Growth Far from Equilibrium: Examples from III-V Semiconductors

Transcription

1 Growth Far from Equilibrium: Examples from III-V Semiconductors Thomas F. Kuech 1, Susan E. Babcock 2, and Luke Mawst 3 1 Department of Chemical and Biological Engineering 2 Department of Materials Science and Engineering ³ Department of Electrical and Computer Engineering University of Wisconsin-Madison Madison, WI USA Abstract The development of new applications has driven the field of materials design and synthesis to investigate materials that are not thermodynamically stable phases. Materials which are not thermodynamically stable can be synthesized and used in many applications. These materials are kinetically stabilized during use. The formation of such metastable materials requires both an understanding of the associated thermochemistry and the key surface transport processes present during growth. Phase separation is most easily accomplished at the growth surface during synthesis where mass transport is most rapid. These surface transport processes are sensitive to the surface stoichiometry, reconstruction and chemistry as well as the growth temperature. The formation of new metastable semiconducting alloys with compositions deep within a compositional miscibility gap serve as a model systems for the understanding of the surface chemical and physical processes controlling their formation. The GaAs 1-y Bi y system is used here to elucidate the role of surface chemistry in the formation of a homogeneous metastable composition during the chemical vapor deposition of the alloy system. 1

2 1. Introduction: State of the Art In the world of advanced electronics and opto-electronics, new applications are almost always preceded by the development of new materials with increased function or flexibility. These qualities are achieved by manipulations of the composition, strain state, microstructure, and ultimately, through them, the critical properties of the material. The devices that enable these new applications generally integrate oxides, metals, and semiconductor materials in monolithic structures that are often layered. Their function, however, is established primarily by the selected sets of elemental and compound semiconductors with highly-controlled electronic and optical properties that they contain. Despite the broad variety of applications in which semiconducting electronic and optical devices are used, most devices are predominantly based on just a few materials, specifically elemental Si and the compounds GaAs, and InP. These materials generally are used in thin film form. They are typically formed through epitaxial growth, a process in which constituent atoms arriving at a surface react to form a single crystalline layer of submicron thickness that maintains crystallographic registry with the underlying substrate. In this thickness range, substantial elastic strain can be imparted to the epitaxial layer, which is described as pseudomorphic when a mismatch between the layer and substrate lattice parameters is elastically accommodated. Controlled pseudomorphic growth captures the ability to manipulate materials properties that vary with strain state, for example, band gap energy, charge carrier mobility, and in some cases, solubility. However, the range of properties obtained through this limited set of base materials and utilizing pseudomorphic growth is quite limited relative to the diversity and versatility that semiconductor alloys potentially offer. 2

3 In fact, exploration and development of semiconductor alloy systems is driving a transformation within the electronics and communications industries. The III-V compound semiconductor alloys present a very broad compositional space for the design of materials, structures, and devices with very specific properties tailored for specific functions. In general, each additional constituent within an alloy delivers an added degree of freedom in the design of the material. The principal materials properties that are critical to application of semiconductor materials in devices are the bandgap energy, the lattice parameter, the availability of dopants to generate p-and n-type conductivity, and the specific energy band offsets that arise at the interfaces of dissimilar materials. Semiconducting heterostructures are, in fact, ubiquitous in advanced device structures. For example, spatial control over the band structure, achieved through nanometer scale changes in composition at heterointerfaces, is the key design feature of optical devices, such as lasers and light-emitting diodes. Device heterostructures generally are monolithic single crystal materials throughout which the composition is controlled in depth and, increasingly, in the lateral dimensions as well, as is the case for buried heterostructure lasers and nanowires. Figure 1 is a representation of the range of semiconductor materials that currently are employed in applications. Points indicate the lattice parameters (specifically a o and a for the zinc blende and wurtzite structured materials, respectively) and band gap energies for the elemental and binary compound semiconductors. Red lines indicate solid solution alloys that are used in device structures. With the exception of InAs- GaSb, these lines all represent ternary solutions composed of three elements. The gray shaded regions and line connecting InAs and GaSb indicate quaternary alloys that are specifically used in the formation of long wavelength optical communication lasers. The lattice parameters and compositions of the commercially-available substrates that are used most commonly for epitaxial 3

4 growth are indicted by vertical black lines. They include Si, Ge, GaAs, GaP, InP, InAs and GaSb. There are effectively only four different lattice parameters to serve as the platform for growth. Note elastic strains that develop in pseudomorphically-grown materials can cause the lattice parameters, band gap energy, and other features of the electronic structure to differ from their values in strain-free material. Figure 1 can also be considered to represent the underutilized composition space within the III-V semiconductor landscape. Several causes contribute to the limited number of ternary, quaternary, and higher constituent number alloys that are currently employed. The need to Figure 1: Schematic of The range of available semiconducting alloys. Red lines represent ternary alloys; shaded regions represent quaternary alloys. Black vertical lines indicate the common commercially available substrates. 4

5 minimize defect concentrations, for example, drives a preference for materials with lattice parameters close to those of the available substrates. High synthesis and processing temperatures often limit the selection of alloys to those that are thermodynamically stable with respect to phase decomposition. The advent of more controlled processing with an emphasis on thin-film heterostructure and nanostructure formation has naturally led to the realm of low-temperature processing. Under low temperature conditions, kinetic processes, rather than thermodynamic properties, dominate the materials formation pathways. Kinetically-controlled synthesis, in which surface chemical and transport processes are manipulated, opens the range of possible materials compositions that can be formed to include those outside of the constraint of thermodynamic stability. Kinetically-stabilized alloys have been used in a variety of commercial applications. For example, In x Ga 1-x As y P 1-y exhibits a miscibility gap, yet solid solution materials within the gap are widely used in long wavelength communication lasers 1. GaAs y Sb 1-y exhibits a broad miscibility gap as well. 2,3. However, theoretical and experimental studies show that the strains developed during pseudomorphic growth reduce the critical temperature associated with the miscibility gap and stabilize this alloy to lower temperatures. As a result, single-phase materials with compositions across the entire GaAs y Sb 1-y phase diagram have been synthesized and used successfully in a variety of device structures 4,5. This present paper explores the aspects of thermodynamics, surface chemistry, mass transport, and reaction kinetics that must be understood and/or manipulated to take advantage of the wide-ranging potential offered by metastable compound semiconductor solutions. 2. Thermodynamics and film formation 5

6 Thermodynamic properties play a central role in the design of new materials and the processes to form them. For example, small differences in the free energy of formation among many of the clathrates leads to difficulty in the synthesis of materials with high phase purity 6. Similarly, the thermodynamic properties of the particular host and guest components of a clathrate compound often make control of the final clathrate composition a challenging problem in materials design and formation. In the case of compound semiconductor materials, an epitaxial single crystal of precisely controlled and uniform composition is required in most applications. For planar devices, the synthetic challenge is to produce this phase over large area substrates. Ideally, this phase is also thermodynamically stable over a range of chemical activities of its constituents, as the final materials properties can be, and often are, a function of the constituent activities during synthesis and subsequent processing. The group V anions: N, P, As, Sb and Bi, in binary III-V compound semiconductors have much higher vapor pressures than the group III cations: B, Al, Ga, and In. Consequently, the crystal quality, defect concentrations, and properties of the III-V compounds are established by controlling the anion activity during synthesis and processing. In GaAs, for example, the concentration of As antisite defects (As Ga, an EL2-type defect), is dependent on the As activity during growth through mass action considerations 7, /2 i i AI As2 As g As As K P (1) /2 As Ga Ga VA As2 As g As V V K P As V As As K As V i Ga Ga Ga AG i Ga 2) (3) 6

7 Inserting Eqs. (1) and (2) into eq. (3) yields for [As Ga ]: AsGa KAI KVAK AGPAs K 2 AGPAs 2 (4) where AG S k H kt K e e with S = x 10-3 ev/k and H = ev 8. Since H is negative (exothermic), K AG and by extension, [As Ga ], decreases with temperature 9. These mass action relationships are more complicated and the defect populations increasingly interrelated to the processing conditions as the chemical complexity of the material increases 8,10. While such influences are ever present in the formation of all materials, the use of lower synthesis temperatures to promote formation of metastable compounds with three or more components from groups III and V can alter the defect populations dramatically, as well as the kinetics of synthesis. The stability of a compound semiconductor alloy depends on the thermodynamic relationships among all of the constituents. Evaluation of its stability becomes more complicated as the number of constituent elements increases, relies on the availability of thermodynamic data for the pair-wise sub-systems, and requires the determination of the enthalpy and entropy of mixing associated with formation from components. Formally, the free energy of formation is: ideal solution G G Gmix x G RT x ln x G i i i i i mix i (5) where the G i are the partial molar free energies of the components, typically considered to be the corresponding binary compound semiconductors; the x i are their mole fractions; and RT xiln xi is the configurational entropy. The free energy of mixing term, i Gmix Hmix T Smix, contains all the various interaction terms describing the deviation from ideal or non-interacting behavior. 7

8 The difficulties in predicting the phase behavior of a given set of constituents that potentially might form a complete solid solution or phase segregate into two or more compositions, lie in the prediction of ΔG mix. Several models of ΔG mix for alloy semiconductors are present in the literature. Perhaps the most intuitive approach is that given by Stringfellow 11,12. In this quasiempirical model for ternary compounds, the free energy of mixing is argued to be most easily parameterized by the difference in lattice parameters of the two endpoint phases, specifically two constituent binary III-V compounds with the zinc blende crystal structure. The enthalpy of mixing in this model follows a regular solution theory with the interaction parameter, AB, fit to the existing body of data: H X X (6) mix A B AB a 4.375K (7) a AB where a0 is the difference in the lattice parameters of the binary endpoints, a, is the average of the binary lattice parameters, and the fitted parameter, K, was determined to be equal to 1.26x10 7 cal/mole/å 2.5 The exact value of K depends on choice of the data used in its determination. This model has the advantage of providing an analytic expression for the enthalpy of mixing. In the regular solution model, there is no additional entropy of mixing beyond the configurational entropy term. Although typically considered a minor term, the entropy of mixing will be a function of composition, particularly in systems where there is a large difference in the characteristics of the substitute and host-replaced atoms, where there is local ordering, or where other deviations from homogeneous alloy formation occur. Extensions of Stringfellow s analytic model to quaternary alloy systems generally show good agreement with experimental data 12,13. But while these quasi-empirical approaches to 8

9 determining phase equilibria have been successful for many systems, they can sometimes have difficulties predicting the exact structure when dealing with wide miscibility gaps and potentially ordered structures 14. Computational approaches to phase diagram determination for these alloy semiconductors provide a means to interrogate their potential. Early approaches were pioneered by Zunger and co-workers 2,3,15. In their models, the influence of strain generated by pseudomorphic growth to a specific in-plane lattice parameter was included in the calculation of the free energy of a phase as a function its composition: ideal solution G G Gmix Gstrain x G RT x ln x G G ( c,, ) i i i i i mix strain ij i (8) The term, G ( c,, ), represents the elastic energy generated when a thin film of the alloy strain ij strains to match the lattice parameter of the substrate, as occurs in pseudomorphic growth, that is dependent on the crystal structures, lattice parameters, and relative crystallographic orientation of the substrate and the epitaxial layer. This additional term can dramatically alter the location, in composition, of the phase boundaries between single-phase and two-phase phase fields that define the regions of immiscibility in the phase diagram. In the case of GaAs 1-y Sb y, the strainfree alloy has an upper critical temperature of 1245K, leading to a broad miscibility gap, while strained to InP this temperature drops to 713K 2. Phase diagram modifications of this type are present in most compound semiconductor alloy systems. Figure 2 illustrates this behavior in Ga x In 1-x As and GaN y As 16 1-y, where a negative critical temperature indicates that the single phase of this composition is metastable at all temperatures. An examination of phase diagrams for multinary alloy systems indicates that most include large regions of immiscibility 12,17. Empirical rules also have been used to predict broad miscibility in alloy systems. In the case of metal 9

10 alloys, they are embodied in the Hume-Rothery rules, which should be applicable to semiconductor alloys as well. By extension and considering the binary semiconductors as the endpoint components being mixed, the basic factors impeding their miscibility are 1) a difference in their equilibrium crystal structure, 2.) large differences in atomic size between atoms that would Figure 2: Calculated critical temperatures for mixed cation and anion systems as a function of composition. The solid dark lines correspond to strain-free material. The other results assume the strains that would be induced by pseudomorphic heteroepitaxial growth on the noted substrates 16. Reprinted from Reference 16, Copyright 1999, with permission from Elsevier. substitute for one another in a solution, 3) a difference in valence between the cations and anions being mixed on their respective lattices, and 4) large differences in electronegativity of the anions and cations, respectively, which would the shift the bond character from covalent and to partially ionic. The above discussion has focused on regular solution models. The determination of the interaction parameters, AB, as well as other non-regular solution approaches, also has been developed by employing large-scale computational approaches to ab initio calculations 18,19. Various interaction parameters can be developed through the use of quantum chemical 10

11 approaches, such as density functional theory (DFT) 19,20. A general observation based both on experiment and these calculations is that almost all compound semiconductor alloy systems have regions of miscibility at the temperatures used for synthesis of epitaxial films. The growth of homogeneous, metastable, single-phase materials with compositions well within the multi-phase phase fields of highly immiscible alloy systems can be achieved by molecular beam epitaxy (MBE) 21 or metal organic vapor phase epitaxy (MOVPE) 22. Success is based on presenting a locally homogenous flux of reactants to the growth front while simultaneously averting atomic mass transport within the grown layer and on its surface. Typically, these metastable solutions are synthesized at temperatures below that optimized for synthesis of the host material. For example, the MOVPE growth of GaAs is usually carried out at C 23 ; MBE GaAs is grown at somewhat lower temperatures of ~580 C 24. Metastable solutions such as GaAs 1-y Bi y or GaAs 1-y N y, are grown using these same techniques at C, far below the optimized growth temperatures for the host material. The self-diffusion of Ga in GaAs, though dependent on the background carrier concentration, is extremely low at these temperatures, with D Ga 2 22 cm 10 at 600 C and a large activation energy of EGa 4.65 ev. s The As self-diffusion coefficient is even lower 25. The extrapolated value of the diffusion coefficient at 400 C would be D Ga cm s. Assuming that a solute, such as Bi or N, would diffuse by similar mechanisms with a similar activation energy and at similar rates, there should be negligible bulk diffusion of the solute in the film at the growth temperature. Experimental values of surface diffusion coefficients are difficult to obtain, but, in general, mass transport processes are much faster on surfaces than in the bulk and could enable phase separation and/or composition modulation. For Ga adatoms on a GaAs c(4x4) reconstruction, the activation energy 11

12 for diffusion is reported to be only 0.74 ev, about a factor of six lower than the bulk value 26. In a typical adatom residence time of ~1 s, a Ga atom can travel several nm across the surface with the bulk diffusion being negligible. These diffusional pathways and rates are also affected by the presence of various chemical overlayers as well. In the case of GaAs 1-y Bi y, Bi metal will segregate on the surface leading to one-to-several monolayers of Bi on the surface and altering the reconstruction This surface-segregated layer then serves as the diffusional surface and can lead to changes in the rates of diffusion. Diffusion on such surfaces, often assumed to be quite rapid, is difficult to study experimentally and has not been investigated in detail. The most likely pathway to phase separation is therefore at the surface during growth. The surface diffusion pathways are often complex even on a pristine surface. The surface composition, temperature and reconstruction affect the surface mass transport processes. The reconstructions present result from the temperature and the activities of the various constituents at the surface. These interrelated factors (temperature, composition, reconstruction, and activities), therefore all must be optimized in order to prevent phase separation during synthesis. The presence of chemical species that "dirty" the surface can alter the surface reconstructions and affect the accessibility of surface sites for diffusion. Intentional modifications to the surface chemistry that reduce mass transport, through steric and other effects, have been combined successfully with low surface temperature to inhibit phase separation and form technologicallyuseful, single phase materials with homogeneous compositions within the miscibility gap of an alloy system 29,30. Aside from the compositional variation over atomic-to-mesoscopic distances on the surface, there is also the presence of local atomic ordering which has been attributed to the surface step structure and chemistry. For example, the formation of a CuPt B-type ordering in the In x Ga 1-x P system is due to specific surface reconstructions existing under different gas phase 12

13 stoichiometric conditions 31. The case study described below highlights the role of the surface chemistry in dictating the phase formation and film homogeneity at the nanoscale to achieve such a material. 3. A model system: Homologous GaAs 1-y X y ternary alloys with X=N, P, Sb or Bi Highly immiscible alloy systems are of great interest. The optical and electronic structure and properties of the metastable solutions that can be formed in them are highly sensitive to alloy composition in ways that offer potential for new and improved devices. Furthermore, as discussed above, the solute concentration achieved in the metastable solution often can be enhanced via control of the elastic strain produced in pseudomorphically grown films. The homologous series of alloys formed by anion substitution into GaAs provides a model system for exploring the influences of strain, composition, surface structure, and surface kinetic processes on the formation and structure of metastable single-phase thin films. The endpoints of this set of alloy systems, GaAs 1-y N y and GaAs 1-y Bi y, exhibit the least solubility for anion substituting solute, but the alloy electronic structure is highly tunable via small changes in the solute concentrations. In the alloy system at one end of the series, the extensively studied GaAs 1-y N y "dilute nitrides," nitrogen is only sparingly soluble; 32 yet the small N concentrations that can be realized in metastable materials 33,34,35 cause large decreases in the conduction band energy relative to the vacuum level and, consequently, the bandgap energy 33. The reduction in the bandgap of the material of ~250 mev at y 0.02 has been observed. This sensitivity of the band gap energy to nitrogen concentration makes GaAs 1-y N y an attractive material for a variety of applications, including solar cells. The electronic structure changes observed in this system have been described by a band anti-crossing model that associates an impurity-to-band state transition for the incorporated nitrogen states 36 with a strong decrease in 13

14 the conduction band edge. At the other end of the series, the incorporation of Bi changes the GaAs band structure by the movement of the valence band to higher energies. This behavior that is of interest for applications as well. Specifically, when y in GaAs 1-y Bi y approaches 0.12, the spin orbit splitting within the valence band structure is predicted to exceed the band gap energy 37. This unusual band structure suppresses Auger recombination, which should result in higher device efficiency when this material is applied in long wavelength laser devices 38. The changes in the band gap are accompanied by extreme band bowing as well. The introduction of strain into these alloys, through pseudomorphic epitaxial growth, can alter the critical temperature for the miscibility gap and facilitate formation of metastable solutions with appreciable solute concentration. In pseudomorphic growth, an elastically strained layer of epitaxial material is grown at any thickness up to a critical thickness 39 that is characteristic of substrate material layer material pair. At the critical thickness, the stored elastic strain energy is released through the introduction of dislocations, cracks, and other extended defects, and the elastic strain dissipates. Alteration of the thermodynamic phase diagram by pseudomorphic-growth-induced elastic strain has been investigated for several alloy systems, including GaAs 1-y N y, GaAs 1-y Sb y and GaAs 1-y Bi y. GaAs 1-y N y has been studied in the greatest detail as a material system which can be integrated into a GaAs platform. The small size and high electronegativity of N leads to highly local ionic bonds between Ga and N, as well as a tensile strain in pseudomorphic layers on GaAs. Methods to incorporate up to several mole percent of N on the anion site have been reported 40, well above the equilibrium solubility limit. The addition of Bi to GaAs leads to complementary effects. As with N, Bi is sparingly soluble in GaAs. However, Bi has a low electronegativity and is an extremely large atom relative to As. As a result, a compressive strain arises in pseudomorphic GaAs 1-y Bi y layers on GaAs, and 14

15 the presence of Bi leads to substantial changes in the valence band structure of the alloy due to both the Bi and any associated pseudomorphic strain. These combined effects lead to shifts in the band gap energy of approximately ~83 mev per (Δy = 0.01) 41. GaAs 1-y Bi y is therefore a material in which band gap reductions are achieved with moderate associated elastic strain. GaBi is not a stable compound, and therefore the lattice parameter of zincblende GaBi has been calculated to be nm, but not confirmed experimentally. This lattice parameter is much larger than that of GaAs ( nm). An approximate critical thickness for GaAs 1-y Bi y on GaAs with y=0.05 would be nm. Thus, high strains could develop within very thin layers. Highly strained thin layers of this type are useful in a wide variety of optical and electronic devices that utilize strain induced changes in bandgap energy, as well as compositionally induced ones. A number of controllable factors can influence the metastability of a GaAs 1-y Bi y solution. The thermodynamic stability of the alloy upon Bi incorporation was examined for both unconstrained (strain-relaxed) and pseudomorphically-strained materials using density functional theory (DFT)-based simulations in a previous study 19. The difference in anion size, and, correspondingly, between the lattice parameters of GaAs and GaBi was shown to manifest itself in strong changes in Bi solubility with the strain state of the material. Bi solubility was also found to depend on the chemical potential of the second phase that was considered to be in equilibrium with the alloy, 19 indicating that Bi solubility can be enhanced through control of the phase or phases to which the solution can decompose. The binary compound, GaBi, unlike GaAs, is not a thermodynamically stable compound and has not be synthesized to the authors knowledge. Estimates of its thermochemistry, crystal structure, and lattice parameter however have been made and used successfully to explain observed behaviors

16 The results of density functional theory based calculations of Bi's solubility, y, in GaAs 1-y Bi y thin films as a function of substrate lattice parameter relative to GaAs are reproduced in Figure For pseudomorphically grown material, Bi solubility increases as the substrate lattice parameter is increased due to reduced compressive elastic strain. Two curves are presented for both the strain-free and the pseudomorphically strained alloy, as the lattice parameter of the substrate is increased. These curves differ in the second phase chosen to be in equilibrium with the alloy: either Bi or GaBi. As with GaAs 1-y Sb 2 y, reduction in elastic strain increases the solubility of Bi in the alloy. Potentially, the tetrahedral distortion of the alloy unit cell when pseudomorphically strained to GaAs provides a change in local bonding arrangements to accommodate the larger Bi atom which can also assist in accommodating a higher concentration of Bi. The second significant factor in increasing the solubility in the system is the choice of the second phase that is in equilibrium with the alloy. If the alloy is forced to phase separate into GaBi (or a GaBi-rich phase) rather than Bi, the solubility is increased by potentially several orders of magnitude depending on the Bi concentration of in the metastable solution. 16

17 These behaviors provide critical insight into synthetic routes to form and stabilize the metastable solutions. Decomposition within the bulk of the material must Figure 3: Solubility of Bi in GaAs versus the strain in the GaAs lattice parameter at 400 C under Ga-rich conditions, using both Bi metal and GaBi as the reference state for Bi. Figure modified from Reference 19 with permission from the American Physical Society occur through solidstate diffusion that would result in, initially, Bi-rich regions with compositions approaching GaBi and greatly increased coherent strain in their vicinity. Solid-state diffusion is very slow under the thermal processing conditions associated with typical synthesis and processing and would not occur extensively in the bulk. Furthermore, decomposition to GaBi has a smaller thermodynamic driving force than to Bi metal. Separation into Bi-deficient GaAs 1-x Bi y and Bi metal can happen easily on the surface during synthesis. If Bi is not incorporated into the growing film it can segregate and accumulate on the growth front. Control of the surface structure and the chemical kinetics associated growth is thus required to synthesize these materials as metastable solid solutions. Once synthesized, they can be processed further using established methods to fabricate devices such as lasers 44 and solar cells 45. The roles of surface chemistry and kinetics in determining the composition and 17

18 compositional homogeneity of a growing, metastable epitaxial material are thus the subject of the remainder of this paper. 3.1 Chemical Vapor Deposition (CVD) formation of GaAs 1-y Bi y A principal chemical route to the formation of epitaxial materials for applications in electronic devices is chemical vapor deposition (CVD). In CVD, gas phase precursors are introduced into a reactor and mass transported to a surface, where they react to form the film. Film formation thus proceeds through both interactions in the gas phase and chemical reactions on the growth surface. The gas phase environment within the reactor precludes use of many of the surface sensitive diagnostic tools available for determination of the chemical and physical state of the growth front, in operando. The most productive approaches therefore have been detailed characterizations of the grown materials combined with computational chemistry and fluid dynamics analysis. In our work, GaAs 1-y Bi y was grown using simple growth chemistries which are amenable to this combined growth-characterization-computation approach. Growth of GaAs 1-y Bi y occurs under quite different gas-phase conditions from those optimized for synthesize of the host material, GaAs, in addition to lower temperature. GaAs is typically grown from trimethylgallium (TMGa, (CH 3 ) 3 Ga) or triethylgallium (TEGa, (C 2 H 5 ) 3 Ga) and tertiarybutylarsine (tbas, C 4 H 9 AsH 2 ) or AsH 46,47 3. However, the growth of alloys containing an anion site-substituted solute requires a large deviation in the gas phase stoichiometry from that used to grow GaAs. The gas phase anion-to-cation ratio (V/III ratio) for the optimal growth of GaAs is typically high, though it depends on the reactor pressure. Particularly at elevated temperatures, thermodynamic stability of the GaAs requires a minimum activity (partial pressure) of As 2 or As 4 over the surface 23. This partial pressure of As is supplied through the decomposition of the As precursor 18

19 in the gas phase or at the surface. Empirically, materials with improved surface morphology, enhanced luminescence efficiency, and reduced carrier concentration result when the partial pressure of the anion source is well in excess of that required for thermodynamic equilibrium. For GaAs growth by MOVPE, V/III ratios of 10 to over 100 typically are employed. In stark contrast, a V/III ratio close to unity is often required 4,48-50 for growth of solutions within the miscibility gap of an alloy system, as is the case for GaAs 1-y Sb y and GaAs 1-y Bi y, in particular. The cation typically exhibits a very low vapor pressure, and therefore, the decomposition of the cation source at the surface is generally the rate-limiting step to film growth. A V/III ratio approaching unity forces the surface cation to bond to those available anions that are present at near stoichiometric ratios, slows the growth reaction processes, and can lead to phase separation of the cation to droplets on the surface. Under these conditions, the choice of precursor chemicals, and specifically their decomposition pathways and rates, has a strong influence on the growth rate and composition of the film. These considerations motivated studies of GaAs 1-y Bi y growth using TEBi, in addition to the more commonly employed TMBi, as the Bi precursor. The results described in the following were obtained from films grown using TEGa, TMBi or TEBi, and tbas in a cold wall, inductively-heated MOVPE system held at a pressure of 0.1 bar. The growth surface was a GaAs (001) wafer placed on a graphite susceptor. A hydrogen carrier gas was used at a total flow rate of ~7slpm (~2.8x10 5 µmole/min) within the 76 mm diameter reactor. When TEGa, TMBi and TBAs were used, the molar flow rates were typically 61.4 xtmbi µmole/min, 5.5 µmole/min and 356 µmole/min, respectively, such that x x TMBi TMGa and V/III = 6 49,51. Because TEBi reacts more rapidly at the growth front than TMBi, the molar flow rate of the TEBi Bi source was ~0.62 µmole/min 50. The growth temperatures ( C) were 19

20 typical of those used for GaAs 1-y Bi y growth by MOVPE, but well below that optimized for GaAs (~600 C). For some studies, single layers of thickness nm were grown. In these cases, all precursors were introduced into the reactor simultaneously. For others, superlattice structures composed of 5-20 nm thick layers of GaAs 1-y Bi y separated by thicker layers of GaAs were the targets of the growth protocols. The GaAs 1-y Bi y layers in the superlattices were grown by counter pulsing the Ga and Bi sources into the reactor chamber, along with a continuous supply of the As precursor and hydrogen 51. X-ray diffraction was used to determine strain state and composition of the grown materials. The surface morphology was investigated by secondary electron imaging in a scanning electron microscope (SEM). The distribution of Bi within the superlattice samples, was determined using the high angle annular dark-field (HAADF), or z-contrast, imaging method in an aberration-corrected scanning transmission electron microscope (STEM). Crosssectional STEM samples were prepared using the wedge-polishing method and ion-milling. GaAs grown using TEGa as the Ga source exhibits a temperature dependent growth rate at growth temperatures below ~500 C that is characterized by an apparent activation energy of ~26 kcal/mol. 22 Above 500 C, the growth rate is relatively independent of growth temperature and growth is characterized by a mass-transport-limited behavior due to the rapid surface reactions. GaAs 1-y Bi y shows markedly different growth characteristics and more complex growth behavior. Its growth rate exhibits a strong dependence on temperature, as shown in Figure 4. This figure plots the thickness of the period of a superlattice consisting of GaAs 1-y Bi y /GaAs quantum well (QW)/barrier bilayers repeated 14 times in the growth direction grown using TEGa\TEBi\TBAs. The period of the superlattice increases approximately linearly with 20

21 increasing growth temperature. SEM studies of the sample surfaces indicated there is a maximum bismuth concentration that can be incorporated at each temperature and that an oversupply of Bi causes Bi-rich deposits to form on the surface. In all cases, it is believed Figure 4: The growth behavior of MOVPEbased GaAs\GaAs 1-y Bi y superlattice structures as a function of temperature. The growth rate increases with increasing temrpature but the Bi content decreases as Bi is rejected from the solid. that a monolayer of Bi persists on the surface, which mediates Bi incorporation and reactivity 27,52,53. A Bi-terminated (2x1) reconstruction is seen in MBE growth under As-lean conditions, which favors Bi incorporation and is thought to be present during MOVPE growth 53. Bi-termination of the surface alters the growth behavior and results in alloy formation being dependent on the specific chemical reactions associated with the surface Bi atoms. The modification of the growth behavior due to the chemical composition of the solid surface during growth can lead to unexpected trends in growth rate and composition, particularly in chemical vapor deposition. The more revealing case is when TMBi is used as the Bi source. A record of the growth behavior realized with the TMBi source is present in the composition profile of the superlattice shown in Figure 5. The sample was grown at 420 o C. The detailed compositional profile in the sample was obtained from HAAFF STEM images, in which the image intensity is most directly related to the local composition of the sample. This figure highlights several key aspects of the growth behavior that a surface kinetic model must capture. 21

22 Specifically, because the GaAs 1-y Bi y was grown using 7 counterpulses of the Bi and Ga sources, the seven closely-spaced peaks in the concentration profile undoubtedly correspond to growth during the flow of the Bi source. However, in each bilayer of the superlattice, the maximum in the Bi concentration is displaced from the seven peaks. The Bi therefore must have been incorporated primarily during the cycles when the Bi source was turned off. Figure 5: Z-contrast STEM image of multilayer sample grown using TMBi, which shows the Bi distribution through a section of the GaAs 1-y Bi y /GaAs superlattice structure grown at 420 C. Bi incorporation is lower during the nominal GaAs 1-y Bi y growth period, and higher after the TMBi flux terminates during the nominal GaAs layer growth step 54. Reprinted with permission from Reference 49. Copyright AIP Publishing LLC. Furthermore, the film growth rate with TMBi present in the reactor is lower than that for pure GaAs under the same conditions of temperature and reactor conditions. Thus, perhaps counterintuitively, the cessation of TMBi introduction into the reactor leads to both accelerated growth and the formation of Bi-rich layer within the sample. These observations imply that Bi 22

23 segregates on the surface in the presence of the TMBi and slows the growth rate. The surface segregated Bi is incorporated in the film when TMBi is removed from the reactor and the growth resumes. Integration of the Bi compositional profile indicates that the Bi incorporated into the subsequent GaAs layer is equivalent to approximately one monolayer of Bi, which would be expected from the Bi-terminated (2x1) reconstruction. These observations imply a controlling role for the Bi in the growth behavior that depends explicitly on its specific chemical form on the surface. This unusual behavior has been investigated further both experimentally and computationally. To develop a full chemical kinetic model, both the gas phase and surface chemistry must be considered. The gas phase chemistry is known for most of the metal organic compounds and hydrides that are commonly used in chemical vapor deposition, including TMGa, TEGa, and the others. It can thus be embedded into a computational fluid dynamics model of the reactor that produces accurate temperature and flow profiles and therefore accurately describes the thermal environment of the reactants as they progress to the growth surface. The extent of gas phase reaction will depend on the average time at temperature for these reactants as they approach the growth front. At these substrate temperatures and within a typical MOVPE reactor, a small but non-negligible gas phase decomposition of the reactants is expected. Homogeneous gas phase reactions generally lead to extremely reactive radical products. In the case of GaAs 1-y Bi y, the relevant gas phase reaction chemistry has been revealed through density functional theory and experiment. When combined with a computational fluid flow model of the reactor, this information enables determination of the chemical composition of the gas phase near the substrate surface and that interacts with the growth front. Results for the composition of the gas near the growth front of GaAs 1-y Bi y grown using TMBi, TBAs, and TEGa 23

24 are shown in Figure The substrate temperature was ~400 C for these calculations. The residence time (time spent near the heated substrate) is quite short, on the order of 1 to 10 ms. During this time, however, several percent of reactive intermediates and reaction byproducts are formed in in the gas phase near the growth surface and can interact with it. A complete reaction network was developed for the case of the reactants studied in Figure 6. This analysis encompasses all the most likely gas phase reaction products resulting from both unimolecular decomposition and molecular reactions. Some of the species indicated in Figure 6 result from the unimolecular decomposition of the host species: C H AsH C H AsH C H AsH Bi CH CH CH Bi Ga C H C H GaH C H (9) There are many other reaction byproducts. Species such as AsH 2 and CH 3 are highly reactive radicals which can play a key role in the surface chemistry even when present at low concentration in the gas phase. 3.2 Reaction Model of GaAs 1-y Bi y growth The unusual growth behavior shown in Figures 4 and 5 is a result of the interaction of the various surface reactants, in this case TMGa, TMBi, and TBAs and their reaction byproducts, and the low growth temperatures. These interactions determine the incorporation of Ga, As and Bi into the growing film. Due to the low solubility of Bi in GaAs 1-y Bi y, Bi deposited on the surface will segregate and form an eventual monolayer on the surface. The Bi monolayer is noted in the MBE growth as forming a (2x1) Bi-terminated surface reconstruction 53. It is the interaction of the chemical species in this surface Bi-segregation layer that controls the film growth. This Bi- 24

25 terminated layer interacts strongly with the methyl radicals generated on the surface and from adsorption and repopulation from the gas phase. As growth proceeds, the surface becomes terminated by a Bi-CH 3 species, which controls the adsorption of other species from the gas phase and hence the growth rate and alloy composition. DFTbased calculations indicate that the lowest free energy state of the (100) GaAs 1-y Bi y surface is that of the surface with complete monolayer coverage of Bi-CH 3. This population of the surface by a specific chemical species leads to the lack of Figure 6: Species and their concentration relative to the input source precursor concentration, C 0, predicted to be arriving to the growth front during GaAs 1-y Bi y growth. The gas phase chemistry can produce reactive intermediates at the relevant growth temperature and short residence time of the reactants within the heated region of the system. This figure is adapted from reference 55. open surface adsorption sites for adsorption and reaction of the Ga source. The methyl groups on the Bi atoms do have a finite lifetime on the surface, which has been measured and is on the order of 1 sec at the growth temperature 56. Each methyl radical desorbed from the surface opens a surface site for adsorption and reaction of the Ga source. However, all gas phase species compete for these sites. The locally significant concentration of methyl radicals in the gas phase and the high reactive sticking coefficient of these groups ensures 25

26 that the surface remains Bi-CH 3 terminated leading to the low growth rates observed and low Bi incorporation. The removal of methyl groups from the gas phase, through the secession of the TMBi flow into the reactor, leads to methyl group desorption from the surface with these sites now becoming available for growth reactants. These dynamics lead to the anomalous Bi profiles shown in Figure 5 wherein the Bi concentration is highest during the GaAs growth, i.e. no TMBi in the gas phase. The exchange of TEBi for TMBi as the gas phase reactant eliminates the source of methyl radicals and changes the growth kinetics and Bi incorporation. Ethyl radicals, should they exist on the surface, possess a different reaction network which permits multiple reaction desorption paths. As a result, ethyl groups desorb at a much higher rate allowing open surface sites for reaction. The use of TEBi as the Bi precursor chemical results in higher rates of growth and higher efficiency of Bi incorporation. 2.3 Structure and Characteristics of GaAs 1-y Bi y Epitaxial Layers Several structural issues arise when developing metastable thin film materials. The thermodynamic tendency of the film to phase separate provides a driving force for the formation of composition fluctuations at the nano-to-mesoscopic level. The most apparent inhomogeneity is the rejection of one of the constituents at the growth front. In the case of GaAs 1-y Bi y, the formation of Bi-rich droplets has been noted under many growth conditions signifying that the flux of Bi to the surface is in excess of what can be incorporated into the growing film or be used to form the surface monolayer 49,57. Beyond the phase segregation during growth, nanoscopic inhomogeneity of the alloy can critically impact its function in device applications. Atomic scale compositional variations can lead to localized changes in the band structure, altering the optical properties and potentially increasing carrier scattering and reducing carrier mobility. Both STEM 26

27 and atom probe tomography (APT) have been used to discover and interrogate the nature of any local composition variations that exist. Aberration-corrected STEM allows evaluation of the composition atomic column-by-atomic column in the plane of the STEM specimen, but integrated in depth through the TEM specimen. 54,58 This technique is thus sensitive to local average variations on the atomic scale in the growth direction and on the scale of a few 10s of nm in the growth plane, assuming cross-sectional TEM samples are investigated. APT yields three-dimensional analysis of composition on the nm or better scale. 59 Statistical analysis of the APT data is particularly useful for the discovery (or not) of solute clustering on the nanoscale as well as other spatial non-uniformities of composition. 60 Combining these approaches has suggested that the Bi distribution is uniform within the plane perpendicular to the growth direction at the nm scale in as-grown samples, 61 indicating that there is no measurable phase separation or clustering on the growth front during growth. This alloy system, as well as the related alloy system of GaAs 1-y N y, exhibits optical and electrical properties that differ from the host material. Sub-optimized temperature growth of most materials leads to incorporation of point defects or defect complexes in excess of that seen in the host material grown at the optimal temperature. These defects often act as non-radiative recombination sites within the material and diminish the minority carrier lifetime. A reduced minority carrier lifetime leads to both lower efficiencies in applications such as solar cells as well as higher threshold currents in solid-state lasers. The specific structural nature of these defects is difficult to ascertain. Electronic signatures, however, are evident in techniques such as deep level transient spectroscopy (DLTS). In the case of GaAs 1-y Bi y, studies have identified several defect states within the band gap and associated them with arsenic antisite, As Ga, defects 62. Post-growth annealing of the layer is often used to ameliorate such defects. When effective, 27

28 these annealing treatments are not sufficient in time and temperature to cause phase separation but do improve properties, such as the photoluminescence intensity, and control over the carrier concentration. The annealing treatments are conjectured to lead to the elimination of local high energy defect complexes through short range diffusive jumps and shuffles 63. Extended annealing, particularly at high annealing temperatures, can and does lead to phase separation with the formation of Bi-rich precipitates 64. The incorporation of electrically active impurities, particularly carbon that is often introduced during MOVPE growth, also can affect the properties of these materials. The concentration of carbon contaminants that are inevitable increases with decreasing growth temperature. Removal of the carbon-based ligands from the growth surface at elevated temperatures is well understood and involves the reaction of the hydrides, AsH 3, NH 3, or PH 3 that are commonly used as the anion source, with the hydrocarbon radicals 65. These reactions are not as fast at low temperatures. Furthermore, other competing pathways occur for the reduction of the hydrocarbon radical on the surface, leading to increased carbon incorporation. Thus, the carbon concentration is highly dependent on the sources used during growth as well as the growth temperature 46,50,51. Improvement in materials properties and control over the unintentional impurity incorporation requires detailed knowledge of the growth chemistry and processes. Predictive and descriptive models for these critical aspects of growth are only beginning to be established even for the more well-studied ternary systems. Even greater flexibility in the design of materials can be accessed through the inclusion of additional elements in the alloy, both as cations and anions. Materials such as Ga 1-x In x As 1-y N y and Ga 1-x In x As 1-y-z N y Sb z, as well as the wide variety of other quaternaries and quinternary alloys, 35,66,67 have been investigated to some extent. In general, 28

29 each additional element offers a new degree of freedom in the design of the material. These design attributes include the lattice parameter, the band gap, and various heterostructure band alignments, as well as detailed features of the band structure. Unfortunately, the compositions of these alloys generally lie within a miscibility gap of the system. Their development thus requires more extensive models for their growth behavior and structure-property relationships. 4. Extension to Other Alloy Systems The approaches to synthesizing metastable ternary alloys involving low temperatures and control over surface stoichiometry and chemistry have been extended to other more complex quaternary and quinternary alloy systems. Typically, the formation of these more complex alloys have used known conditions to produce a specific ternary alloy, for example GaSb 1-y Bi 68 y, InP 1-69 ybi y, GaP 1-y Bi 70 y and then extended the compositional range by incremental additions of additional constituents. Studies have been extended beyond the ternary systems discussed here. GaSb 1-y Bi y, InP 1-y Bi y, GaP 1-y Bi 70 y among other systems have been investigated. Many of the more complex alloys have incorporated a strain-compensating element to extend the critical thickness without adversely affecting the desired optical and electronic properties. For example, nitrogen has been added to GaAs 1-y Sb y to form GaAs 1-y Sb y N 30,67,71 z which can be latticematched to GaAs or a GaSb substrate by coordinated adjustment of y and z to reduce the lattice mismatch strain and increase the critical thickness of pseudomorphic layers. Other systems that have been reported include In 1-x Ga x As 1-y N 72 y, GaAs 1-y-z Bi y N 73 z, In 1-x Ga x As 1-y Bi 74, B x Ga 1-x As 1- yn 75 y, and GaAs 1-y-z P y Bi 76 z. These systems are of interest for applications where lower band gap energies are required along with the constraint of low strain. In the case of MOVPE growth, the systematic trends in alloy formation with chemistry, growth temperature, and gas phase stoichiometric ratios that have been described for GaAs 1-y sbi y are also followed by these more 29

30 complex alloys. Specifically, low growth temperature and stabilization of the growth front through the adsorption of chemical ligands or a surfactant layer comprised of a segregated element can lead to the formation of metastable solutions within the miscibility gap of their respective alloy system. 5. Summary The formation of metastable electronic and optical materials relies on a detailed understanding of the interplay of the thermodynamics of the material system and the kinetic processes on the growth surface during synthesis, as phase separation is most likely to occur on the growth surface during the film formation. Therefore, the most direct approach to producing homogeneous single-phase materials with compositions within a miscibility gap of an alloy system is to minimize mass transport on the surface. A low growth temperature typically is the front line approach to impeding mass transport, but control of the interplay of chemical species at the growth front with the mobile adatoms can augment its effectiveness. Low growth temperatures often also lead to the incorporation of defects and, potentially, chemical impurities. Post-growth treatments, such as annealing, have resulted in improved properties (increased photoluminescence intensity, minority carrier lifetime and carrier mobility), presumably through amelioration of point defects and defect complexes. The use of metastable alloy materials within device structures can expand the range of optical and electronic properties. The flexibility in materials design afforded by metastable materials opens opportunity for exciting new device areas that drives efforts to understand and optimize their synthesis, stabilization and optimization. 30

31 Acknowledgments: This research was primarily supported by NSF through the University of Wisconsin Materials Research Science and Engineering Center (DMR ). The authors would also like to acknowledge Ryan Lucas (MS, Chemical Engineering, UW-Madison) and his thesis work for development of the chemical models described in Section

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