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In Situ Characterization of Epitaxy
29
In Situ Characterization of Epitaxy April S. Brown DEPARTMENT OF ELECTRICAL AND COMP UT ER ENGI NE ERING, PRATT SCHOOL OF ENGINEERING, DUKE UNIVERSITY, DURHAM, NC, USA
Maria Losurdo NATIONAL C OUNC IL OF RESEARCH, INSTITUTE OF INORGANI C METHODOLOGIES AND OF P L A S MA S , CN R - I M I P, VI A O R A B O N A 4, 70 12 6 B A R I , IT AL Y
CHAPTER OUTLINE 29.1 Introduction ............................................................................................................................. 1169 29.2 Measurement Modalities ....................................................................................................... 1171 29.2.1 Photon-Based Techniques (or Optical Probes) ......................................................... 1172 29.2.1.1 Reflectometry and Interferometry .................................................................... 1172 29.2.1.2 Spectroscopic Ellipsometry ............................................................................... 1174 29.2.1.3 Reflectance Anisotropy Spectroscopy .............................................................. 1185 29.2.2 Particle-Based Techniques (or Diffraction Probes)................................................... 1190 29.2.2.1 Reflection High-Energy Electron Diffraction ..................................................... 1190 29.2.2.2 X-Ray Diffraction and Scattering...................................................................... 1198 29.2.2.3 Reflection Mass Spectrometry.......................................................................... 1198 29.3 Future Techniques................................................................................................................... 1203 References......................................................................................................................................... 1204
29.1 Introduction It is difficult to imagine the development of molecular beam epitaxy (MBE) or metal–organic chemical vapor deposition (MOCVD) without the extensive use of in situ diagnostics. During the past four decades, these techniques have evolved with the epitaxial tools development and use. This chapter describes key in situ characterization approaches applicable to MBE and MOCVD, and provides examples of their use aimed toward (1) revealing fundamental processes underlying the growth of planar and nanostructured films, (2) process characterization for device applications, and (3) closed-loop feedback control of layer thickness and composition. Handbook of Crystal Growth. http://dx.doi.org/10.1016/B978-0-444-63304-0.00029-7 Copyright © 2015 Elsevier B.V. All rights reserved.
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Impinging atomic beams
Crystal surface lattice site Surface diffusion
Desorption Surface diffusion
Ts substrate
Lattice incorporation
Overgrowth
Interdiffusion Surface aggregation (nucleation)
FIGURE 29.1 Surface processes during molecular beam epitaxy. Ref. [1].
When considering these techniques, we must first understand their use in terms of similarities and differences in the epitaxial process and growth environment for MBE and MOCVD. Epitaxy is, fundamentally, a surface process, and therefore techniques designed to reveal the underlying molecular/atomistic processes are ideally differentially sensitive to surface chemical and physical properties. The near-surface region is, however, significantly different for MBE, a physical vapor deposition approach carried out in an ultra-high vacuum environment, and MOCVD, a chemical vapor deposition approach carried out in a gas flow environment typically near or at atmospheric pressure. The decomposition of metal–organics and hydrides can happen on or very near the surface, and the surface boundary layer has concentration gradients of incident species and products. Figure 29.1 shows a schematic of the key surface processes determining film composition, uniformity, microstructure, and defect density. Although this figure is specific to the MBE process in terms of the incoming flux from atomic or molecular beams, the surface processes are the same for MOCVD with, as stated earlier, the addition of chemical reactions at the surface/ near-surface region. Hence, considering the growth of GaAs as an example, measuring the concentrations of surface species, such as gallium (Ga) adatoms and arsenic (As) molecules, as well as the rates of key processes, such as diffusion, nucleation, and desorption, provides crucial insights into the growth process and, therefore, means of modification of growth conditions to achieved desired epitaxial layer properties. Common to both growth techniques, and crucial in determining the composition and defect densities of epitaxial films, is the fact that incorporation is mediated through a
Chapter 29 • In Situ Characterization of Epitaxy
InP
(2 × 1) θP = 1 ML
β2 (2 × 4) θP = 0.75 ML
InAs
σ (2 × 4) θP = 0.25 ML
MD (2 × 4) θP = 0.125 ML P atom
γ (2 × 4) θAs = 1 ML
β (2 × 4) θAs = 0.75 ML
In-rich (4 × 2) θAs = 0.25 ML
[110] – [110]
In atom
α (2 × 4) θP = 0.5 ML
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As atom
α (2 × 4)
θAs = 0.5 ML
FIGURE 29.2 Schematic representation of the atomic arrangement for the different surface reconstructions of InP and InAs (001). The coverage of V-group element atoms, expressed in monolayers (ML), is indicated with the corresponding reconstruction. Note that the more In-rich InP surface (MD (2 4)) contains In-P mixed dimers along ½110. Ref. [2].
reconstructed surface. The reconstructed surface is a consequence of surface energy minimization and is established by growth temperature and the relative abundance of group III and group V surface species. Figure 29.2 shows atomic configurations associated with a range of InP and InAs surface reconstructions as a function of the relative arsenic, As, or phosphorus, P, coverage (qP or qAs) [2]. The dimer density and orientation (group V or III dimers and/or heterodimers) have a significant impact on incorporation and surface diffusion. As we show in this chapter, a range of in situ and real-time monitoring techniques is available that enables the characterization of surface crystal and electronic structure, composition, morphology, strain, and surface dynamic processes. With the advent of recent interest in creating nanostructures also comes a refocusing of in situ analysis techniques from the growth of planar structures to nanostructure formation and evolution. Such refocusing will certainly lead to new techniques as well. The organization of this chapter is based on the fundamental modality of a class of in situ techniques, some of them probing the gas phase in the near-surface reaction region and some probing the surface of the growing sample directly, with a description of the approach and examples of use.
29.2 Measurement Modalities We begin the description of techniques and applications exploiting light–sample interactions because these approaches are extremely powerful and applicable to both MOCVD and MBE growth environments.
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29.2.1
Photon-Based Techniques (or Optical Probes)
Optical techniques can be exploited over wide pressure ranges and can be tuned spectrally to access specific ranges of depths in samples. A comprehensive review of linear and nonlinear light–sample interactions in relation to in situ diagnostic techniques has been written by Pemble et al. [3]. A number of optical techniques has been developed and explored for use in revealing key surface processes during epitaxy, including dynamic optical reflectivity, spectroscopic ellipsometry (SE), IR absorption spectroscopy, laser light scattering (LLS), reflectance difference spectroscopy (RDS) or reflectance anisotropy spectroscopy (RAS), and second harmonic generation (SHG). As Pemble et al. [3] point out, the desire to enhance surface-to-bulk response with these techniques led to their classification as “epioptic” techniques by McGilp during the late 1980s [4], an unfortunate naming resulting from the dual reference of “epi” to optical surface science and epitaxial growth. These techniques all hinge on fundamental light–matter interactions that are described by frequency- and wave vector-dependent surface and bulk polarization responses to incident electromagnetic radiation. The polarization is modified through the susceptibility comprised of linear (e.g., reflection and absorption) and nonlinear (e.g., second-harmonic generation) terms. In LLS, the measured property is the diffusive scattering that occurs if the surface becomes rough. SHG is based on the secondharmonic light that is generated when an intense photon beam interacts with the sample. In RDS, the measured property is the sample anisotropy, and in SE the change of light polarization is characterized. The application of nonlinear techniques to characterizing growth is still rare because spectral capabilities are not readily available. The linear response is key to three important and highly successful means of in situ analysis: dynamic optical reflectance (or laser interferometry), SE, and RDS or RAS. Herein, we concentrate on the linear techniques, SE and RAS, that exploit the polarization of light. RAS is surface specific because the surface has different symmetry than the bulk. The sensitivity of RAS is now significantly better than 0.01 monolayer (ML). Although surface analysis is necessary for understanding growth mechanisms, there are also “bulk” properties (or, more appropriately, “thin film”), such as thickness, composition, and buried interfaces, that must be characterized using bulk-oriented probes such as spectral reflectometry and SE. Reflectance and SE are described in detail next, with examples of their use as “bulk” techniques, and RAS as a more surface-specific probe.
29.2.1.1 Reflectometry and Interferometry A primary goal of in situ characterization is to obtain key device-relevant film characteristics such as thickness, composition, and homogeneity. Reflectance measurements are relatively simple to implement, requiring minimal modifications to MBE or MOCVD reactors [5]. Although the majority of in situ reflectance measurements reported in the literature use single-wavelength He–Ne laser light sources (laser reflectance), multiwavelength reflectance (spectroreflectometry) using broadband sources has also been
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FIGURE 29.3 (a) Typical laser interferogram acquired using the 633-nm laser during the metal–organic chemical vapor deposition growth of GaN; (A)–(B) is nucleation; (B)–(C) is annealing; (C)–(E) is coalescence, followed by homogeneous two-dimensional growth. (b) Typical interferogram acquired during the growth of the AlAs/GaAs/ AlGaAs multilayer using two different probing wavelengths. Rearranged from ref [6]
used as an in situ monitor of, for example, the MOCVD growth of GaAs, AlAs, and AlGaAs. The entire spectrum or selected wavelengths sensitive to different properties or film thicknesses/depths can be used for process control or for postgrowth analysis [6,7]. Normal-incidence reflectance can be used to monitor film growth by measuring the interference between light reflected from the film surface– and light reflected from underlying interfaces, assuming the coherence length of the light is greater than the optical thickness of the film. Figure 29.3 is an example of a typical interferogram recorded using an He–Ne laser during the MOCVD growth of gallium nitride (GaN) using Ga(CH3)3 trimethylgallium (TMGa) and ammonia (NH3) sources. The nucleation of GaN leads to the observed initial increase in reflectivity (A–B), whereas subsequent annealing at 1000 C in NH3 causes the formation of rough, hexagonal GaN islands, which are detected through an observed decrease in the reflectivity (B–C). At C, TMGa is introduced again, after the anneal, initiating the high-temperature growth of GaN. The increasing reflectivity at D is associated with the lateral and vertical growth of GaN islands until full coalescence is achieved (D–E) and, last, at E, conversion from three-dimensional to two-dimensional growth is observed. The amplitude and period of the interference are used to determine and control the refractive index, n, and thickness, d, of the growing GaN layer, using the following relationship: d¼
m pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi 2Dn n2 sin2 f
where m is the number of fringes in the selected wave number window and f is the angle of incidence. Furthermore, if the amplitude remains constant, a smooth surface can be inferred from the data, whereas damping of the interference amplitude indicates the development of surface roughness. The same approach also works for more complex structures, including the growth of alloys, as shown in Figure 29.3(b), which is the spectral reflectance from a three-layer test structure comprised of AlAs, GaAs, and Al0.5Ga0.5As. Compositional differences in
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the films show up clearly as different patterns in the image. Interestingly, the GaAs fringes at 673 nm are practically nonexistent because the preceding AlAs layer is very close to an even number of quarter-wave thicknesses, producing what is referred to as an absentee layer, allowing the monitoring of only the subsequent Al0.5Ga0.5As layer. The wavelengths producing the highest intensity fringes for the GaAs layer are those that terminate the AlAs in an odd number of quarter wavelengths, as shown at 805 nm. An advantage of spectral reflectance detection over single-wavelength monitoring is apparent in this example based on the flexibility to choose appropriate wavelengths to monitor that exhibit the highest sensitivity to layer thickness and interface structure for layers of arbitrary optical thickness.
29.2.1.2 Spectroscopic Ellipsometry SE has been used for decades to characterize the optical properties of a range of materials, including semiconductors, enabling the discovery of key phenomena relating thin-film synthesis and properties. A particular strength of SE is the ability to characterize changes in the thicknesses of surface layers with sub-0.1 Angstrom sensitivity [8]. A system schematic diagram is shown in Figure 29.4. A linearly 45-polarized source of tunable light (e.g., example from the deep ultraviolet to the near IR (191–2700 nm)) is incident onto the sample surface with a spot size from a few millimeters to hundreds of microns for the analysis of nanostructures. Ellipsometry measures modifications to the amplitude ratio, j, and phase difference, D, of the two polarized components (p- and s-) of the light reflected from the surface. For a single, semi-infinite material layer (two-phase system comprised of a substrate, or thick film, and the ambient assumed to be air), the polarization of the reflected light satisfies the Fresnel equation and the dielectric function can be extracted directly from the SE response. For a multilayer film, such as a semiconductor film on a substrate, which is thinner than the absorption depth of the incident
FIGURE 29.4 Spectroscopic ellipsometry schematic.
Chapter 29 • In Situ Characterization of Epitaxy
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FIGURE 29.5 Pseudodielectric function of GaN on sapphire; the different information that can be derived by the analysis of the various regions of the spectra is indicated at the top. On the right it is schematized how from fitting pseudodielectric spectra to a layered model, the various properties of the layer can be derived.
light, the extracted dielectric function, referred to as the pseudodielectric function hεi ¼ hε1 i þ ihε2 i and represented with brackets, hi, is given by the following relation: "
0
00
hεi ¼ hε i þ ihε i ¼ sin f 1 þ tan f 2
2
ð1 rÞ2 ð1 þ rÞ2
#
D E ¼ ðn þ ikÞ2
where r is tan JeiD and f is the incident angle of the light, which should be at the Brewster angle of the material under analysis and is, for most semiconductors, around 70 . The reflected light can be acquired as a spectrum or under kinetic (time-varying) conditions at one or more wavelengths across the spectrum. The time resolution is in the millisecond range. The pseudodielectric function is dependent on the composition, thickness, microstructure, and specific optical properties of the multilayer film. As described later, SE provides a means of creating a model of the film, including layer thicknesses, composition, and surface–interface “smoothness.” With kinetic data, the film’s evolving thickness and surface morphology, and the formation of buried interfaces and abrupt or graded overlayers can be observed, such as the evolution of the metallic adlayers present in the MBE growth of group III-rich III-N materials. Figure 29.5 shows the real and imaginary parts of hεi for a GaN film, as a representative example, and how the different photon energy region of the spectrum relate to the film’s optical properties, thereby providing information on different film properties [9,10]. Although SE is a powerful technique for in situ and real-time characterization of growth, the use of complementary data for calibration purposes with SE is essential for achieving useful results because of its model-based nature. The most general method for modeling layered structures including interfaces and imperfect surfaces is the use of an effective-medium approximation (EMA) [11,11a,11b]. This model describes materials as a composite of regions, each with its own dielectric response. As an example, a rough surface is described as a mixture of
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material consisting of the film and voids. Different EMA models have been developed. The most common are the Bruggeman (BEMA) and Maxwell Garnett (MG) approximations. The MG theory applies to composites in which the inclusions are a small volumetric fraction of the host material and are well separated. The Bruggeman formula is symmetric with respect to interchanging the components, which is attractive for dealing with materials of comparable volume fractions in the mixture and of any shape. The BEMA applies to the modeling of surface adlayers and roughness because the pseudodielectric function depends sensitively on the model, especially near the material critical points (i.e., the bandgap and other higher absorption maxima characterizing the band structure) [12]. An important consideration in using an EMA is the “size” of the composite regions; if the sizes are comparable with or larger than the wavelength l/n of incident radiation, then scattering is important and an EMA is not appropriate. The EMA does not apply to modeling alloys or interfaces with atomic-scale detail, such as the atomic content in an alloy or interdiffusion across an interface. Dielectric function models of alloy materials are created through parametric models comprised of Gaussian-broadened polynomials corresponding to each of the critical points. Recent work in SE modeling compares errors associated with the application of the EMA, alloy, or graded-layer models across interfaces where atomic-scale materials variations exist [13]. Existing alloy material models can be implemented and modified to describe the optical properties and thicknesses of alloy layers. SE has been applied successfully to characterize and control the growth of many materials. To give a broad perspective of its use and potential, we focus on applications that have very high composition accuracy requirements, such as the MBE growth of AlxGa1xAs and InxGa1xAs films lattice-matched to InP for high-speed electronics, and HgxCd1xTe films for infrared detectors [14]. Thickness control using SE was first achieved by Aspnes et al. [15] and was based on a virtual substrate approximation. This method constrains the underlying epitaxial layer parameters into a virtual “substrate” and only models, or fits, the properties of the growing layer at the surface. A measure of the growth rate is obtained directly. Figure 29.6 shows an example of real-time monitoring of the MBE growth of GaN on silicon carbide (SiC) enabling GaN thickness control. For every wavelength below the bandgap of GaN, where the epitaxial film is transparent, oscillations in the dielectric function (or the ellipsometric parameter J and D), as shown in Figure 29.6, are recorded as a function of growth time. The oscillations are a result of the change in thickness of the epitaxial layer, which has a different index of refraction than the “substrate.” Second, the thickness of the layer represented by the period of the oscillations is a function of the optical constants of the growing layer, wavelength, and the angle of incidence; using the period and amplitude of the oscillations, the refractive index and thickness can be determined. Last, as growth proceeds, the amplitude of the oscillation decays more rapidly for shorter wavelengths, and disappears altogether for optically thick layers. The latter phenomenon emphasizes the importance of the spectroscopic kinetic mode for accessing wavelength-dependent information. Indeed,
Chapter 29 • In Situ Characterization of Epitaxy
1177
2 eV
4.5 eV
0
2000
4000
6000
8000 10,000 12,000 14,000 16,000 Time (s)
FIGURE 29.6 Typical temporal evolution of the real and imaginary parts of the pseudodielectric function recorded at two different probing photon energies of 2 eV and 4.5 eV during molecular beam epitaxy growth of GaN on silicon carbide.
progress in fast-acquisition characterization and modeling capabilities has allowed new approaches to characterizing epitaxial mechanisms, as described later. The initiation of epitaxy is a crucial process in which the surface must be prepared for epitaxy by the removal of its native oxide (for III–V materials), followed by film nucleation. Nucleation determines microstructure and depends on surface chemical and electronic properties. Using SE, we studied the impact of both the oxide removal and the unintentional nitridation of SiC substrates prior to GaN nucleation on the resulting film properties [16,16a,16b,16c,16d]. Such an experiment is exactly suited to the strengths of SE, in which sensitivity to the presence of surface overlayers can be very high. Oxide removal is determined with SE for absorbing films by seeking maxima and minima in the real and imaginary parts of hεi, for GaN above the band edge, as a function of process conditions. For nonabsorbing materials, the shift in interference fringes between the layer and its substrate, and the variation in their amplitudes, can be used to characterize the presence and absence of overlayers [17]. In the case of heteroepitaxy of GaN on SiC, our work specifically demonstrated the effectiveness of a commonly used oxide removal technique: the exposure of the oxidecovered SiC surface to cycles of Ga deposition and desorption at a high temperature (825 C), to reduce and desorb the oxide as volatile GaO. The process can be evaluated by observing the SE trajectory (Figure 29.7(a)) and noting the near convergence of the Ga desorption signal for the second exposure cycle and the adsorption signal for the third cycle. (Note that the cycle describes the desorption/adsorption of Ga on the surface.) This indicates that the surface is nearly equivalent, in comparison with the same signals for the
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FIGURE 29.7 (a) Spectroscopic ellipsometry trajectory during oxide removal. (b) Impact of Ga oxide removal on the silicon carbide (SiC)–GaN interface. (c) Transmission electron micrograph of a GaN cubic inclusion in buffer layer. Ref. [18].
first and second cycles, and provides evidence that the oxide is removed. Using an array of techniques, we found that oxide removal depends on the integrated Ga flux to the surface, the number of exposure cycles, and the specific polytype of the SiC substrate (4H- or 6H-), as well as its polarity. Furthermore, the Ga dosage during the oxide removal phase affected the interface formation during the subsequent growth of GaN on the Gaprocessed SiC. Figure 29.7(b) shows an SE-derived model of the interface. The presence of cubic phase (c-GaN) inclusions was verified, as shown in Figure 29.7(c) using transmission electron microscopy (TEM) [18]. In addition, nitridizing the surface after oxide removal was found to be crucial to GaN nucleation and coalescence, resulting in part from the competition between unintentional nitridation of the SiC surface and GaN nucleation before coalescence. Using a relatively low-temperature (200 C) nitridation step for 4H-SiC (0001)Si yielded a well-ordered Si3N4 layer (<0.4 nm), resulting in improved Ga wetting and lower cubic-phase inclusion density. Figure 29.8 shows J-D trajectories (at 3 eV) during GaN growth on SiC nitridized under different conditions. The faster increase in D results from more effective Ga wetting and faster coalescence, leading to a lower defect density. Comparing SE spectra at coalescence (corresponding to w12 nm), this GaN nucleation layer has a steeper absorption edge and narrower exciton feature. These studies illustrate the usefulness of the J-D trajectory, corresponding to the J-D values at a single wavelength and as a function of time, and using its shape to describe or infer a variety of synthesis phenomena and properties, most simply the vertical homogeneity of the film’s optical properties during epitaxy (Figure 29.9). A cyclical trajectory observed at 2.7 eV during the growth of a 0.6-mm-thick GaN film is observed in Figure 29.9(a), indicating homogeneous optical properties during growth. In contrast, the J-D trajectory observed for the film grown on a poorer quality nucleation layer (nitridation
Chapter 29 • In Situ Characterization of Epitaxy
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FIGURE 29.8 Real time trajectory in the j-D plane at the photon energy of 3 eV for GaN nucleation at the silicon carbide substrate temperature of 710 C on SiC nitrided at: (a) 200 C in RP-MOCVD, (b) 200 C in MBE, (c) at 700 C in MBE and (d) 700 C unintentionally in MBE. The C-point indicates the coalescence point. The different shape of trajectories indicates different nucleation of GaN depending on SiC nitrided surface. Ref. [19].
at higher temperature) shifts continuously toward greater values of J (Figure 29.9(b)), indicating a continuous refractive index change. The observed narrowing in the D “loop” is the result of an increase in film absorption resulting from defects in the growing film. We have also studied the epitaxy of GaN on HVPE GaN (0001) templates and described the oxide removal and the impact of the Ga/N flux ratio and growth temperature on the inferred GaN growth mode [19]. Our work demonstrated the sensitivity of SE in optimizing the temperature for the thermal oxide desorption from a GaN surface in MBE. Considering the incongruent thermal preferential loss of nitrogen from GaN at high temperature, it is crucial to find the right temperature and time in order to complete oxide desorption without inducing roughening of the GaN surface. This was achieved using SE as shown in Figure 29.10 in which hεi of GaN (with the native oxide) is captured at various temperatures at 4 eV. At 710 C, the flatness of hεi indicates that the temperature is insufficient for thermal desorption of the oxide, whereas at 750 C, the hε2 i decrease signals native oxide removal followed by surface roughening after oxide removal and as the temperature is increased. Hence, an optimal end point associated with the transition between surface cleaning and roughening can be identified. A thermal decomposition diagram based on the change in hε2 i—that is, dhε2 i=dT (at 4 eV)— can be constructed and is shown in Figure 29.10(e). The rate of surface roughening increases around 750 C as a result of the removal of the oxide, as corroborated with
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FIGURE 29.9 Trajectories associated with GaN film evolution on different buffer layers: 200 C nitridation (a) and 710 C nitridation (b).
(a)
(b)
No reacƟon
O-desorpƟon/roughening
710°C
(c) 2.1
4eV 1.95
O-desorpƟon
Roughening
4eV
2.05
1.85
2 1.9
1.95
1.8
<ε2>
<ε2>
<ε2>
Roughening 760°C
1.9
1.85
1.85 1.75
0
100
(d)7
200
300 400 Time (s)
500
600
Cleaning end point
8 1.8 0
50 100 150 200 250 300 350 400 450 500 Time (s)
(e)
1.8 0
200
400 600 Time (s)
800
1.000
6
AŌer annealing
5
<ε1>
4 5 3
<ε2>
IniƟal
Δε2/Δt(s-1)
6
Oxide 4
GaN Sapphire
2
1 3 2
3
4 5 Photon energy (eV)
6
FIGURE 29.10 (a–c) Real-time variation of hε2 i during annealing at various temperatures during molecular beam epitaxy of a GaN template. (d) Spectroscopic ellipsometry spectra of the GaN template before and after native oxide removal. (e) Rate of variation of hε2 i with the increase of temperature from which regimes of oxide desorption and surface roughening are identified and corroborated also by reflection high-energy electron diffraction patterns. Rearranged from ref. [19]
Chapter 29 • In Situ Characterization of Epitaxy
(a)
1181
(b)
FIGURE 29.11 Real-time variation of hε2 i during molecular beam epitaxy growth of GaN at 750 C under various III/V ratios. (b) Corresponding (J–D) trajectories identifying the different III/V flux ratio-dependent growth regimes.
reflection high-energy electron diffraction (RHEED). At w820 C, the roughening rate increases again, but more rapidly, as a result of Ga desorption enhanced by defectlocalized surface decomposition. Figure 29.11 shows the hε2 i variation in time (Figure 29.11(a)) and the corresponding J-D trajectories (Figure 29.11(b)) obtained during growth over a range of Ga/N flux ratios: from N-rich to Ga-rich with Ga droplets present on the surface. The changes observed in the J-D trajectories are related to the formation of Ga adlayers that terminate the growth surface. Well-known GaN growth phenomena related to Ga/N flux ratios are apparent. N-rich growth yields a trajectory remaining near its initial position, but shifting toward greater J values as a result of surface roughening. As the Ga/N ratio increases, the growth mode evolves from a layer-by-layer mode with pit formation to the step-flow growth mode achieved with a stable Ga overlayer. We have been able to characterize and quantify the Ga adlayer formation and its thickness (w2.5 ML) using SE studies of Ga adsorption and desorption from various polar and nonpolar surfaces by monitoring the change in hεi at 4 eV [20,20a,20b]. The same process has been applied to In overlayer formation as well [21]. These findings have been replicated/extended by a number of groups [22,22a,22b]. Thin-film nucleation and grain growth have been explored with SE in application to the synthesis of a variety of substrate-supported materials, including microcrystalline Si [23], growth and bonding in diamond films [24], Ge homoepitaxy [25], and, in addition to our work discussed earlier, GaN grown by MOCVD [26]. The shape of the J-D trajectory provides, in many cases, an effective means of differentiating geometric models. This was demonstrated recently during Ge homoepitaxy [18]. This study effectively used a graded-layer EMA model that included both the geometric shape of the growing
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pyramidal islands and the distribution of the ensemble properties of these islands. Different island shapes and distributions were differentiated with this approach. Nucleation studies specific to III-N heteroepitaxy have focused primarily on strain relaxation. Early work describes the growth of AlN on GaN and GaN on AlN in terms of common dynamic features comprised of platelet formation—that is, the nucleation of islands of a few monolayers in height and 10–20-nm lateral extension, subsequent partial coalescence, and the formation of dislocations at platelet edges. Reversible relaxation occurs through the dynamics of the platelets and the filling of troughs between them. Plastic relaxation results from dislocation formation [27]. Nucleation dynamics depend critically on the V/III ratio and growth temperature during growth. An example of this is clear in recent work extending the description of island dynamics applied to the catalystfree synthesis of GaN nanowires (NWs) using N-rich growth and a high substrate temperature. In this case, initial GaN spherical islands are nucleated, which exhibit shape transformations, thereby minimizing strain energy—first through a pyramidal structure, followed conversion by to a NW shape that then grows [28]. The characterization and modeling of nucleation is, of course, an example of using ellipsometry at the nanoscale. Numerous current devices exploit low-dimensional nanostructures, for example, quantum dots (QDs), quantum wires, or nanocolumns (NCs). In recent years, SE has been used extensively to investigate the growth mechanisms of these nanostructures. As an example, Wang et al. [29] investigated the growth mechanisms of InN NCs on GaN templates using ellipsometry and RHEED. The SE characterization, as shown in Figure 29.12, showed that the InN NCs epitaxy was initiated from the growth of InN QDs in the Stranski–Krastanov growth mode. The InN nuclei were formed at an InN coverage of approximately 10 ML. The subsequent InN growth NC growth was found to be based on In adatom migration to the NCs and then diffusion up the sidewalls. The prospect of achieving self-assembled and coherent QD arrays based on the growth of highly lattice-mismatched systems in the Stranski–Krastanov growth mode is the driving force for a number of studies (see, for example, [30] and references therein). In this context, SE has been useful in obtaining a better understanding of the growth of QDs and, ultimately, their controlled synthesis by both MBE and MOCVD. As an example, Steimetz et al. [31] concentrated on the growth of InAs QDs on GaAs. Although phenomenologically the SE signal directly yields information on the coverage and roughness resulting from the evolving QD ensemble density and geometry, quantitative analysis requires careful application of the appropriate EMA model. Using an EMA, the optical response of the QDs can be treated as surface roughness associated with anisotropic, noncoalescing indium arsenide (InAs) clusters if their characteristic lengths can be assumed to be smaller than the wavelength of light (i.e., light-scattering effects can be neglected). To model the mean geometry of the QDs with an MG EMA, the main axes (x, y, h) of these ellipsoids are adjusted to the averaged QD parameters, base length x along the ½110 direction, base length y along the [110]-direction, and QD height, h. Typically, the dielectric function of the QDs is assumed to be the same as the bulk
Chapter 29 • In Situ Characterization of Epitaxy
1183
Quantum dots formation Embrionic NCs Growth of NCs Point D [nm] 15 0 0.5
Point E [nm] 30 0.0
1.0
1.5
1.5
2.0
2.5
(a) (b) (c)
0
0.5 1.0
1.5
2.0
[μm]
2.5
(d)
0.0
0.5 1.0
1.5
2.0
2.0
2.5
0.5 1.0
2.5 [μm]
(e)
Lattice constant (Å)
3.6
Free standing InN 3.4
3.2 55
Free standing GaN Intensity of RHEED 3.5
<ε ]>
45 3.0 40
<ε1>
RHEED intensity (a.u.)
50
35
2.5
30 2.0
25 20
1.5 0
50
100
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200
250
Growth time (s) FIGURE 29.12 In situ investigation of the growth of InN nanocolumns by reflection high-energy electron diffraction (RHEED) and spectroscopic ellipsometry. (a) Evolution of the in-plane lattice constant of InN as a function of growth time. (b) In situ change of RHEED intensity and of the real part of the pseudodielectric function, hε1 i, at l ¼ 1600 nm as a function of growth time. (a)–(e) mark significant growth transition points. AFM and scanning electron micrographic images of the nanocolumns are also shown. Ref. [29].
material, which is not necessarily a good approximation, because quantum effects may yield a size-dependent dielectric function [32]. Therefore, being able to determine or parameterize the dielectric function of nanostructures as a function of size and geometry remains a key challenge. Figure 29.13 shows typical results obtained by applying an MG EMA analysis to InAs QDs grown on GaAs. The QDs are assumed to be comprised of 3 ML of InAs seeded on a 1-ML-thick InAs wetting layer that covers the GaAs substrate. The height, h, of the QDs corresponds to a thickness, d, which is the effective roughness;
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(b)
(a)
GaAs substrate
25
0
TMI on 0.085 Pa 0.17 Pa 0.34 Pa
5
20
Expected for layer-by-layer growth
20
<ε2>
15
20 4.8eV
<ε2>
h in ML
10
18 Influenced by light scattering
16
5 QDs of height h on wetting layer: calculated ellipsometry spectra
0
2
3
4
10 5
15
20
25
30
35
40
45
Time [s]
Photon energy [eV]
FIGURE 29.13 Spectroscopic ellipsometry spectra of InAs QDs modeled using a Maxwell–Garnett EMA. Both density f and height h of the QDs are varied with the constraint fh ¼ 3 ML. (b) hε2 i variation during InAs QDs growth at three different growth rates. Ref. [31]
and the volume fraction, f, of InAs is determined by constraining the product: fh ¼ 3 ML. The ellipsometric hε2 i spectra are modified only marginally by the initial layer-by-layer growth of the 1–2-ML wetting layer, but are changed significantly when the QDs are nucleated resulting from the roughness, which decreases the amplitude significantly in the vicinity of the E2 bulk critical point (i.e., at approximately 4.5 eV) (Figure 29.13(a)). The temporal variation of hε2 i (Figure 29.13(b)) indicates that the initial growth of the strained InAs proceeds in two-dimensional island growth mode. The sharp decrease observed in hε2 i indicates the transition from the Frank–van der Merwe growth mode to the Stranski–Krastanov growth mode. As stated earlier, as long as the island dimensions are smaller than the wavelength of light, the effective medium theory describes the optical response of the QD layer adequately. For larger islands, light-scattering effects become important. Recently, the integration or growth of metal nanoparticles (NPs) with semiconductors for plasmonic or optical antenna applications has emerged as an exciting new device platform of interest for sensing, catalysis, and optoelectronics. One example of the use of SE to characterize these metal–semiconductor integrated systems is the characterization of the deposition of Au NPs on Si. This system is complicated by interfacial reactions leading to gold silicides (AuSix). Figure 29.14 shows the evolution of the pseudoextinction coefficient as a function of Au sputtering time. The surface plasmon resonance peak associated with incident wave coupling into the localized surface plasmon modes of the evolving Au NP ensemble redshifts as the average particle size increases, as expected. As the Au NP coverage increases, the E1 and E2 critical points of the Si substrate are damped. Models were developed based on corroborating XPS and TEM data, and on including an evolving interfacial silicide layer that grows in thickness as the NPs grow in size [33]. A comprehensive discussion of the use of SE for the synthesis of plasmonic platforms was published recently by Oates et al. [34] and is a vital resource in this area.
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3 SPR
25 nm
2
E1
20 nm
E2
18 nm
1
15 nm
1
(a)
15 nm
(b)
2
3 4 5 Photon energy (eV)
(c)
18 nm
20 nm
6
(d)
25 nm
FIGURE 29.14 Pseudoextinction coefficient, hki, of the NPs ensembles of various diameters during sputtering of different amount of gold on a silicon substrate. The corresponding 500 500-nm AFM is also shown at the bottom. The average diameters are from AFM line profiles scanned at various points of each image. Ref. [33].
29.2.1.3 Reflectance Anisotropy Spectroscopy Like SE, RAS, also referred to as reflectance difference spectroscopy (RDS), is suitable for both MBE and MOCVD environments and has been well developed during the past two decades. RAS is based on determining the difference in reflectance of normal-incidence light between two orthogonal directions in the plane of the sample surface, Dr/r, in the range of 105: Dr r½110 r½110 ¼ r r½110 þ r½110
A system schematic is shown in Figure 29.15. In materials in which the bulk is optically isotropic, RAS becomes extremely surface sensitive because only the surface can produce an anisotropic signal. The anisotropic surface dielectric response is caused primarily by oriented surface dipoles originating primarily from dimer bonds in the reconstructed surface. From both the real and imaginary part of the RAS signal, and the bulk dielectric function of the underlying semiconductor, the surface dielectric function anisotropy Dε0 can be calculated according to Dε0 d ¼
lðεb 1Þ Dr $ 4pi r
where d is the thickness of the surface layer, l is the wavelength of incident light, and εb is the bulk dielectric function.
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FIGURE 29.15 Schematic of reflection anisotropy spectroscopy system. http://www.physik.tu-berlin.de/institute/IFFP/ richter/new/research/method_ras.shtml.
The sampled size is typically in the square millimeter range, and measurements can be modulated at the output using a piezoelastic modulator, or at the input using an electrooptic modulator. As stated earlier, RAS is highly surface sensitive because it works on the basis of the symmetry reduction associated with surface reconstruction works and, for cubic materials, the bulk isotropic linear contributions cancel [3]. The difference in the near-normal incidence reflectivity results from surface structure (i.e., the reconstruction), as stated earlier, and surface chemistry. As a result, it has been highly effective in determining the surface concentrations of adsorbed species. In addition to surface species identification and relative concentrations, interfaces can also be assessed because their symmetries are broken as a result of potential gradients of strain fields. Like SE, the effectiveness of using RAS to identify surfaces species rests on cross-technique calibrations and studies. RAS exploits RHEED (measured for MBE) effectively and has enabled the assessment of surface reconstruction during MOCVD growth. RAS is also supported by complementary ab initio calculations [35,35a,35b] and models [36]. RAS was first applied to MBE in 1991, and was determined early on to be sensitive to 0.01 ML [37]. In MBE, changing the surface reconstruction is readily achieved through tuning the surface stoichiometry, and early studies showed the clear relationship between RAS response and the As–Ga surface coverage. Aspnes et al. [38] mapped known MBE-based reconstructions determined by RHEED to RAS responses observed during MOCVD growth. This important first observation of reconstructions during MOCVD growth was obtained by mapping responses of GaAs in an ultrahigh vacuum to those in atmospheric pressure H2, He, and N2 environments, thus obtaining the first experimental verification of dimer formation during MOCVD growth [39]. RAS measurements are shown in Figure 29.16, comparing the change from an Asterminated (2 4) to a Ga-terminated (4 2) GaAs surface for MBE (top) and MOCVD
Chapter 29 • In Situ Characterization of Epitaxy
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(001) GaAs - MBE (2×4) → (4×2)
8
103∆[(R110-R110)/R]
4 0 4 0 –4
(001)GaAs-OMCVD AsH3→TMG
–8
6°→(111)A SINGULAR
–12
6°→(111)B 2
3 E (eV)
4
FIGURE 29.16 (Top) Spectral dependence of the change in RD signal as coverage of an (001) GaAs molecular beam epitaxy MBE surface at 580 C is changed from As-terminated (2 4) to Ga-terminated (4 2). (Bottom) Same, but for an (001) GaAs metal–organic chemical vapor deposition OMCVD surface at 370 C as the atmospheric-pressure ambient is changed from H2 containing 320 Pa AsH3 to H2 containing 13.6 Pa TMG. Ref. [38].
(bottom) growth under the conditions shown in the figure caption. Although the spectra are clearly different, it can be observed that 2.5 eV is a useful energy for characterizing this surface chemical change. This high sensitivity of such spectral fingerprints to reconstruction can be used to differentiate Ga–Ga and As–As dimers, because the maximum signal differences between the (2 4) As-terminated and (4 2) Ga- and Alterminated surfaces of GaAs and AlAs are found at 2.0–2.5 eV and 3.5 eV, respectively [33]. By slowly rotating (w0.1 Hz) a sample during MBE-based RAS measurements, the noise associated with fixed system issues, such as birefringent windows, could be minimized to obtain very high-quality data. In this case, the dielectric functions of the samples could be obtained from the RAS data and compared for different surface reconstructions (Figure 29.17). Using models of the electronic properties of the surface, the signals at 1.8 eV and 2.5 eV could be assigned to transitions related to Ga and As dimers, respectively [40]. More recently, RAS has been applied to GaN growth on Si to determine GaN thickness and refractive index [41]. Newer studies have extended the use of RAS measurements. Tanaka et al. [42] showed that carrier concentrations can be measured with RAS. n-type and p-type carrier concentrations from 1016 to 1018/cm3 were differentiated based on the ability of RAS to measure the surface electric field resulting from the linear electro-optic effect associated with E1 to E1 þ D1 transitions (near 3 eV) with respect to a reference undoped sample. Temperature-dependent measurements showed sensitivities of 1017/cm3 at 400 C to
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40 (001) GaAs: S, 580 °C 5 s, (4 × 2) 4s 3s 2s 1s
– ) d (Å) Im(ε110 – ε110
20
0
–20 (2 × 4) α (2 × 4) β, 510 °C –40 2
3
4
5
E (eV) FIGURE 29.17 Surface dielectric anisotropy spectra D(ε2d) of various reconstruction on (001) GaAs. Ref. [38].
1 1018/cm3 at 600 C [42]. Relating the signal to surface coverage, RAS has also been used to monitor dopant (As) segregation during Si growth [43]. Recent work by Bruckner et al. [44] showed that key details associated with As adsorption and termination of Ge, such as dimer orientation, as well as the surface step structure can be differentiated using RAS by careful experiments and complementary STM, XPS, and low-energy electron diffraction (LEED) characterization, as shown in Figure 29.18. Recent work has also shown that RAS can be used to monitor the hydrogen termination of Ge during annealing in N2 (Figure 29.19) [45]. Similar to RHEED (as described later), RAS signals exhibit periodic changes in time associated with periodic surface structural and chemical changes during layer-by-layer growth [46]. The nucleation of GaInP on Ge (100) has been studied, and surface morphological changes associated with growth mode changes from island nucleation to layer-by-layer growth were characterized [47]. Recent work has shown that RAS can be used to track critical aspects of Stranski–Krastanov-based growth of InAs QDs on GaAs [48]. Figure 29.20 shows the key processes that could be determined with measurement at 4.2 eV. The RAS signal increases with increasing V/III ratio for InAs QD formation. Also, as a result of the observation that the signal intensity increases with As concentration for InAs growth and decreases with As concentration for GaAs growth, In diffusion could be followed during QD growth. By associating the critical thickness with the rapid increase of QD density and determining the second-order derivatives of the RAS spectra with respect to wavelength, changes in the GaAs band edge light-hole- and heavy-hole-related transition energies could be followed during wetting layer formation. The linear redshift in these energies is associated with In incorporation during two-dimensional growth. Kinks in the derivative spectra appear on transition to the
Chapter 29 • In Situ Characterization of Epitaxy
1189
FIGURE 29.18 In situ RAS of Ge (100):As 6 with predominant (2 1) (red) and (1 2) (green) surface reconstruction domains where dimers are oriented parallel (Ge (100):Asjj) or perpendicular (Ge (100):Ast) to the step edges, respectively. For comparison, the flipped and scaled (factor 1.38) RA spectrum of Ge (100):As 6 with predominant (2 1) reconstruction is also depicted. The insets illustrate the major As dimer orientation on the surface with respect to the step edges. (For interpretation of the references to color in this figure legend, the reader is referred to the online version of this book.) Ref. [44].
FIGURE 29.19 In situ RAS spectra of the monohydride-terminated (thin red line) and the clean (thick black line) Ge (100) surface with 6 toward the [011] prepared in MOVPE ambient. The dash-dotted thin gray line represents the RAS spectrum of an ultrahigh vacuum-prepared Ge (100) surface and the dotted black line corresponds to the scaled RAS spectrum of the MOVPE-prepared clean Ge (100) surface (i.e., thick black line). Vertical lines indicate the critical point energies of Ge (100) at 320 K. The STM image (Vsample ¼ –1201.2 mV, Iz ¼ –0.650 nA) corresponds to the monohydrideterminated Ge (100) surface. (For interpretation of the references to color in this figure legend, the reader is referred to the online version of this book.) Ref. [45].
three-dimensional or QD growth mode. Continued changes in the spectra can be related to the diffusion and incorporation of In as a function of growth conditions [49]. Lastly, recent work reported the use of microreflectance difference spectroscopy to resolve RAS signals at a resolution of square microns [50]. Laterally patterned Si was used as a substrate to grow GaP with layers of alternating orientations as a result of differences in the GaP sublattice occupancy from antiphase domain differences created at steps. By comparing spectra above and below the band edge of GaP (2.78 eV), an anisotropy
HANDBOOK OF CRYSTAL GROWTH
Re(dr/r) (10–3)
3
2
1
0
V/III ratio during InAs deposition {6} Restored GaAs E V/III = 0.5 {2} GaAs β2(2×4) F V/III = 1 G V/III = 2 {3} Start of QD {1} InAs QD formation dissolution growth interuption
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{5} Capped QDs {4} InAs surface
InAs 0
20
WT
Growth marker
GaAs CL
40 60 Growth time (s)
80
100
In migration {1}
{2}
{3}-{4}
{5}
{6}
FIGURE 29.20 Time-resolved RAS signal taken at 4.2 eV during the InAs QD and GaAs capping layer (CL) growth. Samples differ only in the partial TBA pressure during InAs growth and during the waiting time (WT) for QD formation. The beginning of InAs deposition was set as time 0. Proposed model of the growth {1}–{6} according to RAS data is shown at the bottom. Ref. [48].
topographic map of the surface and buried interface could be generated, as shown in Figure 29.21 [51].
29.2.2
Particle-Based Techniques (or Diffraction Probes)
29.2.2.1 Reflection High-Energy Electron Diffraction Particle-based techniques have been exploited only in MBE as a result of the requirement of an ultrahigh vacuum environment. RHEED has been the workhorse and benefited from the significant LEED body of work in crystallography. The geometry of RHEED used in MBE exploits the surface sensitivity realized by glancing incidence. Because RHEED has been used for so long and was developed hand-in-hand with the MBE process, strong reviews exist in the literature; hence, this topical coverage is light and focuses on specific applications. As RHEED has matured in concert with MBE, the full extent of the information that can be derived has grown significantly [52,52a,52b,52c,53]. An excellent early review of RHEED appeared in 1990 by Joyce [54], a pioneer in both MBE and the RHEED technique.A brief description of the basis of the technique is given here (Figure 29.22). A perfect crystalline surface gives rise to integral diffraction lines, and the reconstructed surface, to fractional ordered beams. The intensity of the beams contains extensive information on the perfection and crystalline structure of the surface. Surface imperfections, such as domains or steps, broaden the reciprocal lattice rods, thereby broadening and elongating the diffraction features. Splitting of the streaks can also occur when these features are ordered [55]. Representative RHEED and LEED patterns are shown in Figure 29.23 for III–V materials.
Chapter 29 • In Situ Characterization of Epitaxy
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FIGURE 29.21 Optical anisotropies maps for ten monolayers of Al0.5Ga0.5P followed by 500 nm GaP grown on laterally patterned silicon, obtained by fitting the RDS spectra of the structure. (a) map of the stripes height of the pattern. (b) map induced for the buried structure GaP/Al0.5Ga0.5P/Si. Ref. [51].
The RHEED signal is characterized by its intensity and phase. The intensity depends on a number of diffraction processes and, although often modeled using a kinematic approximation, is modeled more accurately as a multiple-scattering process including beam emergence effects, thermal diffuse scattering, normal diffuse scattering, and surface resonances [54]. The intensity of the diffracted beams and specular spot oscillates with time [57,57a,57b], with a period equal to the growth rate (i.e., the completion of 1 ML of growth). RHEED oscillations are therefore used extensively to calibrate the growth rate in addition to revealing surface static and dynamic processes [58]. Alloy composition can also be inferred from RHEED oscillations under conditions of group V-rich growth, in which all group III elements are incorporated. Taking AlxGa1–xAs as an example, the increase of growth rate with increasing Al flux is directly proportional to the composition, x.
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FIGURE 29.22 (a) Schematic showing a Ewald sphere with radius K0 cutting into surface reciprocal rods, leading to a diffraction pattern. (b) Top view of the geometric setup showing the reciprocal points along the perpendicular-to-beam direction are laying on the Ewald sphere, forming the zeroth zone streaks on the reflection high-energy electron diffraction screen. Both the Ewald sphere and the reciprocal mesh are for illustration purposes only and are not drawn to scale. Ref. [56].
A simple model of the origin of RHEED oscillations is based on the change in surface coverage with time as a single layer is grown. Assuming a two-dimensional layer-by-layer growth mode, the process is initiated with the nucleation of islands on the surface and the time-dependent filling of a single layer as the islands coalesce. As nucleation and growth proceed, the intensity of the signal decreases as the smooth surface roughens with island formation and growth, and then increases as the layer fills in. Damping of the oscillation results from the simultaneous growth and nucleation over multiple layers. The intensity changes in the beams are therefore proportional to the changing step density on the surface. Growth modes that develop steady-state step densities on the surface, such as step-flow growth, therefore yield no oscillations. In a seminal experiment, this model was used successfully to determine adatom diffusion lengths as a function of growth temperature (Figure 29.24) [54]. Using vicinal substrates with a known terrace width, the gradual transition from island nucleation to step-flow growth with increasing growth temperature was identified by the damping of oscillations. The growth mode change, in turn, was related to the increasing adatom diffusion length with respect to the terrace width. When the diffusion length is equal to or greater than the terrace width, step-flow growth is generally preferred as a result of favorable incorporation at the step edges. As shown in the Figure 29.24, this process can be modeled as a gradual transition between the growth modes. RHEED intensities are also found to increase in intensity, or “recover,” on the termination of growth. This observation was first interpreted as a smoothing of the surface resulting from the postgrowth rearrangement of atoms. As such, this effect is dependent on the sample temperature and the presence or absence of a group V flux. An important observation made by Yoshinaga et al. [59] was that the recovered intensity
Chapter 29 • In Situ Characterization of Epitaxy
1193
FIGURE 29.23 Reflection high-energy electron diffraction and low-energy electron diffraction (LEED) examples for III–V (1n00)(1 1) and (2 1) surfaces, with possible atomic arrangements. The reciprocal lattice of an unconstructed III–V (100)(1 1) surface is identical to that of the bulk plane. The vectors, defined by the (00) and (10) spots and the (00) and (01) spots, represent the reciprocal lattice vectors for the bulk plane, as visualized by LEED. For a reconstructed III–V (100)(2 1) surface, the two vectors defined by the (00) and (1/2 0) spots, and the (00) and (01) spots determine the reciprocal lattice of a surface layer. The gray square and rectangle represent the surface lattice cells. Ref. [52c]
depends on the specific phase of the oscillation signal at which the growth was terminated. In addition, the recovery was found to be comprised of a fast and slow component that were initially interpreted as the filling of the unfilled next to the last layer of the sample, and the longer timescale to breaking of bonds and other reactions associated with atomic rearrangement [59]. The ability to smooth the surface through growth interruption, the periodic termination of growth at temperature with an impinging group V flux, was subsequently exploited in many studies and led to new approaches of growth, such as migration-enhanced epitaxy and atomic-layer epitaxy. As Joyce [54] points out, however, simple interpretations of RHEED intensity in relation to surface smoothness can be misleading. For example, migration-enhanced epitaxy RHEED intensity changes will result from reconstruction changes associated with the change from As-rich to Garich growth for GaAs, for example, and not as a result of surface smoothing. RHEED studies have also been used to examine surface segregation and the resulting compositionally graded interfaces that result from growing a layer on top of an alloy with a surface-segregating component. For example, Joyce [54] observed that when shuttering
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FIGURE 29.24 (a) Reflection high-energy electron diffraction intensity oscillations showing the first maximum delay near the transition temperature on vicinal GaAs (001) misoriented by 2n toward [010]. The bottom trace was measured on a singular GaAs surface. (b) Schematic illustration to explain the growth mode transition that occurs on vicinal surfaces, and the origin of the first maximum delay. The grayscale represents the height of the surface. Ref. [54].
the Al cell during AlGaAs growth (i.e., growing GaAs on top of AlGaAs), the RHEED oscillation period increased as expected for the lower growth rate of GaAs, but through an intermediate stage with growth rate intermediate to that of AlGaAs and GaAs, and related to the difference in the cation surface diffusion rates. Later, Braun and Ploog [60] compared the RHEED oscillation behaviors for the growth of AlAs on both GaAs and AlAs with identical growth interruptions at the interface. They observed a negative phase shift for the growth of AlAs on GaAs, compared with that on AlAs, and in a similar experiment on the growth of GaAs, a positive phase shift for the growth of GaAs on AlAs [60]. The phase shift saturates after the growth of 11 ML for AlAs on GaAs, the so-called “normal” interface, and after approximately 1 ML for the “inverted” interface: GaAs on AlAs. By examining different diffraction conditions and dependences on substrate temperature and As overpressure, the results support a Ga segregation process that includes lateral segregation and smoothing.
Chapter 29 • In Situ Characterization of Epitaxy
1195
Despite the success in using RHEED oscillations to determine growth rate and diffusion lengths, in a review article published in 1990, Joyce wrote, “(RHEED) is a technique which is remarkably simple to apply, but is difficult to interpret and can be misleading in the hands of the unwary” [54]. The statement is based on an understanding of the complexity of the diffraction processes and the dependence of beam intensities on the specific diffraction conditions. Rocking curve characterization is the variation of the diffracted intensity of a beam as the incident angle of the primary beam is changed at a fixed azimuth. Such measurements support the need to base RHEED analysis on a multiple-scattering model. Two specific observations are related to this. The dependence of the intensity change with surface morphology depends on the diffraction conditions and processes. For example, the maximum in intensity does not necessarily correspond to a completion of a ML of growth, and oscillations with twice the periodicity can be observed with different diffraction processes that are out of phase. That said, kinematic approaches have been used extensively. Island sizes and step distributions on GaAs were quantified using a kinematic scattering analysis of the shape of measured diffracted beams [61,61a,61b,61c]. Recent work articulates the usefulness of an efficient MATLAB-based model [56]. The program can be used to calculate onedimensional line intensity profiles and quasi-two-dimensional streak intensity maps, and was shown to reconstruct successfully key features of the Ga-rich surface reconstruction of GaN under conditions of Mn adsorption (Figure 29.25). In Figure 29.25, two structural models are compared: the first (BL) substitutes Mn for Ga in the outer layer of a bilayer of Ga terminating GaN; the second (HD) substitutes Mn into the top layer and the Ga atoms rearrange into a 30 rotated and contracted state. Although the
FIGURE 29.25 (a)–(c) Side view (a) and top views (b and c) of the HD and BL models. The black rhombus indicates the surface nit cell. Orange hexagons (solid and dashed) indicate the Ga configurations (first and second layer, respectively). (d) Experimentally obtained reflection high-energy electron diffraction pattern along the ½1100 azimuth. (e and f) Simulated patterns for the HD and BL models, respectively. Ref. [56].
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FIGURE 29.26 Surface reconstruction maps for GaAs (001) (a) and GaAs1-xBix (001) (b) for substrate temperatures from 250 to 425 C and As2:Ga flux ratios from 0 to 3 (As2:Ga BEP ratio from 0 to 9.4). The growing GaAs1-xBix surface has an incident Bi BEP of 3 10–9 Torr. Ref. [62].
reconstruction (three times along the ½1100 and one time along the ½1120) is the same, the intensity modulation along the streaks is different, and comparison with experimentation indicates a better match to the HD configuration. RHEED-based surface phase diagrams are a useful means of condensing the dependence of reconstructions on growth conditions, typically substrate temperature, group V/group III flux ratio, and/or growth rate, and providing a map to guide crystal growth. A recent example (Figure 29.26) provides guidelines for the successful growth of GaAsBi. GaAsBi is particularly challenging to grow because of the size and electronegativity mismatches between As and Bi. Bi has a tendency to surface segregate and is a good surfactant at temperatures in the high 400 C range. At lower temperatures, incorporation is achieved but is typically less than w10%. The greatest incorporation occurs when grown with a (1 2) reconstruction. By comparing the reconstruction maps for GaAs and GaAsBi, it is seen that the (1 2) is not observed for GaAs growth and is therefore associated with a significant modification of the surface structure by Bi [62]. Another use of the surface phase diagram is to provide a reference for comparing growth conditions across equipment given that the substrate temperature and flux measurements will contain varying degrees of inaccuracy. Newstead et al. [63] suggested that referencing conditions to a boundary between reconstructions is a particularly good use of surface phase diagram information. One challenge to exploiting RHEED fully during MBE growth is the difficulty in carrying out measurements with substrate rotation. Growth rate measurements are
Chapter 29 • In Situ Characterization of Epitaxy
1197
FIGURE 29.27 Azimuthal reflection high-energy electron diffraction scan of the GaAs c(4 4) surface immediately before MnAs deposition. The corners of the surface nit cell are marked by circles [65].
inaccurate unless measured directly in the center as a result of the lack of rotation. With rotation, in addition to the change in intensity of the specular spot with azimuthal angle, measurement noise is introduced from vibrations and nonuniformities from substrate wobble and misorientation. One efficient approach to achieving RHEED measurements with rotation is to use gated measurements wherein the image is captured at the same angle during each rotation [64]. This technique enables the capture of azimuthal scans, as shown in Figure 29.27(a) [65]. The sample is rotated slowly to capture the intersection of the reciprocal lattice with the Ewald sphere. The diffraction pattern in a plane parallel to the surface can be determined by capturing the line intensity parallel to the shadow edge at a fixed reciprocal lattice distance. A half rotation is shown and a complete pattern is captured. An example of its use was the study of MnAs) nucleation on GaAs. Figure 29.27(b) shows the azimuthal RHEED scan of GaAs c(4 4) before exposure to MnAs. The evolution of the scan tracked different stages of the MnAs nucleation from random island orientation to oriented growth first along the [110] direction and then in the ½110 direction (at 2 ML).
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29.2.2.2 X-Ray Diffraction and Scattering Real-time in situ X-ray diffraction is based on measuring extremely asymmetric Bragg reflections [66,67] using slightly divergent X-ray radiation and a multichannel detector. Because X-rays penetrate gaseous environments, they can be applied directly to both MOCVD and MBE processes, providing important parameters such as composition, built-in strain, thickness, and mechanisms of relaxation. However, high-intensity X-ray sources are needed. Very successful experiments have been reported using synchrotron radiation sources during MBE. An overview of the potential of surface X-ray scattering and reflectivity during the MBE growth process is given by Ploog’s group using the X-ray source installed at BESSY [68]. They observed intensity oscillations during layerby-layer homoepitaxial growth on the GaAs (001)b(2 4) surface. Using an MBE system coupled directly to an X-ray diffractometer at the synchrotron radiation facility, SPring-8 beamline 11XU, a real-time study was performed during lattice-mismatched In0.12Ga0.88As/GaAs (001) MBE growth to investigate strain relaxation mechanisms [69]. The use of synchrotron radiation and a two-dimensional CCD camera enabled the high-resolution X-ray reciprocal space mapping of (004) diffraction at intervals of 6.2-nm film thickness. This method, in turn, enabled the simultaneous observation of transient behavior associated with residual strain, relaxation, and dislocation nucleation as a function of InGaAs thickness. A key barrier to exploiting X-ray characterization during growth is the challenge of using synthesis equipment in a synchrotron environment. Conventional high-resolution systems are not compatible with required monitoring over MOCVD process times. Experiments based on in situ X-ray reflectivity measurements using an energy-dispersive setup yielded information on the surface morphology as opposed to the composition of epitaxial layers [70]. Nevertheless, real-time X-ray scattering and diffraction using a conventional X-ray source in the configuration depicted in Figure 29.28 have been used to study the MOCVD growth of cubic GaN on a GaAs/GaN/AlGaN template [71]. As shown in the figure, the GaN (224) and AlGaN (224) diffraction peaks were acquired as a function of growth time. During MOCVD growth, the GaN Bragg peak intensity was found to increase and shift continuously, corresponding to a decrease in the lattice ˚ . The observed variation of parameter normal to the GaN surface of about Dat ¼ 0.015 A the GaN lattice parameter was associated with relaxation of the layer during growth. The nucleation of cubic GaN on SiC (001) during MOCVD has also been investigated and, from the diffracted intensity from the GaN film, the growth rate and microstructure from a submonolayer coverage to 350 nm were determined [72].
29.2.2.3 Reflection Mass Spectrometry The earliest studies of III–V growth by MBE exploited modulated beam techniques to determine the fundamental interactions between Ga and As species at the GaAs surface [73]. By identifying and measuring the time-varying intensities of desorbed products, important parameters affecting epitaxy were determined, such as adatom/admolecule surface lifetimes and reaction orders. Current configurations for the technique exploit a
Chapter 29 • In Situ Characterization of Epitaxy
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FIGURE 29.28 (a) Setup of an X-ray diffractometer with a conventional X-ray source integrated on a metal–organic chemical vapor deposition (MOCVD) system. (b) X-ray diffraction spectra recorded as a function of time during the MOCVD of cubic GaN on a GaN/AlGaN template. Each spectrum was collected in 10 s. The peak position shows a clear shift with increasing layer thickness. This corresponds to a decrease Dat of the average lattice parameter normal to the GaN surface, as shown in (c). Rearranged from Ref. [71].
line-of-sight configuration by mounting a mass spectrometer head in an effusion cell port (for MBE), or centrally if such a port exists (often used for a pyrometer to measure temperature). During growth, reflected beam signals such as those resulting from an excess group V flux and/or desorbed group III species are measured. The technique has been called reflection mass spectrometry and desorption mass spectrometry (DMS) [74]. To reduce the noise associated with background pressure, for example, periodic modulation of the input and gated detection of the output signal (amplitude and phase) with a lock-in amplifier improved the technique significantly [75]. Signal averaging approaches based on signal processing techniques offered additional improvements over phase-sensitive approaches. DMS has been used extensively to elucidate surface chemical reactions during MOCVD, to identify surface-segregating species during alloy growth, and to study nucleation kinetics. Some key examples are given next. Early studies on the decomposition of triethylgallium, TMGa, and trimethylindium, TMIn, on GaAs were carried out using DMS [78]. These studies were based on dosing GaAs surfaces with the species and then measuring reaction products. Kinetic models for GaAs growth by MOCVD using these precursors were derived from these data. Figure 29.29(a) shows DMS measurements of reflected As, intensity versus time, during AlGaAs growth by MBE and the corresponding RHEED intensity captured concurrently. Before growth, a high As signal is measured relative to growth because the As is not consumed. The signal decreases when growth is initiated, as can be seen when the Ga shutter is opened, followed by the Al shutter. The Ga-to-Al incorporation ratio can be determined by comparing As consumption [76]. Figure 29.29(b) shows how DMS was used to track the Al concentration in AlGaAs during the growth of a parabolic layer based on measuring the Ga desorbed flux with time [77]. The incorporation of mixed group V alloys, such as GaAsSb, is a significant challenge as a result of the nonunity sticking coefficients of each element. DMS can
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FIGURE 29.29 (a) Time-dependent REMS mass 150 signal (top) and time-dependent specular reflection highenergy electron diffraction intensity (bottom) during AlGaAs growth [76]. The sequence of shutter openings and closings is indicated. (b) Observed and desired Ga desorption rate Fd vs time profiles (top), and calculated and desired Al fraction vs thickness profiles (bottom) during DMS-controlled growth of parabolic AlGaAs well [77].
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be used in a similar fashion as that described earlier for AlGaAs to determine the relative incorporation of As to antimony (Sb). Early experiments demonstrated the closed-loop control of GaAsSb composition to yield a sinusoidally varying composition profile by measuring the Sb desorbed signal and controlling the As flux [79]. Compositional control enabling the synthesis of complex structures is a strength of DMA. However, fundamental surface processes can also be characterized. For example, by measuring the As consumed after creation of a group III-rich surface (e.g., a Ga droplet-covered surface created during growth with a high III/V flux ratio), the time dependence of As consumption depends on the temperature-dependent migration length of Ga. The DMS signal from desorbing As during growth is found to oscillate with the same frequency observed using RHEED [80]. In desorption, signals measured during MBE growth of InGaAs over a range of temperatures yielded data differentiating and characterizing In segregation, incorporation, and desorption [81]. Anion exchange can also be characterized. By measuring the desorbed Sb from the surface of InAs and InAsSb during growth, the displacement of Sb by As resulting from subsurface exchange can be characterized [82]. DMS has been applied successfully to III-N compound growth, during which the dependence of nucleation and growth on the III/V flux ratio, growth rate, and N species is much more complex than III–Vs such as GaAs. Early work determined the incorporation behavior of Ga during GaN growth using NH3. Distinct growth regimes associated with Ga incorporation were identified based on complete to partial Ga consumption and Ga adlayer and/or droplet formation [83]. For example, Brown et al. [84] studied the desorption of Ga from a Ga-rich GaN surface at the onset of the characteristic in-plane relaxation and surface roughening associated with the onset of Stranski-Krastanov growth mode of QDs during GaN growth on AlN. Figure 29.30 shows the RHEED Bragg spot intensity, the determined lattice spacing from the RHEED streak separation, and the desorbed Ga during the growth of GaN QDs. A steady-state Ga surface population is created before exposure of the surface to N (at 60 s). The transition from GaN planar growth to the Stranski-Krastanov growth mode is identified by the change in lattice spacing associated with relaxation. By integrating the DMS signal over time, the total coverage of Ga can be obtained to determine that the Stranski-Krastanov growth mode transition occurs under these conditions at a GaN coverage of 2–3 ML. Nanowires, NWs, present an extreme challenge to in situ characterization because of their geometry and size, and the interplay of surface processes on multiple crystal planes (e.g., on the evolving NW surface and sidewalls). DMS has been used to characterize the growth of catalyst-free GaN NWs. The nucleation of the NW takes place at high temperatures and a high V/III flux ratio, and is characterized by an incubation time. Limbach et al. [85] studied the impact of magnesium (Mg) doping on NW nucleation time using DMS to measure Ga desorption. Results were correlated with the density of the resulting NW ensemble. Mg was found to decrease the incubation time and enhance the lateral growth rate, thus enhancing coalescence. Figure 29.31(a) shows the Ga DMS
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FIGURE 29.30 In situ data during 60-s pregrowth Ga wetting, 19-s GaN growth, subsequent SK transition, and Ga–adsorbate desorption with a 707 C substrate temperature. The Ga flux was 5 nm/min. The N fluence corresponded to 3.0 ML nominal GaN coverage. The conventional GaN SK transition occurred during GaN growth. The total Ga–adsorbate coverage was 0.75 ML. (a) Reflection high-energy electron diffraction (RHEED) Bragg spot intensity variation. (b) RHEED in-plane lattice spacing along the ½1100 azimuth. (c) QMS desorption Ga flux. Ref. [84].
signal with and without incident Mg flux. The incubation time is characterized by a constant Ga signal. On nucleation, the desorbing Ga decreases on consumption as the nuclei form and grow. Figure 29.31(b) shows that Mg increases the nucleation rate significantly and its dependence on growth temperature was also used to characterize the growth of the composition of InGaN NWs during growth. By measuring the In desorption, an apparent activation energy of 2.5 eV could be determined associated with In dynamics, including InN decomposition, and In desorption and reincorporation [86]. As a final example, laser single-photon ionization time-of-flight (TOF) mass spectrometry has been used to measure the desorbing fluxes of Ga and As species from GaAs. In work reported by Ott et al., [87] the system is configured with the laser ionization photons propagating along the same axis of the RHEED electrons, but in the opposite direction. The incident photons are at 355 nm with a 100-Hz repetition rate of pulses of 20–30 mJ and a 3-ns duration. These pulses are focused into a Xe:Ar gas cell for frequency tripling to produce 118-nm photons. The TOF mass signals result from ionization by the 118-nm photons and are proportional to the densities of the detected species, and can be converted to fluxes with appropriate factors. The Ga TOF signal agreed well with growth rate determined by RHEED, and by comparing incorporation under a variety of temperatures and As fluxes leads to a precursor-mediated adsorption model for Ga desorption [86].
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FIGURE 29.31 (a) The partial pressure of 69Ga as detected by LS-QMS is plotted vs the growth time for two samples, one with (blue) and one without (green) an Mg supply. (b) Arrhenius plot of s as defined in (a) for samples grown with (blue squares) and without (green circles) an Mg supply. Both data sets were fitted (solid line) with the exponential function sðTs1 Þ A $ expðDE $ ðkB TS Þ1 Þ. Ref. [85].
29.3 Future Techniques As devices’ dimensions and architectures move toward the nanoscale, the need to control manufacturing as well as improve process development will drive the creation of new in situ monitoring techniques and tools. Although layer thickness is important to monitor during the growth of traditional devices, accuracy of measurements at the nanometer scale in all three dimensions is increasingly important. As an example, we can consider the characterization of the growth of an ensemble of NWs. A full set of parameters to be controlled with in-line metrology may include NW radial and vertical composition, alignment to substrate, diameter, spacing, length, and density. Today, realtime process control and characterization techniques cannot meet these needs.
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A trend in future techniques exploits the concept of combining information from correlated techniques. Such measurements are performed at the same position on the sample. An example is given by SOPRALAB, which has developed a new approach that combines two nondestructive characterization techniques on the same instrument— namely, SE and grazing X-ray reflectometry (GXR). GXR and SE measurements can be acquired quasi-simultaneously at exactly the same sample location. Analysis of complementary data from both techniques with the same physical model leads to unprecedented accuracy in measurement. With increasing integration of correlated tools supported by common physically based models and signal processing techniques, we envision significant progress in characterizing the growth of complex structures.
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In Situ Characterization of Epitaxy April S. Brown DEPARTMENT OF ELECTRICAL AND COMP UT ER ENGI NE ERING, PRATT SCHOOL OF ENGINEERING, DUKE UNIVERSITY, DURHAM, NC, USA
Maria Losurdo NATIONAL C OUNC IL OF RESEARCH, INSTITUTE OF INORGANI C METHODOLOGIES AND OF P L A S MA S , CN R - I M I P, VI A O R A B O N A 4, 70 12 6 B A R I , IT AL Y
CHAPTER OUTLINE 29.1 Introduction ............................................................................................................................. 1169 29.2 Measurement Modalities ....................................................................................................... 1171 29.2.1 Photon-Based Techniques (or Optical Probes) ......................................................... 1172 29.2.1.1 Reflectometry and Interferometry .................................................................... 1172 29.2.1.2 Spectroscopic Ellipsometry ............................................................................... 1174 29.2.1.3 Reflectance Anisotropy Spectroscopy .............................................................. 1185 29.2.2 Particle-Based Techniques (or Diffraction Probes)................................................... 1190 29.2.2.1 Reflection High-Energy Electron Diffraction ..................................................... 1190 29.2.2.2 X-Ray Diffraction and Scattering...................................................................... 1198 29.2.2.3 Reflection Mass Spectrometry.......................................................................... 1198 29.3 Future Techniques................................................................................................................... 1203 References......................................................................................................................................... 1204
29.1 Introduction It is difficult to imagine the development of molecular beam epitaxy (MBE) or metal–organic chemical vapor deposition (MOCVD) without the extensive use of in situ diagnostics. During the past four decades, these techniques have evolved with the epitaxial tools development and use. This chapter describes key in situ characterization approaches applicable to MBE and MOCVD, and provides examples of their use aimed toward (1) revealing fundamental processes underlying the growth of planar and nanostructured films, (2) process characterization for device applications, and (3) closed-loop feedback control of layer thickness and composition. Handbook of Crystal Growth. http://dx.doi.org/10.1016/B978-0-444-63304-0.00029-7 Copyright © 2015 Elsevier B.V. All rights reserved.
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Impinging atomic beams
Crystal surface lattice site Surface diffusion
Desorption Surface diffusion
Ts substrate
Lattice incorporation
Overgrowth
Interdiffusion Surface aggregation (nucleation)
FIGURE 29.1 Surface processes during molecular beam epitaxy. Ref. [1].
When considering these techniques, we must first understand their use in terms of similarities and differences in the epitaxial process and growth environment for MBE and MOCVD. Epitaxy is, fundamentally, a surface process, and therefore techniques designed to reveal the underlying molecular/atomistic processes are ideally differentially sensitive to surface chemical and physical properties. The near-surface region is, however, significantly different for MBE, a physical vapor deposition approach carried out in an ultra-high vacuum environment, and MOCVD, a chemical vapor deposition approach carried out in a gas flow environment typically near or at atmospheric pressure. The decomposition of metal–organics and hydrides can happen on or very near the surface, and the surface boundary layer has concentration gradients of incident species and products. Figure 29.1 shows a schematic of the key surface processes determining film composition, uniformity, microstructure, and defect density. Although this figure is specific to the MBE process in terms of the incoming flux from atomic or molecular beams, the surface processes are the same for MOCVD with, as stated earlier, the addition of chemical reactions at the surface/ near-surface region. Hence, considering the growth of GaAs as an example, measuring the concentrations of surface species, such as gallium (Ga) adatoms and arsenic (As) molecules, as well as the rates of key processes, such as diffusion, nucleation, and desorption, provides crucial insights into the growth process and, therefore, means of modification of growth conditions to achieved desired epitaxial layer properties. Common to both growth techniques, and crucial in determining the composition and defect densities of epitaxial films, is the fact that incorporation is mediated through a
Chapter 29 • In Situ Characterization of Epitaxy
InP
(2 × 1) θP = 1 ML
β2 (2 × 4) θP = 0.75 ML
InAs
σ (2 × 4) θP = 0.25 ML
MD (2 × 4) θP = 0.125 ML P atom
γ (2 × 4) θAs = 1 ML
β (2 × 4) θAs = 0.75 ML
In-rich (4 × 2) θAs = 0.25 ML
[110] – [110]
In atom
α (2 × 4) θP = 0.5 ML
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As atom
α (2 × 4)
θAs = 0.5 ML
FIGURE 29.2 Schematic representation of the atomic arrangement for the different surface reconstructions of InP and InAs (001). The coverage of V-group element atoms, expressed in monolayers (ML), is indicated with the corresponding reconstruction. Note that the more In-rich InP surface (MD (2 4)) contains In-P mixed dimers along ½110. Ref. [2].
reconstructed surface. The reconstructed surface is a consequence of surface energy minimization and is established by growth temperature and the relative abundance of group III and group V surface species. Figure 29.2 shows atomic configurations associated with a range of InP and InAs surface reconstructions as a function of the relative arsenic, As, or phosphorus, P, coverage (qP or qAs) [2]. The dimer density and orientation (group V or III dimers and/or heterodimers) have a significant impact on incorporation and surface diffusion. As we show in this chapter, a range of in situ and real-time monitoring techniques is available that enables the characterization of surface crystal and electronic structure, composition, morphology, strain, and surface dynamic processes. With the advent of recent interest in creating nanostructures also comes a refocusing of in situ analysis techniques from the growth of planar structures to nanostructure formation and evolution. Such refocusing will certainly lead to new techniques as well. The organization of this chapter is based on the fundamental modality of a class of in situ techniques, some of them probing the gas phase in the near-surface reaction region and some probing the surface of the growing sample directly, with a description of the approach and examples of use.
29.2 Measurement Modalities We begin the description of techniques and applications exploiting light–sample interactions because these approaches are extremely powerful and applicable to both MOCVD and MBE growth environments.
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29.2.1
Photon-Based Techniques (or Optical Probes)
Optical techniques can be exploited over wide pressure ranges and can be tuned spectrally to access specific ranges of depths in samples. A comprehensive review of linear and nonlinear light–sample interactions in relation to in situ diagnostic techniques has been written by Pemble et al. [3]. A number of optical techniques has been developed and explored for use in revealing key surface processes during epitaxy, including dynamic optical reflectivity, spectroscopic ellipsometry (SE), IR absorption spectroscopy, laser light scattering (LLS), reflectance difference spectroscopy (RDS) or reflectance anisotropy spectroscopy (RAS), and second harmonic generation (SHG). As Pemble et al. [3] point out, the desire to enhance surface-to-bulk response with these techniques led to their classification as “epioptic” techniques by McGilp during the late 1980s [4], an unfortunate naming resulting from the dual reference of “epi” to optical surface science and epitaxial growth. These techniques all hinge on fundamental light–matter interactions that are described by frequency- and wave vector-dependent surface and bulk polarization responses to incident electromagnetic radiation. The polarization is modified through the susceptibility comprised of linear (e.g., reflection and absorption) and nonlinear (e.g., second-harmonic generation) terms. In LLS, the measured property is the diffusive scattering that occurs if the surface becomes rough. SHG is based on the secondharmonic light that is generated when an intense photon beam interacts with the sample. In RDS, the measured property is the sample anisotropy, and in SE the change of light polarization is characterized. The application of nonlinear techniques to characterizing growth is still rare because spectral capabilities are not readily available. The linear response is key to three important and highly successful means of in situ analysis: dynamic optical reflectance (or laser interferometry), SE, and RDS or RAS. Herein, we concentrate on the linear techniques, SE and RAS, that exploit the polarization of light. RAS is surface specific because the surface has different symmetry than the bulk. The sensitivity of RAS is now significantly better than 0.01 monolayer (ML). Although surface analysis is necessary for understanding growth mechanisms, there are also “bulk” properties (or, more appropriately, “thin film”), such as thickness, composition, and buried interfaces, that must be characterized using bulk-oriented probes such as spectral reflectometry and SE. Reflectance and SE are described in detail next, with examples of their use as “bulk” techniques, and RAS as a more surface-specific probe.
29.2.1.1 Reflectometry and Interferometry A primary goal of in situ characterization is to obtain key device-relevant film characteristics such as thickness, composition, and homogeneity. Reflectance measurements are relatively simple to implement, requiring minimal modifications to MBE or MOCVD reactors [5]. Although the majority of in situ reflectance measurements reported in the literature use single-wavelength He–Ne laser light sources (laser reflectance), multiwavelength reflectance (spectroreflectometry) using broadband sources has also been
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FIGURE 29.3 (a) Typical laser interferogram acquired using the 633-nm laser during the metal–organic chemical vapor deposition growth of GaN; (A)–(B) is nucleation; (B)–(C) is annealing; (C)–(E) is coalescence, followed by homogeneous two-dimensional growth. (b) Typical interferogram acquired during the growth of the AlAs/GaAs/ AlGaAs multilayer using two different probing wavelengths. Rearranged from ref [6]
used as an in situ monitor of, for example, the MOCVD growth of GaAs, AlAs, and AlGaAs. The entire spectrum or selected wavelengths sensitive to different properties or film thicknesses/depths can be used for process control or for postgrowth analysis [6,7]. Normal-incidence reflectance can be used to monitor film growth by measuring the interference between light reflected from the film surface– and light reflected from underlying interfaces, assuming the coherence length of the light is greater than the optical thickness of the film. Figure 29.3 is an example of a typical interferogram recorded using an He–Ne laser during the MOCVD growth of gallium nitride (GaN) using Ga(CH3)3 trimethylgallium (TMGa) and ammonia (NH3) sources. The nucleation of GaN leads to the observed initial increase in reflectivity (A–B), whereas subsequent annealing at 1000 C in NH3 causes the formation of rough, hexagonal GaN islands, which are detected through an observed decrease in the reflectivity (B–C). At C, TMGa is introduced again, after the anneal, initiating the high-temperature growth of GaN. The increasing reflectivity at D is associated with the lateral and vertical growth of GaN islands until full coalescence is achieved (D–E) and, last, at E, conversion from three-dimensional to two-dimensional growth is observed. The amplitude and period of the interference are used to determine and control the refractive index, n, and thickness, d, of the growing GaN layer, using the following relationship: d¼
m pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi 2Dn n2 sin2 f
where m is the number of fringes in the selected wave number window and f is the angle of incidence. Furthermore, if the amplitude remains constant, a smooth surface can be inferred from the data, whereas damping of the interference amplitude indicates the development of surface roughness. The same approach also works for more complex structures, including the growth of alloys, as shown in Figure 29.3(b), which is the spectral reflectance from a three-layer test structure comprised of AlAs, GaAs, and Al0.5Ga0.5As. Compositional differences in
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the films show up clearly as different patterns in the image. Interestingly, the GaAs fringes at 673 nm are practically nonexistent because the preceding AlAs layer is very close to an even number of quarter-wave thicknesses, producing what is referred to as an absentee layer, allowing the monitoring of only the subsequent Al0.5Ga0.5As layer. The wavelengths producing the highest intensity fringes for the GaAs layer are those that terminate the AlAs in an odd number of quarter wavelengths, as shown at 805 nm. An advantage of spectral reflectance detection over single-wavelength monitoring is apparent in this example based on the flexibility to choose appropriate wavelengths to monitor that exhibit the highest sensitivity to layer thickness and interface structure for layers of arbitrary optical thickness.
29.2.1.2 Spectroscopic Ellipsometry SE has been used for decades to characterize the optical properties of a range of materials, including semiconductors, enabling the discovery of key phenomena relating thin-film synthesis and properties. A particular strength of SE is the ability to characterize changes in the thicknesses of surface layers with sub-0.1 Angstrom sensitivity [8]. A system schematic diagram is shown in Figure 29.4. A linearly 45-polarized source of tunable light (e.g., example from the deep ultraviolet to the near IR (191–2700 nm)) is incident onto the sample surface with a spot size from a few millimeters to hundreds of microns for the analysis of nanostructures. Ellipsometry measures modifications to the amplitude ratio, j, and phase difference, D, of the two polarized components (p- and s-) of the light reflected from the surface. For a single, semi-infinite material layer (two-phase system comprised of a substrate, or thick film, and the ambient assumed to be air), the polarization of the reflected light satisfies the Fresnel equation and the dielectric function can be extracted directly from the SE response. For a multilayer film, such as a semiconductor film on a substrate, which is thinner than the absorption depth of the incident
FIGURE 29.4 Spectroscopic ellipsometry schematic.
Chapter 29 • In Situ Characterization of Epitaxy
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FIGURE 29.5 Pseudodielectric function of GaN on sapphire; the different information that can be derived by the analysis of the various regions of the spectra is indicated at the top. On the right it is schematized how from fitting pseudodielectric spectra to a layered model, the various properties of the layer can be derived.
light, the extracted dielectric function, referred to as the pseudodielectric function hεi ¼ hε1 i þ ihε2 i and represented with brackets, hi, is given by the following relation: "
0
00
hεi ¼ hε i þ ihε i ¼ sin f 1 þ tan f 2
2
ð1 rÞ2 ð1 þ rÞ2
#
D E ¼ ðn þ ikÞ2
where r is tan JeiD and f is the incident angle of the light, which should be at the Brewster angle of the material under analysis and is, for most semiconductors, around 70 . The reflected light can be acquired as a spectrum or under kinetic (time-varying) conditions at one or more wavelengths across the spectrum. The time resolution is in the millisecond range. The pseudodielectric function is dependent on the composition, thickness, microstructure, and specific optical properties of the multilayer film. As described later, SE provides a means of creating a model of the film, including layer thicknesses, composition, and surface–interface “smoothness.” With kinetic data, the film’s evolving thickness and surface morphology, and the formation of buried interfaces and abrupt or graded overlayers can be observed, such as the evolution of the metallic adlayers present in the MBE growth of group III-rich III-N materials. Figure 29.5 shows the real and imaginary parts of hεi for a GaN film, as a representative example, and how the different photon energy region of the spectrum relate to the film’s optical properties, thereby providing information on different film properties [9,10]. Although SE is a powerful technique for in situ and real-time characterization of growth, the use of complementary data for calibration purposes with SE is essential for achieving useful results because of its model-based nature. The most general method for modeling layered structures including interfaces and imperfect surfaces is the use of an effective-medium approximation (EMA) [11,11a,11b]. This model describes materials as a composite of regions, each with its own dielectric response. As an example, a rough surface is described as a mixture of
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material consisting of the film and voids. Different EMA models have been developed. The most common are the Bruggeman (BEMA) and Maxwell Garnett (MG) approximations. The MG theory applies to composites in which the inclusions are a small volumetric fraction of the host material and are well separated. The Bruggeman formula is symmetric with respect to interchanging the components, which is attractive for dealing with materials of comparable volume fractions in the mixture and of any shape. The BEMA applies to the modeling of surface adlayers and roughness because the pseudodielectric function depends sensitively on the model, especially near the material critical points (i.e., the bandgap and other higher absorption maxima characterizing the band structure) [12]. An important consideration in using an EMA is the “size” of the composite regions; if the sizes are comparable with or larger than the wavelength l/n of incident radiation, then scattering is important and an EMA is not appropriate. The EMA does not apply to modeling alloys or interfaces with atomic-scale detail, such as the atomic content in an alloy or interdiffusion across an interface. Dielectric function models of alloy materials are created through parametric models comprised of Gaussian-broadened polynomials corresponding to each of the critical points. Recent work in SE modeling compares errors associated with the application of the EMA, alloy, or graded-layer models across interfaces where atomic-scale materials variations exist [13]. Existing alloy material models can be implemented and modified to describe the optical properties and thicknesses of alloy layers. SE has been applied successfully to characterize and control the growth of many materials. To give a broad perspective of its use and potential, we focus on applications that have very high composition accuracy requirements, such as the MBE growth of AlxGa1xAs and InxGa1xAs films lattice-matched to InP for high-speed electronics, and HgxCd1xTe films for infrared detectors [14]. Thickness control using SE was first achieved by Aspnes et al. [15] and was based on a virtual substrate approximation. This method constrains the underlying epitaxial layer parameters into a virtual “substrate” and only models, or fits, the properties of the growing layer at the surface. A measure of the growth rate is obtained directly. Figure 29.6 shows an example of real-time monitoring of the MBE growth of GaN on silicon carbide (SiC) enabling GaN thickness control. For every wavelength below the bandgap of GaN, where the epitaxial film is transparent, oscillations in the dielectric function (or the ellipsometric parameter J and D), as shown in Figure 29.6, are recorded as a function of growth time. The oscillations are a result of the change in thickness of the epitaxial layer, which has a different index of refraction than the “substrate.” Second, the thickness of the layer represented by the period of the oscillations is a function of the optical constants of the growing layer, wavelength, and the angle of incidence; using the period and amplitude of the oscillations, the refractive index and thickness can be determined. Last, as growth proceeds, the amplitude of the oscillation decays more rapidly for shorter wavelengths, and disappears altogether for optically thick layers. The latter phenomenon emphasizes the importance of the spectroscopic kinetic mode for accessing wavelength-dependent information. Indeed,
Chapter 29 • In Situ Characterization of Epitaxy
1177
2 eV
4.5 eV
0
2000
4000
6000
8000 10,000 12,000 14,000 16,000 Time (s)
FIGURE 29.6 Typical temporal evolution of the real and imaginary parts of the pseudodielectric function recorded at two different probing photon energies of 2 eV and 4.5 eV during molecular beam epitaxy growth of GaN on silicon carbide.
progress in fast-acquisition characterization and modeling capabilities has allowed new approaches to characterizing epitaxial mechanisms, as described later. The initiation of epitaxy is a crucial process in which the surface must be prepared for epitaxy by the removal of its native oxide (for III–V materials), followed by film nucleation. Nucleation determines microstructure and depends on surface chemical and electronic properties. Using SE, we studied the impact of both the oxide removal and the unintentional nitridation of SiC substrates prior to GaN nucleation on the resulting film properties [16,16a,16b,16c,16d]. Such an experiment is exactly suited to the strengths of SE, in which sensitivity to the presence of surface overlayers can be very high. Oxide removal is determined with SE for absorbing films by seeking maxima and minima in the real and imaginary parts of hεi, for GaN above the band edge, as a function of process conditions. For nonabsorbing materials, the shift in interference fringes between the layer and its substrate, and the variation in their amplitudes, can be used to characterize the presence and absence of overlayers [17]. In the case of heteroepitaxy of GaN on SiC, our work specifically demonstrated the effectiveness of a commonly used oxide removal technique: the exposure of the oxidecovered SiC surface to cycles of Ga deposition and desorption at a high temperature (825 C), to reduce and desorb the oxide as volatile GaO. The process can be evaluated by observing the SE trajectory (Figure 29.7(a)) and noting the near convergence of the Ga desorption signal for the second exposure cycle and the adsorption signal for the third cycle. (Note that the cycle describes the desorption/adsorption of Ga on the surface.) This indicates that the surface is nearly equivalent, in comparison with the same signals for the
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FIGURE 29.7 (a) Spectroscopic ellipsometry trajectory during oxide removal. (b) Impact of Ga oxide removal on the silicon carbide (SiC)–GaN interface. (c) Transmission electron micrograph of a GaN cubic inclusion in buffer layer. Ref. [18].
first and second cycles, and provides evidence that the oxide is removed. Using an array of techniques, we found that oxide removal depends on the integrated Ga flux to the surface, the number of exposure cycles, and the specific polytype of the SiC substrate (4H- or 6H-), as well as its polarity. Furthermore, the Ga dosage during the oxide removal phase affected the interface formation during the subsequent growth of GaN on the Gaprocessed SiC. Figure 29.7(b) shows an SE-derived model of the interface. The presence of cubic phase (c-GaN) inclusions was verified, as shown in Figure 29.7(c) using transmission electron microscopy (TEM) [18]. In addition, nitridizing the surface after oxide removal was found to be crucial to GaN nucleation and coalescence, resulting in part from the competition between unintentional nitridation of the SiC surface and GaN nucleation before coalescence. Using a relatively low-temperature (200 C) nitridation step for 4H-SiC (0001)Si yielded a well-ordered Si3N4 layer (<0.4 nm), resulting in improved Ga wetting and lower cubic-phase inclusion density. Figure 29.8 shows J-D trajectories (at 3 eV) during GaN growth on SiC nitridized under different conditions. The faster increase in D results from more effective Ga wetting and faster coalescence, leading to a lower defect density. Comparing SE spectra at coalescence (corresponding to w12 nm), this GaN nucleation layer has a steeper absorption edge and narrower exciton feature. These studies illustrate the usefulness of the J-D trajectory, corresponding to the J-D values at a single wavelength and as a function of time, and using its shape to describe or infer a variety of synthesis phenomena and properties, most simply the vertical homogeneity of the film’s optical properties during epitaxy (Figure 29.9). A cyclical trajectory observed at 2.7 eV during the growth of a 0.6-mm-thick GaN film is observed in Figure 29.9(a), indicating homogeneous optical properties during growth. In contrast, the J-D trajectory observed for the film grown on a poorer quality nucleation layer (nitridation
Chapter 29 • In Situ Characterization of Epitaxy
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FIGURE 29.8 Real time trajectory in the j-D plane at the photon energy of 3 eV for GaN nucleation at the silicon carbide substrate temperature of 710 C on SiC nitrided at: (a) 200 C in RP-MOCVD, (b) 200 C in MBE, (c) at 700 C in MBE and (d) 700 C unintentionally in MBE. The C-point indicates the coalescence point. The different shape of trajectories indicates different nucleation of GaN depending on SiC nitrided surface. Ref. [19].
at higher temperature) shifts continuously toward greater values of J (Figure 29.9(b)), indicating a continuous refractive index change. The observed narrowing in the D “loop” is the result of an increase in film absorption resulting from defects in the growing film. We have also studied the epitaxy of GaN on HVPE GaN (0001) templates and described the oxide removal and the impact of the Ga/N flux ratio and growth temperature on the inferred GaN growth mode [19]. Our work demonstrated the sensitivity of SE in optimizing the temperature for the thermal oxide desorption from a GaN surface in MBE. Considering the incongruent thermal preferential loss of nitrogen from GaN at high temperature, it is crucial to find the right temperature and time in order to complete oxide desorption without inducing roughening of the GaN surface. This was achieved using SE as shown in Figure 29.10 in which hεi of GaN (with the native oxide) is captured at various temperatures at 4 eV. At 710 C, the flatness of hεi indicates that the temperature is insufficient for thermal desorption of the oxide, whereas at 750 C, the hε2 i decrease signals native oxide removal followed by surface roughening after oxide removal and as the temperature is increased. Hence, an optimal end point associated with the transition between surface cleaning and roughening can be identified. A thermal decomposition diagram based on the change in hε2 i—that is, dhε2 i=dT (at 4 eV)— can be constructed and is shown in Figure 29.10(e). The rate of surface roughening increases around 750 C as a result of the removal of the oxide, as corroborated with
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FIGURE 29.9 Trajectories associated with GaN film evolution on different buffer layers: 200 C nitridation (a) and 710 C nitridation (b).
(a)
(b)
No reacƟon
O-desorpƟon/roughening
710°C
(c) 2.1
4eV 1.95
O-desorpƟon
Roughening
4eV
2.05
1.85
2 1.9
1.95
1.8
<ε2>
<ε2>
<ε2>
Roughening 760°C
1.9
1.85
1.85 1.75
0
100
(d)7
200
300 400 Time (s)
500
600
Cleaning end point
8 1.8 0
50 100 150 200 250 300 350 400 450 500 Time (s)
(e)
1.8 0
200
400 600 Time (s)
800
1.000
6
AŌer annealing
5
<ε1>
4 5 3
<ε2>
IniƟal
Δε2/Δt(s-1)
6
Oxide 4
GaN Sapphire
2
1 3 2
3
4 5 Photon energy (eV)
6
FIGURE 29.10 (a–c) Real-time variation of hε2 i during annealing at various temperatures during molecular beam epitaxy of a GaN template. (d) Spectroscopic ellipsometry spectra of the GaN template before and after native oxide removal. (e) Rate of variation of hε2 i with the increase of temperature from which regimes of oxide desorption and surface roughening are identified and corroborated also by reflection high-energy electron diffraction patterns. Rearranged from ref. [19]
Chapter 29 • In Situ Characterization of Epitaxy
(a)
1181
(b)
FIGURE 29.11 Real-time variation of hε2 i during molecular beam epitaxy growth of GaN at 750 C under various III/V ratios. (b) Corresponding (J–D) trajectories identifying the different III/V flux ratio-dependent growth regimes.
reflection high-energy electron diffraction (RHEED). At w820 C, the roughening rate increases again, but more rapidly, as a result of Ga desorption enhanced by defectlocalized surface decomposition. Figure 29.11 shows the hε2 i variation in time (Figure 29.11(a)) and the corresponding J-D trajectories (Figure 29.11(b)) obtained during growth over a range of Ga/N flux ratios: from N-rich to Ga-rich with Ga droplets present on the surface. The changes observed in the J-D trajectories are related to the formation of Ga adlayers that terminate the growth surface. Well-known GaN growth phenomena related to Ga/N flux ratios are apparent. N-rich growth yields a trajectory remaining near its initial position, but shifting toward greater J values as a result of surface roughening. As the Ga/N ratio increases, the growth mode evolves from a layer-by-layer mode with pit formation to the step-flow growth mode achieved with a stable Ga overlayer. We have been able to characterize and quantify the Ga adlayer formation and its thickness (w2.5 ML) using SE studies of Ga adsorption and desorption from various polar and nonpolar surfaces by monitoring the change in hεi at 4 eV [20,20a,20b]. The same process has been applied to In overlayer formation as well [21]. These findings have been replicated/extended by a number of groups [22,22a,22b]. Thin-film nucleation and grain growth have been explored with SE in application to the synthesis of a variety of substrate-supported materials, including microcrystalline Si [23], growth and bonding in diamond films [24], Ge homoepitaxy [25], and, in addition to our work discussed earlier, GaN grown by MOCVD [26]. The shape of the J-D trajectory provides, in many cases, an effective means of differentiating geometric models. This was demonstrated recently during Ge homoepitaxy [18]. This study effectively used a graded-layer EMA model that included both the geometric shape of the growing
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pyramidal islands and the distribution of the ensemble properties of these islands. Different island shapes and distributions were differentiated with this approach. Nucleation studies specific to III-N heteroepitaxy have focused primarily on strain relaxation. Early work describes the growth of AlN on GaN and GaN on AlN in terms of common dynamic features comprised of platelet formation—that is, the nucleation of islands of a few monolayers in height and 10–20-nm lateral extension, subsequent partial coalescence, and the formation of dislocations at platelet edges. Reversible relaxation occurs through the dynamics of the platelets and the filling of troughs between them. Plastic relaxation results from dislocation formation [27]. Nucleation dynamics depend critically on the V/III ratio and growth temperature during growth. An example of this is clear in recent work extending the description of island dynamics applied to the catalystfree synthesis of GaN nanowires (NWs) using N-rich growth and a high substrate temperature. In this case, initial GaN spherical islands are nucleated, which exhibit shape transformations, thereby minimizing strain energy—first through a pyramidal structure, followed conversion by to a NW shape that then grows [28]. The characterization and modeling of nucleation is, of course, an example of using ellipsometry at the nanoscale. Numerous current devices exploit low-dimensional nanostructures, for example, quantum dots (QDs), quantum wires, or nanocolumns (NCs). In recent years, SE has been used extensively to investigate the growth mechanisms of these nanostructures. As an example, Wang et al. [29] investigated the growth mechanisms of InN NCs on GaN templates using ellipsometry and RHEED. The SE characterization, as shown in Figure 29.12, showed that the InN NCs epitaxy was initiated from the growth of InN QDs in the Stranski–Krastanov growth mode. The InN nuclei were formed at an InN coverage of approximately 10 ML. The subsequent InN growth NC growth was found to be based on In adatom migration to the NCs and then diffusion up the sidewalls. The prospect of achieving self-assembled and coherent QD arrays based on the growth of highly lattice-mismatched systems in the Stranski–Krastanov growth mode is the driving force for a number of studies (see, for example, [30] and references therein). In this context, SE has been useful in obtaining a better understanding of the growth of QDs and, ultimately, their controlled synthesis by both MBE and MOCVD. As an example, Steimetz et al. [31] concentrated on the growth of InAs QDs on GaAs. Although phenomenologically the SE signal directly yields information on the coverage and roughness resulting from the evolving QD ensemble density and geometry, quantitative analysis requires careful application of the appropriate EMA model. Using an EMA, the optical response of the QDs can be treated as surface roughness associated with anisotropic, noncoalescing indium arsenide (InAs) clusters if their characteristic lengths can be assumed to be smaller than the wavelength of light (i.e., light-scattering effects can be neglected). To model the mean geometry of the QDs with an MG EMA, the main axes (x, y, h) of these ellipsoids are adjusted to the averaged QD parameters, base length x along the ½110 direction, base length y along the [110]-direction, and QD height, h. Typically, the dielectric function of the QDs is assumed to be the same as the bulk
Chapter 29 • In Situ Characterization of Epitaxy
1183
Quantum dots formation Embrionic NCs Growth of NCs Point D [nm] 15 0 0.5
Point E [nm] 30 0.0
1.0
1.5
1.5
2.0
2.5
(a) (b) (c)
0
0.5 1.0
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2.0
[μm]
2.5
(d)
0.0
0.5 1.0
1.5
2.0
2.0
2.5
0.5 1.0
2.5 [μm]
(e)
Lattice constant (Å)
3.6
Free standing InN 3.4
3.2 55
Free standing GaN Intensity of RHEED 3.5
<ε ]>
45 3.0 40
<ε1>
RHEED intensity (a.u.)
50
35
2.5
30 2.0
25 20
1.5 0
50
100
150
200
250
Growth time (s) FIGURE 29.12 In situ investigation of the growth of InN nanocolumns by reflection high-energy electron diffraction (RHEED) and spectroscopic ellipsometry. (a) Evolution of the in-plane lattice constant of InN as a function of growth time. (b) In situ change of RHEED intensity and of the real part of the pseudodielectric function, hε1 i, at l ¼ 1600 nm as a function of growth time. (a)–(e) mark significant growth transition points. AFM and scanning electron micrographic images of the nanocolumns are also shown. Ref. [29].
material, which is not necessarily a good approximation, because quantum effects may yield a size-dependent dielectric function [32]. Therefore, being able to determine or parameterize the dielectric function of nanostructures as a function of size and geometry remains a key challenge. Figure 29.13 shows typical results obtained by applying an MG EMA analysis to InAs QDs grown on GaAs. The QDs are assumed to be comprised of 3 ML of InAs seeded on a 1-ML-thick InAs wetting layer that covers the GaAs substrate. The height, h, of the QDs corresponds to a thickness, d, which is the effective roughness;
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(b)
(a)
GaAs substrate
25
0
TMI on 0.085 Pa 0.17 Pa 0.34 Pa
5
20
Expected for layer-by-layer growth
20
<ε2>
15
20 4.8eV
<ε2>
h in ML
10
18 Influenced by light scattering
16
5 QDs of height h on wetting layer: calculated ellipsometry spectra
0
2
3
4
10 5
15
20
25
30
35
40
45
Time [s]
Photon energy [eV]
FIGURE 29.13 Spectroscopic ellipsometry spectra of InAs QDs modeled using a Maxwell–Garnett EMA. Both density f and height h of the QDs are varied with the constraint fh ¼ 3 ML. (b) hε2 i variation during InAs QDs growth at three different growth rates. Ref. [31]
and the volume fraction, f, of InAs is determined by constraining the product: fh ¼ 3 ML. The ellipsometric hε2 i spectra are modified only marginally by the initial layer-by-layer growth of the 1–2-ML wetting layer, but are changed significantly when the QDs are nucleated resulting from the roughness, which decreases the amplitude significantly in the vicinity of the E2 bulk critical point (i.e., at approximately 4.5 eV) (Figure 29.13(a)). The temporal variation of hε2 i (Figure 29.13(b)) indicates that the initial growth of the strained InAs proceeds in two-dimensional island growth mode. The sharp decrease observed in hε2 i indicates the transition from the Frank–van der Merwe growth mode to the Stranski–Krastanov growth mode. As stated earlier, as long as the island dimensions are smaller than the wavelength of light, the effective medium theory describes the optical response of the QD layer adequately. For larger islands, light-scattering effects become important. Recently, the integration or growth of metal nanoparticles (NPs) with semiconductors for plasmonic or optical antenna applications has emerged as an exciting new device platform of interest for sensing, catalysis, and optoelectronics. One example of the use of SE to characterize these metal–semiconductor integrated systems is the characterization of the deposition of Au NPs on Si. This system is complicated by interfacial reactions leading to gold silicides (AuSix). Figure 29.14 shows the evolution of the pseudoextinction coefficient as a function of Au sputtering time. The surface plasmon resonance peak associated with incident wave coupling into the localized surface plasmon modes of the evolving Au NP ensemble redshifts as the average particle size increases, as expected. As the Au NP coverage increases, the E1 and E2 critical points of the Si substrate are damped. Models were developed based on corroborating XPS and TEM data, and on including an evolving interfacial silicide layer that grows in thickness as the NPs grow in size [33]. A comprehensive discussion of the use of SE for the synthesis of plasmonic platforms was published recently by Oates et al. [34] and is a vital resource in this area.
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3 SPR
25 nm
2
E1
20 nm
E2
18 nm
1
15 nm
1
(a)
15 nm
(b)
2
3 4 5 Photon energy (eV)
(c)
18 nm
20 nm
6
(d)
25 nm
FIGURE 29.14 Pseudoextinction coefficient, hki, of the NPs ensembles of various diameters during sputtering of different amount of gold on a silicon substrate. The corresponding 500 500-nm AFM is also shown at the bottom. The average diameters are from AFM line profiles scanned at various points of each image. Ref. [33].
29.2.1.3 Reflectance Anisotropy Spectroscopy Like SE, RAS, also referred to as reflectance difference spectroscopy (RDS), is suitable for both MBE and MOCVD environments and has been well developed during the past two decades. RAS is based on determining the difference in reflectance of normal-incidence light between two orthogonal directions in the plane of the sample surface, Dr/r, in the range of 105: Dr r½110 r½110 ¼ r r½110 þ r½110
A system schematic is shown in Figure 29.15. In materials in which the bulk is optically isotropic, RAS becomes extremely surface sensitive because only the surface can produce an anisotropic signal. The anisotropic surface dielectric response is caused primarily by oriented surface dipoles originating primarily from dimer bonds in the reconstructed surface. From both the real and imaginary part of the RAS signal, and the bulk dielectric function of the underlying semiconductor, the surface dielectric function anisotropy Dε0 can be calculated according to Dε0 d ¼
lðεb 1Þ Dr $ 4pi r
where d is the thickness of the surface layer, l is the wavelength of incident light, and εb is the bulk dielectric function.
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FIGURE 29.15 Schematic of reflection anisotropy spectroscopy system. http://www.physik.tu-berlin.de/institute/IFFP/ richter/new/research/method_ras.shtml.
The sampled size is typically in the square millimeter range, and measurements can be modulated at the output using a piezoelastic modulator, or at the input using an electrooptic modulator. As stated earlier, RAS is highly surface sensitive because it works on the basis of the symmetry reduction associated with surface reconstruction works and, for cubic materials, the bulk isotropic linear contributions cancel [3]. The difference in the near-normal incidence reflectivity results from surface structure (i.e., the reconstruction), as stated earlier, and surface chemistry. As a result, it has been highly effective in determining the surface concentrations of adsorbed species. In addition to surface species identification and relative concentrations, interfaces can also be assessed because their symmetries are broken as a result of potential gradients of strain fields. Like SE, the effectiveness of using RAS to identify surfaces species rests on cross-technique calibrations and studies. RAS exploits RHEED (measured for MBE) effectively and has enabled the assessment of surface reconstruction during MOCVD growth. RAS is also supported by complementary ab initio calculations [35,35a,35b] and models [36]. RAS was first applied to MBE in 1991, and was determined early on to be sensitive to 0.01 ML [37]. In MBE, changing the surface reconstruction is readily achieved through tuning the surface stoichiometry, and early studies showed the clear relationship between RAS response and the As–Ga surface coverage. Aspnes et al. [38] mapped known MBE-based reconstructions determined by RHEED to RAS responses observed during MOCVD growth. This important first observation of reconstructions during MOCVD growth was obtained by mapping responses of GaAs in an ultrahigh vacuum to those in atmospheric pressure H2, He, and N2 environments, thus obtaining the first experimental verification of dimer formation during MOCVD growth [39]. RAS measurements are shown in Figure 29.16, comparing the change from an Asterminated (2 4) to a Ga-terminated (4 2) GaAs surface for MBE (top) and MOCVD
Chapter 29 • In Situ Characterization of Epitaxy
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(001) GaAs - MBE (2×4) → (4×2)
8
103∆[(R110-R110)/R]
4 0 4 0 –4
(001)GaAs-OMCVD AsH3→TMG
–8
6°→(111)A SINGULAR
–12
6°→(111)B 2
3 E (eV)
4
FIGURE 29.16 (Top) Spectral dependence of the change in RD signal as coverage of an (001) GaAs molecular beam epitaxy MBE surface at 580 C is changed from As-terminated (2 4) to Ga-terminated (4 2). (Bottom) Same, but for an (001) GaAs metal–organic chemical vapor deposition OMCVD surface at 370 C as the atmospheric-pressure ambient is changed from H2 containing 320 Pa AsH3 to H2 containing 13.6 Pa TMG. Ref. [38].
(bottom) growth under the conditions shown in the figure caption. Although the spectra are clearly different, it can be observed that 2.5 eV is a useful energy for characterizing this surface chemical change. This high sensitivity of such spectral fingerprints to reconstruction can be used to differentiate Ga–Ga and As–As dimers, because the maximum signal differences between the (2 4) As-terminated and (4 2) Ga- and Alterminated surfaces of GaAs and AlAs are found at 2.0–2.5 eV and 3.5 eV, respectively [33]. By slowly rotating (w0.1 Hz) a sample during MBE-based RAS measurements, the noise associated with fixed system issues, such as birefringent windows, could be minimized to obtain very high-quality data. In this case, the dielectric functions of the samples could be obtained from the RAS data and compared for different surface reconstructions (Figure 29.17). Using models of the electronic properties of the surface, the signals at 1.8 eV and 2.5 eV could be assigned to transitions related to Ga and As dimers, respectively [40]. More recently, RAS has been applied to GaN growth on Si to determine GaN thickness and refractive index [41]. Newer studies have extended the use of RAS measurements. Tanaka et al. [42] showed that carrier concentrations can be measured with RAS. n-type and p-type carrier concentrations from 1016 to 1018/cm3 were differentiated based on the ability of RAS to measure the surface electric field resulting from the linear electro-optic effect associated with E1 to E1 þ D1 transitions (near 3 eV) with respect to a reference undoped sample. Temperature-dependent measurements showed sensitivities of 1017/cm3 at 400 C to
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40 (001) GaAs: S, 580 °C 5 s, (4 × 2) 4s 3s 2s 1s
– ) d (Å) Im(ε110 – ε110
20
0
–20 (2 × 4) α (2 × 4) β, 510 °C –40 2
3
4
5
E (eV) FIGURE 29.17 Surface dielectric anisotropy spectra D(ε2d) of various reconstruction on (001) GaAs. Ref. [38].
1 1018/cm3 at 600 C [42]. Relating the signal to surface coverage, RAS has also been used to monitor dopant (As) segregation during Si growth [43]. Recent work by Bruckner et al. [44] showed that key details associated with As adsorption and termination of Ge, such as dimer orientation, as well as the surface step structure can be differentiated using RAS by careful experiments and complementary STM, XPS, and low-energy electron diffraction (LEED) characterization, as shown in Figure 29.18. Recent work has also shown that RAS can be used to monitor the hydrogen termination of Ge during annealing in N2 (Figure 29.19) [45]. Similar to RHEED (as described later), RAS signals exhibit periodic changes in time associated with periodic surface structural and chemical changes during layer-by-layer growth [46]. The nucleation of GaInP on Ge (100) has been studied, and surface morphological changes associated with growth mode changes from island nucleation to layer-by-layer growth were characterized [47]. Recent work has shown that RAS can be used to track critical aspects of Stranski–Krastanov-based growth of InAs QDs on GaAs [48]. Figure 29.20 shows the key processes that could be determined with measurement at 4.2 eV. The RAS signal increases with increasing V/III ratio for InAs QD formation. Also, as a result of the observation that the signal intensity increases with As concentration for InAs growth and decreases with As concentration for GaAs growth, In diffusion could be followed during QD growth. By associating the critical thickness with the rapid increase of QD density and determining the second-order derivatives of the RAS spectra with respect to wavelength, changes in the GaAs band edge light-hole- and heavy-hole-related transition energies could be followed during wetting layer formation. The linear redshift in these energies is associated with In incorporation during two-dimensional growth. Kinks in the derivative spectra appear on transition to the
Chapter 29 • In Situ Characterization of Epitaxy
1189
FIGURE 29.18 In situ RAS of Ge (100):As 6 with predominant (2 1) (red) and (1 2) (green) surface reconstruction domains where dimers are oriented parallel (Ge (100):Asjj) or perpendicular (Ge (100):Ast) to the step edges, respectively. For comparison, the flipped and scaled (factor 1.38) RA spectrum of Ge (100):As 6 with predominant (2 1) reconstruction is also depicted. The insets illustrate the major As dimer orientation on the surface with respect to the step edges. (For interpretation of the references to color in this figure legend, the reader is referred to the online version of this book.) Ref. [44].
FIGURE 29.19 In situ RAS spectra of the monohydride-terminated (thin red line) and the clean (thick black line) Ge (100) surface with 6 toward the [011] prepared in MOVPE ambient. The dash-dotted thin gray line represents the RAS spectrum of an ultrahigh vacuum-prepared Ge (100) surface and the dotted black line corresponds to the scaled RAS spectrum of the MOVPE-prepared clean Ge (100) surface (i.e., thick black line). Vertical lines indicate the critical point energies of Ge (100) at 320 K. The STM image (Vsample ¼ –1201.2 mV, Iz ¼ –0.650 nA) corresponds to the monohydrideterminated Ge (100) surface. (For interpretation of the references to color in this figure legend, the reader is referred to the online version of this book.) Ref. [45].
three-dimensional or QD growth mode. Continued changes in the spectra can be related to the diffusion and incorporation of In as a function of growth conditions [49]. Lastly, recent work reported the use of microreflectance difference spectroscopy to resolve RAS signals at a resolution of square microns [50]. Laterally patterned Si was used as a substrate to grow GaP with layers of alternating orientations as a result of differences in the GaP sublattice occupancy from antiphase domain differences created at steps. By comparing spectra above and below the band edge of GaP (2.78 eV), an anisotropy
HANDBOOK OF CRYSTAL GROWTH
Re(dr/r) (10–3)
3
2
1
0
V/III ratio during InAs deposition {6} Restored GaAs E V/III = 0.5 {2} GaAs β2(2×4) F V/III = 1 G V/III = 2 {3} Start of QD {1} InAs QD formation dissolution growth interuption
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{5} Capped QDs {4} InAs surface
InAs 0
20
WT
Growth marker
GaAs CL
40 60 Growth time (s)
80
100
In migration {1}
{2}
{3}-{4}
{5}
{6}
FIGURE 29.20 Time-resolved RAS signal taken at 4.2 eV during the InAs QD and GaAs capping layer (CL) growth. Samples differ only in the partial TBA pressure during InAs growth and during the waiting time (WT) for QD formation. The beginning of InAs deposition was set as time 0. Proposed model of the growth {1}–{6} according to RAS data is shown at the bottom. Ref. [48].
topographic map of the surface and buried interface could be generated, as shown in Figure 29.21 [51].
29.2.2
Particle-Based Techniques (or Diffraction Probes)
29.2.2.1 Reflection High-Energy Electron Diffraction Particle-based techniques have been exploited only in MBE as a result of the requirement of an ultrahigh vacuum environment. RHEED has been the workhorse and benefited from the significant LEED body of work in crystallography. The geometry of RHEED used in MBE exploits the surface sensitivity realized by glancing incidence. Because RHEED has been used for so long and was developed hand-in-hand with the MBE process, strong reviews exist in the literature; hence, this topical coverage is light and focuses on specific applications. As RHEED has matured in concert with MBE, the full extent of the information that can be derived has grown significantly [52,52a,52b,52c,53]. An excellent early review of RHEED appeared in 1990 by Joyce [54], a pioneer in both MBE and the RHEED technique.A brief description of the basis of the technique is given here (Figure 29.22). A perfect crystalline surface gives rise to integral diffraction lines, and the reconstructed surface, to fractional ordered beams. The intensity of the beams contains extensive information on the perfection and crystalline structure of the surface. Surface imperfections, such as domains or steps, broaden the reciprocal lattice rods, thereby broadening and elongating the diffraction features. Splitting of the streaks can also occur when these features are ordered [55]. Representative RHEED and LEED patterns are shown in Figure 29.23 for III–V materials.
Chapter 29 • In Situ Characterization of Epitaxy
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FIGURE 29.21 Optical anisotropies maps for ten monolayers of Al0.5Ga0.5P followed by 500 nm GaP grown on laterally patterned silicon, obtained by fitting the RDS spectra of the structure. (a) map of the stripes height of the pattern. (b) map induced for the buried structure GaP/Al0.5Ga0.5P/Si. Ref. [51].
The RHEED signal is characterized by its intensity and phase. The intensity depends on a number of diffraction processes and, although often modeled using a kinematic approximation, is modeled more accurately as a multiple-scattering process including beam emergence effects, thermal diffuse scattering, normal diffuse scattering, and surface resonances [54]. The intensity of the diffracted beams and specular spot oscillates with time [57,57a,57b], with a period equal to the growth rate (i.e., the completion of 1 ML of growth). RHEED oscillations are therefore used extensively to calibrate the growth rate in addition to revealing surface static and dynamic processes [58]. Alloy composition can also be inferred from RHEED oscillations under conditions of group V-rich growth, in which all group III elements are incorporated. Taking AlxGa1–xAs as an example, the increase of growth rate with increasing Al flux is directly proportional to the composition, x.
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FIGURE 29.22 (a) Schematic showing a Ewald sphere with radius K0 cutting into surface reciprocal rods, leading to a diffraction pattern. (b) Top view of the geometric setup showing the reciprocal points along the perpendicular-to-beam direction are laying on the Ewald sphere, forming the zeroth zone streaks on the reflection high-energy electron diffraction screen. Both the Ewald sphere and the reciprocal mesh are for illustration purposes only and are not drawn to scale. Ref. [56].
A simple model of the origin of RHEED oscillations is based on the change in surface coverage with time as a single layer is grown. Assuming a two-dimensional layer-by-layer growth mode, the process is initiated with the nucleation of islands on the surface and the time-dependent filling of a single layer as the islands coalesce. As nucleation and growth proceed, the intensity of the signal decreases as the smooth surface roughens with island formation and growth, and then increases as the layer fills in. Damping of the oscillation results from the simultaneous growth and nucleation over multiple layers. The intensity changes in the beams are therefore proportional to the changing step density on the surface. Growth modes that develop steady-state step densities on the surface, such as step-flow growth, therefore yield no oscillations. In a seminal experiment, this model was used successfully to determine adatom diffusion lengths as a function of growth temperature (Figure 29.24) [54]. Using vicinal substrates with a known terrace width, the gradual transition from island nucleation to step-flow growth with increasing growth temperature was identified by the damping of oscillations. The growth mode change, in turn, was related to the increasing adatom diffusion length with respect to the terrace width. When the diffusion length is equal to or greater than the terrace width, step-flow growth is generally preferred as a result of favorable incorporation at the step edges. As shown in the Figure 29.24, this process can be modeled as a gradual transition between the growth modes. RHEED intensities are also found to increase in intensity, or “recover,” on the termination of growth. This observation was first interpreted as a smoothing of the surface resulting from the postgrowth rearrangement of atoms. As such, this effect is dependent on the sample temperature and the presence or absence of a group V flux. An important observation made by Yoshinaga et al. [59] was that the recovered intensity
Chapter 29 • In Situ Characterization of Epitaxy
1193
FIGURE 29.23 Reflection high-energy electron diffraction and low-energy electron diffraction (LEED) examples for III–V (1n00)(1 1) and (2 1) surfaces, with possible atomic arrangements. The reciprocal lattice of an unconstructed III–V (100)(1 1) surface is identical to that of the bulk plane. The vectors, defined by the (00) and (10) spots and the (00) and (01) spots, represent the reciprocal lattice vectors for the bulk plane, as visualized by LEED. For a reconstructed III–V (100)(2 1) surface, the two vectors defined by the (00) and (1/2 0) spots, and the (00) and (01) spots determine the reciprocal lattice of a surface layer. The gray square and rectangle represent the surface lattice cells. Ref. [52c]
depends on the specific phase of the oscillation signal at which the growth was terminated. In addition, the recovery was found to be comprised of a fast and slow component that were initially interpreted as the filling of the unfilled next to the last layer of the sample, and the longer timescale to breaking of bonds and other reactions associated with atomic rearrangement [59]. The ability to smooth the surface through growth interruption, the periodic termination of growth at temperature with an impinging group V flux, was subsequently exploited in many studies and led to new approaches of growth, such as migration-enhanced epitaxy and atomic-layer epitaxy. As Joyce [54] points out, however, simple interpretations of RHEED intensity in relation to surface smoothness can be misleading. For example, migration-enhanced epitaxy RHEED intensity changes will result from reconstruction changes associated with the change from As-rich to Garich growth for GaAs, for example, and not as a result of surface smoothing. RHEED studies have also been used to examine surface segregation and the resulting compositionally graded interfaces that result from growing a layer on top of an alloy with a surface-segregating component. For example, Joyce [54] observed that when shuttering
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FIGURE 29.24 (a) Reflection high-energy electron diffraction intensity oscillations showing the first maximum delay near the transition temperature on vicinal GaAs (001) misoriented by 2n toward [010]. The bottom trace was measured on a singular GaAs surface. (b) Schematic illustration to explain the growth mode transition that occurs on vicinal surfaces, and the origin of the first maximum delay. The grayscale represents the height of the surface. Ref. [54].
the Al cell during AlGaAs growth (i.e., growing GaAs on top of AlGaAs), the RHEED oscillation period increased as expected for the lower growth rate of GaAs, but through an intermediate stage with growth rate intermediate to that of AlGaAs and GaAs, and related to the difference in the cation surface diffusion rates. Later, Braun and Ploog [60] compared the RHEED oscillation behaviors for the growth of AlAs on both GaAs and AlAs with identical growth interruptions at the interface. They observed a negative phase shift for the growth of AlAs on GaAs, compared with that on AlAs, and in a similar experiment on the growth of GaAs, a positive phase shift for the growth of GaAs on AlAs [60]. The phase shift saturates after the growth of 11 ML for AlAs on GaAs, the so-called “normal” interface, and after approximately 1 ML for the “inverted” interface: GaAs on AlAs. By examining different diffraction conditions and dependences on substrate temperature and As overpressure, the results support a Ga segregation process that includes lateral segregation and smoothing.
Chapter 29 • In Situ Characterization of Epitaxy
1195
Despite the success in using RHEED oscillations to determine growth rate and diffusion lengths, in a review article published in 1990, Joyce wrote, “(RHEED) is a technique which is remarkably simple to apply, but is difficult to interpret and can be misleading in the hands of the unwary” [54]. The statement is based on an understanding of the complexity of the diffraction processes and the dependence of beam intensities on the specific diffraction conditions. Rocking curve characterization is the variation of the diffracted intensity of a beam as the incident angle of the primary beam is changed at a fixed azimuth. Such measurements support the need to base RHEED analysis on a multiple-scattering model. Two specific observations are related to this. The dependence of the intensity change with surface morphology depends on the diffraction conditions and processes. For example, the maximum in intensity does not necessarily correspond to a completion of a ML of growth, and oscillations with twice the periodicity can be observed with different diffraction processes that are out of phase. That said, kinematic approaches have been used extensively. Island sizes and step distributions on GaAs were quantified using a kinematic scattering analysis of the shape of measured diffracted beams [61,61a,61b,61c]. Recent work articulates the usefulness of an efficient MATLAB-based model [56]. The program can be used to calculate onedimensional line intensity profiles and quasi-two-dimensional streak intensity maps, and was shown to reconstruct successfully key features of the Ga-rich surface reconstruction of GaN under conditions of Mn adsorption (Figure 29.25). In Figure 29.25, two structural models are compared: the first (BL) substitutes Mn for Ga in the outer layer of a bilayer of Ga terminating GaN; the second (HD) substitutes Mn into the top layer and the Ga atoms rearrange into a 30 rotated and contracted state. Although the
FIGURE 29.25 (a)–(c) Side view (a) and top views (b and c) of the HD and BL models. The black rhombus indicates the surface nit cell. Orange hexagons (solid and dashed) indicate the Ga configurations (first and second layer, respectively). (d) Experimentally obtained reflection high-energy electron diffraction pattern along the ½1100 azimuth. (e and f) Simulated patterns for the HD and BL models, respectively. Ref. [56].
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FIGURE 29.26 Surface reconstruction maps for GaAs (001) (a) and GaAs1-xBix (001) (b) for substrate temperatures from 250 to 425 C and As2:Ga flux ratios from 0 to 3 (As2:Ga BEP ratio from 0 to 9.4). The growing GaAs1-xBix surface has an incident Bi BEP of 3 10–9 Torr. Ref. [62].
reconstruction (three times along the ½1100 and one time along the ½1120) is the same, the intensity modulation along the streaks is different, and comparison with experimentation indicates a better match to the HD configuration. RHEED-based surface phase diagrams are a useful means of condensing the dependence of reconstructions on growth conditions, typically substrate temperature, group V/group III flux ratio, and/or growth rate, and providing a map to guide crystal growth. A recent example (Figure 29.26) provides guidelines for the successful growth of GaAsBi. GaAsBi is particularly challenging to grow because of the size and electronegativity mismatches between As and Bi. Bi has a tendency to surface segregate and is a good surfactant at temperatures in the high 400 C range. At lower temperatures, incorporation is achieved but is typically less than w10%. The greatest incorporation occurs when grown with a (1 2) reconstruction. By comparing the reconstruction maps for GaAs and GaAsBi, it is seen that the (1 2) is not observed for GaAs growth and is therefore associated with a significant modification of the surface structure by Bi [62]. Another use of the surface phase diagram is to provide a reference for comparing growth conditions across equipment given that the substrate temperature and flux measurements will contain varying degrees of inaccuracy. Newstead et al. [63] suggested that referencing conditions to a boundary between reconstructions is a particularly good use of surface phase diagram information. One challenge to exploiting RHEED fully during MBE growth is the difficulty in carrying out measurements with substrate rotation. Growth rate measurements are
Chapter 29 • In Situ Characterization of Epitaxy
1197
FIGURE 29.27 Azimuthal reflection high-energy electron diffraction scan of the GaAs c(4 4) surface immediately before MnAs deposition. The corners of the surface nit cell are marked by circles [65].
inaccurate unless measured directly in the center as a result of the lack of rotation. With rotation, in addition to the change in intensity of the specular spot with azimuthal angle, measurement noise is introduced from vibrations and nonuniformities from substrate wobble and misorientation. One efficient approach to achieving RHEED measurements with rotation is to use gated measurements wherein the image is captured at the same angle during each rotation [64]. This technique enables the capture of azimuthal scans, as shown in Figure 29.27(a) [65]. The sample is rotated slowly to capture the intersection of the reciprocal lattice with the Ewald sphere. The diffraction pattern in a plane parallel to the surface can be determined by capturing the line intensity parallel to the shadow edge at a fixed reciprocal lattice distance. A half rotation is shown and a complete pattern is captured. An example of its use was the study of MnAs) nucleation on GaAs. Figure 29.27(b) shows the azimuthal RHEED scan of GaAs c(4 4) before exposure to MnAs. The evolution of the scan tracked different stages of the MnAs nucleation from random island orientation to oriented growth first along the [110] direction and then in the ½110 direction (at 2 ML).
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29.2.2.2 X-Ray Diffraction and Scattering Real-time in situ X-ray diffraction is based on measuring extremely asymmetric Bragg reflections [66,67] using slightly divergent X-ray radiation and a multichannel detector. Because X-rays penetrate gaseous environments, they can be applied directly to both MOCVD and MBE processes, providing important parameters such as composition, built-in strain, thickness, and mechanisms of relaxation. However, high-intensity X-ray sources are needed. Very successful experiments have been reported using synchrotron radiation sources during MBE. An overview of the potential of surface X-ray scattering and reflectivity during the MBE growth process is given by Ploog’s group using the X-ray source installed at BESSY [68]. They observed intensity oscillations during layerby-layer homoepitaxial growth on the GaAs (001)b(2 4) surface. Using an MBE system coupled directly to an X-ray diffractometer at the synchrotron radiation facility, SPring-8 beamline 11XU, a real-time study was performed during lattice-mismatched In0.12Ga0.88As/GaAs (001) MBE growth to investigate strain relaxation mechanisms [69]. The use of synchrotron radiation and a two-dimensional CCD camera enabled the high-resolution X-ray reciprocal space mapping of (004) diffraction at intervals of 6.2-nm film thickness. This method, in turn, enabled the simultaneous observation of transient behavior associated with residual strain, relaxation, and dislocation nucleation as a function of InGaAs thickness. A key barrier to exploiting X-ray characterization during growth is the challenge of using synthesis equipment in a synchrotron environment. Conventional high-resolution systems are not compatible with required monitoring over MOCVD process times. Experiments based on in situ X-ray reflectivity measurements using an energy-dispersive setup yielded information on the surface morphology as opposed to the composition of epitaxial layers [70]. Nevertheless, real-time X-ray scattering and diffraction using a conventional X-ray source in the configuration depicted in Figure 29.28 have been used to study the MOCVD growth of cubic GaN on a GaAs/GaN/AlGaN template [71]. As shown in the figure, the GaN (224) and AlGaN (224) diffraction peaks were acquired as a function of growth time. During MOCVD growth, the GaN Bragg peak intensity was found to increase and shift continuously, corresponding to a decrease in the lattice ˚ . The observed variation of parameter normal to the GaN surface of about Dat ¼ 0.015 A the GaN lattice parameter was associated with relaxation of the layer during growth. The nucleation of cubic GaN on SiC (001) during MOCVD has also been investigated and, from the diffracted intensity from the GaN film, the growth rate and microstructure from a submonolayer coverage to 350 nm were determined [72].
29.2.2.3 Reflection Mass Spectrometry The earliest studies of III–V growth by MBE exploited modulated beam techniques to determine the fundamental interactions between Ga and As species at the GaAs surface [73]. By identifying and measuring the time-varying intensities of desorbed products, important parameters affecting epitaxy were determined, such as adatom/admolecule surface lifetimes and reaction orders. Current configurations for the technique exploit a
Chapter 29 • In Situ Characterization of Epitaxy
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FIGURE 29.28 (a) Setup of an X-ray diffractometer with a conventional X-ray source integrated on a metal–organic chemical vapor deposition (MOCVD) system. (b) X-ray diffraction spectra recorded as a function of time during the MOCVD of cubic GaN on a GaN/AlGaN template. Each spectrum was collected in 10 s. The peak position shows a clear shift with increasing layer thickness. This corresponds to a decrease Dat of the average lattice parameter normal to the GaN surface, as shown in (c). Rearranged from Ref. [71].
line-of-sight configuration by mounting a mass spectrometer head in an effusion cell port (for MBE), or centrally if such a port exists (often used for a pyrometer to measure temperature). During growth, reflected beam signals such as those resulting from an excess group V flux and/or desorbed group III species are measured. The technique has been called reflection mass spectrometry and desorption mass spectrometry (DMS) [74]. To reduce the noise associated with background pressure, for example, periodic modulation of the input and gated detection of the output signal (amplitude and phase) with a lock-in amplifier improved the technique significantly [75]. Signal averaging approaches based on signal processing techniques offered additional improvements over phase-sensitive approaches. DMS has been used extensively to elucidate surface chemical reactions during MOCVD, to identify surface-segregating species during alloy growth, and to study nucleation kinetics. Some key examples are given next. Early studies on the decomposition of triethylgallium, TMGa, and trimethylindium, TMIn, on GaAs were carried out using DMS [78]. These studies were based on dosing GaAs surfaces with the species and then measuring reaction products. Kinetic models for GaAs growth by MOCVD using these precursors were derived from these data. Figure 29.29(a) shows DMS measurements of reflected As, intensity versus time, during AlGaAs growth by MBE and the corresponding RHEED intensity captured concurrently. Before growth, a high As signal is measured relative to growth because the As is not consumed. The signal decreases when growth is initiated, as can be seen when the Ga shutter is opened, followed by the Al shutter. The Ga-to-Al incorporation ratio can be determined by comparing As consumption [76]. Figure 29.29(b) shows how DMS was used to track the Al concentration in AlGaAs during the growth of a parabolic layer based on measuring the Ga desorbed flux with time [77]. The incorporation of mixed group V alloys, such as GaAsSb, is a significant challenge as a result of the nonunity sticking coefficients of each element. DMS can
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FIGURE 29.29 (a) Time-dependent REMS mass 150 signal (top) and time-dependent specular reflection highenergy electron diffraction intensity (bottom) during AlGaAs growth [76]. The sequence of shutter openings and closings is indicated. (b) Observed and desired Ga desorption rate Fd vs time profiles (top), and calculated and desired Al fraction vs thickness profiles (bottom) during DMS-controlled growth of parabolic AlGaAs well [77].
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be used in a similar fashion as that described earlier for AlGaAs to determine the relative incorporation of As to antimony (Sb). Early experiments demonstrated the closed-loop control of GaAsSb composition to yield a sinusoidally varying composition profile by measuring the Sb desorbed signal and controlling the As flux [79]. Compositional control enabling the synthesis of complex structures is a strength of DMA. However, fundamental surface processes can also be characterized. For example, by measuring the As consumed after creation of a group III-rich surface (e.g., a Ga droplet-covered surface created during growth with a high III/V flux ratio), the time dependence of As consumption depends on the temperature-dependent migration length of Ga. The DMS signal from desorbing As during growth is found to oscillate with the same frequency observed using RHEED [80]. In desorption, signals measured during MBE growth of InGaAs over a range of temperatures yielded data differentiating and characterizing In segregation, incorporation, and desorption [81]. Anion exchange can also be characterized. By measuring the desorbed Sb from the surface of InAs and InAsSb during growth, the displacement of Sb by As resulting from subsurface exchange can be characterized [82]. DMS has been applied successfully to III-N compound growth, during which the dependence of nucleation and growth on the III/V flux ratio, growth rate, and N species is much more complex than III–Vs such as GaAs. Early work determined the incorporation behavior of Ga during GaN growth using NH3. Distinct growth regimes associated with Ga incorporation were identified based on complete to partial Ga consumption and Ga adlayer and/or droplet formation [83]. For example, Brown et al. [84] studied the desorption of Ga from a Ga-rich GaN surface at the onset of the characteristic in-plane relaxation and surface roughening associated with the onset of Stranski-Krastanov growth mode of QDs during GaN growth on AlN. Figure 29.30 shows the RHEED Bragg spot intensity, the determined lattice spacing from the RHEED streak separation, and the desorbed Ga during the growth of GaN QDs. A steady-state Ga surface population is created before exposure of the surface to N (at 60 s). The transition from GaN planar growth to the Stranski-Krastanov growth mode is identified by the change in lattice spacing associated with relaxation. By integrating the DMS signal over time, the total coverage of Ga can be obtained to determine that the Stranski-Krastanov growth mode transition occurs under these conditions at a GaN coverage of 2–3 ML. Nanowires, NWs, present an extreme challenge to in situ characterization because of their geometry and size, and the interplay of surface processes on multiple crystal planes (e.g., on the evolving NW surface and sidewalls). DMS has been used to characterize the growth of catalyst-free GaN NWs. The nucleation of the NW takes place at high temperatures and a high V/III flux ratio, and is characterized by an incubation time. Limbach et al. [85] studied the impact of magnesium (Mg) doping on NW nucleation time using DMS to measure Ga desorption. Results were correlated with the density of the resulting NW ensemble. Mg was found to decrease the incubation time and enhance the lateral growth rate, thus enhancing coalescence. Figure 29.31(a) shows the Ga DMS
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FIGURE 29.30 In situ data during 60-s pregrowth Ga wetting, 19-s GaN growth, subsequent SK transition, and Ga–adsorbate desorption with a 707 C substrate temperature. The Ga flux was 5 nm/min. The N fluence corresponded to 3.0 ML nominal GaN coverage. The conventional GaN SK transition occurred during GaN growth. The total Ga–adsorbate coverage was 0.75 ML. (a) Reflection high-energy electron diffraction (RHEED) Bragg spot intensity variation. (b) RHEED in-plane lattice spacing along the ½1100 azimuth. (c) QMS desorption Ga flux. Ref. [84].
signal with and without incident Mg flux. The incubation time is characterized by a constant Ga signal. On nucleation, the desorbing Ga decreases on consumption as the nuclei form and grow. Figure 29.31(b) shows that Mg increases the nucleation rate significantly and its dependence on growth temperature was also used to characterize the growth of the composition of InGaN NWs during growth. By measuring the In desorption, an apparent activation energy of 2.5 eV could be determined associated with In dynamics, including InN decomposition, and In desorption and reincorporation [86]. As a final example, laser single-photon ionization time-of-flight (TOF) mass spectrometry has been used to measure the desorbing fluxes of Ga and As species from GaAs. In work reported by Ott et al., [87] the system is configured with the laser ionization photons propagating along the same axis of the RHEED electrons, but in the opposite direction. The incident photons are at 355 nm with a 100-Hz repetition rate of pulses of 20–30 mJ and a 3-ns duration. These pulses are focused into a Xe:Ar gas cell for frequency tripling to produce 118-nm photons. The TOF mass signals result from ionization by the 118-nm photons and are proportional to the densities of the detected species, and can be converted to fluxes with appropriate factors. The Ga TOF signal agreed well with growth rate determined by RHEED, and by comparing incorporation under a variety of temperatures and As fluxes leads to a precursor-mediated adsorption model for Ga desorption [86].
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FIGURE 29.31 (a) The partial pressure of 69Ga as detected by LS-QMS is plotted vs the growth time for two samples, one with (blue) and one without (green) an Mg supply. (b) Arrhenius plot of s as defined in (a) for samples grown with (blue squares) and without (green circles) an Mg supply. Both data sets were fitted (solid line) with the exponential function sðTs1 Þ A $ expðDE $ ðkB TS Þ1 Þ. Ref. [85].
29.3 Future Techniques As devices’ dimensions and architectures move toward the nanoscale, the need to control manufacturing as well as improve process development will drive the creation of new in situ monitoring techniques and tools. Although layer thickness is important to monitor during the growth of traditional devices, accuracy of measurements at the nanometer scale in all three dimensions is increasingly important. As an example, we can consider the characterization of the growth of an ensemble of NWs. A full set of parameters to be controlled with in-line metrology may include NW radial and vertical composition, alignment to substrate, diameter, spacing, length, and density. Today, realtime process control and characterization techniques cannot meet these needs.
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A trend in future techniques exploits the concept of combining information from correlated techniques. Such measurements are performed at the same position on the sample. An example is given by SOPRALAB, which has developed a new approach that combines two nondestructive characterization techniques on the same instrument— namely, SE and grazing X-ray reflectometry (GXR). GXR and SE measurements can be acquired quasi-simultaneously at exactly the same sample location. Analysis of complementary data from both techniques with the same physical model leads to unprecedented accuracy in measurement. With increasing integration of correlated tools supported by common physically based models and signal processing techniques, we envision significant progress in characterizing the growth of complex structures.
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