Epitaxial growth paradigms

Epitaxial growth paradigms can be generally grouped under three classes: homomorphic, pseudomorphic, and metamorphic.^{Reference Kuech5} These growth paradigms are briefly reviewed, as all three are widely employed in modern heterostructures.

Homomorphic growth, or homoepitaxy, is the first category, both because of its historic significance in the development of epitaxial crystal growth and surface science and because of its relative simplicity. Homomorphic epitaxy is the growth of a single-crystal thin film on a single-crystal substrate that is composed of the same material. The single-crystal substrate acts as the seed crystal that enables the growth of a coherent overlayer (i.e., no broken bonds at the interface). Because the film and substrate are identical, the two are perfectly lattice matched with zero misfit strain. The ability to grow high-quality homomorphic materials is important from a technological perspective, because changes in doping (e.g., p-type, n-type) along the growth direction can be used to create functionality, such as p–n junction diodes or n–p–n bipolar junction transistors. Additionally, homoepitaxial layers are extensively used as buffer layers to bury residual contamination from the substrate surface prior to device growth.

The second paradigm, pseudomorphic growth (e.g., InGaAs on GaAs) or lattice-matched heteroexpitaxy (e.g., AlGaAs on GaAs), is the growth of a single-crystal film on a single-crystal structure composed of different materials, but with fully coherent atomic bonds. The freedom to engineer the alloy composition of the epitaxial layer directly led to the demonstration of the double heterostructure laser,^{Reference Alferov6–Reference Holonyak8} high-brightness visible light-emitting diodes (LEDs),^{Reference Rupprecht, Woodall and Pettit9} and numerous other semiconductor devices of commercial significance.^{Reference Kuech5,Reference Farrow, Bunshah and McGuire10} However, in order to maintain a fully coherent crystal structure that is not highly defective, the epitaxial layers must be chosen to maintain similar crystal structures and nearly identical lattice constants to that of the substrate; they must reside on a nearly vertical line (see Figure 2). For strained layers, there is a critical thickness beyond which the formation of misfit dislocations becomes energetically favorable. The misfit dislocations allow the layer to relax by plastic deformation. This can greatly reduce the technical value of materials in both electronic and optoelectronic applications if care is not taken. Most pseudomorphic layers are designed to be as lattice matched as technically possible with residual misfit strains below 0.1%; but thin strained layers with misfit strain of approximately 1% are often designed as quantum wells and conduction channels.

Figure 2. Graph displaying the bandgaps and lattice constants of III–V compound semiconductor and silicon-germanium alloys. Dots and line segments that are blue indicate direct-gap materials. Indirect materials with sixfold conduction-band symmetry are shown in red, and materials with eightfold conduction-band symmetry are shown in green. The vertical colored bars represent common commercial substrates. The width of each bar represents the range of lattice constants that produce up to 1% strain, indicating the range of alloys that can be grown nearly lattice matched. Without metamorphic growth, the conventional pairing of substrates and epitaxial layers that are vertically aligned necessitates a variety of substrate materials in order to design devices with different bandgaps.

The limitation of nearly lattice-matched materials drove early device designers to develop quaternary alloys (e.g., GaInAsP, AlGaInAs), such that the bandgap could be varied over a wider design space without changing the lattice constant; quaternary alloys are critical to the operation of telecommunication devices grown on InP substrates.^{Reference Farrow, Bunshah and McGuire10} Today, state-of-the-art lasers reported in the scientific literature include quinary alloys, which have up to five III–V compound semiconductor elements, to enable engineered control of the lattice constant, bandgap, and the valence-band offset.^{Reference Bank, Wistey, Goddard, Yuen, Lordi and Harris11,Reference Belenky, Shterengas, Wang, Kipshidze and Vorobjev12} Device designers are also increasingly looking to further manipulate semiconductor band extrema by deliberately growing heavily strained layers that may have elastic strain approaching 3%. However, this is an extremely challenging approach because layers with this amount of strain are on the edge of stability; to remain dislocation free, these layers can only be grown a few monolayers thick.^{Reference Tansu and Mawst13} The use of increasing numbers of alloy components and highly strained layers with critical thickness on the order of monolayers demonstrates the desire to increase the degree of freedom that can be employed to produce enhanced epitaxial materials.

The third growth paradigm, and the subject of this issue of MRS Bulletin, is metamorphic epitaxial growth or growth of fully relaxed, lattice-mismatched materials. Metamorphic layers are grown thicker than the critical thickness that limits design grown within the pseudomorphic paradigm. In metamorphic systems, there is, in principle, no limit to the degree of lattice mismatch that can be accommodated. Early studies in this area found that misfit dislocations that accommodate the lattice mismatch between an epitaxial layer and substrate often generate threading dislocations.^{Reference Matthews14} Since dislocations cannot terminate within crystals (unless as a loop), threading dislocations that terminate at the film surface are typically “left behind” from the relaxation process. Threading dislocation density (TDD) is generally determined by the kinetics of dislocation nucleation and glide, as threading dislocation segments contribute relatively little to strain relaxation; threading dislocations are often nearly vertical, and the amount of strain relieved by a dislocation is proportional to its length projected onto the interface plane. Since they act as nonradiative recombination centers, contribute to carrier scattering, and create spatial inhomogeneities that can lead to early device failure, one of the most important metrics for metamorphic epitaxial materials is a low TDD. The TDD of commercial substrates is typically very low for Si, Ge, GaAs, and InP, with specified TDD values of ∼0 cm^–2, <3 × 10² cm^–2, <5 × 10³ cm^–2, and <6 × 10⁴ cm^–2, respectively.^15–17 While not extensively explored in this issue, it is interesting to note that nitride semiconductors are commonly grown metamorphically on silicon or sapphire; many commercial devices based on nitrides offer high performance despite TDD values exceeding 10⁸ cm^–2 in the active region, making them relatively unique compared to other semiconductor material systems.

Accordingly, relaxing strain through misfit dislocations while maintaining low TDD in the device region is the defining challenge of metamorphic growth. The study of misfit dislocations, dislocation interactions, and dislocation motion has seen considerable attention in II–VI, III–V, and SiGe material systems.^{Reference Matthews14,Reference Goldman, Kavanagh, Wieder, Ehrlich and Feenstra18–Reference Fitzgerald20} Three primary approaches to reducing the TDD have emerged: abrupt interfaces, buffer layers, and structured interfaces; each has seen a different level of success in different material systems.^{Reference Wang, Liu, Lee, Pozzi and Seeds4,Reference Belenky, Shterengas, Wang, Kipshidze and Vorobjev12,Reference Fitzgerald, Watson, Proano, Ast, Kirchner, Pettit and Woodall21–Reference Yang, Bhattacharya and Mi27}

An abrupt interface is an atomically abrupt transition from the substrate material to the thin-film layer that is overgrown. This approach has seen success in the growth of dissimilar III–V semiconductors as the growth conditions have been optimized to facilitate the formation of misfit dislocations. In the literature, dislocation densities of abrupt interfaces have been reported to be below 1 × 10⁷ cm^–2.^{Reference Richardson, He, Apiratikul, Siwak and Leavitt25} The x-ray diffraction (XRD) full width at half maximum for reciprocal space maps of two perfect crystals coherently joined through an array of dislocations was evaluated theoretically, and it was shown that 60° mixed character threading dislocations have a different XRD spot shape than 90° pure-edge misfit dislocations.^{Reference Kaganer, Köhler, Schmidbauer, Opitz and Jenichen28} While this diffraction spot shape is thickness dependent, the aspect ratio of the elliptical shape was determined to be independent of the sample thickness and therefore, can be used to assess the relative degree to which strain is accommodated by the 90° misfit dislocations.^{Reference Richardson, He and Kanakaraju26}

The XRD width of abrupt metamorphic III–V semiconductors can be very narrow, as shown in Figure 3a, and high-quality devices have been fabricated by a number of research groups. A cartoon of a rigid model abrupt interface depicting strain relaxation through a periodic array of misfit dislocations aligned to the [110] direction is shown in Figure 3b. The distance between misfit dislocations is determined by the ratio of the Burgers vector and the misfit strain between the thin film and substrate. It is common for either strained superlattices^{Reference Nozawa and Horikoshi29} or quantum dot structures^{Reference Yang, Bhattacharya and Mi27} to be included in device heterostructures to act as dislocation filtering structures that reduce the TDD penetrating the device layers.

Figure 3. (a) Graph of 004 x-ray diffraction peaks of several abrupt metamorphic III–V semiconductors. Adapted with permission from Reference Reference Richardson, He and Kanakaraju26. © 2011 American Institute of Physics. Note: FWHM, full width at half maximum; the x-ray diffractometer angle designations for the sample, ω, and detector, θ, and intensity recorded in counts per second. (b) A rigid model cartoon showing an abrupt metamorphic interface between two III–V compound semiconductors looking down the [110] direction. The green balls represent the Group III atom, and blue and yellow balls represent different Group V atoms that result in significantly different lattice constants of the film and substrate. The substrate bonds are shown in blue, the film bonds in green, and the highly distorted interface bonds in gray. The misfit dislocation lines lie perpendicular to this view, aligned with the green atoms that are depicted with no bonds.

Compositionally graded buffer layers have been heavily investigated for achieving high strain relaxation while maintaining low TDD. The basic premise of a graded buffer is to maximize dislocation glide velocity and minimize dislocation nucleation, thus allowing each threading dislocation to do maximum work (i.e., glide very long lengths). Figure 4 illustrates the dislocation network created through one particular design of a compositionally graded buffer with a cartoon and cross-sectional transmission electron micrograph. The strategy attempts to maintain a low density of glissile threads while minimizing any kinetic barriers to dislocation glide, such as compositional inhomogeneity or excessive surface roughness. While compositionally graded buffers can be very effective in producing dislocation densities as low as 10⁴–10⁶ cm^–2,^{Reference Fitzgerald, Xie, Green, Brasen, Kortan, Michel, Mii and Weir22,Reference Lee and Fitzgerald30} they often require several micrometers of thickness and come with significant surface roughening in the form of crosshatch roughness.

Figure 4. (a) Schematic and (b) bright-field transmission electron microscope image of compositionally graded SiGe buffer layer on Si, where threading dislocations may be “recycled” at many mismatched interfaces.

Structured or patterned interfaces make up the last broad class for manipulating dissimilarities in structure between the substrate and thin film. The involved techniques for creating these interfaces include selective area growth, where growth occurs on a pedestal or rib such that the dislocations are able to terminate at a free sidewall before the device region is grown.^{Reference Fitzgerald, Watson, Proano, Ast, Kirchner, Pettit and Woodall21,Reference Li, Bai, Park, Adekore, Fox, Carroll, Lochtefeld and Shellenbarger23,Reference Merckling, Waldron, Jiang, Guo, Collaert, Caymax and Vandervorst24} Figure 5 illustrates InP grown selectively on a 300-mm-diameter Si in nanoscale trenches.^{Reference Merckling, Waldron, Jiang, Guo, Collaert, Caymax and Vandervorst24} These techniques are being advanced in facilities combining growth and nanofabrication capabilities to create metamorphic materials in a deterministic fashion.

Figure 5. InP/Si heterostructure grown in “v-grooved” 50-nm-width trenches with optimized nucleation conditions: (a) (upper) Tilted view scanning electron microscope image and (lower) high-magnification cross-sectional transmission electron microscope image of the orange box area in (c). (b) Perpendicular view showing a twinned region at the InP/Si interface. (c) Parallel view showing a very uniformly grown and low-defect density InP layer with Moiré fringes at the InP/Si bottom interface in inset. {111}A denotes In-terminated plane and {111}B denotes P-terminated plane. Reproduced with permission from Reference Reference Merckling, Waldron, Jiang, Guo, Collaert, Caymax and Vandervorst24. © 2014 American Institute of Physics. Note: W, trench width.

Common metamorphic epitaxial thin-film growth techniques

Metamorphic epitaxial materials have been grown using a variety of techniques, each tailored to the specific material system. Chemical vapor deposition (CVD) uses gaseous precursors and a thermally driven reaction at the substrate surface to grow material. CVD is widely applied in industry and has been used for both SiGe and III–V compound semiconductor materials, including GaN. The relatively fast growth rate (∼3–10 µm/h) is an attractive attribute for growing linearly graded buffers that are conventionally designed to mitigate 1% strain per micrometer of buffer.^{Reference Kuech5}

Molecular beam epitaxy (MBE), a highly precise form of physical vapor deposition, has been the other major technique used in metamorphic materials research. While best known as a research tool, MBE is used commercially for the growth of amplifiers for cell phones and wireless devices, as well as laser diodes. In MBE, atomic or molecular beams are generated via effusion cells, electron-beam evaporators, or even pulsed lasers and directed toward a heated substrate in an ultrahigh vacuum environment. Hybrid techniques are also possible, where beam fluxes are generated from hydride or metallorganic gas precursors (i.e., gas-source MBE and chemical beam epitaxy).^{Reference Kuech5}

The relative success of a growth technique typically depends on the thermodynamic and kinetic processing windows of the final material. Accessible growth rate and operating temperatures have a significant impact on these quantities, and the system parameters that are expressed as a strength in one materials system can translate into a weakness in another material. As an example, most MBE systems employ a relatively low growth rate (typically 1–2 µm/h), which is a disadvantage for growing buffer layers. But precise flux control of MBE facilitates growth of materials that are very sensitive to the V/III ratio, such as III–antimonide compounds.^{Reference Kuech5,Reference Farrow, Bunshah and McGuire10} In general, all modes of growth technologies—from liquid-phase epitaxy to hydride vapor-phase epitaxy—have opportunities to contribute to developing novel metamorphic epitaxial materials.

Record-setting performance

In several technology areas, metamorphic epitaxial materials provide state-of-the-art performance. For example, in photovoltaics, metamorphic multijunction solar cells have set many records for efficiency over the past 10 years. The design freedom that metamorphic materials enable allows device designers to tailor the bandgap of the absorbing layers to match the solar spectrum better than what is possible through lattice-matched designs. Most recently, a 45.7%-efficient four-junction concentrator solar cell with two metamorphic junctions was demonstrated;³¹ concentrator cells are typically <40% efficient.^{Reference Kinsey32} The future of metamorphic solar cells may lie in the integration of III–V materials with Si, enabling high-efficiency and low-cost solar cells for 1-sun or low-concentration applications. High-efficiency metamorphic solar cells are currently under active commercial development for space applications. In this issue, France et al. discuss the importance of metamorphic materials in both ultrahigh-efficiency devices that operate with efficiencies that are beyond the current commercial state of the art, and in low-cost, high-efficiency solar cells with theoretical efficiencies near 40%.

Metamorphic transistors may soon become important for applications in electronics that push higher performance and higher energy efficiency beyond the capabilities of silicon. It is possible that the complementary metal oxide semiconductor industry will move toward metamorphic nonplanar 3D multigate field-effect transistor devices for next-generation logic devices such as FinFETs or tri-gate transistors. Metamorphic transistors may also drive the capabilities of high-speed, mixed-signal applications and high-power devices, allowing new integrated circuit technologies to impact our electronics infrastructure. In their article, Lee and Fitzgerald discuss how these integrated circuits of the future are expected to impact applications in wireless communication, power electronics, and smart systems that could be used in solid-state lighting, printing, displays, and appliance computing.

Advances in metamorphic semiconductor lasers will include both quantum-well and quantum dot active regions to reach new wavelength regimes using semiconductor devices. Metamorphic III–V lasers on Si may also serve as a critical enabler for Si-integrated photonics, where high-performance digital logic and high-speed optical communication are intimately coupled. Tournié et al. review current progress and the future promise of metamorphic lasers.

Opportunities and outlook

The final article in this issue by Deelman et al. discusses the applications of metamorphic materials in the area of quantum computing, currently one of the most challenging and exciting areas of research. Precise strain engineering of silicon quantum wells on metamorphic SiGe is needed to remove the conduction-band degeneracy such that electrons occupy only one valley. In addition, low-loss superconducting materials and novel superconductor/semiconductor epitaxial nanowires are being created from metamorphic epitaxial materials that may help propel quantum computing out of the research laboratory. This article reviews the challenges and materials progress toward creating quantum-bit (qubit) devices for quantum information applications that hold promise for ultrafast computation and unbreakable cryptography.

We hope that this issue will help materials scientists and engineers as well as those who use advanced materials to create devices, circuits, and systems to understand how new engineered, single-crystal semiconductor materials offer new opportunities. Technological value resides in the increased design freedom that results from relaxing the requirement that device layers be lattice-matched to a commercially available substrate; metamorphic growth allows essentially all of the space on Figure 2 to be used in device design and may facilitate epitaxial growth of other materials that are not shown. Already, the advantage of this increased design space has produced devices that have set new performance records and are moving toward commercial relevance.