Threading dislocation reduction mechanisms in low-temperature-grown GaAsS. K. Mathis, X.-H. Wu, A. E. Romanov, and J. S. Speck Citation: Journal of Applied Physics 86, 4836 (1999); doi: 10.1063/1.371450 View online: http://dx.doi.org/10.1063/1.371450 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/86/9?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Defect reduction in epitaxial GaSb grown on nanopatterned GaAs substrates using full wafer block copolymerlithography Appl. Phys. Lett. 95, 062104 (2009); 10.1063/1.3204013 Low temperature growth of InGaAs layers on misoriented GaAs substrates by metalorganic vapor phase epitaxy Appl. Phys. Lett. 80, 2054 (2002); 10.1063/1.1463210 Residual strain and threading dislocation density in InGaAs layers grown on Si substrates by metalorganic vapor-phase epitaxy Appl. Phys. Lett. 78, 93 (2001); 10.1063/1.1338502 Reduction of threading dislocations by InGaAs interlayer in GaAs layers grown on Si substrates Appl. Phys. Lett. 73, 2917 (1998); 10.1063/1.122629 Dislocation-free InSb grown on GaAs compliant universal substrates Appl. Phys. Lett. 71, 776 (1997); 10.1063/1.119642

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Threading dislocation reduction mechanismsin low-temperature-grown GaAs

S. K. Mathisa) and X.-H. Wub)

Materials Department, College of Engineering, University of California, Santa Barbara, California 93106

A. E. RomanovA. F. Ioffe Physico-Technical Institute, Russian Academy of Sciences, 194021 St. Petersburg, Russia

J. S. SpeckMaterials Department, College of Engineering, University of California, Santa Barbara, California 93106

~Received 21 December 1998; accepted for publication 21 July 1999!

In these studies, we have investigated the role of low-temperature growth in the reduction ofthreading dislocation~TD! densities in large mismatch heteroepitaxy. Low- and high-temperature~LT! and~HT! GaAs growths on highly mismatched substrates were used to find the mechanism ofenhanced TD reduction in LT grown~250 °C! GaAs. LT templates have symmetric~equal! TDsubdensities on the$111%A and $111%B planes, whereas HT templates have asymmetric TDsubdensities. A model based on TD reactions was applied to the experimental results and confirmedthe beneficial role of symmetric TD subdensities in LT GaAs TD reduction. A ductile-to-brittletransition in dislocation behavior was observed at;400 °C. © 1999 American Institute of Physics.@S0021-8979~99!02821-2#

I. INTRODUCTION

Dislocations in semiconductors are detrimental to deviceperformance. Threading dislocations~TDs!, which passthrough the interior of a heteroepitaxial film to the surface,reduce mobilities and act as mid-band-gap states. TDs can bereduced with increasing growth thickness. This is due todislocation–dislocation reactions, where two dislocations re-act to form either a single dislocation or annihilate, removingboth dislocations from the system. Two important issues forTD reduction are~i! understanding the mechanism of TDgeneration, and~ii ! the development of experimental tech-niques that diminish the existing TD density. Currently,buffer layers are used in heteroepitaxial growth to reduce TDdensity for devices that do not have an available lattice-matched substrate.1

In this article, we will concentrate on low-temperature-grown @~LT!, Tgrowth'250 °C]GaAs. LT grown arsenidesare nonstoichiometric, containing excess arsenic in the formof AsGa andVGa.2 It has been shown that LT growth reducesTD density in step-graded InGaAs buffer layers.3 Grideret al. showed that LT~300 °C! InGaAs buffers grown onGaAs substrates have improved heterojunction FET~HFET!device performance over HT grown buffers. Low-temperature~77 K! Hall mobilities in HFET devices in-creased by a factor of four when compared with devicesgrown on high-growth-temperature~500 °C! InGaAs gradedbuffers. Cross-section TEM showed that the LT gradedbuffer reduced TD densities dramatically, although a mecha-nism for this greater reduction was not proposed.3

In the current work, we attempt to understand the resultsin TD reduction in LT GaAs buffers. Specifically, the aim of

the experiments is to understand why TD densities are re-duced faster in LT GaAs and to enhance this reductionmechanism in other systems, with the goal of reducing thethickness of buffer layers. We have interpreted our data interms of a model based on TD reactions in growing bufferlayers.

II. BACKGROUND

Because we are concentrating on the mechanism of TDreduction in LT GaAs, we review two topics in this section:~i! a model for TD reduction based on dislocation reactions,and ~ii ! the origin of TD density asymmetry on the$111%Aand B planes of GaAs.

A. TD modeling and reduction

Elastic strain energy of the coherent film scales with thefilm thicknessh as Cem

2 h,where C is the combination ofelastic moduli andem is the misfit strain. The energy of arelaxed film~with MDs at the film/substrate interface! has aweaker logarithmic dependence on film thickness. When thefilm thickness reaches the critical value ofhc the relaxed~semicoherent! state of the film/substrate system becomesenergetically favorable.4–6 Therefore, MDs are equilibriumdefects for h.hc . In low-mismatch thin films ~misfit,;1%!, there may be a large difference between the equi-librium and kinetic critical thicknesses~the thickness wheremisfit relaxation is experimentally observed!.1,4 In large mis-match films, relaxation happens near to the equilibrium criti-cal thickness.4 MDs relieve strain and lie in the interfacebetween a mismatched film and the substrate. TDs are at-tached to MDs and thread to the film surface, as shown inFig. 1~a!.

As TD densities change with increasing film thickness,there are three experimentally observed regimes of TD den-

a!Electronic mail: smathis@engineering.ucsb.edub!Current address: Headway Technologies, Milpitas, CA.

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sity evolution.7 Soon after dislocation generation, high TDdensities are present in the entanglement regime. In the fall-off regime, TD density reduces with thickness (h)as 1/h dueto TD reactions. This has been observed in films of uniformcomposition in several systems, including InAs/GaAs, GaAs/Ge/Si, GaAs/InP, and InAs/InP.8 Saturation is the last re-gime, and results when TD reactions slow and TD densitybecomes a weak function of the height of the film. TD den-sity may plateau during the saturation regime due to a netlocal Burgers vector content in thin films.4,9,10

The following scenario can be applied to the process ofTD generation and reduction in growing constant-composition buffer layers. After the film grows thick enoughto relax, dislocations may be generated at the film surface.Additionally, dislocation multiplication may be involved inproducing high TD densities in the entanglementregimes.11,12 Once the film has extensively relaxed, there iseither no net stress or a very small net stress; therefore, glideand climb of dislocations should primarily be induced whenTDs are close enough to be affected by mutual elastic inter-action. Relative dislocation motion takes place with increas-ing film thickness since TDs are inclined with respect to thefilm normal.9,10 Figure 1~a! shows how inclined TDs canapproach one another as growth proceeds. Dislocation den-sities are reduced when TDs meet and react with one an-other.

Threading dislocations will react with one another whenthey approach within a characteristic interaction distance.Once they are close enough, they may either annihilate orfuse if their line energy is reduced by reaction. The defectline energy is proportional tob2 for a dislocation, whereb isthe magnitude of the dislocation’s Burgers vector. The reac-tion condition is thatb1

21b22>b3

2 ~theb2 criterion9,13!, where

b35b11b2 is the Burgers vector of the resulting dislocation.The reaction radius,r I , is the distance at which the interac-tion force between dislocations becomes larger than the fric-tion resistance of the lattice~caused by the Peierls stresssp).The reaction distance depends on the material proper-ties, ~such as shear modulusm! the Burgers vectors of thedislocations, and the type of reaction~annihilationr A or fu-sion r F). For annihilation, the reaction radius isr A andfollows7

r A'mb

2psp. ~1!

Overall, Specket al. found that the effective range of anni-hilation radii in cubic semiconductors was from 500 to 5000Å using this relation.7 Experimental TD falloff data was fit-ted ~including GaAs/Si, GaAs/InP, and InAs/InP!, showingthat the dislocation reaction radius is approximately 500–1000 Å for a range of III–V semiconductors.7

A quantitative model incorporating threading dislocationreactions and their relative motion during thin film growthhas been developed by Romanovet al.9,10 This model suc-cessfully predicts therTD}1/h behavior in constant compo-sition buffer layers on~001! semiconductors. There are 24possible Burgers vector/slip plane combinations in the zinc-blende system in this geometry. For each unique pair of dis-locations, theb2 criterion was applied, and it was determinedwhether the pair of TDs would annihilate, fuse, or have noreaction. The line direction of each TD was also considered,and the reaction probabilities were calculated from these linedirections. From this analysis, a set of 24 coupled differentialequations was developed to determine the thickness depen-dence of the TD density. Using various initial TD subdensi-ties, the overall solution for total TD densityrTD confirmsthe experimentally observed behavior:

rTD51

K~h1h!. ~2!

Here,K}r A and it is a function of the ratior A /r F and othergeometrical factors on the order of 1. The constanth is aparameter corresponding to the initial TD density, i.e.,

rTD~h50!51

Kh. ~3!

B. a/b asymmetry

GaAs has crystallographically distinct$111% planes.Each$111% plane is composed to an As/Ga bilayer.$111%Aplanes have Ga~group III! layers uppermost in a@001# ori-ented substrate, while$111%B has As~group V! layers upper-most when viewed along the surface normal direction. Figure1~b! shows the four$111% slip planes in zinc-blende semi-conductors and identifies them as A or B type. Dislocationslying on the$111%A planes are referred to asa dislocations,and those on$111%B are referred to asb dislocations. Anasymmetry in thea and b TD subdensities on the$111%Aand $111%B planes has been observed in cross-sectionTEM.14 This has been attributed to different dislocationnucleation barriers on$111%A and B in undoped GaAs.15 The

FIG. 1. ~a! Schematic of threading dislocations and misfit dislocations inmismatched thin film. As growth proceeds, TDs approach one another dueto their inclined line directions. TDs annihilate when their Burgers vectorsare antiparallel, fuse when components of their Burgers vectors are antipar-allel, and can repel one another when their Burgers vectors are parallel.~b!The set of$111% slip planes in zinc-blende semiconductors. Dislocationslying on $111%A planes are referred to asa dislocations, while dislocationslying on $111%B planes are referred to asb dislocations.

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bilayer ordering leads to an asymmetry in the core structureof TDs sincea andb dislocations are terminated by differentatomic species.14,16,17 The result of the asymmetric corestructures is thata andb dislocations have different veloci-ties under applied stress and different subdensities. We willuse these properties to explain the more efficient TD reduc-tion in LT GaAs since the asymmetry in TD density is re-moved when TDs are generated at low temperature.

III. EXPERIMENTAL TECHNIQUE

Threading dislocation templates~TD templates! wereused in this study to provide regrown layers of GaAs withthe same starting surface and TD density. The layers weregrown in a Varian Gen-II molecular beam epitaxy~MBE!machine. The native InP oxide was desorbed at 545 °C underan As2 flux from a valved, cracked solid arsenic source. Tosmooth the surface, 0.1mm of AlInAs was grown latticematched to InP. GaAs was then grown to a thickness muchgreater than the critical thickness (hc'17 Å for GaAs grownon InP! at 1 mm/h growth rate. The surface was then passi-vated for subsequent regrowth using metallic antimony. Theantimony was deposited using a Sb4 effusion cell at a sub-strate temperature of 200 °C according to a previously pub-lished method.18,19 The substrate could then be removedfrom the growth chamber, sectioned, and reintroduced forregrowth without surface exposure to air. The Sb metal wasdesorbed at 350 °C under an As2 flux, typically leaving lessthan one monolayer of antimony on the surface.18,19 Thistemplate could then be used to study TD reduction underdifferent growth conditions but with the same initial TD den-sity.

Two separate experiments were carried out on TD tem-plates. Experiment I investigated the effect of excess arsenicantisite defects and gallium vacancies on TD reduction farfrom the interface where the TDs and MDs were generated@see Fig. 2~a!#. This was accomplished using a 1-mm-thickTD template of GaAs grown at 520 °C and passivated usingthe method described above. Regrowths were carried out onthe TD template at six different temperatures: 250, 300, 350,425, and 580 °C. Substrate temperatures above 450 °C weremeasured using a pyrometer, while growth temperatures be-low 450 °C were measured using a thermocouple placed nearto the substrate holder. Each layer was grown 5mm thick for

a total of 6 mm of GaAs except in the case of the lowestregrowth temperature, 250 °C, where reflection high energyelectron diffraction~RHEED! showed indications of poly-crystalline growth at 4mm of regrowth, so growth wasstopped after a total of 5mm including the TD templatelayer.

Experiment II was performed to study the effects of low-and high-temperature dislocation formation on the subse-quent TD reduction mechanism. Two 0.1-mm-thick tem-plates were grown on InP, where the substrate temperaturewas the only difference between the two growths. The tem-peratures were 250 °C~LT template! and 580 °C~HT tem-plate! as shown by the growth structure in Fig. 2~b!. Afterthe templates were grown, the wafers were removed from thegrowth chamber and reintroduced on the same wafer holderfor simultaneous regrowth. Regrowth was done at 1mm/h at580 °C to a thickness of 3mm for a total of 3.1mm GaAs.

A. Threading dislocation density measurements

1. X-ray diffraction

Samples from experiment I and II were first processedvia wet chemical etching into stepped mesa structures. Thesteps were;5 mm wide and;0.5 mm high as characterizedusing a Dektak profilometer, which allowed for x-ray diffrac-tion ~XRD! measurements at each step.

A theory developed for polycrystalline metals by Gay,Hirsch, and Kelly describes the x-ray peak broadening ex-pected from dislocations.20 The general relation between dis-location density (r') and peak width, full width at halfmaximum~FWHM! is r'

1/2}FWHM.This model was appliedto zinc-blende thin films by Ayers for the measurement ofTD density using several different rocking curve widths.21 Inour experiments, however, only the general form derived byGay, Hirsh, and Kelly was used. A single 004 rocking curvepeak width was measured for each thickness using a Bedex-ray diffraction system with a single crystal monochromatorwith Cu Ka radiation ~l51.54 Å!. Each peak fit was per-formed using a Gaussian–Lorentzian function. Plan viewtransmission electron microscopy~PVTEM! was used to de-termine the TD density at the growth surface and thus findthe proportionality constantM @wherer'5M•(FWHM)2].

2. TEM

TEM samples were prepared using the wedge technique.Plan view samples were mechanically thinned from the sub-strate side, then polished on the substrate side to electrontransparency using a bromine-methanol solution. Cross-section samples were prepared for observation along the twoorthogonal@110# directions by a mechanical polish on eachside of the sample. Both plan view and cross-section TEMsamples were thinned and cleaned using Ar1ions at 3.5 keVin a Gatan PIPS ion mill. The cross-section samples weremilled from both sides, while care was taken to ensure thatonly the back side of the plan view samples were exposed tothe ion beam, thus ensuring that the TD density was countedat the top surface of the film.

Plan view and cross-section TEM~XTEM! experimentswere carried out in a JEOL 2000FX TEM microscope with

FIG. 2. Threading dislocation template and regrowth structure.~a! A 1 mmGaAs template was grown at a single temperature, and regrowths were doneon the same template at five different temperatures.~b! 1000 Å GaAs tem-plates were grown at two different temperatures. Regrowths on these tem-plates were done at a single temperature at the same time.

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200 keV electrons. Plan view TEM for each sample wasdone at the final growth surface. Threading dislocations werecounted over an area of 10310 mm. About 5% of the dislo-cations had dissociated at the surface of the material intopartial dislocations and associated stacking faults.

In experiment II, the TD subdensities on$111%A and Bplanes were measured. TDs were counted at several thick-nesses in the micrographs. The number of TDs was dividedby the length over which they were counted and by the filmthickness. The thickness of the film was determined usingconvergent beam electron diffraction~CBED! according tothe method described in Ref. 22. TDs inclined at 60° to thefilm–substrate interface were assumed to be on the$111%planes lying along the viewing direction. All other TDs wereassumed to be on the set of$111% planes facing the viewingdirection. The four crystallographically distinct types of$111% planes are shown in Fig. 1~b!. For example, if theviewing direction is assumed to be@110#, the planes lyingalong the viewing direction are$111%B planes and include~111! and ~111!, while the $111% planes facing the viewingdirection are$111%A planes and include~111! and~111!. Themeasurements were made along both the perpendicular^110&directions lying in the~001! plane.

IV. RESULTS AND DISCUSSION

Figure 3~a! shows the TD density calculated from XRDand calibrated at the surface using PVTEM. Curve fits in Fig.3~a! are from Eq. ~2!. Regrowths at high temperatures

(Tgrowth.;400 °C)show low TD density and similar reduc-tion to the regrowth at HT (Tgrowth5580 °C).Regrowths attemperatures less than;400 °C have higher TD densitiesthroughout the thickness of the material than higher regrowthtemperatures. The lowest temperature regrowth does displayslightly lower TD densities than regrowth at 350 °C.

The annihilation radiusr Awas calculated by fitting theTD density falloff data with Eq.~2! and takingK'r A . Thevariation in annihilation radius with regrowth temperature isshown in Fig. 3~b!. At temperatures higher than 400 °C, theannihilation radius was an average of approximately 1000 Å,while below 400 °C, the effective annihilation radius de-creased to about 100 Å. We term LT material ‘‘brittle’’ sinceits dislocations are immobilized and unable to easily movetogether to react. Thus, we have observed a ductile-to-brittletransition temperature atTgrowth;400 °C in GaAs. The re-duction in r A shows that low growth temperature does notresult in greater dislocation mobility.

Prior investigation has shown that dislocation glide mo-tion is retarded in GaAs at low temperatures.23,24 In the in-vestigation of Tachikawa and Mori, as relaxed GaAs/Si wascooled from the growth temperature, the thermal expansionmismatch of GaAs and Si created a thermal stress in theGaAs film. Near the growth temperature, TD glide motiongenerated MD length to relax this stress. Below;350°–450 °C, the film behaved in a brittle manner: TD glide mo-tion was suppressed and thermal stresses again built up untilthe critical stress for dislocation generation was reached.23,24

At very low regrowth temperature, the high point defectdensity may have an effect on TD reduction. The regrowth at350 °C had a lower TD density for all thicknesses than theregrowth at 350 °C, despite the increasing difficulty of glidemotion of dislocations. The high point defect density mayaffect TD reduction in two ways. First, the supersaturation ofpoint defects can initiate more frequent dislocation climb.The same growth chamber used in these experiments previ-ously gave LT GaAs with AsGa concentrations of 6.531019 cm23 at a growth temperature of 250 °C.25 The pointdefect density increases quickly with decreasing growth tem-perature below 350 °C.2 Second, high concentrations of pointdefects result in lattice expansions up to 0.15% atTgrowth5225 °C and 0.075% atTgrowth5250 °C when com-pared with stoichiometric GaAs.25 This may lead to disloca-tion motion and interaction due to additional net stress dur-ing regrowth. However, the effect of nonstoichiometric pointdefects during LT regrowth is not significant compared to themobilities of TDs at high regrowth temperatures (Tgrowth

.;400 °C).A comparison between the low- and high-temperature

initiated growths of experiment II is shown in Fig. 4~a!. To-tal TD densities were measured with XRD and calibrated atthe final growth surface with PVTEM. Curve fits are againfrom Eq. ~2!. The measurements show that LT nucleation ofTDs and MDs gives lower TD densities for all thicknessesthan HT nucleation of dislocations. The PVTEM sampleswere also checked for evidence of subgrain formation~cel-lular structure and/or tilt boundaries!, but none was found.

Threading dislocation subdensities for experiment IIwere measured using XTEM. ‘‘Subdensity’’ refers to the

FIG. 3. ~a! Falloff in TD density with thickness on TD template in experi-ment I. The TD densities were measured by usingrTD}FWHM2 and cali-brated by PVTEM at the surface of the material. Growth temperatures above400 °C lay near to the 580 °C TD densities, while growth temperaturesbelow 350 °C showed increasing TD densities. The exception wasTgrowth5250 °C, which had a lower TD density than of the 350 °C-grownsample.~b! Annihilation radius variation with growth temperature for ex-periment A. Note the reduced annihilation radius for growth temperaturesbelow 400 °C.

4839J. Appl. Phys., Vol. 86, No. 9, 1 November 1999 Mathis et al.

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portion of the total TD density on the$111%A and B planes~a or b dislocations, respectively!. The subdensities in LTinitiated growths are shown in Fig. 4~b!~i! and the subdensi-ties in HT initiated growths are shown in Fig. 4~b!~ii !. HTinitiated growths had asymmetric TD densities, while LTinitiated growths had symmetric TD densities on the twotypes of $111% planes. The total TD densities measured viaXTEM and CBED varies from the total density measured viaPVTEM.

In semiconductors, dislocation formation energies, ve-locities, and densities are affected by the Fermi level of thematerial.26 These effects were first investigated for silicon,where it was found that dislocation velocities were increasedat constant stress by doping withn- or p-type dopants atordinary doping levels when compared with unintentionallydoped material.27 The motion was not enhanced by increas-ing the rate of dislocation climb; the doping levels in thesesilicon samples were too low to provide enough point defectsto enhance climb rates. Theoretical treatments of this phe-nomenon rely on changing the energies of formation andmigration of charged double kinks. Dislocations move byintroducing double kinks, which then propagate along thedislocation line, moving it from one lattice position to thenext. Several theories describing Fermi level effects on dis-locations have been described critically in two reviews byHirsch.26,28However, these theories have not been applied tozinc-blende materials, although differences in dislocation ve-locities and nucleation barriers have been observed in dopedmaterial when compared with undoped material.

Experimentally, it has been observed that bulk grownzinc-blende crystals doped with electrically active impuritieshave lower dislocation densities than undoped crystals.29

Yonenaga and Sumino showed that point defects located ongroup III lattice positions, such as silicon, increased the bar-

rier dislocation formation.15 On a single crystal bend speci-men of GaAs,$111%A and $111%B dislocations nucleated at ahigher stress than in undoped GaAs.15 Choi and Mihara mea-sured the relative velocities ofa and b dislocations in Si-,Te-, and Zn-doped bulk GaAs specimens, showing that theZn-doped,p-type GaAs had nearly equal dislocation veloci-ties on the$111%A and B planes.30 In Te- and Si-dopedn-type GaAs, the velocities of theb dislocations was slowerthan thea dislocations by two to three orders of magnitude.Doping GaAs eithern- or p-type slowed dislocation veloci-ties for a given applied stress when compared to undopedspecimens.30 We believe that LT generation of TDs in GaAsleads to symmetric dislocation nucleation barriers andsymmetric TD densities. It has been shown that as-grownLT GaAs has both donor and acceptor concentrations atordinary doping levels~;1017/cm3acceptors and;1018/cm3

donors!.31 We speculate that the combination of slower dis-location glide motion during low temperature growth andformation of excess carriers of both types may modify dis-location generation and motion in a manner that equalizesthe TD densities on both the$111%A and B planes. However,as with most high misfit systems, a complete picture of thedetails of misfit and threading dislocation generation ispoorly understood.

V. MODELING

The effect of an asymmetric initial TD density was in-vestigated using the model of Romanovet al.9,10 For com-pleteness, the essential features of this model are detailedhere.

The 24 unique dislocation types in zinc-blende thin filmswere considered, and all energetically possible TD reactionswere determined using theb2 criterion. Annihilation reac-tions, where the Burgers vectors of the two reacting disloca-tions are equal and opposite, remove both TDs from the ma-terial. Fusion reactions produce a single dislocation from twoTDs. A 24324 matrix was developed showing the possiblereactions and new dislocations, including those reactions thatwere geometrically unlikely considering their line directions.From this reaction matrix, 24 coupled differential equationsthat describe the evolution of specific TD subdensities werewritten and solved numerically.9 These equations took intoaccount annihilation and fusion reactions that reduced theparticular TD subdensity, and fusion reactions that increasedthe TD subdensity. Twelve of the 24 dislocations had$111%Aslip planes, while the other twelve had$111%B slip planes.These coupled differential equations were numericallysolved simultaneously for increasing thicknesses.

The model was used to determine whether the reductionin TD density in LT initiated buffer layers could be attrib-uted to the symmetric initial TD density. Symmetric andcompletely asymmetric initial TD subdensities were mod-eled. For the symmetric case, each TD family was given thesame initial density, which meant that the TD density wasdistributed evenly between$111%A and $111%B planes. Theasymmetric case was analyzed by determining which TDs inthe reaction matrix had$111%A slip planes and placing all ofthe initial TD density on those planes. The total initial TD

FIG. 4. ~a! Falloff in TD density with thickness in experiment II. The TDdensities were measured by using x-ray diffraction and calibrated byPVTEM at the surface of the material. Low-temperature TD generationclearly reduced TD densities for all thicknesses in the material.~b! XTEMmeasurement of the TD densities on the two different$111% planes for~i! LTGaAs initiated growth and~ii ! HT GaAs initiated growth.

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density was chosen to be the same for the two cases. Becauseof the regrowth conditions in experiment II~the regrowthswere done at the same growth temperature!, a constant anni-hilation radius was assumed for the modeling. The chosenasymmetric case is a limiting case and is not the assumedexperimental condition.

Results from the model are shown in Fig. 5, whichshows the falloff of the total TD density with increasing filmthickness for the asymmetric and symmetric initial TD den-sities. The case of symmetric initial TD density falls offfaster than the cases of asymmetric initial TD density. How-ever, fusion reactions produce TDs that have$111%B slipplanes, and the final TD densities should and do approachone another at large thicknesses.

Threading dislocations lying in only one type of$111%plane approach one another less often than TDs lying onboth A- and B-type slip planes. Two TDs approaching oneanother on a$111%A and $111%B slip plane are shown in Fig.1~a!. Asymmetric TD subdensities lead to less interactionamong TDs and less opportunity to react. Figure 1~b! showsthe four possible slip planes; the$111%A planes intersect oneanother along a110& direction in the~001! plane, as do the$111%B planes. When the TD density is asymmetric, most ofthe TDs lie on one of the two types of slip planes, so theseintersections are the primary way TDs can meet. For a sym-metric TD density, the likelihood of two TDs meeting isincreased, since the$111%A planes intersect the$111%Bplanes along two more110& directions that do not lie in the~001! plane. For a constant total TD density, this increasesthe likelihood of TD interaction. This is one advantage ofinitiating mismatched growth at low temperature in GaAs.

VI. CONCLUSION

In conclusion, we have developed a TD template tech-nique to investigate TD reduction in highly lattice-mismatched III–V materials. The current experiments andmodeling have shown the following:

~1! The reduction in TD density in low-temperaturegrown GaAs, when compared to high-temperature grownGaAs, is not directly due to increased dislocation mobility

from nonstoichiometric defects. When TDs are nucleated inlow-temperature initiated GaAs, a symmetric distribution ofTDs is obtained. This is in contrast to HT GaAs, where dis-locations have a well-known asymmetry in density, which isdue to the difference in their velocity and formation energyon the$111%A and $111%B planes. Modeling of the TD den-sity reduction for symmetric and asymmetric distributionsconfirmed that the symmetric distribution of TDs on$111%Aand B planes leads to increased TD reaction probability andto lower TD density during the initial stages of TD reduction.

~2! The effective annihilation radius of the threading dis-locations at high temperature was determined by fitting ex-perimental data to be 1200 Å, which compares well with atheoretical estimate of 500–5000 Å. By applying this ap-proach, the ductile-to-brittle transition temperature was de-termined for GaAs films to lie between 350° and 425 °C.

ACKNOWLEDGMENTS

The authors would like to thank Z. Lillinetal-Weber forhelpful suggestions. This work was supported by the AirForce Office of Scientific Research through the PRET Centerat UCSB~Dr. Gerald Witt contract monitor!. Travel supportfor J.S.S. and S.K.M. was provided by the travel program ofNSF under Award No. INT-9603242.

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FIG. 5. Modeling of falloff in TD density for symmetric and asymmetricinitial TD densities. Total initial density and annihilation radius are heldconstant to model conditions in experiment II. The case of isotropic initialTD density~like LT GaAs! attains a lower value at large thicknesses. TheTD densityrTD is normalized by multiplying byr A

2 and the film thickness isnormalized by dividing byr A . These data correspond to the case ofr A

51000 Å,rTD0 5109 cm22 and a maximum thickness of 5mm.

4841J. Appl. Phys., Vol. 86, No. 9, 1 November 1999 Mathis et al.

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