears to be the primary basis for future silicon heterostructures.

8.6.3.2 Ultrahigh-Vacuum Chemical-Vapor Deposition (UHV/CVD)

This relatively new process pioneered by Meyerson (Refs. 60, 61) challenges our conventional notions regarding CVD processes, particularly the high-temperature epitaxial deposition of silicon. As noted in Section 6.3.2, Si epitaxy is normally practiced well above 1000°C in atmospheric or sometimes in low-pressure (10–100 torr) reactors. Desorption of water vapor and oxygen contaminants as well as native oxide from the silicon surface, so necessary for high-quality epitaxy, is a result of the high temperatures employed. But, such temperatures also cause troublesome redistribution of dopants between the substrate and epitaxial layer being grown (autodoping). The evolution of silicon technology to ever-smaller dimensions coupled with heavily doped patterned substrates has made it imperative to limit diffusion by reducing the so-called thermal budget, e.g., 1000°C for 30 min, for epitaxy. Rather than high-temperature surface cleaning a novel approach was to passivate the Si surface ex situ by etching in HF. This simple step produces a monolayer of hydrogen that passivates the Si surface and reduces its tendency to react with H₂O and O₂ by some 13 orders of magnitude (Ref. 60)! As a result, native oxide does not form; instead the passivated surface can now be exposed to SiH₄, which displaces the adsorbed hydrogen and directly reacts with the substrate to produce epitaxial Si. By this strategy an atomically clean Si surface can be obtained at deposition temperatures of ∼ 500°C. To maintain surface cleanliness, the UHV/CVD reactor is typically first pumped to the 10⁻⁹ torr range while film growth is carried out at a pressure of ∼ 10⁻³ torr or lower. In addition to silane, simultaneous gas flows of GeH₄, B₂H₆, and PH₃ are used, the first to produce Ge_xSi_1–x films and the latter two to dope them. With respect to the latter, excellent control of boron content in Si is achieved through variation of the diborane flow. In addition to Ge_xSi_1–x/Si superlattices shown in Fig. 8-29, similar defect-free, highly doped, metastable 10 at.% B–Si/Si multilayer structures have been grown.

Figure 8-29 (a) Cross-sectional TEM image of Gea4Sia6-Si strained-layer superlattice. (b) High-resolution lattice image.

(Courtesy of J. C. Bean and R. Hull, AT&T Bell Laboratories.)

The major application for SiGe technology is the base region of heterojunction bipolar transistors (HBTs). In this device the highly doped Ge_xSi_1–x base is pseudomorphically grown over an n-doped Si collector and then covered with a polysilicon emitter. A typical configuration merges these HBTs with their high-frequency capability and Si CMOS for digital applications. Other potential applications for SiGe ranging from wireless communications to optoelectronics including traditional (CMOS) and quantum (resonant tunneling diode) devices have been discussed in the literature (Refs. 61, 62). It now appears that high-speed devices based on SiGe are competitive with those derived from III–V compound semiconductors. The often quoted observation that "GaAs is the material of the future… and it always will be" may have added significance now that SiGe has boosted the performance of Si devices.

8.6.4.1 Molecular Beam Allotaxy (MBA)

In this method a buried heteroepitaxial layer is formed upon annealing a subsurface precipitate layer. The MBA process (Ref. 63) can be understood by considering the formation of an epitaxial Si/CoSi₂/(100)Si structure. Because of the small lattice mismatch between CoSi₂ and Si noted earlier (Section 8.2.3.2), this is a model MBA system. To produce the trilayer epitaxial structure a buffer homoepitaxial Si film is first deposited on a Si wafer within an MBE system at 500– 700°C. Then as the Si flux is maintained constant, Co metal is coevaporated first at a steadily increasing rate, then at a constant rate for some time, and finally at a rate that ramps down to zero. A Si top layer completes the structure. In effect a trapezoidal depth profile of Co in the form of small-to-large-to-small CoSi₂ precipitates buried within the Si matrix results. When these precipitates are annealed to temperatures of 1100–1200°C they coalesce into CoSi₂ layers with flat and atomically abrupt interfaces. The growth mechanisms, i.e., Ostwald ripening and sintering, already discussed (Section 7.4.5) are responsible for the enlargement of the bigger precipitates at the expense of the smaller ones. A similar continuous buried β-FeSi₂ layer has been prepared by MBA. However, the Si cap layer contained many twins and is considerably more defective than is the case for CoSi₂.

8.6.4.2 Mesotaxy

The same objective, buried disilicide layers embedded in silicon, can also be realized by an ion-implantation process known as mesotaxy. In the case of CoSi₂ 200 keV Co ⁺ ions are implanted into Si at fluences of ∼ 2 × 10¹⁷ ions/cm² resulting in a Gaussian distribution of metal atoms. This is followed by annealing treatments at 1000°C during which time the Co concentration profile narrows by similar coalescence phenomena while the surrounding lattice damage is significantly reduced. Abrupt epitaxial silicide layers buried 1000Å beneath the Si surface have been produced this way (Ref. 64).

Through similar ion implantation of oxygen ions into silicon at high energies and fluences, followed by annealing, highly insulating, subsurface layers of amorphous SiO₂ films have been produced. Ion-beam synthesis of buried SiO₂ is known as SIMOX (separation by implanted oxygen). Together with MBA and mesotaxy they represent important potential processes for the eventual realization of three-dimensional integrated circuits.

8.6.4.3 van der Waals Epitaxy

We have already noted the severe restriction on heteroepitaxy imposed by lattice mismatch between materials containing strong ionic or covalent bonds. However, one might imagine conditions for epitaxy to be relaxed on substrate surfaces that do not contain the dangling electrons which promote chemical bonding across interfaces. In the absence of the latter we speak of an epitaxy based on weak van der Waals interactions (Ref. 65). Suitable surfaces for such purposes stem from easily cleaved materials, or semiconductors whose bonds are terminated by specific atoms, e.g., S or Se on (111) GaAs, H on Si(111), and F on CaF₂. Among the inorganic film/substrate van der Waals epitaxy systems that have been studied are Se/Te; TMX₂/SnS₂; TMX₂/mica; TMX₂/S–GaAs(111); GaSe/Se–GaAs(111); and GaSe/H–Si(111), where TM is a transition metal, e.g., Mo, Nb, and X is S, Te, or Se. Epitaxial organic films, e.g., phthalocyanines/TMX₂ and C₆₀/TMX₂, have also been prepared. In virtually all cases large lattice mismatches are involved, but good epitaxial growth has been claimed.

8.6.4.4 Colloidal Epitaxy

The concept of epitaxy has extended beyond merely arranging atoms on a crystalline substrate, to depositing colloidal particles on a geometrically patterned substrate template. In this way, colloidal silica particles with a 0.525 μm radius have been made to controllably settle onto a substrate lithographically patterned with an FCC (100) planar array of accommodating holes (Ref. 66). The result is a periodic three-dimensional, microporous dielectric structure known as a photonic crystal. These crystals have unique optical properties and are claimed to "manipulate light the way superconductors manipulate electrons" (Ref. 67).

8.7.2.1 Kinetics of Adsorption and Desorption

Since the first step in MBE film growth involves surface adsorption, let us first consider a beam of Ga atoms incident on a GaAs surface. Below about 480°C Ga atoms readily physisorb on the surface but above this temperature Ga both adsorbs and desorbs. Time-resolved mass-spectroscopy measurements of the magnitude of the atomic flux desorbing from the substrate have revealed details of GaAs film-growth mechanisms (Ref. 69). The instantaneous Ga surface concentration, n_Ga, is increased by the incident Ga beam flux, (Ga), and simultaneously reduced by a first-order kinetics desorption process. Therefore,

     (8-15)

where τ(Ga) is the Ga adatom lifetime and n_Ga/τ(Ga) represents the Ga desorption flux, •_des(Ga). Integrating Eq. 8-15 yields

     (8-16)

For a rectangular pulse of incident Ga atoms the detected desorption flux closely follows the dependence of Eq. 8-16. Similarly, when the Ga beam is abruptly shut off, the desorption rate decays as exp – (t/τ(Ga)). The exponential rise and decay of the signal is shown schematically in Fig. 8-30a.

Figure 8-30 Deposition and desorption pulse shapes on (111) GaAs for (a) Ga, (b) As₂, (c) As₂ on a Ga-covered surface.

(After Ref. 69.)

In the case of As₂ molecules incident on a GaAs surface, the lifetime is extremely short so that the desorption pulse profile essentially mirrors that for deposition (Fig. 8-30b), i.e., _des(As₂) = (As₂). However, on a Ga-covered GaAs surface, τ(As₂) becomes appreciable with desorption increasing only as the available Ga is consumed (Fig. 8-30c). These observations indicate that in order to adsorb As₂ on GaAs, Ga adatoms are essential.

8.7.2.2 Mechanisms

Detailed models for epitaxial growth on (100) GaAs with both As₂ and As₄ precursors have been reviewed more recently by Joyce (Ref. 70). In the case of incident Ga plus As₂ fluxes on a Ga-stabilized GaAs surface (defined later), the As₂ molecules are first adsorbed into a mobile, weakly bound precursor state that has a residence time of ∼ 10⁻⁵ s. First-order dissociative chemisorption on Ga atoms enables As incorporation into the growing film. If the Ga flux is less than half the As₂ flux, one As atom sticks to each Ga atom. At low substrate temperatures, association of As₂ produces As₄ molecules which then slowly desorb. Similarly, when films are grown employing an As₄ flux, these molecules are also first adsorbed as a mobile, weakly bound precursor state. This entity migrates along the surface with a diffusive activation energy of 0.25 eV, while its residence time is temperature dependent with a desorption activation energy of 0.4 eV. The sticking coefficient of As never exceeds 0.5, even with a completely covered Ga surface or when the Ga flux exceeds the As₄ flux. This fact is explained by assuming a pairwise dissociation of the As₄ molecules chemisorbed on adjacent Ga atoms in a second-order reaction. During GaAs growth it is suggested that when two As₄ molecules react, four As atoms are incorporated while the other four desorb as As₄. For either As precursor under conventional deposition conditions the film growth-rate determining step is the migration rate of Ga adatoms to appropriate lattice sites where reaction occurs. In summary these adsorption/desorption effects strongly underscore the kinetic rather than thermodynamic nature and control of MBE growth.

8.7.2.3 Stabilized and Reconstructed Surfaces

Normally, III–V compound-semiconductor films are grown with a two- to tenfold excess of the group V element. This maintains the elemental V/III impingement flux ratio > 1. For GaAs and Al_xGa_1–x As, this condition results in stable stoichiometric film growth for long deposition times. In contrast to the preceding so-called As-stabilized growth, there is Ga-stabilized growth which occurs when the flux ratio is approximately 1. An excess of Ga atoms is generally avoided, however, because they tend to cluster into molten droplets.

The (100) and (111) surfaces of GaAs and related compounds exhibit a variety of reconstructed surface geometries dependent on growth conditions and subsequent treatments (Ref. 55). For As- and Ga-stabilized growth, (2 × 4) and (4 × 2) reconstructions, respectively, have been observed on (100) GaAs. Other structures, i.e., C(2 × 8) As and C(8 × 2) Ga, have also been reported for the indicated stabilized structures. To complicate matters further, intermediate structures, e.g., (3 × 1), (4 × 6), and (3 × 6), as well as mixtures also exist within narrow ranges of growth conditions. The complex issues surrounding the existence and behavior of these surface reconstructions are continuing subjects of research.

8.7.2.4 Mechanism of Growth in GaInAsP

During epitaxial film deposition of multicomponent semiconductors the mechanisms of substrate chemical reactions and atomic incorporation can be quite complex. For example, a proposed model of sequential deposition of the first two monolayers of GaInAsP on an InP substrate is depicted in Fig. 8-31 for the hydride process (Ref. 71). The first step is suggested to involve adsorption of P and As atoms. Then GaCl and InCl gas molecules also adsorb in such a way that the Cl atoms dangle outward from the surface. Next, gaseous atomic hydrogen adsorbs and reacts with the Cl atoms forming HCl molecules, which then desorb. Now the process repeats with P and As desorption and when the cycle is completed, another bilayer of quaternary alloy film deposits. This picture accounts for single-crystal film growth and the development of variable As/P and Ga/In stoichiometries.

Figure 8-31 Atomic mechanisms involved in the sequential deposition of GaInAsP on InP.

(Reprinted with permission from J. Wiley & Sons. From Ref. 71.)

8.7.3.1 Selective Epitaxy in Silicon Materials

There is a history of SEG in Si dating back to the early 1960s (Ref. 72). This effort has almost entirely been devoted to fostering nucleation and growth of epitaxial Si on Si surfaces and suppressing these processes on adjoining SiO₂ or silicon nitride mask surfaces. It is usually accomplished by CVD processes involving H2 reduction of a chlorosilane, e.g., SiCl₄, Si₂ Cl₂ H₂, to deposit Si, and with simultaneous HCl additions to etch away spurious Si nuclei before they coalesce and grow. In an LPCVD-based SEG study using a Si₂Cl₂H₂/HCl/H₂ mixture, as many as 10⁵ hemispherical, 0.5 sized cap-shaped Si nuclei per cm² deposited on dielectric rather than Si surfaces (Ref. 73). Elimination of such an intolerable defect density is critical before any of the applications suggested for selective epitaxy, e.g., filling deep trenches and contact holes, formation of emitter windows in bipolar transistors, processing of DRAM cells and three-dimensional integrated circuits, can be realized. More recently (Ref. 74) selective heteroepitaxial deposition of SiGe films has been studied and the effects of SiO₂/Si area ratio, HCl flow rates, temperature, and doping on film growth explored. In contrast to Si the growth of SiGe at low temperatures is strongly dependent on oxide coverage.

8.7.3.2 Selective Epitaxy in Compound Semiconductors

In general, compound semiconductor devices require fewer processing steps than their silicon-based counterparts. A great advantage of selective deposition is the further reduction in the number of steps. In fact, the fabrication of a semiconductor laser wholly by selective epitaxy processing has already been demonstrated (Ref. 75).

In the remainder of this section only III–V semiconductors used for photonic devices will be considered and selective MBE, MOCVD, and MOMBE techniques for their deposition briefly reviewed.

8.7.4.1 LEED

In LEED a low-energy electron beam (10–1000 eV) impinges normally on the film surface and only penetrates a few angstroms below the surface. Bragg’s law for both lattice periodicities in the surface plane results in cones of diffracted electrons emanating along forward and backscattered directions. Simultaneous satisfaction of the diffraction conditions means that constructive interference occurs where the cones intersect along a set of lines or beams radiating from the surface. These backscattered beams are intercepted by a set of grids raised to different electric potentials. The first grids encountered retard the penetration of low-energy inelastic electrons. Diffracted (elastic) electrons of higher energy pass through and, accelerated by later grids, produce illuminated spots on the hemispherical fluorescent screen.

Both LEED and RHEED patterns of the (7 × 7) structure of the Si (111) surface are shown in Fig. 8-33. To obtain some feel for the nature of these diffraction patterns it is useful once again to think in terms of the reciprocal space. Arrays of reciprocal latice points form rods or columns of reciprocal-lattice planes shown as vertical lines pointing normal to the real surface.

Figure 8-33 (a) LEED pattern of Si surface (38 eV electron energy, normal incidence). (b) RHEED pattern of Si surface (5 keV electron energy, along <112> azimuth).

(Courtesy of H. Gossmann, AT&T Bell Laboratories.)

They are indexed as (10), (20), etc., in Fig. 8-34. Consider now an electron wave of magnitude 2π/λ, propagating in the direction of the incident radiation and terminating at the origin of the reciprocal lattice. Following Ewald we draw a sphere of radius 2π/λ, about the center. A property of this construction is that the only possible directions of the diffracted rays are those which intersect the reflecting sphere at reciprocal lattice points as shown. To prove this we note that the normal to the reflecting plane is the vector connecting the ends of the incident and diffracted rays. But this vector is also a reciprocal lattice vector. Its magnitude is 2π/α, where a is the interplanar spacing for the diffracting plane in question. It is obvious from the geometry that

Figure 8-34 Ewald sphere construction for LEED and RHEED methods. The film plane is horizontal, and reciprocal planes are vertical lines.

     (8-17)

which reduces to Bragg’s law, the requisite condition for diffraction. When the electron energies are small as in LEED, the wavelength is relatively large, yielding a small Ewald sphere. A sharp spot diffraction pattern is the result. The intense hexagonal spot array of Fig. 8-33a reflects the sixfold symmetry of the (111) plane while the six fainter spots in between are the result of the (7 × 7) surface reconstruction.

8.7.4.2 RHEED

An immediate advantage of RHEED is that the measurement apparatus does not physically interfere with deposition sources in an MBE system the way LEED does. This is one reason why RHEED has become the overwhelmingly preferred real-time film characterization accessory in MBE systems. In RHEED the electron beam is incident on the film surface at a grazing angle of a few degrees at most. Electron energies are much higher than for LEED and range from 5 to 100 keV. From the standpoint of diffraction, the high electron energies lead to a very large Ewald sphere (Fig. 8-34). The reciprocal lattice rods have finite width due to lattice imperfections and thermal vibrations; likewise, the Ewald sphere is of finite width because of the incident electron-energy spread. Therefore, the intersection of the Ewald sphere and rods occurs for some distance along their height, resulting in a streaked rather than spotty diffraction pattern. During MBE film growth both spotted and streaked patterns can be observed; spots occur as a result of three-dimensional volume diffraction at islands or surface asperities while streaks characterize smooth layered film growth. These features can be seen in the RHEED patterns obtained from MBE-grown GaAs films (Fig. 8-35).

Figure 8-35 RHEED patterns [40 keV, (110) azimuth] and corresponding electron micrograph replicas (38,400 ×) of same GaAs surface. (a) Polished and etched GaAs substrate heated in vacuum to 580°C for 5 min. (b) 150 Å film of GaAs deposited; (c) 1 of GaAs deposited.

(From Ref. 69. Courtesy of A. Y. Cho, AT&T Bell Laboratories.)

8.7.4.3 RHEED Oscillations

An important attribute of the RHEED technique is that the diffracted beam intensity is relatively immune to thermal attenuation arising from lattice vibrations. This makes it possible to observe the so-called RHEED oscillations during MBE growth of epitaxial semiconductor films. In the case of GaAs the intensity of the specular RHEED beam undergoes variations which track the step density of Ga on the growing surface layer. If we consider Fig. 8-36 and associate the maximum beam intensity with the flat surface where the fractional coverage = 0 (or = 1), then the minimum intensity corresponds to = 0.5. During deposition of a complete monolayer, the beam intensity, initially at the crest, falls to a trough and then crests again. Film growth is, therefore, characterized by an attenuated, sinelike wave with a period equal to the monolayer formation time. Under optimal conditions the oscillations persist for many layers and serve to conveniently monitor film growth with atomic resolution. The temperature above which RHEED oscillations are expected can be easily estimated. To allow a few atomic jumps to occur in order to smooth terraces before they are covered by a monolayer (per second) requires a diffusivity of roughly 10⁻¹⁵ cm²/s. By the example given in Section 7.4.3, RHEED oscillations are predicted to occur above 0.2T_M, 0.12T_M, and 0.03T_M on group IV element, metal, and alkali halide substrates, respectively, in rough qualitative agreement with experiment.

Figure 8-36 Real space representation of the formation of a single complete monolayer. θ is the fractional layer coverage. Corresponding RHEED oscillation signal is shown.

What we have said strictly applies to MBE growth on unstepped or singular planes. But what about growth on vicinal surfaces roughened by steps and terraces of length h? At low temperatures, the surface-diffusion length of adatoms is less than h and two-dimensional nucleation of monolayer islands occurs as on a singular plane. These are the conditions that lead to RHEED oscillations. However, at elevated temperatures the adatom migration length exceeds h and step edges now become a favored sink for adatoms (Ref. 70). Instead of island formation and coalescence with a progressive buildup of , film growth now proceeds by step propagation across a featureless terrain ( = 0). Under these conditions RHEED oscillations vanish. By noting the disappearance of RHEED oscillations (Ref. 66) in GaAs, the transition temperature (T_c) separating the two-dimensional nucleation and step propagation regimes was experimentally measured to be 590°C. Estimates of Tc based on random walk, i.e., h² = 2Dτ, where Dand τ are the adatom diffusion coefficient and lifetime, respectively, are consistently ∼ 150–200 K lower than observed. A probable reason for the underestimate is the effective reduction in D due to adatom reactions at step edges.