Low-Temperature and Metamorphic Buffer Layers

25 Low-Temperature and Metamorphic Buffer Layers John E. Ayers EL ECTRICAL AND COMP UT ER ENGINE ERING DEP ART ME NT, UNIVERSITY OF CONNECTICUT, STORR S, CT , USA

CHAPTER OUTLINE 25.1 Introduction ............................................................................................................................. 1008 25.2 Uniform Buffer Layers............................................................................................................ 1010 25.2.1 Critical Layer Thickness in the Uniform Buffer ........................................................ 1011 25.2.2 Strain Relaxation in the Uniform Buffer .................................................................. 1011 25.2.3 Misfit and Threading Dislocations in the Uniform Buffer...................................... 1011 25.2.4 Crystallographic Tilting in the Uniform Buffer ........................................................ 1013 25.2.5 Surface Roughening and Cross-Hatch in the Uniform Buffer ................................ 1014 25.2.6 Device Applications of Uniform Buffers ................................................................... 1014 25.3 Step-Graded Buffer Layers..................................................................................................... 1015 25.3.1 Lattice Relaxation and Residual Strain in Step-Graded Buffers............................. 1016 25.3.2 Misfit and Threading Dislocations in Step-Graded Buffers .................................... 1018 25.3.3 Morphology and Surface Roughening in Step-Graded Buffers ............................. 1022 25.3.4 Crystallographic Tilting in Step-Graded Buffers ...................................................... 1024 25.3.5 Device Applications of Step-Graded Buffers ............................................................ 1024 25.4 Linearly-Graded Buffer Layers............................................................................................... 1025 25.4.1 Approaches to Linear Grading .................................................................................. 1026 25.4.2 Misfit Dislocations and Strain in Linearly Graded Buffers...................................... 1028 25.4.3 Threading Dislocations in Linear Buffers.................................................................. 1031 25.4.4 Crystallographic Tilting in Linear Buffers ................................................................. 1035 25.4.5 Surface Roughening and Cross-Hatch in Linear Buffers ......................................... 1036 25.4.6 Dual-Slope and Tandem Graded Buffers.................................................................. 1037 25.4.7 Device Applications of Linear Buffers....................................................................... 1038 25.5 Nonlinear Buffers.................................................................................................................... 1041 25.5.1 Sublinear and Superlinear Grading........................................................................... 1041 25.5.2 S-Graded Buffer Layers............................................................................................... 1043 25.6 Superlattice Buffers ................................................................................................................ 1043

Handbook of Crystal Growth. http://dx.doi.org/10.1016/B978-0-444-63304-0.00025-1 Copyright © 2015 Elsevier B.V. All rights reserved.

1007

1008

HANDBOOK OF CRYSTAL GROWTH

25.7 Low-Temperature Buffer Layers and Two-step Growth .................................................... 1044 25.7.1 III-Nitrides on Sapphire Substrates ............................................................................ 1045 25.7.2 ZnO ............................................................................................................................... 1046 25.7.3 Heteroepitaxy on Si .................................................................................................... 1046 25.8 Conclusion................................................................................................................................ 1047 References......................................................................................................................................... 1047

25.1 Introduction Modern semiconductor devices require materials with a diversity of lattice constants, thermal expansion coefficients, chemical properties, and even crystal orientation or structure [1]. Because of the wide range of semiconductors utilized in devices, and the limited choice of single-crystal substrates on which to fabricate them, their manufacture almost always requires lattice-mismatched heteroepitaxial growth [2]. Mismatched epitaxy brings with it a host of challenges, including strain [3], misfit dislocations [4] and the associated threading dislocations which propagate through device regions [5], crystallographic tilt induced during relaxation [6], and the possible degradation of morphology due to three-dimensional nucleation [7] or stress-induced surface roughening [8]. Foremost among these problems is the density of threading dislocations, which can exceed 109 cm
2 and strongly influences the performance and reliability of devices utilizing the defected material [9]. Considerable effort and much progress has been made toward the goal of controlling threading dislocations in lattice-mismatched devices. Approaches involving patterning, such as epitaxial lateral overgrowth (ELO) [10,11], pendeoepitaxy [12], and dislocation sidewall gettering (DSG), also known as patterned heteroepitaxial processing (PHeP) [13], have demonstrated effectiveness in removing threading dislocations from latticerelaxed materials. ELO involves photolithographic definition of ridges which allows the lateral growth of cantilevered material under conditions for which anisotropic growth prevails [11]. Because the threading dislocations are steeply inclined to the growth interface, they grow out of the material and laterally grown regions are dislocation free. Pendeoepitaxy is similar except that the lateral growth occurs over silicon dioxide rather than in cantilevered fashion [12]. Continuous films may be achieved by ELO/ pendeoepitaxy, but geometrically necessary defects are introduced along the intersections of the laterally grown semiconductor regions. Even though ELO has been successfully adapted to several combinations of epilayer/substrate [10,14–16], it is not universally applicable due to the need for a strong orientation dependence of the growth rate. DSG/PHeP eliminates dislocations by image-force induced glide to sidewalls of mesa-patterned material either during growth or post-growth annealing, but the need for mesa patterning is quite restrictive except in applications where regular arrays of similar devices are to be defined, such as focal plane arrays of detectors [17]. Due to the device design restrictions imposed by patterning and the difficulties in

Chapter 25 • Low-Temperature and Metamorphic Buffer Layers

1009

obtaining continuous films with patterning techniques, planar approaches are preferred for the development of lattice-mismatched devices. A planar approach, which involves only changes in composition and/or growth conditions along the growth direction, can simplify the fabrication sequence, increasing yield and lowering cost, while maintaining general applicability to all types of devices regardless of their size or shape. Two distinct planar strategies involve pseudomorphic or metamorphic growth [2]. In the pseudomorphic case, all layers in the structure are restricted in thickness and composition so that they grow coherently strained, and entirely free of misfit dislocations. One problem with this approach is that the limited choice of substrates greatly restricts device design. For example, InxGa1
xAs layers on GaAs substrates may not employ greater than 20% indium composition if coherency is to be maintained [18]; more generally, the thickness-mismatch product is restricted to less than w0.04 nm for individual layers within pseudomorphic structures [19]. Another problem is that some device structures may not be grown pseudomorphically because there is no lattice-matched substrate, and an important example is the III-Nitride blue LED, usually fabricated on sapphire substrates. The metamorphic approach, in which layers of the structure relax partially by the introduction of misfit dislocations, allows great flexibility in choosing compositions and thicknesses of semiconductor layers [20]. The key to successful realization of a metamorphic semiconductor device structure is the design of an appropriate buffer layer which can relax the lattice mismatch existing between the substrate and device. Compositional grading [5] is the most commonly used strategy, but low-temperature growth [20–24] and temperature grading [25–27] are increasingly used as well. The ideal buffer layer is completely lattice relaxed, has an in-plane lattice constant which may be chosen arbitrarily, takes on the same orientation as the substrate, blocks the propagation of threading dislocations into the active device regions above, and has a perfectly smooth surface. Moreover, its properties are not compromised by the subsequent growth of device layers. Figures of merit for a metamorphic buffer or device structure are, therefore, the threading dislocation density (or X-ray rocking curve width), the residual strain, the crystallographic tilt, and the root mean square (rms) surface roughness. The threading dislocation density is determined by cross-sectional transmission electron microscopy (XTEM) [20,28,29], plan-view transmission electron microscopy (PVTEM) [2], high-resolution X-ray diffraction [30], or etch pit density measurements [2]. XTEM and PVTEM have a detection limit of about 108 cm
2 [31]; therefore, material with no visible dislocations may still have a high density. It has been argued that the PVTEM technique may be extended to lower dislocation densities by averaging over a number of images, and essentially increasing the observed area [2]. High-resolution X-ray diffraction determination involves calculation of the dislocation density from the rocking curve full width at half maximum, D z (b/4.36b)2, where b is the full width at half maximum (FWHM), and b is the length of the Burgers vector [1], or from a more exact analysis involving a number of reflections from different crystal planes [30,32]. The X-ray analysis is applicable to a wide range of dislocation densities, 106–1010 cm
2, but involves geometric factors which are not known with better than

1010

HANDBOOK OF CRYSTAL GROWTH

factor-of-two accuracy, so often the FWHM value is quoted rather than D [33]. Etch pit density measurements are well suited to dislocation densities less than 107 cm
2, but care must be taken to avoid missing some types of dislocations or counting features which are not associated with dislocations [1]. Residual strains, compositions, and crystallographic tilts are determined using X-ray rocking curves or reciprocal space maps [34]. Surface morphology is typically assessed using Nomarski contrast microscopy [35] and the rms surface roughness may be studied by atomic force microscopy (AFM) [36–39]. Compositional grading is commonly employed to control dislocation densities and strain, while low-temperature growth has been used to improve the surface smoothness and block threading dislocations. The following sections will describe various approaches to metamorphic and lowtemperature buffer layers. Much of the modeling work focusses on equilibrium descriptions, and even though the threading dislocation behavior is dictated largely by kinetics, an equilibrium model provides the basis for understanding that behavior. We will also draw upon the wealth of empirical results and relate them to the modeling work. First, uniform-composition buffers will be considered, including their lattice relaxation and misfit dislocation behavior. Compositionally graded layers will be discussed, starting with step-graded buffers, and then continuously graded layers, including linear, sublinear, and superlinear profiles. Superlattice buffers will be discussed for the control of the dislocation density and surface roughness. Lowtemperature growth of graded buffer layers has been shown to be important for control of the morphology and dislocation density and will be discussed along with the various buffer layer grading approaches.

25.2 Uniform Buffer Layers By the use of a uniform composition buffer layer, the entire lattice mismatch between device and substrate may be accommodated at a single, abrupt interface. This results in the smallest possible critical layer thickness for the onset of lattice relaxation, apart from the use of reverse grading. Another advantage of the uniform buffer layer is minimum residual strain for a given buffer thickness. There are two important drawbacks. First, an abrupt interface with a large lattice mismatch usually gives rise to three-dimensional nucleation, with the associated surface roughening, but use of a thin low-temperature (LT) buffer can alleviate this difficulty [40]. Second, even in the absence of a threedimensional growth mode, uniform buffers contain very high surface densities of threading dislocations (>108 cm
2) which require the use of additional uniform, superlattice, or graded buffers for their reduction. Increasing the layer thickness decreases the thread density, and some studies have found an inverse relationship between buffer thickness and dislocation density [9,41,42], but in most cases impracticably thick layers would be necessary to achieve sufficiently low defect densities for optoelectronic devices.

Chapter 25 • Low-Temperature and Metamorphic Buffer Layers

25.2.1

1011

Critical Layer Thickness in the Uniform Buffer

By balancing the line tension and strain forces on a grown-in substrate dislocation for a cubic semiconductor grown with (001) orientation, Matthews and Blakeslee [4] found the critical layer thickness for the uniform buffer to be hc ¼


   bð1
n cos2 aÞ hc ln þ1 ; 8pjf jð1 þ nÞcos l b

(25.1)

where b is the length of the Burgers vector, v is the Poisson ratio, a is the angle between the Burgers vector and line vector, f is the lattice mismatch, and l is the angle between the Burgers vector and that direction in the interface which is perpendicular to the intersection of the glide plane and the interface. As a first-order approximation, the critical layer thickness is inversely proportional to the lattice mismatch; for InxGa1
xAs/ GaAs (001), the critical layer thickness is 34 nm with 5% indium and 14.5 nm with 10% indium. The Matthews and Blakeslee model is only applicable up to approximately 2% lattice mismatch; beyond that three-dimensional growth tends to prevail.

25.2.2

Strain Relaxation in the Uniform Buffer

For a metamorphic layer with a thickness greater than hc, the equilibrium residual in-plane strain may be calculated on the basis of the Matthews and Blakeslee force balance model [4] and is εjj ¼


  fbð1
ncos2 aÞ h þ1 ; ln b jf j8phð1 þ nÞcos l

(25.2)

where the sign convention is given by f ¼ (as
ae)/ae, where as and ae are the substrate and epitaxial layer lattice constants, respectively, and the coherency strain is equal to the mismatch. As a first-order approximation, the equilibrium strain is inversely proportional to the layer thickness. For example, in Si0.9Ge0.1/Si (001) the equilibrium strain is
8.2  10
4 for a 200 nm layer and
4.5  10
4 for a 400 nm layer. This corresponds to 80% and 89% lattice relaxation, respectively. Often the residual strain is found to exceed the equilibrium value due to kinetic limitations. For example, in some work the residual strain was reported to have a reciprocal square root dependence on thickness [43,44]. The relaxation dynamics can be manipulated to a large degree by choice of the buffer layer material, doping of the buffer layer, inclusion of a low-temperature buffer, or preimplantation of the substrate [45]. Despite the presence of finite residual strain, a uniform buffer can be designed with mismatch exceeding that of the device layer (compositional overshoot) so that it matches the in-plane lattice constant of the device [46].

25.2.3

Misfit and Threading Dislocations in the Uniform Buffer

Uniform buffers tend to contain high densities of surface dislocations; in part this comes about because the misfit dislocations are concentrated within a network at the substrate interface, maximizing pinning interactions, and because the low built-in strain provides

1012

HANDBOOK OF CRYSTAL GROWTH

a weak force to elongate misfit dislocations [47a,47b]. For growth in the (001) direction in a diamond or zinc blende semiconductor, there are two orthogonal networks of misfit dislocations along [110] and ½110 directions, and their linear density along one of the [110] directions is rL ¼

d ; b sin a cos 4

(25.3)

where d is the amount of mismatch relaxed by dislocations and f is the angle between the slip plane and the interface. Generally, only a small fraction of the lattice mismatch may be relaxed by bending over substrate defects, so most misfit dislocations are associated with half loops which glide from the surface down {111} planes toward the interface [44]. Each half loop contains a misfit segment and two threading segments. Accounting for the two orthogonal systems of misfit segments and assuming the average length of misfit segments is Lave the density of threading dislocations is D¼

4rL : Lave

(25.4)

It follows that reduction of the threading dislocation density requires growth under conditions which favor the glide of threading dislocations to create the longest possible misfit segments, either by maximizing glide forces, or minimizing pinning interactions, or some combination of the two. Consider the example of a 400 nm layer of uniform In0.1Ga0.9As/GaAs (001) with equilibrium strain. The linear density of misfit dislocations is 3.3  105 cm
1 and to achieve a threading dislocation density less than 106 cm
2, the misfit segments would need to have an average length of over 1.3 cm. This is roughly 400,000 times the distance between misfit dislocations, so dislocation interactions might be expected to prevent the growth of misfit segments to this length in a uniform layer. In uniform buffer layers, the effective average length of misfit segments and, therefore, the threading dislocation density, is controlled by the annihilation and coalescence reactions between threading dislocations, because no further misfit dislocations are needed above the substrate interface. The change in dislocation density with distance from the interface is given by [9,41] dD ¼
2Ca D2
Cc D2 ¼
aD2 ; dy

(25.5)

where Ca quantifies the annihilation reaction between two threading dislocations, Cc quantifies the coalescence reaction between two threading dislocations to form a single dislocation, and a ¼ 2Ca þ Cc. The solution is D¼

1 1 z ; ay þ 1=D0 ay

 y[1 aD0 :

(25.6)

Therefore, the surface threading dislocation density is inversely proportional to the layer thickness. For InxGa1
xAs/GaAs (001), Jeong et al. found a z 1.4  10
5 cm
1, corresponding to a threading dislocation density of about 7  108 cm
2 in a 1 mm-thick layer [39].

Chapter 25 • Low-Temperature and Metamorphic Buffer Layers

1013

The applicability of uniform buffer layers has been extended somewhat by thermal annealing and low-temperature growth. Several reports have shown that post-growth thermal annealing can reduce the threading dislocation density, by promoting annihilation and coalescence reactions, but in some of these studies the reduction was limited to about a factor of two [48]. Low-temperature growth can also help block the propagation of threading dislocations to the surface. The mechanisms are not clearly established but may be related to interactions with the high nonequilibrium density of point defects that could affect the generation, motion, or interactions of dislocations. Mi et al. [49] used low-temperature growth (390  C) combined with a high-temperature anneal (700  C) of a 0.6 mm uniform In0.15Ga0.85As buffer layer on a GaAs substrate to fabricate a quantum dot laser having peak emission at 1.45 mm and a low threshold density of 63 A cm
2, suggesting a relatively low threading dislocation density.

25.2.4

Crystallographic Tilting in the Uniform Buffer

Generally a metamorphic buffer layer takes on a crystallographic tilt with respect to its substrate during the relaxation process. This is due to the preferential introduction of misfit dislocations having one tilt component over the other [6]. This mechanism differs from the one which is active in pseudomorphic layers [50], involving coherency strain at steps giving rise to tilt of the opposite sign. In the metamorphic layer, misfit dislocations which glide to the interface necessarily have a Burgers component perpendicular to the interface. If rþ and r
are the linear densities of misfit dislocations giving rise to positive and negative tilt,1 respectively, and if the misfit dislocations have misfit-relieving and tilt components of bε and bþ (dislocations producing positive tilt) and bε and b
(for those producing negative tilt), the strain relaxation will be d ¼ bε ðrþ þ r
Þ;

(25.7)

and the crystallographic tilt with respect to the substrate will be [28] Df ¼ bþ rþ
b
r


(25.8)

If the imbalance in misfit dislocation densities is caused entirely by the offcut of the substrate, then the misorientation of the epitaxial layer is expected to be about the same axis [48].2 Positive tilt and negative tilt are associated with relaxation in tensile and compressive buffers, respectively. The extent of the tilt is determined by the dislocation dynamics [48]. In type I relaxation, all slip systems become active, though some are more stressed and exhibit greater glide velocity, resulting in a slight imbalance in the populations of misfit dislocations with positive and negative tilt components. In type II relaxation, only the most stressed slip systems (MSSs) are active, so that either rþ or r
is 1

Here we define “positive” tilt as inclination in the sense that adds to that of the vicinal substrate and “negative” tilt with the sense that subtracts from the substrate tilt. 2 In the case of an “on axis” substrate, with only a small unintentional offcut, the tilt direction may be determined by an imbalance in the dislocation multiplication sources, but this behavior is incompletely understood at the present time.

1014

HANDBOOK OF CRYSTAL GROWTH

zero, and the tilt may be sizable. Type II relaxation can occur when the MSSs become active before the critical layer thickness for the least stressed slip systems (LSSs) has been reached, so that LSSs are excluded altogether. The resulting misorientation with the substrate may cause a degradation in crystal quality or difficulties in characterization and device fabrication if cleaved facets, anisotropic etching, or other orientationdependent processing is to be employed. Typically metamorphic buffers with uniform composition exhibit type I relaxation and relatively small misorientations, so that only their characterization is affected.

25.2.5

Surface Roughening and Cross-Hatch in the Uniform Buffer

Metamorphic buffer layers typically exhibit “cross-hatch” morphology. The troughs and crests of this pattern are aligned with the h110i directions, but the roughening may be highly anisotropic, leading to corrugations aligned with one of the two directions. Crosshatch is associated with the misfit dislocations aligned with these same directions for (001) heteroepitaxy of zinc blende semiconductors. The dislocations cause strain nonuniformities at the growing surface which can cause compositional or thickness variations [51]. There is a tendency for this type of surface roughening to diminish with layer thickness in a uniform layer, which buries the misfit dislocations at the substrate interface [52]. However, the height variations on the surface may persist to a considerable thickness, well beyond the effective range of the misfit dislocations (MD) strain fields which gave rise to them in the first place,3 if there are compositional or height variations which create secondary strain variations at the surface. Low-temperature growth can suppress the cross-hatch by reducing the surface mobility of adatoms [53]. In addition to strain-induced cross-hatch, other sources of surface roughening include three-dimensional growth, second-nucleation, and pits associated with threading dislocations. Typically, the cross-hatch gives rise to roughening on a scale of mm, whereas the other sources of roughening occur on a smaller scale. Fourier analysis of the surface roughness can therefore separate these effects.

25.2.6

Device Applications of Uniform Buffers

Uniform buffer layers have been utilized in a number of metamorphic devices, including InxGa1
xAs quantum well laser diodes grown on GaAs by metalorganic vapor phase epitaxy (MOVPE) [46,54–57] and molecular beam epitaxy (MBE) [58], InxGa1
xAs quantum dot lasers on GaAs by MBE [49], and MBE-grown InxGa1
xAs/InyAl1
yAs high electron mobility transistors (HEMTs) on GaAs [59]. Although uniform buffers tend to exhibit higher dislocation densities than graded buffers, some studies of metamorphic HEMTs suggest that the buffer layer surface smoothness plays a more important role than the threading dislocation density in 3

The strain fields surrounding misfit dislocations tend to cancel at distances greater than one-half their separation, which is on the order of 5–50 nm for uniform layers having moderate lattice mismatch (0.2–2%).

Chapter 25 • Low-Temperature and Metamorphic Buffer Layers

1015

determining the two-dimensional electron gas (2DEG) mobility. The cross-hatch and corrugations associated with metamorphic growth can give rise to significant electron scattering and lower the 2DEG mobility if the interface roughness has a lateral scale similar to the Fermi wavelength, given by lF ¼ (2p/ns)1/2, where ns is the sheet electron concentration [36]. Thomas et al. [60] grew InAs/AlxGa1
xSb QWs on GaAs substrates using uniform 2 mm-thick uniform buffers of either GaSb or AlSb by MBE. Both types of structures contained w108 cm
2 threading dislocations, but the one with the GaSb buffer exhibited much higher 2DEG mobility at 12 K: 944,000 cm2 V
1 s
1 with ns ¼ 1.3  1012 cm
2 compared to 244,000 cm2 V
1 s
1 with the AlSb buffer, with the same 2DEG concentration of ns ¼ 1.3  1012 cm
2. This difference was attributed to the smoother morphology of the structure with the GaSb buffer due to the higher surface mobility of Ga adatoms. There have been several reports of metamorphic lasers fabricated on GaAs substrates using uniform buffer layers [58,61]. Quantum dot and quantum dash lasers appear to be less sensitive than quantum well devices to the threading dislocation density, and in the case of quantum dots it is possible to remove those containing defects by selective evaporation [62–65]. Good operating performance has been obtained in these metamorphic lasers despite the relatively high threading defect densities. Arai et al. [57] demonstrated the highest temperature operation (200  C pulsed) for a metamorphic laser on GaAs emitting at 1.3 mm, with T0 ¼ 200 K, by MOVPE. Nonetheless, reliability and lifetime remain important issues due to the presence of dislocations in the active device regions.

25.3 Step-Graded Buffer Layers In a step-graded buffer, the overall change in lattice constant is divided between several uniform layers, in steps which may be equal (linear step grading) or varied (nonlinear step grading). This approach has two advantages relative to the uniform buffer: the individual steps in lattice constant may be made small enough to preserve layer-by-layer growth, and the misfit dislocations are spread out in the growth direction by placing them at multiple abrupt interfaces. Step-graded buffers have been investigated in a number of material systems including InxGa1
xAs [27,28,66–69], InxAl1
xAs [24,39,68,70–80], InxAlyGa1
x
yAs [19,35,80], and AlxGa1
xSbyAs1
y [52,81] on GaAs (001) substrates, InAsyP1
y [29,82–84] on InP (001), and InxAl1
xSb [85] on GaSb (001). There has been relatively little modeling work with step-graded buffers, and their theoretical behavior is less firmly established than for the linearly graded case, but some important properties are known regarding their dislocation and strain behavior. Abrahams et al. [5] considered a simple model for a step-graded structure and argued that the threading dislocation density would reach a steady-state value which depends on the average grading coefficient, similar to the case of linear grading. This model is illustrated in Figure 25.1, in which MDs are created by the jogging of threading

1016

HANDBOOK OF CRYSTAL GROWTH

FIGURE 25.1 Abrahams model for the step-graded buffer, predicting a steady-state threading dislocation density proportional to the average grading coefficient [5]. Reprinted from Abrahams MS et al. J. Mater. Sci. 1969;4:223-35. With permission. Copyright 1969 Springer.

dislocations (TDs) at each step interface. If the average length of MD segments is fixed, the steady-state TD density will be proportional to the amount of mismatch at each step (the average grading coefficient). Experimental results have tended to bear this out, and show the absence of misfit dislocations above the top step interface. Experiments have also shown greater residual strain in the topmost layer of a step-graded buffer, and this is to be expected if lattice relaxation proceeds with the deposition of each successive step [28]. Experiments with InxAl1
xAs on GaAs showed that step-graded and linearly graded buffers had similar values of residual surface strain [77]. Therefore, we can identify several similarities to linearly graded layers: (1) misfit dislocations are absent from the topmost portion of the buffer, in a misfit dislocation free zone (MDFZ); (2) there is a relatively large built-in strain in the topmost layer; and (3) overshoot of the buffer layer composition (in other words, a reverse step of the device layer) should allow growth of a nearly strain-free device layer, if its relaxed lattice constant matches the in-plane lattice constant of the strained layer at the top of the buffer. An important difference between step-graded and linearly graded buffers is that the step-graded buffer contains an MDFZ in each step, whereas a linearly graded buffer contains only two MDFZs. Experimental investigations of step-graded buffers have involved 10 or more steps [29,39,76] and as few as two steps [69]. If a large number of small steps is employed, the behavior of the step-graded layer will approach that of the linear buffer [76], but otherwise we should expect the abrupt interfaces to give rise to characteristics unique to step grading.

25.3.1

Lattice Relaxation and Residual Strain in Step-Graded Buffers

Considering force balance on a grown-in dislocation, one can see that the average residual strain is the same as that in a uniform layer with the same total thickness. The

Chapter 25 • Low-Temperature and Metamorphic Buffer Layers

1017

deposition of each successive step gives rise to lattice relaxation of the underlying layers [75] to maintain the inverse relationship between average strain and thickness. Therefore, the residual strain is concentrated in the top layer of the step-graded buffer. For example, in a step-graded InAsyP1
y structure grown on InP (001) by MOVPE for the realization of a mid-IR laser diode, Kirch et al. [86] found that the top layer (500 nm InAs0.68P0.32) was 90% relaxed and, therefore, contained 10% of the coherency strain. The built-in strain at the top of the step-graded buffer helps sweep out threading dislocations, generally leading to a reduced threading dislocation density compared to the case of a uniform buffer. In order to avoid new misfit dislocations in the device layer, the buffer can be designed with compositional overshoot so that the relaxed device layer matches the in-plane lattice constant of the buffer layer [75,76,78,86]. For InxGa1
xAs/ InyAl1
yAs quantum wells on GaAs substrates, it is possible to control the residual strain in the quantum wells by varying the amount of overshoot in the step-graded buffer [76]. Exact matching is difficult to achieve in practice, unless the relaxation dynamics can be predicted accurately, but could be aided by the use in in situ stress measurements using a multibeam optical stress sensor (MOSS) [75]. The residual strain and lattice relaxation in step-graded buffers are usually assessed by ex situ X-ray measurements including X-ray reciprocal space maps (RSM)s and highresolution X-ray rocking curves (HRXRC). Dynamical simulations of HRXRCs allow depth profiling of composition and strain as long as symmetrical and asymmetrical reflections are used [87–89]. Recently this method has been extended to include the profiling of dislocation densities [90,91]. In most cases, the dynamical simulations are made necessary by the lack of a one-to-one correspondence between X-ray diffraction peaks and lattice constants present in the sample [87]. In some step-graded layers, though, a separate peak may be resolved for each layer, and it becomes possible to extract approximate strain data directly from the peak positions. This is the case for the HRXRC of Figure 25.2, measured from an overshoot step-graded InxAl1
xAs structure FIGURE 25.2 A 004 high-resolution X-ray diffraction (HRXRD) rocking curve for 1 mm In0.75Al0.25As grown on a stepgraded InxAl1
xAs buffer layer with an indium compositional overshoot of Dxos ¼ 0.1 [78]. Reprinted from Jiang Z. et al. Appl. Surf. Sci. 2008;254:5241-6. With permission. Copyright 2008 Elsevier

1018

HANDBOOK OF CRYSTAL GROWTH

grown on GaAs (001) by MBE and incorporating nine 100 nm steps with indium mole fractions of 0.05, 0.15, 0.25, 0.35, 0.45, 0.55, 0.65, 0.75, and 0.85. A 1 mm uniform layer of In0.75Al0.25As layer was grown on top of the step-graded buffer. Analysis of the X-ray rocking curve, after canceling out the effect of crystallographic tilting by use of the rocking curves measured at opposing azimuths, revealed that the top (device) layer was 98% relaxed using this overshoot design [78]. In situ stress measurements are also of great interest, because the ex situ X-ray measurements do not reveal the time evolution of the stress or strain. One method is the MOSS, in which multibeam laser illumination of the growing surface allows determination of the sample curvature, and indirectly, the average stress in the growing film. Although depth-profiling is not possible with the MOSS technique, it does allow determination of the average stress as a function of thickness while the structure is being grown, and this can provide valuable insight into the relaxation dynamics of metamorphic buffers. Lynch et al. [75] applied MOSS to step-graded InxAl1
xAs buffers with 250 nm thick steps on GaAs substrates to show that (1) the relaxation of underlying layers proceeds with the deposition of each successive step, and (2) each step quickly reaches a near-constant stress early in its growth, so that it might be possible to use much thinner steps. Figure 25.3 shows the compositional grading profile, the stressthickness product as a function of thickness, and the average stress as a function of thickness for this InxAl1
xAs step-graded buffer. Some studies have revealed nearly complete relaxation in step-graded buffers and the device layers grown on top, even without the use of overshoot, as long as the device layer is sufficiently thick, but these structures may contain misfit dislocations in the device layers. Shang et al. [24] utilized X-ray reciprocal space mapping for a step-graded InxAl1
xAs structure (100 nm steps, Dx ¼ 0.1) with a 1 mm uniform layer of In0.52Al0.48As on top to show that all layers were w98% relaxed without using overshoot. Alternatively, use of thick layers in the step-graded buffer results in a high degree of lattice relaxation at the top of the buffer, removing the need for overshoot. Chen et al. [92] demonstrated 96% relaxation in the top layer of an InxGa1
xAs step-graded buffer grown on GaAs by MBE using relatively thick (0.3 mm) step layers and achieved excellent 2DEG mobility (mn ¼ 35,000 cm2 V
1 s
1 with ns ¼ 1.21  1012 cm
2 with x ¼ 0.3 at 77 K) without the need for overshoot.

25.3.2

Misfit and Threading Dislocations in Step-Graded Buffers

An important question for the design of metamorphic device structures involves the choice of step-graded or continuously graded buffer layers for optimum reduction of the threading dislocations. Though there have been few direct comparisons, the answer seems to depend on the material system and the ending composition. Some results suggest that step grading can be superior, confining dislocations to lower layers if the defects move more easily or have lower energy in material with those compositions. Arguments of this type have been made on the basis of yield strength and hardness.

Chapter 25 • Low-Temperature and Metamorphic Buffer Layers

(a)

Layer:

1

2

3

4

5

6

Inverse

Nominal XIn

0.6 0.5 0.4 0.3 0.2 0.1

(b)

1019

FIGURE 25.3 (a) Compositional grading profile, (b) stress-thickness product as a function of thickness, and (c) average stress as a function of thickness for an InxAl1
xAs step-graded structure. The stress-thickness product was determined by MOSS measurements. [75]. Reprinted from Lynch C. et al. J. Vac. Sci. Technol. B 2004;22:153943. With permission. Copyright 2004, American Vacuum Society.

0

Stress-thickness (GPa-Å)

–500

(c)

–1000 –1500 –2000 –2500 –3000 0 –0.1

Average stress (GPa)

–0.2 –0.3 –0.4 –0.5 –0.6 –0.7 –0.8 –0.9 –1

0

4000

8000 12000 Thickness (Å)

16000

For step-graded InxGa1
xAs on GaAs (001), Krishnamoorthy et al. [66] showed that new dislocations were absent from the topmost layer as long as the change in composition was less than 0.18 per step, and they attributed this to the increasing yield strength with indium content. However, this approach was only effective up to an indium mole fraction of w0.50, beyond which the yield strength actually decreases. Jeong et al. made similar observations with step-graded InxAl1
xAs on GaAs (001). Though step grading

1020

HANDBOOK OF CRYSTAL GROWTH

was effective in reducing the threading dislocation density up to an alloy composition of w0.50, they found that step-graded layers with higher indium concentrations yielded threading dislocation densities which were similar to those for uniform buffers having the same total thickness. They attributed this effect to alloy hardening, which results in maximum hardness in the middle of the compositional range. Based on the results above, it is interesting to consider the behavior of step-graded InxGa1
xAs or InxAl1
xAs with high indium content, which have been investigated by Gozu et al. [93], Mendach et al. [73], Heyn et al. [74], and Jiang et al. [78]. Gozu et al. [93] fabricated an In0.75Ga0.25As/In0.75Al0.25As HEMT on GaAs using a step-graded InxAl1
xAs buffer, and although no threading dislocation densities were given the device exhibited very high mobility, mn ¼ 397,000 cm2 V
1 s
1 with ns ¼ 1.0  1012 cm
2 at 4.2 K. Mendach et al. [73] grew an In0.75Ga0.25As/In0.75Al0.25As quantum well on a step-graded InxAl1
xAs buffer on GaAs (001) having 100 nm steps with indium mole fractions of 0.15, 0.25, 0.35, 0.45, 0.55, and 0.65. The surface threading dislocation density was measured by PVTEM to be 3.6  109 cm
2. In an otherwise similar structure containing an strained-layer superlattice (SLS) under the step-graded buffer, a lower threading dislocation density of 1.0  109 cm
2 was obtained and under illumination the 2 K Hall mobility was mn ¼ 400,000 cm2 V
1 s
1 with ns ¼ 5.6  1011 cm
2. Heyn et al. [74] used this same step-graded structure with the inserted strained-layer superlattice to fabricate a shallowchannel InAs HEMT, with the channel 16.5 nm below the surface and exhibiting 4 K channel mobility under illumination of mn ¼ 160,000 cm2 V
1 s
1 with ns ¼ 6.3  1011 cm
2 at 4.2 K. Figure 25.4 shows XTEM images of these structures (a) with and (b) without the SLS, showing the difference in TD behavior. Jiang et al. grew a uniform 1 mm In0.75Al0.25As layer on a step-graded buffer incorporating overshoot with a maximum indium concentration of 0.85 [78]. XTEM revealed that most threading dislocations were confined to the step-graded buffer, but the surface dislocation density was still a relatively high 2  108 cm
2. The threading dislocation densities reported in these studies are similar to those that would be expected with uniform buffers having the same total thickness, suggesting weak dislocation reduction behavior in these highindium materials, even though high electron mobilities have been obtained at cryogenic temperatures using these buffers. Quaternary step-graded buffers have also been investigated, such as AlxGa1
xAs1
ySby on GaAs for the realization of InAs quantum dot (QD) lasers [81]. Using eight steps having fixed aluminum (x ¼ 0.5) and a maximum antimony mole fraction y ¼ 0.24, Xin et al. showed by XTEM that dislocations were absent from the top layer, which was partially relaxed. Balakrishnan et al. [52] demonstrated InAs quantum dashes with room temperature emission at w2.0 mm on a step-graded Al0.5Ga0.5As1
ySby buffer with 16 steps and a top composition of y ¼ 0.46. This structure had a low threading dislocation density at the top of the step-graded buffer, <105 cm
2, as determined by TEM. The steady-state threading dislocation density is reached in the early stages of growth, so the conditions of growth at the first interface are critical in determining the surface dislocation density. Sometimes, the first step in composition is made smaller than the

Chapter 25 • Low-Temperature and Metamorphic Buffer Layers

1021

FIGURE 25.4 XTEM images of step-graded InxAl1
xAs structures grown on GaAs (001) substrates by MBE: (a) with an inserted strained-layer superlattice, and (b) without a strained-layer superlattice [74]. Reprinted from Heyn Ch. et al. J. Cryst. Growth 2003;251:832-6. With permission. Copyright 2003 Elsevier.

rest, or grown at a lower temperature, to optimize the dislocation density. It has also been clearly shown that the insertion of a strained-layer superlattice below a step-graded buffer establishes longer misfit segments, enhances lattice relaxation in the buffer, and reduces the surface dislocation density [73,74,79]. Several studies have shown that low-temperature growth helps to confine threading dislocations to the metamorphic buffer. Grider et al. [20] showed that, for InxGa1
xAs HEMTs (0.2  x  0.5) grown on GaAs substrates by MBE with a step-graded InxGa1
xAs

1022

HANDBOOK OF CRYSTAL GROWTH

buffer, low-temperature buffer growth at 300  C resulted in a structure in which threading dislocations were confined to the buffer and the 77 K electron mobility was >22,000 cm2 V
1 s
1 at x ¼ 0.4. When the buffer was grown at the same temperature as the device, 500  C, there was a high density of threading dislocations propagating through the device as seen by PVTEM, and the 77 K mobility was lower by about a factor of three. In some studies, high-temperature annealing has been applied between layers of the step-graded buffer to control threading dislocation propagation and reduce the surface density. Huo et al. [94] used in situ annealing at 500–540  C between layers of an InxGa1
xAs step-graded buffer grown on GaAs by MBE at 400  C. After growth of four 200 nm steps, with a top indium mole fraction of 0.4, a coherently strained 10 nm layer of Ge was grown on top, and no threading dislocations were observed in the Ge by XTEM, indicating that the surface density of dislocations was less than 108 cm
2. Mi et al. [49] inserted 1.5 nm AlAs layers between the steps of a low-temperature (390  C) stepgraded InxGa1
xAs buffer grown on a GaAs substrate by MBE to allow hightemperature (700  C) annealing of the InxGa1
xAs layers. This resulted in a sufficiently low threading dislocation density for the fabrication of a quantum dot laser diode emitting at 1.52 mm. Some evidence indicates that lower threading dislocation densities may be obtained by reducing the average grading coefficient, either by using small compositional steps or thicker step layers. Typical step thicknesses are 100 nm, and typical average grading coefficients are 500 cm
1 to 1000 cm
1. As an example, a step-graded InxAl1
xAs buffer with 100 nm steps and an increment in the indium composition of Dx ¼ 0.1 has an average grading coefficient of w700 cm
1. Czaban et al. [83] found, for uniform InAsyP1
y material grown on an InP substrate with a step-graded InAsxP1
x buffer, that doubling the step thickness (from 50 to 100 nm) increased the room temperature photoluminescence (PL) intensity from the device layers by 40%. He et al. [27] reported an extremely low etch pit density (EPD) of 5.0  103 cm
2, comparable to the GaAs substrates, for a laser structure on a step-graded InxGa1
xAs buffer using thick steps (200 nm) and a small increment in the indium mole fraction (Dx ¼ 0.02), resulting in an average grading coefficient of w70 cm
1.

25.3.3

Morphology and Surface Roughening in Step-Graded Buffers

Step-graded device structures typically exhibit cross-hatch morphology with corrugations along the [110] and ½110 directions [20], as shown in the optical micrograph of Figure 25.5 for a mid-IR laser diode on an InP (001) substrate with a step-graded InAsyP1
y buffer layer [29]. It has been shown that the average period of surface undulations corresponds approximately to the separation of misfit dislocations, projected into the interface and observed by PVTEM [76]. Often, the undulations are asymmetric and indicate asymmetric MD densities. In addition to the normal cross-hatch, deep grooves have been found parallel to the ½110 direction in structures containing tensile residual strain in the device layers [76]. The cross-hatch arises from the influence of the

Chapter 25 • Low-Temperature and Metamorphic Buffer Layers

1023

FIGURE 25.5 Optical micrograph showing cross-hatch pattern on the surface of a 500 nm InAsP/200 nm InGaAs SCH/InAs QW laser diode grown on a step-graded InAsyP1
y buffer layer on an InP (001) substrate [29]. Reprinted from Kirch J. et al. J. Cryst. Growth 2010;312:1165-9. With permission. Copyright 2010 Elsevier.

MD strain fields at the growing surface, which can induce compositional or growth rate variations. In a uniform layer, the MDs are buried at the interface, but the cross-hatch may persist in layers much thicker than the effective range of the misfit strain fields, due to secondary strain fields associated with height and compositional variations. In a step-graded layer, new misfit dislocations are introduced at each step, so the cross-hatch generally becomes more pronounced as the layer is grown. Increasing the separation of MDs also increases the effective range of their strain fields which give rise to cross-hatch. For these reasons, the associated surface roughness tends to be more problematic in graded buffers than in uniform composition layers. The surface roughness associated with cross-hatch may be reduced by lowtemperature growth [22], high-temperature annealing [94], or the use of surfactants as has been shown qualitatively in Nomarski images and quantitatively by AFM. The underlying physics involves manipulation of the surface mobility for adatoms. For stepgraded InxAl1
xAs grown on GaAs by MBE with a sublinear profile and top indium composition of 0.35, studied by Nomarski microscopy, Shen et al. [22] found cross-hatch along both <110> directions for growth at 500  C, corrugations along the ½110 direction for growth at 450 and 350  C, but an absence of corrugations and cross-hatch for lowtemperature growth at 250  C. For sublinear step-graded InxAl1
xAs grown on GaAs (001) by MBE for the fabrication of InxGa1
xAs/InyAl1
yAs HEMTs, Mishima et al. found that reduced temperature growth of step-graded InxAl1
xAs at 350  C resulted in superior morphology compared to deposition at 400  C [71]. For step-graded InxGa1
xAs grown on GaAs by MBE at 400  C and annealed between steps at 500–540  C, Huo et al. [94] found that the rms surface roughness in a 10 nm Ge top layer increased with the number of steps and top indium content, but was only 1.01 nm using four steps and a maximum indium composition of 0.4. Three-dimensional growth is another cause of surface roughening, but lowering the growth temperature has been reported to extend the compositional regime for two-dimensional growth in some mismatched ternary alloys. This behavior has been

1024

HANDBOOK OF CRYSTAL GROWTH

reported in the case of a single In0.1Al0.9As layer on GaAs by MBE, which could be grown in a two-dimensional mode at a low temperature of 300  C [95]. Shen et al. found a similar result for InxAl1
xAs step-graded buffers on GaAs [22]. Use of low-temperature growth can also be helpful in reducing surface roughness associated with phase separation or clustering. Shang et al. [24] studied the influence of temperature and arsenic overpressure on the morphology in step-graded InxAl1
xAs. They found that low-temperature growth at 380  C resulted in the smoothest morphology, with rms roughness of 0.802 nm as determined by AFM using a 5  5 mm observation area. In–As and Al–As have very different bond energies, which can lead to InAs and InAl clustering; Shang et al. attributed the improved smoothness at low temperature to the suppression of InAs–AlAs clustering. Increasing the As overpressure from 5.0  10
6 Torr to 7.6  10
6 Torr gave rise to a three-dimensional growth mode, as seen by the spotty reflection high-energy electron diffraction pattern, and worsened the surface roughness. In some studies it has been reported that growth of a thick, uniform layer on top of the step-graded buffer can reduce the roughness associated with cross-hatch, by burying the misfit dislocations responsible for the cross-hatch. Balakrishnan et al. [52] used a 2 mm uniform layer of Al0.5Ga0.5As0.54Sb0.46 on top of a step-graded Al0.5Ga0.5As1
ySby buffer for this purpose. Though the rms surface roughness was not given, it was amenable to the deposition of InAs quantum dashes.

25.3.4

Crystallographic Tilting in Step-Graded Buffers

Step-graded buffers typically exhibit crystallographic tilt which accumulates at each step [77] and which has been reported to degrade the quality of device layers grown on top [69]. Lee et al. [77] studied crystallographic tilting in step-graded InxAl1
xAs buffer layers grown on GaAs substrates by MBE. The tilt increased with each step of the buffer, and its magnitude was consistent with the assumption that all misfit dislocations were 60 dislocations with the same sign tilt component (type II relaxation). The tilt also decreased at the reverse step of the overshoot graded structure. Gonzalez [69] studied tilting in step-graded InxGa1
xAs buffers having two steps. Crystallographic tilt was present at each of the two interfaces, but the introduction of a graded transition zone at the second interface reduced it greatly. Based on this observation and the reduction of the misfit dislocation density when a transition zone was used, it was proposed that the difference comes about because there is a greater proportion of edge dislocations with the use of a graded transition, and edge dislocations with in-plane Burgers vectors do not introduce any tilt.

25.3.5

Device Applications of Step-Graded Buffers

Step-graded buffers have been successfully applied in device applications including HEMTs [20,35,71–74], QD lasers [27,81], quantum cascade lasers [19], and thermovoltaic cells [84].

Chapter 25 • Low-Temperature and Metamorphic Buffer Layers

1025

The first metamorphic InxGa1
xAs/InxAl1
xAs HEMT to be realized on a GaAs substrate in the range 0.25  x  0.5 was demonstrated by Grider et al. [20] using a stepgraded InxGa1
xAs buffer grown at low temperature (300  C) by MBE. They observed that dislocations were confined to the low-temperature, metamorphic buffer using PVTEM with a detection limit of w108 cm
2 in threading dislocation density. However, use of a similar step-graded buffer grown at 500  C gave rise to a high density of threading dislocations, observable by PVTEM, in the device layers. Quantum dot, quantum dash, and quantum cascade lasers have been fabricated on GaAs substrates using step-graded buffers. He et al. [27] demonstrated an InAs QD laser diode on a GaAs substrate using a temperature-graded, step-graded InxGa1
xAs buffer layer and Balakrishnan et al. demonstrated InAs quantum dashes on GaAs using a stepgraded AlGaSbAs buffer [52]. Mawst et al. [19] realized an InxGa1
xAs/InxAl1
xAs quantum cascade laser on a GaAs substrate using an InxAlyGa1
x
yAs step-graded buffer. Xin et al. utilized a quaternary step-graded AlGaSbAs buffer with eight steps in conjunction with a linearly graded InAlAs buffer for an InAs QD laser on a GaAs substrate [81]. XTEM images showed that threading dislocations did not extend from the stepgraded buffer into the device layers, and pulsed, room temperature operation was achieved with a threshold current density of 304 A cm
2. Hudait et al. [84] demonstrated an InxGa1
xAs thermovoltaic cell on an InP substrate using a step-graded InAsyP1
y buffer. Low threading dislocation densities of 2–4  106 cm
2 were reported from a PVTEM study despite the use of only four compositional steps. Using a novel phosphorus-free InxAl1
xAs window, the thermovoltaic cell achieved w100% efficiency for wavelengths in the range 1.2–1.4 mm. Despite the broad application of step-graded buffers to metamorphic devices, the high dislocation density has been identified as the factor limiting the performance of InxGa1
xAs quantum dot lasers grown on GaAs substrates with two-step buffers [49]. Therefore, it may be possible to achieve better device performance using a greater number of steps or specially engineered continuously graded buffers.

25.4 Linearly-Graded Buffer Layers Buffer layers with linearly-graded composition, and therefore lattice constant, have been extensively investigated in a number of material systems, including InxGa1
xAs/GaAs [25,26,51,96–104], InxAl1
xAs/GaAs [34,75,103,105–110], InxAlyGa1
x
yAs/GaAs [18,19,23,35,80,95,111], Si1
xGex/Si [112–116], InxGa1
xP/GaAs [117–119], InxGa1
xP/ GaP [120], ZnSySe1
y/GaAs [102,121], and InxGa1
xSb/GaSb [122,123]. A possible advantage of continuous grading is that layer-by-layer growth may be maintained without the intrusion of island growth associated with large, abrupt changes in composition [119]. Haupt et al. [35] compared the surface morphologies of In0.52Ga0.48As HEMTs on linear and step-graded InxAl1
xAs buffer layers; as shown in the Nomarski micrographs of Figure 25.6, the structure with the linear buffer exhibited a cross-hatch

1026

HANDBOOK OF CRYSTAL GROWTH

FIGURE 25.6 Nomarski micrographs of In0.52Ga0.48As HEMTs on (a) linear and (b) step-graded InxAl1
xAs buffer layers [35]. Reprinted from Haupt M. et al. Appl. Phys. Lett. 1996;69:412–4. With permission. Copyright 1996, American Institute of Physics.

pattern whereas the step-graded device had rough, irregular morphology which was attributed to three-dimensional growth. In another study involving similar devices on quaternary InxGayAl1
x
yAs buffer layers, Haupt et al. [124] found that devices on linear buffers possessed smoother morphology and significantly higher 77 K mobility (38,000 cm2 V
1 s
1 vs 26,000 cm2 V
1 s
1).

25.4.1

Approaches to Linear Grading

Several approaches to linear compositional grading are shown in Figure 25.7, along with their approximate misfit dislocation density profiles. By far the most studied approach is the “forward-graded” buffer shown in Figure 25.7(a), in which the lattice mismatch is zero at the substrate interface and increases linearly to match the lattice constant of the device layer,4 and the lattice mismatch is given by ¼ Cf y. Although the case of tensile mismatch (Cf > 0) is shown in Figure 25.7(a), the compressive case is simply a mirror image. In the overshoot graded layer shown in Figure 25.7(b), the lattice mismatch in the graded buffer “overshoots” that in the device layer. This can compensate for incomplete relaxation in the graded layer, allowing in-plane lattice matching between the strained buffer layer and relaxed device layer [47a,47b]. The jump-graded buffer [114] of Figure 25.7(c) contains a nonzero interfacial mismatch, ¼ f0 þ Cf y, in which f0 and Cf both have the same sign as the device mismatch. It contains interfacial misfit dislocations, and can quickly reach a steady-state threading dislocation density, but dislocation interactions and pinning can be more pronounced than in the simple forward graded layer. In the reverse-graded approach of Figure 25.7(d), f ¼ f0 þ Cfy, and f0 has the same sign as the device mismatch, but 4 The “device layer” may actually include a series of layers, such as multiple quantum wells and graded layers, as in a graded index separate confinement heterostructure laser diode. For simplicity, we show the device layer as a single uniform layer with the same average lattice constant and total thickness as the actual device structure.

Chapter 25 • Low-Temperature and Metamorphic Buffer Layers

1027

FIGURE 25.7 Approaches to linearly graded buffers are (a) forward graded, (b) overshoot graded, (c) jump graded, and (d) reverse graded. The lattice mismatch is f, r is the misfit dislocation density, and y is the distance from the substrate interface.

Cf has the opposite sign. The relaxation behavior of reverse-graded layers is quite complex [125], exhibiting force balance on grown-in dislocations at up to three critical layer thicknesses [126], but preliminary work with this type of buffer indicates that the reverse grading may allow the bending over of threading dislocations associated with the interfacial mismatch, resulting in a low device threading dislocation density with a minimal buffer thickness [127]. In the following discussions, our focus will be the forward-graded approach illustrated in Figure 25.7(a) unless otherwise noted.

1028

HANDBOOK OF CRYSTAL GROWTH

25.4.2

Misfit Dislocations and Strain in Linearly Graded Buffers

Early experimental studies by Abrahams et al. [5] with vapor phase epitaxial GaAs1
yPy/ GaAs (001) using XTEM revealed that the linearly graded material contained a nearly constant areal density of misfit dislocations rA, that this density of misfit dislocations was proportional to the rate of grading, and that the surface density of threading dislocations D was also proportional to the rate of grading. Sacedon et al. observed similar behavior in linearly graded MBE-grown InxGa1
xAs/GaAs (001), but noted the existence of a MDFZ adjacent to the surface, above the dislocated region with nearly constant rA [97]. Tersoff [47a,47b] developed an approximate model for the equilibrium misfit dislocation density and strain profiles in a linearly graded layer, based on a minimization of strain energy and dislocation line energy. It was assumed that the lattice mismatch, like the composition, varies linearly with distance from the interface and is given by f ð yÞ ¼ Cf y

(25.9)

where Cf is the grading coefficient and y is the distance from the interface. Tersoff showed that misfit dislocations are first introduced at a critical layer thickness given by sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2Fd hc ¼ ; bYCf sin a cos 4

(25.10)

where Fd is the line energy of misfit dislocations and Y is the biaxial modulus,5 which for 2 a zinc blende semiconductor with (001) orientation is given by Y ¼ C11 þ C12
2C12 =C11 , where C11 and C12 are the elastic stiffness constants. Lattice relaxation is accompanied by the introduction of an approximately constant areal (cross-sectional) misfit dislocation density, which is just sufficient to relax the additional misfit introduced by grading. rA ¼

Cf b sin a cos 4

(25.11)

The thickness of the dislocated region, in which this nearly constant misfit dislocation density exists, is given by sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2Fd yd ¼ h
bYCf sin a cos 4

(25.12)

where h is the layer thickness. Above this, there is a MDFZ with thickness equal to hc. In an XTEM study of linearly graded InxGa1
xAs/GaAs (001), Sacedon et al. [97] verified the existence of an MDFZ having a thickness close to that predicted by Tersoff. Bertoli et al. [102] used detailed numerical calculations to reveal small departures from the ideal rectangular profile for misfit dislocations found in the approximate analysis of Tersoff, and these are illustrated in Figure 25.8 for the case of linearly graded 5

Here the term “biaxial modulus” is used to refer to the Young’s modulus for the case of biaxial stress. In other words, it is the ratio of the in-plane stress to in-plane strain for the condition of biaxial stress, Y ¼ sjj/εjj, with sxx ¼ syy ¼ sjj and sxy ¼ syx ¼ syz ¼ szy ¼ szx ¼ sxz ¼0.

Chapter 25 • Low-Temperature and Metamorphic Buffer Layers

1029

FIGURE 25.8 Calculated equilibrium misfit dislocation density profiles for 0.5 mm-thick linearly graded layers of Si1
xGex on Si (001) substrates, with grading coefficients of (a)
50 cm
1, (b)
100 cm
1, and (c)
150 cm
1. The dashed profiles were calculated using the approximate Tersoff model [47a,47b] while the solid profiles were calculated using detailed numerical calculations by Bertoli et al. [102]. Reprinted from Bertoli B. et al. J. Appl. Phys. 2009;106:073519. With permission. Copyright 2009, American Institute of Physics.

Si1
xGex/Si (001). First, there is a second MDFZ adjacent to the interface. This is because the lattice mismatch at the interface is zero, and introducing misfit dislocations there would actually increase the strain energy. The thickness of the interfacial MDFZ is small in the linearly graded layer unless a very small grading coefficient is used, but has been observed by XTEM in InxGa1
xAs on GaAs [28]. Second, the misfit dislocation density is not constant, but tapered, in the dislocated region. The extent of this tapering may be up to 20% using typical material properties and grading coefficients. The underlying physical causes for this tapering are the change in the length of the Burgers vector with the variation in lattice constant, the inherent variation in the grading coefficient with a linear variation in lattice constant, and the reduction in the dislocation line energy with distance from the interface. In InxGa1
xAs and Si1
xGex graded layers, the lattice constant increases with distance from the interface, so the misfit dislocation density decreases in the dislocated region. Additional differences are expected due to differences in the mobility of a and b dislocations, which cause asymmetries in the misfit dislocation densities along the [110] and ½110 directions. This effect, not considered by Tersoff or Bertoli et al., has been observed experimentally in linearly graded layers of InxGa1
xAs/GaAs (001) grown by MBE [101]. In addition, Capotondi et al. showed that the thickness of the surface MDFZ is different for the misfit dislocations along the two 110 directions [76].

1030

HANDBOOK OF CRYSTAL GROWTH

The approximate equilibrium strain profile in the linearly graded layer was found by Tersoff [47a,47b] with the assumptions that (1) the strain is completely relaxed in the dislocated region, and (2) the derivative of the strain in the MDFZ is equal to the grading coefficient, yielding 

εjj ¼

0;

Cf y
yd ;

y  yd ; y > yd :

(25.13)

Therefore the linearly graded layer has a large built-in surface strain which helps to sweep out threading dislocations from the MDFZ, given approximately by sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2Fd Cf : εjj ðhÞ ¼ bY sin a cos 4

(25.14)

Bertoli et al. [102] used detailed numerical calculations for Si1
xGex/Si (001) graded layers and found small departures from the approximate strain relationships given by Tersoff. The presence of the interfacial MDFZ introduces nonzero strain in the dislocated region and also results in a somewhat larger built-in strain at the surface. Implicit in Tersoff’s derivation of the critical layer thickness for the linearly graded layer is the assumption that the dislocation line energy is independent of distance from the interface. Removing this assumption, and minimizing the total energy, Fitzgerald et al. [31] found the critical layer thickness as h2c ¼

  3bð1
n cos2 aÞ ehc   ; ln b 8pCf ð1 þ nÞ2 sin a cos l

(25.15)

where e is the dislocation core energy parameter. By applying a minimum energy approach, Sidoti et al. [115] determined the nonzero separation of the initial misfit dislocations from the interface to be yc ¼

hc
2

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi h4c bð1
nÞð1
n cos2 aÞ ;
  4 4pCf ð1 þ nÞ2 sin a cos l

(25.16)

and this is the thickness of the interfacial MDFZ when the first misfit dislocations are introduced. It is important to note that the thickness of this MDFZ varies as the layer is grown; in general the thickness of the interfacial MDFZ is y1, and this is equal to yc only at the critical layer thickness. The state of strain and crystallographic tilting in a graded heterostructure may be analyzed using high resolution HRXRC. Dynamical simulations are used to predict the rocking curve for the assumed structure, which is refined to obtain the best fit between the simulation and measured rocking curve [87–89]. In this way, the depth profiles of composition and strain may be determined indirectly. A limitation of this method has been the assumption of perfect crystals, which renders it applicable strictly to pseudomorphic structures. Recently the dynamical theory has been extended to metamorphic structures, and can in principle allow the depth profiling of the dislocation density as well as the composition and strain [90,91].

Chapter 25 • Low-Temperature and Metamorphic Buffer Layers

1031

RSM may also be used to assess the state of strain and crystallographic tilting in a metamorphic buffer. As with HRXRC, the tilting is easily determined by using a symmetric reflection measured at two or more azimuths. Once the tilt is accounted for, the RSM shows the variations of the in-plane and out-of-plane lattice constants in the graded structure. For example, Figure 25.9 shows RSM for LED structures on uniform 1 mm-thick InAsySb1
y grown on GaSb using an intermediate linearly graded buffer of InAsxSb1
x and measured around the 335 reflection of the GaSb (001) substrate [123]. The mole fraction of Sb in the top layer was 0.2 (a and b) and 0.44 (c and d). RSMs were measured at azimuths of 0 and 180 with respect to the [110] direction to cancel out any crystallographic tilt. The abscissa and ordinate are 3/2ajj and 5/at, respectively, where ajj and at are the in-plane and out-of-plane lattice constants, respectively. The red line shows the loci of 335 reflections from fully relaxed cubic material with varying lattice constant. The perpendicular blue lines represent constant in-plane lattice constant, coherently grown with the top of the linearly graded buffer. In each of the two structures, the linearly graded buffer gives rise to intensity along the diagonal line, indicating nearly complete relaxation. For the structure with 20% antimony, the uniform layer reciprocal lattice point, indicated by “L,” is off the diagonal line. From its position, the in-plane and out-of-plane lattice constants may be determined, and if the elastic constants are estimated, the relaxed lattice constant and state of strain may be determined. In situ measurements, such as those made using a MOSS, make it possible to study the evolution of the average film stress. Multibeam laser illumination of the growing surface allows determination of the sample curvature, and indirectly, the average stress in the growing film. Figure 25.10 illustrates the application of MOSS to a linearly graded InxAl1
xAs/GaAs (001) structure grown by MBE with overshoot. Figure 25.10(a) shows the compositional profile, Figure 25.10(b) shows the stress-thickness product as a function of thickness, and Figure 25.10(c) illustrates the average stress as a function of layer thickness [75]. Initially, the average stress increases monotonically with thickness, corresponding to pseudomorphic growth. Once the layer starts to relax, at w200 nm, the average stress begins to decrease. In the top of the linearly graded buffer, the average stress increases approximately linearly with thickness, indicating a nearconstant strain in the top MDFZ of the graded buffer. The overshoot design, frequently used in linearly graded metamorphic buffers [25,26,95,128,129], is intended to allow unstrained growth of the uniform layer, but the linear change in average stress during its growth shows that exact lattice matching was not achieved. However, MOSS monitoring could be used to help attain closer lattice matching in overshoot graded structures.

25.4.3

Threading Dislocations in Linear Buffers

The threading dislocation behavior of the linearly graded buffer is not completely understood at the present time. Nonetheless, experimental and modeling studies have shed

1032

HANDBOOK OF CRYSTAL GROWTH

FIGURE 25.9 Reciprocal space maps for LED structures on uniform 1 mm-thick InAsySb1
y grown on GaSb using an intermediate linearly graded buffer of InAsxSb1
x and measured around the 335 reflection of the GaSb (001) substrate. The mole fraction of Sb in the top layer was 0.2 (a and b) and 0.44 (c and d) [123]. Reprinted from Belenky G. et al. Appl. Phys. Lett. 2013;102:111108. With permission. Copyright 2013, American Institute of Physics.

Chapter 25 • Low-Temperature and Metamorphic Buffer Layers

1033

FIGURE 25.10 Application of the in situ multibeam optical stress sensor characterization to a linearly graded InxAl1
xAs/GaAs (001) structure grown by MBE with overshoot, (a) compositional profile, (b) stress-thickness product as a function of thickness, and (c) average stress as a function of layer thickness [75]. Reprinted from Lynch C. et al. J. Vac. Sci. Technol. B 2004;22:1539–43. With permission. Copyright 2004, American Vacuum Society.

some light on this important issue. In their pioneering study of linearly graded GaAs1
yPy/GaAs (001), Abrahams et al. [5] made a number of important observations regarding the types, configurations, and densities of misfit and threading dislocations in linearly graded material. They found that the surface threading dislocation density D varied linearly with the grading coefficient Cf, over two orders of magnitude change, and devised a simple model to explain these findings. Three key concepts were developed in their paper: (1) that the misfit dislocations do not extend from one wafer edge to the other, but are segmented; (2) that there is a set of inclined threading dislocations associated with the segment ends because dislocations may not terminate within a crystal; and (3) that the growing graded layer reaches a steady-state condition in which new misfit segments are produced by the bending over of existing inclined dislocations

1034

HANDBOOK OF CRYSTAL GROWTH

rather than by the introduction of new ones. The cross-sectional density of misfit dislocations is rA ¼

Cf ; bε

(25.17)

where bε is the misfit-relieving component of the Burgers vector. The number of misfit segments per unit volume will be ns ¼

2rA ; Lave

(25.18)

where Lave is the average length of misfit segments. If the density of inclined threading dislocations D reaches steady state after the growth of a thickness equal to the separation
1=2 between misfit segments, rA , then the density will be D ¼ ns r
1=2 ¼ A

2Cf1=2 1=2

Lave bε

;

(25.19)

where Lave is the average length of misfit segments. If it is assumed that this average
1=2 length is proportional to the average distance between misfit dislocations, Lave ¼ mrA , then D¼

2Cf ; mbε

(25.20)

and the density of threading dislocations will be proportional to the grading coefficient. From their TEM measurements of misfit and threading dislocation densities, and accounting for the fact that roughly half of the misfit dislocations were edge type while the other half were mixed 60 type, Abrahams et al. found a value of m z 8. Though this simple model is consistent with the experimental finding that the threading dislocation density is proportional to the grading coefficient in GaAs1
yPy/GaAs (001), it does not include dislocation dynamics phenomena such as thermally activated glide, Peierls forces, dislocation interactions, and pinning. It, therefore, can not explain the influence of temperature or the misfit dislocation free zones. Moreover, it has been shown that the threading dislocation density increases strongly with the total lattice mismatch, even with the grading coefficient fixed, in Si1
xGex/Si (001) [31]. Fitzgerald et al. [2] developed a dislocation dynamics model for a linearly graded metamorphic buffer grown at constant temperature. Key assumptions are that the layer is much greater than the critical layer thickness, that the threading dislocation density has reached a constant, steady-state value, and that dislocation glide is thermally activated with an exponential dependence on the effective stress.6 Hence the glide velocity for threading dislocations was assumed to be v¼B

  m  seff U ; exp
kT s0

(25.21)

6 The effective stress is that component of the stress which is above and beyond the equilibrium value; seff ¼ sjj
seq, where sjj is the actual in-plane stress and seq is the equilibrium in-plane stress.

Chapter 25 • Low-Temperature and Metamorphic Buffer Layers

1035

where B is a constant with units of velocity, seff is the effective stress, s0 is a constant having units of stress, m is a unitless constant generally between 1 and 2, U is the activation energy for dislocation glide, k is the Boltzmann constant, and T is the absolute temperature. If it is assumed that all dislocations are half loops and the misfit segments have 60 character, the rate of lattice relaxation is dd vbD bDB m ¼ ¼ ε dt 2 2 eff

  m  Y U ; exp
s0 kT

(25.22)

where b is the length of the Burgers vector, Y is the biaxial modulus, and εeff is the effective in-plane strain (the actual in-plane strain minus the equilibrium value). With the assumption of a constant rate of strain relaxation, the threading dislocation density may be solved for as D¼

2gCf expðU=kT Þ bBðY=s0 Þm εm eff

(25.23)

where g is the growth rate. This model predicts a threading dislocation density proportional to the grading coefficient, similar to the Abrahams et al. model, but it also predicts a linear dependence on the growth rate. It has been argued on the basis of this model that linearly graded layers will have similar threading dislocation densities because it is not practical to vary the growth rate or the grading coefficient by orders of magnitude and still maintain a practical growth time [2]. An order of magnitude change in growth rate coupled with an order of magnitude variation in the grading coefficient could result in about two orders of magnitude change in the threading density, with all other parameters equal. However, it is becoming increasingly common to insert one or more low-temperature buffer layers in the structure, or to use temperature grading, or non-linear or step- compositional grading, or superlattice buffers, or some combination of these techniques. In such cases the growth rate and grading rate can change significantly during growth, so that a much wider variation of surface dislocation density becomes achievable.

25.4.4

Crystallographic Tilting in Linear Buffers

Similar to step-graded buffers, linearly graded buffers tend to exhibit crystallographic tilt with respect to the substrate due to an imbalance of the populations of misfit dislocations with positive and negative tilt components. However, for the linear buffer the misfit dislocations are distributed throughout much of the thickness, so the tilting is expected to be continuous rather than discrete events confined to step interfaces. In X-ray rocking curves, this shows up as broadening of the buffer layer diffraction profile, and in the reciprocal space map it exhibits as a diagonal spreading of the buffer diffraction contours [77]. Chyi et al. compared the crystallographic tilting in linearly graded and step-graded InxGa1
xAs and InxAl1
xAs [68]. They found smaller tilts in the continuously graded layers, indicating a weaker imbalance between the slip systems. Lee et al. found a similar result in a comparison of linearly and step-graded InxAl1
xAs on GaAs (001) [77].

1036

HANDBOOK OF CRYSTAL GROWTH

Lee et al. also studied crystallographic tilting in MBE-grown single-slope and dual-slope linearly graded InxAl1
xAs buffers by RSMs; they found that the tilt increased superlinearly with indium composition, with sharp increases occurring at approximately x ¼ 0.6 [77]. Ihn et al. used RSMs to show that a tilted low-temperature linearly graded InxAl1
xAs buffer could be brought back in line with the substrate axis by rapid thermal annealing (RTA) for 700  C for 30 s [95]. Apparently the RTA reversed the imbalance in the dislocations with opposite tilt components.

25.4.5

Surface Roughening and Cross-Hatch in Linear Buffers

Similar to other metamorphic buffers, those with linear grading usually exhibit straininduced surface roughening which may take the form of corrugations [25], crosshatch [51], or sometimes irregular surfaces. Cross-hatch is associated with misfit dislocations, and may be present in high-quality material with threading dislocation densities below the detection limit by PVTEM [103]. The roughness may be quite different along the [110] and ½110 directions; for metamorphic high electron mobility transistor (M-HEMT) structures on GaAs substrates with linearly graded InxAl1
xAs buffer layers, Cordier et al. measured rms surface roughness of 1.2–1.6 nm along the [110] direction but 3.2–4.5 nm along the ½110 direction [129]. The surface roughness associated with cross-hatch is strongly affected by the temperature, grading rate, and even doping in the metamorphic buffer. These effects are governed by strain-field-induced surface roughening as described previously, but also by indium segregation in the case of InxGa1
xAs or InxAl1
xAs buffers. The increased indium concentration on the growth front has been modeled by Muraki et al. [130] as xseg ¼

ahCf R ; 1
R

(25.24)

where a is the lattice constant, h is the buffer thickness Cf, is the grading coefficient, and R is the segregation constant. This model predicts increased indium segregation and, therefore, surface roughness, with increasing thickness or grading coefficient. Lowtemperature growth decreases the surface roughness [35,51,100,106,131,132], and this is expected because the reduced surface mobility of adatoms would decrease surface roughening by either mechanism. Haupt et al. [35] measured the rms roughness and 2DEG mobility for In0.53Ga0.47As/In0.53Al0.47As HEMT structures grown on GaAs with linear and step-graded InxAl1
xAs buffers, for different buffer growth temperatures. Reduced buffer growth temperature, in the range 300–400  C, resulted in reduced roughness (Figure 25.11) and improved 77 K mobility (Figure 25.12). Song et al. investigated the influence of doping on surface roughness in low-temperature linearly graded InxGa1
xAs buffers on GaAs [51]. Beryllium doping reduced the surface roughness relative to undoped material, whereas silicon doping increased the surface roughness, as shown in Figure 25.13. These differences were proposed to be due to the influence of dopants on the segregation of indium; whereas silicon enhances this segregation, beryllium has the opposite effect. Surfactants can also modify the adatom mobility and

Chapter 25 • Low-Temperature and Metamorphic Buffer Layers

FIGURE 25.11 Root mean square surface roughness as a function of the buffer growth temperature, for Al0.48In0.52As/ Ga0.47In0.53As heterostructures grown on GaAs substrates with linearly graded or step-graded InxAl1
xAs buffer layers [35]. Reprinted from Haupt et al. Appl. Phys. Lett. 1996;69:412-414. With permission. Copyright 1996, American Institute of Physics.

25 Linear grading (quaternary) Step grading

rms roughness (nm)

20

1037

15

10

5

0 250

300

350 400 TB (°C)

450

500

FIGURE 25.12 Two-dimensional electron gas mobility as a function of the buffer growth temperature for Al0.48In0.52As/ Ga0.47In0.53As heterostructures grown on GaAs substrates with linearly graded or step-graded InxAl1
xAs buffer layers [35]. Reprinted from Haupt et al. Appl. Phys. Lett. 1996;69:412-414. With permission. Copyright 1996, American Institute of Physics.

50000 Linear graded (quaternary) Step graded

µ (cm2 V–1 s–1)

40000 77 K 30000

20000

10000 300 K 250

300

350

400 450 TB (°C)

500

550

600

reduce the surface roughness, as in the self-surfactant effect observed with antimonycontaining graded buffers [133].

25.4.6

Dual-Slope and Tandem Graded Buffers

Several unique graded buffer layers have been created by the use of disparate slopes (dual-slope buffers) or materials (tandem buffers). Capotondi et al. used a dual-slope step-graded InxAl1
xAs buffer for the realization of InxGa1
xAs/InyAl1
yAs quantum wells (QW) on GaAs [76]. In this buffer the average grading coefficient was 510 cm
1 (5.1% per mm) in the first 600 nm and 310 cm
1 in the remaining 600 nm, with 50 nm thick steps. Because of the small step thickness, this

1038

HANDBOOK OF CRYSTAL GROWTH

(a)

(b)

(c)

FIGURE 25.13 Cross-hatch morphology in linearly graded InxGa1
xAs/GaAs (001) grown by MBE: (a) undoped, (b) Be doped, and (c) Si doped [51]. Reprinted from Song Y. et al. J. Appl. Phys. 2009;106:123531. With permission. Copyright 2009, American Institute of Physics.

buffer was considered to approximate a continuous linearly graded layer, and the Tersoff model [47a,47b] was used to understand its behavior. XTEM micrographs showed that the material with the smaller grading coefficient had a lower misfit dislocation density, and that there was a 450 nm thick MDFZ adjacent to the surface. Lee et al. used RSMs to investigate dual-slope continuously graded InxAl1
xAs/GaAs buffer layers, in which the top of each buffer had a larger grading coefficient than the bottom portion [77]. The initial slope in all layers was w300 cm
1, but the final slope was varied. They found that the buffers with a greater final slope exhibited less strain, less tilting, and greater FWHM (mosaic spread). Single-slope and dual-slope buffers exhibited similar behavior, which was controlled by the final grading coefficient. Therefore, in a dual-slope graded buffer, the mosaic spread may be controlled by adjusting the grading coefficient in the topmost portion of the buffer. Yang et al. developed a tandem graded buffer involving MOVPE-grown InxGa1
xAs plus InxGa1
xP for InP-based devices on GaAs substrates [104]. The tandem design was used to avoid the problem of phase separation which leads to surface roughening and high threading dislocation densities in InxGa1
xAs with high indium compositions. The indium mole fraction was graded to 0.3 in the InxGa1
xAs, and to 1.0 in the InxGa1
xP. The InxGa1
xAs buffer was grown at reduced temperature (450  C instead of 750  C) for compositions in the range 0.1  x  0.3 to further suppress phase separation. By this approach, they obtained metamorphic InP on GaAs with a reported threading dislocation density of 7.9  106 cm
2 and an rms surface roughness of 7.4 nm on an AFM image of 40  40 mm.

25.4.7

Device Applications of Linear Buffers

Linearly graded metamorphic buffers have been the widely used in device applications, including HEMTs [18,21,23,105,106,109,110,118,123,129,131,134,135], metal oxide semiconductor high electron mobility transistors (MOS HEMTs) [136], heterojunction bipolar transistors (HBTs) [113,117,118,137], LEDs [31,123], laser diodes [26,81,103,106,122], photodiodes [18,80,108,138,139], and solar cells [119].

Chapter 25 • Low-Temperature and Metamorphic Buffer Layers

1039

Recent work with metamorphic HEMTs has emphasized InxGa1
xAs/InyAl1
yAs quantum wells grown on GaAs (001) substrates by MBE [18,21,23,35,103,118,123, 129,131,135]. Hybrid buffer approaches have also been used, such as a linearly graded buffer along with a superlattice [105,110,134]. Several comparative studies have been made in an attempt to evaluate different buffer layer approaches. Song et al. [51] compared HEMT devices on linearly graded layers with different grading coefficients and doping. They found that moderate grading gave a lower threading dislocation density than either lower or higher grading coefficients and that a Be-doped buffer was superior to a Si-doped buffer in terms of defect density. Cordier et al. [129] also studied the effects of grading coefficient and buffer layer thickness, for In0.33Ga0.67As/In0.34Al0.66As HEMTs on linearly graded InxAl1
xAs with and without overshoot. The inclusion of overshoot resulted in lower residual strain in the device layers, but the strain relaxation, as well as the surface roughness, 77 K electron mobility, and crystallographic tilt changed considerably as the buffer thickness, and therefore grading coefficient, were varied. Some studies have compared the use of InxGa1
xAs and InxAlyGa1
yAs linearly graded buffers. Inoue et al. [21] found that use of the wider bandgap buffer containing aluminum resulted in a lower residual carrier concentration, and higher resistivity, by an order of magnitude. Chyi et al. [68], when comparing linearly graded InxGa1
xAs and InxAl1
xAs buffers, found that the aluminum-containing buffer relaxed less completely, and exhibited less crystallographic tilt, presumably because of differences in dislocation mobility. Choi et al. [109] compared HEMTs on sublinear, linear, and superlinear InxAl1
xAs buffer layers. They found that the sublinear profile gave the lowest threading dislocation density (1.3  108 cm
2), the superlinear profile gave the highest density (2.6  108 cm
2), and the linearly graded device was intermediate. This may indicate the importance of the MDFZ adjacent to the device in reducing the defect density. Some work has considered the use of a superlattice along with a linearly graded buffer to improve the quality of the device layers. Galiev et al. compared a device utilizing a linearly graded layer with overshoot to a similar transistor having a linearly graded buffer plus a superlattice [110]. In their work, inclusion of the superlattice resulted in a lower dislocation density and smoother surface. Mendach et al. [73] and Heyn et al. [74] showed that insertion of a superlattice buffer lowered the threading dislocation density in metamorphic HEMTs with linearly graded buffers and InAs channels. Modern metamorphic HEMTs on GaAs substrates exhibit performance and reliability comparable to pseudomorphic HEMTs fabricated on InP wafers, but with a wider available range of indium mole fraction in the channel layers. Wakita et al. [131] showed that HEMTs, with channel indium mole fraction of 0.53, grown on GaAs using a lowtemperature linearly graded buffer exhibit low-bias reliability similar to P-HEMTs on InP with an extrapolated mean time to failure (MTTF) of 7.5  106 h at 125  C and an activation energy of 1.7 eV. Metamorphic HBTs [117,118,140] and double heterojunction bipolar transistors (DHBTs) [107] have been fabricated on GaAs and Si substrates using linearly graded

1040

HANDBOOK OF CRYSTAL GROWTH

buffers. Yang et al. [117] compared the thermal resistances of InP-based HBTs on GaAs substrates using InxAl1
xAs and InxGa1
xP graded buffers by an experimental and modeling study. They found that the commonly used linearly graded InxAl1
xAs buffer contributed significantly to the device thermal resistance and accounted for 40% of the total thermal resistance in the case of a 250 nm thick buffer. An InxGa1
xP buffer of similar thickness contributed much less to the thermal resistance, rendering it about 20% more than for a pseudomorphic device on an InP substrate. Lew et al. [140] demonstrated an InGaP/GaAs HBT on a Si substrate using a linearly graded Si1
xGex buffer, with a maximum current gain of w25 at a collector current of 100 mA and an offset voltage of 150 mV. Tsai [118] reported the integration of InP/InGaAs HBTs and InGaAs/InP HEMTs on a GaAs substrate using a linearly graded InxGa1
xP buffer layer as shown in Figure 25.14. The HBT exhibited a maximum current gain of 255 with a low offset voltage of 105 mV. Despite the successful application of linearly graded buffers in commercially available metamorphic devices including HEMTs and LEDs, further investigations with low-temperature growth, temperature grading, and novel compositional profiles may

FIGURE 25.14 Integrated metamorphic HBTs and HEMTs utilizing a linearly graded buffer layer on a GaAs substrate [118]. From Tsai J-H, J. Electrochem. Soc. 2011;158:H889-91. Reproduced by permission of ECS-The Electro-Chemical Society.

Chapter 25 • Low-Temperature and Metamorphic Buffer Layers

1041

enable lower defect densities and smoother interfaces for improved device performance.

25.5 Nonlinear Buffers Nonlinear graded buffer layers have been investigated in order to manipulate the MDFZs and their built-in strains, and also to control the steady-state threading dislocation density. The thickness of the MDFZ adjacent to the device may be enhanced by tapering the grading coefficient near the device (sublinear grading) while the thickness of the interfacial MDFZ may be enhanced by tapering the grading coefficient near the substrate (superlinear grading). By the use of tapering at both the bottom and top of the buffer layer, with an erfc or “S-graded” profile, both MDFZs may be enhanced.

25.5.1

Sublinear and Superlinear Grading

The role of the MDFZ adjacent to the device layer in promoting the glide of threading dislocations for the achievement of the longest possible misfit segments is well established [47a,47b]. It is desirable to maintain a thick MDFZ with large residual strain for maximum effectiveness. Modeling and experimental studies have shown that the thickness of this MDFZ may diminish upon growth of the device layer or structure on top of the graded buffer [102]; in other words, there is an undesirable “loading effect” of the device structure on the buffer. In some cases, this MDFZ may disappear entirely due to loading. One solution to the problem is to “overshoot” the average lattice constant of the device layer in the graded buffer, so the in-plane lattice constant of the relaxed device structure matches that of the strained buffer layer. If the device structure is relaxed, it applies no stress to the buffer and the loading effect vanishes. However, this is not applicable in cases where it may be desirable to have built-in strain in the device structure to enhance carrier mobility or shift the emission or absorption wavelength. Another approach is to alter the grading profile to make it less susceptible to loading, and this can be achieved using sublinear grading adjacent to the device layer [141]. Sublinear grading may also taper the steady-state threading dislocation density to a lower value. The models of Abrahams et al. [5] and Fitzgerald et al. [2] show that the steady-state threading dislocation density (TDD) is proportional to the grading coefficient, so a gradual reduction of the grading coefficient in the sublinear buffer can help remove threading dislocations from the top of the buffer. This idea is reinforced by the observation that the threading dislocation density can be controlled by the grading coefficient near the top of a tandem graded buffer [77]. There have been experimental and modeling studies of sublinear continuous grading in the material systems InxGa1
xAs/GaAs [109,142,143], Si1
xGe/Si [102,141], and sublinear step grading has been investigated in the material system InAsyP1
y/ InP [86].

1042

HANDBOOK OF CRYSTAL GROWTH

The use of sublinear grading modifies the critical layer thickness compared to the linear case. Sidoti et al. [142] considered force balance on a grown-in dislocation to determine the critical layer thickness in a sublinearly graded buffer with an exponential lattice mismatch profile given by f ¼ fN(1
e
g/y), where fN is the limiting mismatch, y is the distance from the interface, and g is the grading length constant. The critical layer thickness in such a graded buffer is hc ¼

 
 bð1
n cos2 aÞ hc
yc   þ 1 þ yc þ ge
yc =y
ge
hc =g ; ln b 8pfN ð1 þ nÞ

(25.25)

where yc is the distance from the interface where the first misfit dislocations appear. As a first approximation, the value of yc is the same as for a linear buffer having the same initial slope of the mismatch. Salviati et al. have modeled nonlinear buffers having square root and parabolic profiles with the assumption that the strain energy remains constant after the critical thickness is exceeded [28]. This was based on the experimental finding that the residual strain in uniform layers greater than the critical layer thickness may be fit by the relationship ε2 h ¼ K ;

(25.26)

where ε is the residual strain, h is the layer thickness, and K is a fitting parameter [44,144,145]. To apply the constant strain energy approximation to arbitrarily graded buffers, Salviati et al. assumed composition-independent elastic constants and applied the relationship Z

εdy ¼ K

(25.27)

to buffer layers with power-law type profiles of the form f ¼ Aya, where A is a constant. A key assumption was constant lattice relaxation, g ¼ f – ε ¼ constant. The resulting calculations predicted the largest residual surface strain in the superlinear buffer with a ¼ 2, the smallest surface strain in the sublinear buffer with a ¼ 0.5, and an intermediate value for the linear case with a ¼ 1. In an experimental investigation of MBE-grown InxGa1
xAs/GaAs (001) heterostructures with sublinear, linear, and superlinear grading of the indium composition, Salviati et al. [28] found by XTEM analysis that the misfit dislocation density scaled with the compositional gradient, and that the structure with sublinear grading had the best quality as measured by PL and HRXRD. They also found the residual surface strains and MDFZ thicknesses were similar to those predicted by the constant strain energy model and proposed the use of such a model for the design of graded buffer layers. However, the model does not consider relaxation kinetics and may have limited applicability to low-temperature buffer layers. Choi et al. [109] compared sublinear, linear, and superlinear InxAl1
xAs buffers for the MBE growth of InxGa1
xAs/InyAl1
yAs quantum wells on GaAs (001) substrates. The indium mole fraction profiles were of the form x ¼ x0 þ (xN
x0)( y/h)a, resulting in sublinear grading for a < 1, superlinear grading for a > 1, and linear grading for a ¼ 1.

Chapter 25 • Low-Temperature and Metamorphic Buffer Layers

1043

It was found that use of a sublinear buffer (a ¼ 0.5) resulted in the highest PL intensity and lowest threading dislocation density of the three profiles. The superlinear profile with (a ¼ 2) exhibited the lowest PL intensity and highest TDD, while the sample with linear grading was intermediate. These differences may indicate the importance of the MDFZ adjacent to the device; the sublinear profile would be expected to have the thickest MDFZ while the superlinear profile would have the least MDFZ thickness.

25.5.2

S-Graded Buffer Layers

To obtain the advantages of tapered grading coefficient near the interface and the device layer, Xhurxhi et al. proposed the use of an erfc or “S-graded” compositional profile [146]. The lattice mismatch profile in an S-graded buffer layer is given by     8  
fh m
y m > > pffiffiffi þ erf pffiffiffi ;
erf > > 2 > s 2 s 2 > > > >   < fh ; f ¼ > 2 > > > >     
 > > > fh y
m m > : pffiffiffi þ erf pffiffiffi ; erf 2 s 2 s 2

y < m; y ¼ m;

(25.28)

y > m;

where fh is the limiting mismatch, s is the standard deviation parameter, m is the mean parameter, and y is the distance from the interface. Using minimum energy calculations for InxGa1
xAs/GaAs (001) heterostructures, Xhurxhi et al. showed that S-graded buffer layers are less susceptible to loading by a device layer than linearly graded layers with equal thickness and ending composition [146]. Kujofsa et al. derived expressions for the widths of the MDFZs in an S-graded buffer of arbitrary composition in equilibrium [147]. Further investigations are needed to evaluate the potential advantages of S-graded buffer layers for device applications.

25.6 Superlattice Buffers Superlattice buffers have been used in conjunction with uniform or graded buffer layers to reduce the surface threading dislocation density and improve the surface smoothness of metamorphic material. There are two basic mechanisms for threading dislocation density reduction by superlattice buffers. Dislocation filtering occurs when a superlattice is placed on top of high dislocation density material. Dislocation inhibition occurs in the case of a superlattice placed below a graded buffer to reduce the steady-state density. In either case, surface smoothness can be improved by suppressing strain-induced cross-hatch. The dislocation filtering mechanism has been studied to a great extent in the context of GaAs on Si [148]. Though GaAs on Si typically contains 108–109 cm
2 threading dislocations, this density can be reduced significantly by inserting a SLS. The periodic reversals of strain in the SLS bend dislocations back and forth as they pass through, and

1044

HANDBOOK OF CRYSTAL GROWTH

those with canceling components of the Burgers vector are bent in opposite directions, thereby promoting annihilation and coalescence reactions [79]. Two 60 dislocations with opposite Burgers vectors can participate in an annihilation reaction, or two 60 dislocations with canceling tilt components can coalesce to form a single edge dislocation. Depending on the dislocation sources present, there will always be some net Burgers vector content which cannot be eliminated, so perfect filtering has not been achieved. Yamaguchi et al. demonstrated remarkable reduction of the threading dislocation density in GaAs on Si (001) by a combination of thermal cycle annealing and strainedlayer superlattice dislocation filters [149]. By an experimental and modeling study of InxGa1
xAs/GaAs and InxGa1
xAs/GaAs1
yPy strained-layer superlattices, they clarified the requirements on the SLS thickness for optimum dislocation filtering and showed that the optimum thickness is less than the Matthews and Blakeslee critical layer thickness [4] for a uniform layer with the same average mismatch. The dislocation inhibition mechanism of an SLS comes into play when a superlattice is inserted below a graded buffer, and has been demonstrated for both step-graded [79] and linearly graded buffers [105,110]. In this instance, the bending back and forth of dislocations may enhance the length of misfit segments, by bending dislocations away from pinning defects. This enables the establishment of a lower steady-state dislocation density in the graded buffer above. The inclusion of superlattice buffers can also improve the surface smoothness in device structures [110]. This benefit also arises from the periodic strain reversals in the growth direction, which undermine the small local lateral strain fluctuations responsible for roughening and cross-hatch.

25.7 Low-Temperature Buffer Layers and Two-step Growth In the previous sections, it has been well established that low-temperature growth of continuously graded and step-graded buffer layers can improve their surface smoothness and block the propagation of threading dislocations to the device layers. However, it is not always practical to grade from zero mismatch. In situations which dictate the growth of an abrupt interface with large mismatch, such as GaN/a-Al2O3 or GaAs/Si, the growth mode is three-dimensional, rather than layer-by-layer or step-flow growth. Therefore, the growth proceeds by the nucleation of a high density of islands which then coalesce by lateral growth to form a continuous layer. The coalescence of spherical or faceted islands results in a surface with rms roughness r comparable to the separation of the islands, pffiffiffiffi rfdi z1= ri , where ri is the areal density of islands. The density of islands varies exponentially in both the high-temperature and low-temperature regimes [150] due to the variation of surface mobility and source decomposition, respectively, and peaks at an intermediate value of temperature. Typically, the maximum island density is attained

Chapter 25 • Low-Temperature and Metamorphic Buffer Layers

1045

well below the optimum growth temperature for homoepitaxy due to surface mobility considerations. Therefore, the surface smoothness can be greatly improved by growing a thin low-temperature buffer followed by a thick deposit at a more typical growth temperature. Such a two-step growth process has been used for the growth of GaAs/Si (001) [151], GaAs/GaP (001) [152], InP/Si (001) [153], InP/GaAs (001) [154], ZnTe/GaAs (001) [155], and GaN/a-Al2O3 (0001) [156]. Although two-step growth was originally developed to control the morphology of heteroepitaxial films with a three-dimensional growth mode, use of a thin, lowtemperature buffer has since been shown to have a number of other benefits. These include a reduction of the threading dislocation density [157], enhancement of the lattice relaxation [152,158], and suppression of interdiffusion with the substrate [159]. The following sections describe some important examples of the use of LT buffer layers and two-step growth, but are not meant to be exhaustive.

25.7.1

III-Nitrides on Sapphire Substrates

For the growth of GaN on c-face sapphire substrates, which is important for visible and ultraviolet LEDs, the typical growth process involves deposition of a thin LT buffer, followed by annealing, and then high-temperature (HT) growth of a thick GaN layer. The properties of the thick device layer depend critically on the deposition and annealing conditions for the LT buffer [160]. Early investigations with two-step growth of GaN on sapphire involved AlN buffers. Yoshida et al. [161,162] showed that inclusion of a thin AlN buffer layer improved carrier mobility and cathodoluminescence intensity compared to direct growth by reactive molecular beam epitaxy. Amano et al. [163] found that use of a thin AlN buffer layer avoided cracking associated with the thermal expansion mismatch between GaN and sapphire. Koide et al. demonstrated that a thin (50 nm) low-temperature (800  C) AlN buffer improved the surface smoothness and crystal quality of AlxGa1
xN grown on sapphire by MOVPE [156]. In their work it was shown that the low-temperature AlN nucleation layer was amorphous, thereby inhibiting the growth of columnar islands. Annealing of the amorphous AlN layer by heating to the growth temperature on GaN led to its solid-phase crystallization [156]. In a recent investigation, Hoshino et al. [160] showed that a 25 nm LT-GaN buffer grown at 475  C on sapphire was partially crystallized even before annealing. For such a nonamorphous buffer layer, it was found that the properties of the HT-GaN depended strongly on the island density and size in the LT-GaN buffer. Nakamura et al. [164] applied an LT-GaN buffer (450–600  C) for the growth of GaN on sapphire by MOVPE, and found an optimum buffer layer thickness of 20 nm for maximum Hall mobility. In their study, it was shown that inclusion of the LT buffer resulted in specular morphology, whereas direct growth of HT-GaN led to columnar islands and rough morphology.

1046

HANDBOOK OF CRYSTAL GROWTH

Kuznia et al. [33] compared the use of LT-AlN and LT-GaN buffer layers for the growth of GaN on c-plane sapphire, with buffer layers grown at 550  C to thicknesses in the range of 10–90 nm. By using low-energy electron diffraction, they showed that both materials were amorphous as deposited but transformed to single crystal after a 1 h anneal at 1000  C. Use of either LT buffer layer improved the crystallinity, increased the carrier mobility, and decreased the background doping in the GaN in similar fashion, but the optimum buffer thicknesses were quite different (25 nm for GaN, 50 nm for AlN). The threading dislocation density in GaN on sapphire depends strongly on the properties of the low-temperature buffer, and in recent work Fu et al. have shown that use of multiple alternating MgxNy/GaN buffer layers can reduce the TDD in blue LEDs [165]. Recently, Lee et al. have demonstrated a novel two-step growth method for ð1122Þ GaN on semipolar m-plane sapphire in which the buffer layer was grown in a nitrogen atmosphere but at the normal temperature [168]. This material had specular morphology, whereas conventional two-step growth resulted in a hazy surface; therefore, the morphology is strongly affected by crystal orientation as well as buffer layer. Two-step growth has become the standard approach for growth of heteroepitaxial III-Nitrides on sapphire substrates for blue, violet, and white LEDs.

25.7.2

ZnO

ZnO, a wide bandgap semiconductor of interest for short-wavelength LEDs, has been deposited on a variety of substrates including a-Al2O3 (0001) [166,167], Si (001) [168], Si (111) [168,169], CaF2 (111) [170], and ZnO (0001) [171] and by a number of growth techniques, including MBE [170,171], pulsed laser deposition [168], RF magnetron sputtering [167], and MOVPE [169]. Typically, a two-step growth process is employed using a low-temperature ZnO buffer (200–400  C, 10–20 nm) in order to control the crystallinity [168], orientation [167], and morphology [166] of the high-temperature layer. In most work, the LT buffer is annealed prior to growth of the HT layer to improve its crystallinity [168,169]. Shin et al. [167] investigated the RF magnetron sputtering of ZnO:Ga on c-plane sapphire using 100 nm LT buffers of ZnO, GaN, MgO, or no LT buffer. It was found that the ZnO and GaN LT-buffers resulted in the best film properties, including X-ray FWHM and texture. Direct growth without an LT-buffer gave rise to polycrystalline growth with random in-plane texture [167]. Wang et al. studied the use of a double buffer involving HT-AlN and LT-ZnO for the growth of ZnO on Si (111) [169]. Films grown in this way had some of the best reported X-ray FWHMs (41000 for 002, 132100 for 102) but exhibited cracking due to tensile thermal strain. A unique aspect of ZnO epitaxy is that homoepitaxial growth, on a ZnO (0001) substrate, assumes a threedimensional growth mode unless an LT buffer layer is used [171].

25.7.3

Heteroepitaxy on Si

Direct high-temperature heteroepitaxial growth on Si is usually three-dimensional in character, leading to the common use of a two-step growth process, as in Ge/Si (001)

Chapter 25 • Low-Temperature and Metamorphic Buffer Layers

1047

[150–157], GaAs/Si (001) [151], or InP/Si (001) [153]. In the case of Si1
xGex/Si (001), LT buffers of Si [172], Ge [171], or Si1
xGex [173] have been used. Although the original motivation for using LT buffer layers was control of the island density and surface morphology, it has been found that they can also enhance lattice relaxation and reduce the surface threading dislocation density, perhaps by the same mechanisms active in LT graded buffers. For two-step growth of Ge on Si (001), Shin et al. found that there is a minimum required thickness of LT buffer to obtain a low TDD because of interdiffusion between the LT buffer and silicon [157]. In a variation on conventional two-step growth, Choi et al. found that use of two to four cycles of LT growth, HT growth, and annealing resulted in low threading dislocation density Ge/Si (001) by reduced pressure CVD [174]. Kawano et al. showed that completely relaxed Ge with a thickness of only 54 nm could be grown on Si (001) using an intermediate LT buffer of Fe3Si [158]. The 10 nm Fe3Si buffer accommodated nearly all of the lattice mismatch between Ge and Si.

25.8 Conclusion A wide variety of semiconductor devices including HEMTs, HBTs, LEDs, and lasers may be grown on lattice-mismatched substrates using low-temperature and metamorphic buffer layers. Common challenges in the design of these buffer layers include the high densities of threading dislocations, strain-induced surface roughening and cross-hatch, crystallographic tilting, and three-dimensional nucleation. Compositional grading can be tailored to distribute the misfit dislocations and, therefore, control the threading dislocation density. Low-temperature growth of these graded buffers can improve the surface smoothness and reduce the propagation of threading dislocations to the device layers.

References [1] Ayers JE. Heteroepitaxy of semiconductors: theory, growth, and characterization. Boca Raton, FL: CRC Press; 2007. [2] Fitzgerald EA, Kim AY, Currie MT, Langdo TA, Taraschi G, Bulsara MT. Dislocation dynamics in relaxed graded composition semiconductors. Mater Sci Eng 1999;B67:53–61. [3] van der Merwe JH. Crystal interfaces. Part II. Finite overgrowths. J Appl Phys 1963;34:123–7. [4] Matthews JW, Blakeslee AE. Defects in epitaxial multilayers. I. Misfit dislocations. J Cryst Growth 1974;27:118–25. [5] Abrahams MS, Weisberg LR, Buiocchi CJ, Blanc J. Dislocation morphology in graded heterojunctions: GaAs1
xPx. J Mater Sci 1969;4:223–35. [6] Olsen GH, Smith RT. Misorientation and tetragonal distortion in heteroepitaxial vapor-grown III–V structures. Phys Stat Sol A 1975;31:739–47. [7] Daruka I, Barabasi A-L. Dislocation-free island formation in heteroepitaxial growth: a study at equilibrium. Phys Rev Lett 1997;79:3708–11. [8] Tersoff J. Stress-induced roughening in epitaxial growth. Appl Surf Sci 1996;102:1–2.

1048

HANDBOOK OF CRYSTAL GROWTH

[9] Romanov AE, Pompe W, Mathis S, Beltz GE, Speck JS. Threading dislocation reduction in strained layers. J Appl Phys 1999;85:182–92. [10] McClelland RW, Bozler CO, Fan JCC. A technique for producing epitaxial films on reusable substrates. Appl Phys Lett 1980;37:560–2. [11] Nam OH, Bremser MD, Zheleva TS, Davis RF. Lateral epitaxy of low defect density GaN layers via organometallic vapor phase epitaxy. Appl Phys Lett 1997;71:2638–40. [12] Zheleva T, Smith SA, Thomson DB, Gehrke T, Linthicum KJ, Rajagopal P, et al. Pendeo-epitaxy: a new approach for lateral growth of gallium nitride structures. MRS Internet J Nitride Semicond 1999;4S1. G3.38. [13] Zhang XG, Rodriguez A, Wang X, Li P, Jain FC, Ayers JE. Complete removal of threading dislocations from mismatched layers by patterned heteroepitaxial processing. Appl Phys Lett 2000;77: 2524–6. [14] Jastrzebski L. SOI by CVD: epitaxial lateral overgrowth (ELO) process – review. J Cryst Growth 1983; 63:493–526. [15] Gale RP, McClelland RW, Fan JCC, Bozler CO. Lateral epitaxial overgrowth of GaAs by organometallic vapor phase epitaxy. Appl Phys Lett 1982;41:545–7. [16] Vohl P, Bozler CO, McClelland RW, Chu A, Strauss AJ. Lateral growth of single-crystal InP over dielectric films by orientation-dependent VPE. J Cryst Growth 1982;56:410–22. [17] Molstad JC, Benson JD, Markunas JK, Varesi JB, Boyd PR, Dinan JH. Threading dislocation removal from the near-surface region of epitaxial cadmium telluride on silicon by lithographic patterning of the substrate. J Electron Mater 2005;34:1242–8. [18] Hoke WE, Kennedy TD, Torabi A, Whelan CS, Marsh PF, Leoni RE, et al. Properties of metamorphic materials and device structures on GaAs substrates. J Cryst Growth 2003;251:804–10. [19] Mawst LJ, Kirch JD, Chang C-C, Kim T, Garrod T, Botez D, et al. InGaAs/AlInAs straincompensated superlattices grown on metamorphic buffer layers for low-strain, 3.6 mm-emitting quantum-cascade-laser active regions. J Cryst Growth 2013;370:230–5. [20] Grider DE, Swirhun SE, Narum DH, Akinwande AI, Nohava TE, Stuart WR, et al. Metamorphic InxGa1
xAs/InxAl1
xAs heterostructure field effect transistors grown on GaAs (001) substrates using molecular beam epitaxy. J Vac Sci Technol B 1990;8:301–4. [21] Inoue K, Harmand JC, Matsuno T. High-quality InxGa1
xAs/InAlAs modulation-doped heterostructures grown lattice-mismatched on GaAs substrates. J Cryst Growth 1991;111:313–7. [22] Shen L, Wieder HH, Chang WSC. Low temperature grown thin InAlAs step graded buffers for application on optical modulator at 1.3 mm. Mater Res Soc Symp 1997;379:297–301. [23] Wakita A, Rohden H, Robbins V, Mll N, Su C-Y, Nagy A, et al. Low-noise bias reliability of AlInAs/ GaInAs modulation-doped field effect transistors with linearly graded low-temperature buffer layers grown on GaAs substrates. Jpn J Appl Phys 1999;38:1186–9. [24] Shang XZ, Wu SD, Liu C, Wang WX, Guo LW, Huang Q. Low-temperature step-graded InAlAs/GaAs metamorphic buffer layers grown by molecular beam epitaxy. J Phys D 2006;39:1800–4. [25] Lee B, Baek JH, Lee JH, Choi SW, Jung SD, Han WS, et al. Optical properties of InGaAs linear graded buffer layers on GaAs grown by metalorganic chemical vapor deposition. Appl Phys Lett 1996;68: 2973–5. [26] Tangring I, Ni HQ, Wu BP, Wu DH, Xiong YH, Huang SS, et al. 1.58 mm InGaAs quantum well laser on GaAs. Appl Phys Lett 2007;91:221101. [27] He J-F, Wang H-L, Shang X-J, Li M-F, Zhu Y, Wang L-J, et al. GaAs-based long-wavelength InAs quantum dots on multi-step-graded InGaAs metamorphic buffer grown by molecular beam epitaxy. J Phys D 2011;44:335102.

Chapter 25 • Low-Temperature and Metamorphic Buffer Layers

1049

[28] Salviati G, Ferrari C, Lazzarini L, Franchi S, Bosacchi A, Taiariol F, et al. “TEM and X-ray diffraction studies of III–V lattice mismatched multilayers and superlattices. Inst Phys Conf Ser 1995;146: 337–48. [29] Kirch J, Garod T, Kim S, Park JH, Shin JC, Mawst LJ, et al. InAsyP1
y metamorphic buffer layers on InP substrates for mid-IR diode lasers. J Cryst Growth 2010;312:1165–9. [30] Ayers JE. The measurement of threading dislocation densities in semiconductor crystals by X-ray diffraction. J Cryst Growth 1994;135:71–7. [31] Fitzgerald EA, Xie Y-H, Monroe D, Silverman PJ, Kuo JM, Kortan AR, et al. Relaxed GexSi1
x structures for III–V integration with Si and high mobility two-dimensional electron gases in Si. J Vac Sci Technol B 1992;10:1807–19. [32] Chang J, Godo K, Song J, Oh D, Lee C, Yao T. High quality ZnTe heteroepitaxy layers using lowtemperature buffer layers. J Cryst Growth 2003;251:596–601. [33] Kuznia JN, Khan MA, Olsen DT. Influence of buffer layers on the deposition of high quality single crystal GaN over sapphire substrates. J Appl Phys 1993;73:4700–2. [34] Olsen JA, Hu EL, Lee SR, Fritz IJ, Howard AJ, Hammons BE, et al. X-ray reciprocal-space mapping of strain relaxation and tilting in linearly graded InAlAs buffers. J Appl Phys 1996;79: 3578–84. [35] Haupt M, Kohler K, Ganser P, Emminger S, Muller S, Rothemund W. Growth of high quality Al0.48In0.52As/Ga0.47In0.53As heterostructures using strain relaxed AlxGayIn1
x
yAs buffer layers on GaAs. Appl Phys Lett 1996;69:412–4. [36] Blank H-R, Thomas M, Wong KC, Kroemer H. Influence of the buffer layers on the morphology and the transport properties in InAs/(Al,Ga)Sb quantum wells grown by molecular beam epitaxy. Appl Phys Lett 1996;69:2080–2. [37] Luo YH, Wan J, Forrest RL, Liu JL, Jin G, Goorsky MS, et al. Compliant effect of low-temperature Si buffer for SiGe growth. Appl Phys Lett 2001;78:454–6. [38] Luo YH, Wan J, Forrest RL, Liu JL, Goorsky MS, Wang KL. High-quality strain-relaxed SiGe films grown with low temperature Si buffer. J Appl Phys 2001;89:8279–83. [39] Jeong Y, Choi H, Suzuki T. Invalidity Graded Buffers InAs Grown GaAs (001) – a comparison between direct and graded-buffer growth. J Cryst Growth 2007;301/302:235–9. [40] Radhadkrishnan K, Yuan K, Hong W. Characterization of InGaAs/InP single quantum well structure on GaAs substrate with metamorphic buffer grown by molecular beam epitaxy. J Cryst Growth 2004;261:16–21. [41] Tachikawa M, Yamaguchi M. Film thickness dependence of dislocation density reduction in GaAs-on-Si substrates. Appl Phys Lett 1990;56:484–6. [42] Ayers JE, Schowalter LJ, Ghandhi SK. Post-growth thermal annealing of GaAs on Si (001) grown by organometallic vapor phase epitaxy. J Cryst Growth 1992;125:329–35. [43] Bellani V, Bocchi C, Ciabattoni T, Franchi S, Frigeri P, Galinetto P, et al. Residual strain measurements in InGaAs metamorphic buffer layers on GaAs. Eur Phys J B 2007;56:217–22. [44] Maree PMJ, Barbour JC, van der Veen JF, Kavanough KL, T Bulle-Lieuwma CW, et al. Generation of misfit dislocations in semiconductors. J Appl Phys 1987;62:4413–20. [45] Hsieh YC, Chang EY, Luo GL, Pikuhn MH, Tang SS, Chang CY, et al. Use of Siþ pre-ionimplantation on Si substrate to enhance the strain relaxation of the GexSi1
x metamorphic buffer layer for the growth of Ge layer on Si substrate. Appl Phys Lett 2007;90:083507. [46] Arai M, Tadokoro T, Fujisawa T, Kobayashi W, Nakashima K, Yuda M, et al. Uncooled (25-85  C) 10 Gb/s operation of 1.3 mm-range metamorphic Fabry-Perot laser on GaAs substrate. Electron Lett 2009;45:359–60.

1050

HANDBOOK OF CRYSTAL GROWTH

[47] [a] Tersoff J. Dislocations and strain relief in compositionally graded layers. Appl Phys Lett 1993;62: 693–5. [b] Tersoff J. Dislocations and strain relief in compositionally graded layers. Appl Phys Lett 1994;64: 2748. [48] Ayers JE, Ghandhi SK, Schowalter LJ. Crystallographic tilting of heteroepitaxial layers. J Cryst Growth 1991;113:430–40. [49] Mi Z, Wu C, Yang J, Bhattacharya P. Molecular beam epitaxial growth and characteristics of 1.52 mm metamorphic InAs quantum dot lasers on GaAs. J Vac Sci Technol B 2008;26:1153–6. [50] Nagai H. Structure of vapor-deposited GaxIn1
xAs crystals. J Appl Phys 1974;45:3789–94. [51] Song Y, Wang S, Tangring I, Lai Z, Sadeghi M. Effects of doping and grading slope on surface and structure of metamorphic InGaAs buffers on GaAs substrates. J Appl Phys 2009;106:123531. [52] Balakrishnan G, Huang S, Rotter TJ, Stintz A, Dawson LR, Malloy KJ, et al. 2.0 mm wavelength InAs quantum dashes grown on a GaAs substrate using a metamorphic buffer layer. Appl Phys Lett 2004;84:2058–60. [53] Song JS, Chang JH, Hong SK, Cho MW, Makino H, Hanada T, et al. Improvement in crystallinity of ZnSe by inserting a low-temperature buffer layer between the ZnSe epilayer and the GaAs substrate. J Cryst Growth 2002;242:95–103. [54] Arai M, Fujisawa T, Kobayashi W, Nakashima K, Yuda M, Kondo Y. High temperature operation of 1.26 mm ridge waveguide laser with InGaAs metamorphic buffer on GaAs substrate. IEEE Intl Semicond Laser Conf 2008:57–8. [55] Arai M, Fujisawa T, Kobayashi W, Nakashima K, Yuda M, Kondo Y. High temperature operation of 1.26 mm Fabry-Perot laser with InGaAs metamorphic buffer layer. Electron Lett 2008;44:1359–60. [56] Arai M, Fujisawa T, Kobayashi W, Nakashima K, Yuda M, Kondo Y. High temperature operation of 1.26 mm ridge waveguide laser with InGaAs metamorphic buffer on GaAs substrate. CLEO Tech Dig 2008. TuB4. [57] Arai M, Kondo Y, Kanazawa S, Tadokoro T, Kohtoku M. Demonstration of high temperature operation in 1.3-mm-range metamorphic InGaAs laser. CLEO Tech Dig 2012. CTu2N. [58] Zhukov AE, Kovsh AR, Mikhrin SS, Semenova ES, A Maleev N, Vasil’ev AP, et al. Alferov, metamorphic lasers for 1.3 mm spectral range grown on GaAs substrates by MBE. Semiconductors 2003; 37:1119–22. [59] Behet M, van der Zanden K, Borghs G. Metamorphic InGaAs/InAlAs quantum well structures grown on GaAs substrates for high electron mobility transistor applications. Appl Phys Lett 1998; 75:2760–2. [60] Thomas M, Blank H-R, Wong KC, Kroemer H. Buffer-dependent mobility and morphology on InAs/(Al,Ga)Sb quantum wells. J Cryst Growth 1997;175/176:894–7. [61] Ledentsov NN, Shchukin VA, Kettler T, Psilovic K, Bimberg D, Karachinsky L Ya, et al. MBE-grown metamorphic lasers for applications at telecom wavelengths. J Cryst Growth 2007;301–302:914–22. [62] Ledentsov NN, Maximov MV, Bimberg D, Maka T, Sotomayor Torres CM, Kochnev IV, et al. Alferov, 1.3 mm luminescence and gain from defect-free InGaAs-GaAs quantum dots grown by metal-organic chemical vapour deposition. Semicond Sci Technol 2000;15:604–7. [63] Sizov DS, Maksimov MV, Tsatsul’nikov AF, Cherkashin NA, Kryzhanovskaya NV, Zhukov AB, et al. The influence of heat treatment conditions on the evaporation of defect regions in structures with InGaAs quantum dots in the GaAs matrix. Semiconductors 2002;36:1020–6. [64] Ledentsov N. Semiconductor device and method of making same. US Patent 6,653,166. 2003. [65] Shchukin V, Ledentsov N. Defect-free semiconductor templates for epitaxial growth and method of making same. US Patent 6,784,074 B2. 2004.

Chapter 25 • Low-Temperature and Metamorphic Buffer Layers

1051

[66] Krishnamoorthy V, Lin YW, Park RM. Application of ‘critical compositional difference’ concept to the growth of low dislocation density (<104/cm2) InxGa1
xAs (x  0.5) on GaAs. J Appl Phys 1992; 72:1752–7. [67] Knall J, Romano LT, Biegelsen DK, Bringans RD, Chui HC, Harris Jr JS, et al. The use of graded InGaAs layers and patterned substrates to remove threading dislocations from GaAs on Si. J Appl Phys 1994;76:2697–702. [68] Chyi J-I, Shieh J-L, Pan J-W, Lin R-M. Material properties of compositional graded InxGa1
xAs and InxAl1
xAs epilayers grown on GaAs substrates. J Appl Phys 1996;79:8367–70. [69] Gonzalez D, Araujo D, Gonzalez L, Gonzalez Y, Aragon G, Garcia R. Advantages of thin interfaces in step-graded buffer structures. Mater Sci Eng 1997;B44:41–5. [70] Gozu S-I, Hong C, Yamata S. Low temperature high electron mobility in In0.75Ga0.25As/In0.75Al0.25As modulation-doped heterostructures grown on GaAs substrate. Jpn J Appl Phys Part 2 1998;37: L1501–3. [71] Mishima T, Higuchi K, Mori M, Kudo M. High Gm In0.5Al0.5As/In0.5Ga0.5As high electron mobility transistors grown lattice-mismatched on GaAs substrates. J Cryst Growth 1995;150:1230–5. [72] Cui LJ, Zeng YP, Wang BQ, Wu J, Zhu ZP, Lin LY. Rapid thermal annealing effects on step-graded InAlAs buffer layer and In0.52Al0.48As/In0.53Ga0.47As metamorphic high electron mobility transistor structures on GaAs substrates. J Appl Phys 2002;91:2429–32. [73] Mendach S, Hu CM, Heyn Ch, Schnull S, Oepen HP, Anton R, Hansen W. Strain relaxation in highmobility InAs inserted-Channel heterostructures with metamorphic buffer. Phys E 2002;13:1204–7. [74] Heyn Ch, Mendach S, Lohr S, Beyer S, Schnull S, Hansen W. Growth of shallow InAs HEMTs with metamorphic buffer. J Cryst Growth 2003;251:832–6. [75] Lynch C, Beresford R, Chason E. Real-time stress evolution during growth of InxAl1
xAs/GaAs metamorphic buffer layers. J Vac Sci Technol B 2004;22:1539–43. [76] Capotondi F, Biasiol G, Ercolani D, Grillo V, Carlino E, Romanato F, et al. Strain induced effects on the transport properties of metamorphic InAlAs/InGaAs quantum wells. Thin Sol Films 2005;484: 400–7. [77] Lee D, Park MS, Tang Z, Luo H, Beresford R, Wie CR. Characterization of metamorphic InxAl1
xAs/ GaAs buffer layers using reciprocal space mapping. J Appl Phys 2007;101:063523. [78] Jiang Z, Wang W, Gao H, Liu L, Chen H, Zhou J. Strain relaxation and surface morphology of high indium content InAlAs metamorphic buffers with reverse step. Appl Surf Sci 2008;254:5241–6. [79] Landgraf B, Slobodskyy T, Heyn Ch, Hansen W. Strain relaxation in metamorphic InAlAs buffers. Mater Sci Eng B 2012;177:762–7. [80] Jang J-H, Cueva G, Hoke WE, Lemonias PJ, Fay P, Adesida I. Metamorphic graded bandgap InGaAs-InGaAlAs-InAlAs double heterojunction P-i-I-N photodiodes. J Lightwave Technol 2002;20: 507–14. [81] Xin Y-C, Vaughn LG, Dawson LR, Stintz A, Lin Y, Lester LF, et al. InAs quantum-dot GaAs-based lasers grown on AlGaAsSb metamorphic buffers. J Appl Phys 2003;94:2133–5. [82] Bui SS, Lee HP, Yu KM. Metamorphic InAsyP1
y (y ¼ 0.30
0.75) and AldIn1
dAsyP1
y buffer layers on InP substrates. Appl Phys Lett 2007;90:212113. [83] Czaban JA, Thompson DA, Robinson BJ. Improved InAsP metamorphic layers grown on an InP substrate using underlying InP grown at low temperatures. Semcond Sci Technol 2007;22:408–12. [84] Hudait MK, Brenner M, Ringel SA. Metamorphic In0.7Al0.3As/In0.69Ga0.31As thermovoltaic devices grown on graded InAsyP1
y buffers by molecular beam epitaxy. Sol State Electron 2009; 53:102–6.

1052

HANDBOOK OF CRYSTAL GROWTH

[85] Plis E, Rotella P, Raghavan S, Dawson LR, Krishna S, Le D, et al. Growth of room-temperature arsenic free infrared photovoltaic detectors on GaSb substrate using metamorphic InAlSb digital alloy buffer layers. Appl Phys Lett 2003;82:1658–60. [86] Kirch J, Kim TW, Konen J, Mawst LJ, Kuech TF, Kuan T-S. Effects of antimony (Sb) incorporation on MOVPE grown InAsyP1
y metamorphic buffer layers on InP substrates. J Cryst Growth 2011;315: 96–101. [87] Halliwell MAG, Lyons MH, Hill MJ. The interpretation of X-ray rocking curves from III–V semiconductor device structures. J Cryst Growth 1984;68:523–31. [88] Bartels WJ, Hornstra J, Lobeek DJW. X-ray diffraction of multilayers and superlattices. Acta Cryst A 1986;42:539–45. [89] Wie CR, Tombrello TA, Vreeland Jr T, Dynamical. X-ray diffraction from nonuniform crystalline films: application to X-ray rocking curve analysis. J Appl Phys 1986;59:3743–6. [90] Rago PB, Suarez EN, Jain FC, Ayers JE. Dynamical X-ray diffraction from ZnSySe1
y/GaAs (001) multilayers and superlattices with dislocations. J Electron Mater 2012. http://dx.doi.org/10.1007/ s11664-012-2012-y. [91] Rago PB, Ayers JE. Dynamical X-ray diffraction from InxGa1
xAs heterostructures with dislocations. J Electron Mater 2012;42:2450–8. [92] Chen J, Fernandez JM, Chang JCP, Kavanagh KL, Wieder HH. Modulation-doped In0.3Ga0.7As/ In0.29Al0.71As heterostructures grown on GaAs by step grading. Semicond Sci Technol 1992;7:601–3. [93] Gozu S, Tsuboki K, Hayashi M, Hong C, Yamada S. Very high electron mobilities at low temperatures in InxGa1
xAs/InyAl1
yAs HEMTs grown lattice-mismatched on GaAs substrates. J Cryst Growth 1999;201/202:749–52. [94] Huo Y, Lin H, Chen R, Makarova M, Rong Y, Li M, et al. Strong enhancement of direct transition photoluminescence with highly tensile-strained Ge grown by molecular beam epitaxy. Appl Phys Lett 2011;98:011111. [95] Ihn S-G, Jo S-J, Oh K-H, Kim TW, Song J-I. Crystalline quality improvement of In0.52Al0.48As/In0. 53Ga0.47As heterostructure on InAlAs/GaAs metamorphic buffer by post-growth rapid thermal annealing. In: 2005 International conference indium phosphide related material; 2005. p. 216. [96] Molina SI, Pacheco FJ, Araujo D, Garcia R, Sacedon A, Calleja E, et al. Strain relief in linearly graded composition buffer layers: a design scheme to grow dislocation-free (<105 cm
2) and unstrained epilayers. Appl Phys Lett 1994;65:2460–2. [97] Sacedon A, Gonzalez-Sanz F, Calleja E, Munoz E, Molina SI, Pacheco FJ, et al. Design of InGaAs linear graded buffer structures. Appl Phys Lett 1995;66:3334–6. [98] Kim S-D, Lord SM, Harris Jr JS. Strain relaxation in compositionally graded epitaxial layers. J Vac Sci Technol B 1996;14:642–6. [99] Bulsara MT, Yang V, Thilderkvist A, Fitzgerald EA, Hausler K, Eberl K. Graded InxGa1
xAs/GaAs 1.3 mm wavelength light emitting diode structures grown with molecular beam epitaxy. J Appl Phys 1998;83:592–4. [100] Tangring I, Wang S, Sadeghi M, Larsson A. 1.27 mm metamorphic InGaAs quantum well lasers on GaAs substrates. Electron Lett 2006;42:691–3. [101] Tangring I, Wang SM, Zhu XR, Larsson A, Lai ZH, Sadeghi M. Manipulation of strain relaxation in metamorphic heterostructures. Appl Phys Lett 2007;90:071904. [102] Bertoli B, Suarez EN, Ayers JE, Jain FC. Misfit dislocation density and strain relaxation in graded semiconductor heterostructures with arbitrary composition profiles. J Appl Phys 2009;106:073519. [103] Lee KE, Fitzgerald EA. High-quality metamorphic compositionally graded InGaAs buffers. J Cryst Growth 2010;312:250–7.

Chapter 25 • Low-Temperature and Metamorphic Buffer Layers

1053

[104] Yang L, Bulsara MT, Lee KE, Fitzgerald EA. Compositionally-graded InGaAs-InGaP alloys and GaAsSb alloys for metamorphic InP on GaAs. J Cryst Growth 2011;324:103–9. [105] Dammann M, Chertouk M, Jantz W, Kohler K, Weimann G. Reliability of InAlAs/InGaAs HEMTs grown on GaAs substrate with metamorphic buffer. Microelectron Reliab 2000;40:1709–13. [106] Semenova ES, Zhukov AE, Mikhrin SS, Egorov AY, Odnoblyudov VA, Vasil’ev AP, et al. Metamorphic growth for application in long-wavelength (1.3–1.55 mm) lasers and MODFET-type structures on GaAs substrates. Nanotechnology 2004;15:S283–7. ˚ [107] Cavus A, Monier C, Cox C, Pascua D, Gutierrez-Aitken A, Noori A, et al. Development of 6.00 A graded metamorphic buffer layers and high performance In0.86Al0.14As/In0.86Ga0.14As heterojunction bipolar transistor devices. J Vac Sci Technol B 2006;24:1492–5. [108] Zhang Y, Gu Y, Tian Z, Li A, Zhu X, Zheng Y. Wavelength extended 2.4 mm heterojunction InGaAs photodiodes with InAlAs cap and linearly graded buffer layers suitable for both front and back illuminations. Infrared Phys Technol 2008;51:316–21. [109] Choi H, Jeong Y, Cho J, Jeon MH. Effectiveness of non-linear graded buffers for In(Ga,Al)As metamorphic layers grown on GaAs (001). J Cryst Growth 2009;311:1091–5. [110] Galiev GB, Vasil’evskii IS, Pushkarev SS, Klimov EA, Imamov RM, Buffat PA, et al. Metamorphic InAlAs/InGaAs/InAlAs/GaAs HEMT heterostructures containing strained superlattices and inverse steps in the metamorphic buffer. J Cryst Growth 2013;366:55–60. [111] Jo SJ, Ihn S-G, Lee G-J, Lee D-H, Song J-I. Carrier lifetime of low-temperature grown In0.53Ga0.47As on GaAs using an InGaAlAs metamorphic buffer. In: 2005 International conference InP related material; 2005. p. 175–77. [112] Liu JL, Wang KL, Moore CD, Goorsky MS, Borca-Tasciuc T, Chen G. Experimental study of a surfactant-assisted SiGe graded layer and a symmetrically strained Si/Ge superlattice for thermoelectric applications. Thin Sol Films 2000;369:121–5. [113] Lew KL, Yoon SF, Tanato H, Chen KP, Dohrman CL, Isaacson DM, et al. InGaP/GaAs heterojunction bipolar transistor grown on Si substrate with SiGe graded buffer layer. Electron Lett 2008; 44:243–4. [114] Ayers JE. Critical layer thickness in compositionally-graded semiconductor layers with non-zero interfacial mismatch. Semicond Sci Technol 2008;23:045018. [115] Sidoti D, Xhurxhi S, Kujofsa T, Cheruku S, Correa JP, Bertoli B, et al. Initial misfit dislocations in a graded heteroepitaxial layer. J Appl Phys 2011;109:023510. [116] Endres J, Danis S, Bauer G. The misfit dislocation density profile in graded SiGe/Si (001) layers prepared at different temperatures. J Phys Cond Matt 2013;25:175802. [117] Yang H, Wang H, Radhakrishnan K, Tan CL. Thermal resistance of metamorphic InP-based HBTs on GaAs substrates using a linearly graded InxGa1
xP metamorphic buffer. IEEE Trans Electron Dev 2004;51:1221–7. [118] Tsai J-H. Study of metamorphic co-integrated heterostructure bipolar and field-effect transistors (BiFETs). J Electrochem Soc 2011;158:H889–91. [119] Zakaria A, King RR, Jackson M, Goorsky MS. Comparison of arsenide and phosphide based graded buffer layers used in inverted metamorphic solar cells. J Appl Phys 2012;112:024907. [120] Odnoblyudov VA, Tu CW. Room-temperature yellow-amber emission from InGaP quantum wells grown on an InGaP metamorphic buffer layer on GaP (100) substrates. J Cryst Growth 2005;279: 20–5. [121] Ocampo JF, Bertoli B, Rago PB, Suarez EN, Shah D, Jain FC, et al. Asymmetric dislocation densities in forward-graded ZnSySe1
y/GaAs (001) heterostructures. J Electron Mater 2010;39:391–9. [122] Hosoda T, Wang D, Kipshidze G, Sarney WL, Shterengas L. 3 mm diode lasers grown on (Al)GaInSb compositionally graded metamorphic buffer layers. Semicond Sci Technol 2012;27:055011.

1054

HANDBOOK OF CRYSTAL GROWTH

[123] Belenky G, Wang D, Lin Y, Donetsky D, Kipshidze G, Shterengas L, et al. Metamorphic InAsSb/ AlInAsSb heterostructures for optoelectronic applications. Appl Phys Lett 2013;102:111108. [124] Haupt M, Kohler K, Ganser P, Muller S, Rothemund W. Molecular beam epitaxy of Al0.48In0.52As/ Ga0.47In0.53As heterostructures on metamorphic AlxGayIn1
x
yAs buffer layers. J Cryst Growth 1997;175/176:1028–32. [125] Bertoli B, Suarez EN, Jain FC, Ayers JE. Dislocations and strain relief in reverse-graded semiconductor layers. Semicond Sci Technol 2009;24:125006. [126] Ayers JE. Multiple critical layer thicknesses in retro-graded heterostructures. Appl Phys Lett 2008; 92:102014. [127] Wong LH, Liu JP, Wong CC, Ferraris C, White TJ, Chan L, et al. Thermal stability of a reversegraded SiGe buffer layer for growth of relaxed SiGe epitaxy. Electrochem Sol State Lett 2006;9: G114–6. [128] Ocampo JF, Suarez E, Jain FC, Ayers JE. Overshoot graded layers for mismatched heteroepitaxial devices. J Electron Mater 2008;37:1035–43. [129] Cordier Y, Chauveau J-M, Ferre D, Dipersio J. Comparison of In0.33Ga0.67As/In0.34Al0.66As on GaAs metamorphic high electron mobility transistors grown by molecular beam epitaxy with normal and inverse step on linear graded buffer layers. J Vac Sci Technol B 2000;18:2513–7. [130] Muraki K, Fukatsu S, Shiraki Y, Ito R. Surface segregation of in atoms during molecular beam epitaxy and its influence on the energy levels in InGaAs/GaAs quantum wells. Appl Phys Lett 1992; 61:557–9. [131] Wakita AS, Rohdin H, Robbins VM, Moll N, Su C-Y, Nagy A, et al. Low-noise bias reliability of AlInAs/GaInAs MODFETs with linearly graded low-temperature buffer layers grown on GaAs substrates. In: 10th international conference indium phosphide related material; 1998. TuP-38. [132] Toikkanen L, Hakkarainen T, Schramm A, Tukiainen A, Laukkanen P, Guina M. Metamorphic growth of tensile strained GaInP on GaAs substrate. J Cryst Growth 2010;312:3105–10. [133] Liu HY, Qiu Y, Jin CY, Walther T, Cullis AG. 1.55 mm InAs quantum dots grown on a GaAs substrate using a GaAsSb metamorphic buffer layer. Appl Phys Lett 2008;92:111906. [134] Hong S-K, Lee H-G, Lee J-J, Kim S-G, Pyun K-E, Park H-M. Molecular beam epitaxy growth of indium-rich InxGa1
xAs/InyAl1
yAs/InP structures towards high channel conductivity for a high electron mobility transistor using a linearly graded buffer layer. J Cryst Growth 1996;169:435–42. [135] Yuan K, Radhakrishnan K, Zheng HQ, I Ng G. Metamorphic In0.52Al0.48As/In0.53Ga0.47As high electron mobility transistors on GaAs with InxGa1
xP graded buffer. J Vac Sci Technol B 2001;19: 2119–22. [136] Lee K-W, Lin H-C, Lee K-L, Hsieh C-H, Wang Y-H. Comprehensive study of InAlAs/InGaAs metamorphic high electron mobility transistor with oxidized InAlAs gate. J Electrochem Soc 2009; 156:H925–9. [137] Sin Y, Presser N, Adams P. A comparative study of metamorphic InP/InGaAs double heterojunction bipolar transistors with InP and InAlP buffer layers grown by molecular beam epitaxy. J Electron Mater 2006;35:266–72. [138] Lin G-R, Kuo H-C, Lin C-K, Feng M. Ultralow leakage In0.53Ga0.47As p-i-n photodetector grown on linearly graded metamorphic InxGa1
xP buffered GaAs substrate. IEEE J Quantum Electron 2005; 41:749–52. [139] Liu SQ, Han Q, Zhu B, Yang XH, Ni HQ, He JF, et al. High-performance metamorphic InGaAs resonant cavity enhanced photodetector grown on GaAs substrate. Appl Phys Lett 2011;98:201104. [140] Lew KL, Yoon SF, Tanoto H, Chen KP, Dohman CL, Isaacson DM, et al. InGaP/GaAs heterojunction bipolar transistor grown on Si substrate with SiGe graded buffer layer. Electron Lett 2008: 0083328.

Chapter 25 • Low-Temperature and Metamorphic Buffer Layers

1055

[141] Bertoli B, Sidoti D, Xhurxhi S, Kujofsa T, Cheruku S, Correa JP, et al. Equilibrium strain and dislocation density in exponentially graded Si1
xGex/Si (001). J Appl Phys 2010;108:113525. [142] Sidoti D, Xhurxhi S, Kujofsa T, Cheruku S, Reed J, Bertoli B, et al. Critical layer thickness in exponentially graded heteroepitaxial layers. J Electron Mater 2010;29:1140–5. [143] Mathews I, O’Mahony D, Gocalinska A, Manganaro M, Palucchi E, Schmidt M, et al. InAlAs solar cell on a GaAs substrate employing a graded InxGa1
xAs-InP metamorphic buffer layer. Appl Phys Lett 2013;102:033906. [144] Drigo AV, Aydinli A, Carnera A, Genova F, Rigo C, Ferrari C, et al. On the mechanisms of strain release in molecular-beam-epitaxy-grown InxGa1
xAs/GaAs single heterostructures. J Appl Phys 1989;66:1975–83. [145] Ferrari C, Franzosi P, Lazzarini L, Salviati G, Berti M, Drigo AV, et al. Mechanisms of strain release in molecular beam epitaxy grown InGaAs/GaAs buffer heterostructures. Mater Sci Eng B 1994;28: 510–4. [146] Xhurxhi S, Obst F, Sidoti D, Bertoli B, Kujofsa T, Cheruku S, et al. S-graded buffer layers for latticemismatched heteroepitaxial devices. J Electron Mater 2011;60:2348–54. [147] Kujofsa T, Antony A, Xhurxhi S, Obst F, Sidoti D, Bertoli B, et al. Design of s-graded buffer layers for metamorphic ZnSySe1
y/GaAs (001) semiconductor devices. J Electron Mater 2013. http://dx.doi. org/10.1007/s11664-013-2771-0. [148] Fischer R, Morkoc H, Nueman DA, Zabel H, Choi C, Otsuka N, et al. Material properties of highquality GaAs epitaxial layers grown on Si substrates. J Appl Phys 1986;60:1640–7. [149] Yamaguchi M, Nishioka T, Sugo M. Analysis of strained-layer superlattice effects on dislocation density reduction in GaAs on Si substrates. Appl Phys Lett 1989;54:24–6. [150] Kim H-W, Shin KW, Lee G-D, Yoon E. High quality Ge epitaxial layers on Si by ultrahigh vacuum chemical vapor deposition. Thin Sol Films 2009;517:3990–4. [151] Akiyama M. Growth of high quality GaAs layers on Si substrates by MOCVD. J Cryst Growth 1986; 77:490–7. [152] Nomura T, Wakatuki K, Miyao M, Hagino M. Characterization of the GaAs buffer layer grown on GaP by MBE for the two-step growth method. Appl Surf Sci 1989;41/42:512–5. [153] Yamamoto A. Optimization of InP/Si heteroepitaxial growth conditions using organometallic vapor phase epitaxy. J Cryst Growth 1989;96:36–377. [154] Takano Y, Sasaki T, Nagaki Y, Kuwahara K, Fuke S, Imai T. Two-step growth of InP on GaAs substrates by metalorganic vapor phase epitaxy. J Cryst Growth 1996;169:621–4. [155] Guo Q, Sueyasu Y, Tanaka T, Nishio M, Cao J. Improvement in the quality of ZnTe epilayers grown on GaAs substrates by introducing a low-temperature buffer layer. Jpn J Appl Phys 2009;48:080208. [156] Koide Y, Itoh N, Itoh K, Sawaki N, Akasaki I. Effect of AlN buffer layer on AlGaN/a-Al2O3 heteroepitaxial growth by metalorganic vapor phase epitaxy. Jpn J Appl Phys 1989;27:1156–61. [157] Shin KW, Kim H-W, Kim J, Yang C, Lee S, Yoon E. The effects of low temperature buffer layer on the growth of pure Ge on Si. Thin Solid Films 2010;518:6496–9. [158] Kawano M, Yamada S, Tanikawa K, Sawano K, Miyao M, Hamaya K. An ultra-thin buffer layer for Ge epitaxial layers on Si. Appl Phys Lett 2013;102:121908. [159] Song JS, Seo SH, Oh MH, Chang JH, Cho MW, Yao T. Suppression of impurity interdiffusion heteroepitaxy by inserting low-temperature buffer layer between epilayer substrate. J Cryst Growth 2004;261:159–63. [160] Hoshino K, Yanagita N, Araki M, Tadatomo K. Effect of low-temperature GaN buffer layer on the crystalline quality of subsequent GaN layers grown by MOVPE. J Cryst Growth 2007;298:232–4.

1056

HANDBOOK OF CRYSTAL GROWTH

[161] Yoshida S, Misawa S, Gonda S. Epitaxial growth of GaN/AlN heterostructures. J Vac Sci Technol B 1983;1:250–3. [162] Yoshida S, Misawa S, Gonda S. Improvements on the electrical and luminescent properties of reactive molecular beam epitaxially grown GaN films by AlN-coated sapphire substrates. Appl Phys Lett 1983;42:427–9. [163] Amano H, Sewaki N, Akasaki I. Metalorganic vapor phase epitaxial growth of a high quality GaN film using an AlN buffer layer. Appl Phys Lett 1986;48:353–5. [164] Nakamura S. GaN growth using GaN buffer layer. Jpn J Appl Phys Part 2 1991;(30):L1705–7. [165] Fu YK, Kuo CH, Tun CJ, Chang LC. Nitride-based light-emitting diodes with multiple MgxNy/GaN buffer layers. Solid State Electron 2010;54:590–4. [166] Jung Y-S, Konenenko O, Kim J-S, Choi W-K. Two-dimensional growth of ZnO epitaxial films on c-Al2O3 (0001) substrates with optimized growth temperature and low-temperature buffer layer by plasma-assisted molecular beam epitaxy. J Cryst Growth 2005;274:418–24. [167] Shin SW, Agawane GL, Kim IY, Kwon YB, Jung IO, Gang MG, et al. Low temperature epitaxial growth and characterization of Ga-doped ZnO thin films on Al2O3 (0001) substrates prepared with different buffer layers. Appl Surf Sci 2012;258:5073–9. [168] Zheng W, Liao Y, Li L, Yu Q, Wang G, Li Y, et al. Structure and properties of ZnO films grown on Si substrates with low temperature buffer layers. Appl Surf Sci 2006;253:2765–9. [169] Wang L, Pu Y, Chen YF, Mo CL, Fang WQ, Xiong CB, et al. MOCVD growth of ZnO films on Si (111) substrate using a thin AlN buffer layer. J Cryst Growth 2005;284:459–63. [170] Ko HJ, Chen YF, Zhu Z, Hanada T, Yao T. Effects of a low-temperature buffer layer on structural properties of ZnO epilayers grown on (111) CaF2 by two-step MBE. J Cryst Growth 2000;208: 389–94. [171] Park SH, Minegishi T, Lee HJ, Oh DC, Ko HJ, Chang JH, et al. Growth mechanism of ZnO lowtemperature homoepitaxy. J Appl Phys 2011;110:053520. [172] Vdovin VJ, Yugova TJ, Rzaev MM, Schaffler F, Mil’vidskii MG. Thermally induced strain relaxation in SiGe-Si heterostructures with low-temperature buffer layers. Phys Stat Sol 2005;2:1938–42. [173] Vdovin VI, Muhlberger M, Rzaev MM, Schaffler F, Yugova TG. Dislocation structure formation in SiGe/Si (001) heterostructures with low-temperature buffer layers. J Phys Cond Matt 2002;14: 13313–8. [174] Choi D, Ge Y, Harris JS, Cagnon J, Stemmer S. Low surface roughness and threading dislocation density Ge growth on Si (001). J Cryst Growth 2008;310:4273–9.