Experiments have shown that the presence of a thin native oxide layer on the surface of a strained SiGe epilayer causes an order of magnitude increase in dislocation velocities during annealing over those observed in atomically clean samples and during crystal growth. This behavior is explained herein by stress-assisted dislocation kink nucleation at the oxide/epilayer interface. Finite element models are used to estimate the magnitude of stress local to steps at this interface due to both intrinsic and thermal expansion stresses, and dislocation theory is used to determine the resulting increase in single kink nucleation

Stach, E.A.

eScholarship - University of California

Lawrence Berkeley National LaboratoryRecent WorkTitleEnhancement of dislocation velocities by stress assisted kink nucleation at the native oxide/SiGe interfacePermalinkhttps://escholarship.org/uc/item/9760x2m5JournalApplied Physics Letters, 79(3)AuthorStach, E.A.Publication Date2001-02-15eScholarship.org Powered by the California Digital LibraryUniversity of CaliforniaStach and Hull Ð Submitted to Appl. Phys. Lett.1Enhancement of dislocation velocities by stress assisted kinknucleation at the native oxide / SiGe interfaceE. A. Stacha)National Center for Electron Microscopy, Materials Sciences Division, Lawrence BerkeleyNational Laboratory, Berkeley, CA 94720.R. HullDepartment of Materials Science and Engineering, University of Virginia, Charlottesville,Virginia 22903;AbstractExperiments have shown that the presence of a thin native oxide layer on the surface of astrained SiGe epilayer causes an order of magnitude increase in dislocation velocities duringannealing over those observed in atomically clean samples and during crystal growth.  Thisbehavior is explained herein by stress-assisted dislocation kink nucleation at the oxide /epilayer interface.  Finite element models are used to estimate the magnitude of stress local tosteps at this interface due to both intrinsic and thermal expansion stresses, and dislocationtheory is used to determine the resulting increase in single kink nucleation.                                                 a Electronic mail: EAStach@LBL.govStach and Hull Ð Submitted to Appl. Phys. Lett.2The rate of strain relaxation in lattice mismatched heterostructures is determined bythe kinetics of dislocation nucleation, propagation and interaction.  Over the past decade thedislocation propagation process in these systems has been studied extensively.1  The majorityof these studies have focused on the rate of dislocation motion during annealing of structuresfollowing the completion of epilayer growth.  Recently, it has been shown in the SiGe / Si(001) system that significant differences exist between the rate of dislocation motion duringepilayer growth and during annealing.2  In particular, it was found that the presence of a thinnative oxide layer on the epilayer surface causes an order of magnitude increase indislocation velocities over those observed during crystal growth and during annealing ofoxide-free samples.  In this Letter, it will be shown that this increase may be explained byconsidering how intrinsic and thermal expansion stresses present at atomic height steps alongthe oxide / epilayer interface alter the rate of single kink nucleation along the dislocation line.Dislocation propagation in strained heterostructures is driven by the net excess stressin the epitaxial layer.  This stress results from the strain caused by the inherent latticemismatch between the epitaxial layer and the substrate minus the stress associated with theself-energy of the dislocation.3  In addition to the driving stress, the periodicity of acrystalline lattice also has a direct influence on the glide motion of dislocations, causing avariation in the self-energy of a dislocation as a function of its position within the lattice.This variation in self-energy results in a periodic force on the dislocation, known as thePeierls force or the Peierls-Nabarro force.4   Because of the strong covalent bonding presentin silicon, germanium and silicon-germanium alloys, the magnitude of the Peierls forces arerelatively large and dislocation propagation is substantially more difficult than in metallicmaterials (with activation energies on the order of 1.0 to 2.5 eV compared to » 0.1 eV forStach and Hull Ð Submitted to Appl. Phys. Lett.3metals).  These high Peierls barriers cause dislocations to lie within the potential energytroughs.  As a result, dislocation glide in semiconductors must occur via the nucleation andpropagation of thermally activated kinks along the dislocation line.5  These kinks are atomicscale disturbances along the dislocation that occur when a small portion of the line is able tosurmount the Peierls barrier through thermal activation and advance one lattice spacing.  Inbulk materials, kink nucleation must necessarily occur in pairs in order to maintain thecontinuity of the dislocation line.  In the case of strained epilayers, however, dislocationkinks may nucleate singly at the epilayer / free surface interface.6  These kinks, oncenucleated, are driven along the length of the dislocation by the applied stress and thus act toadvance the entire dislocation forward by one atomic spacing.  The presence of very highstresses within a material may assist in the likelihood of kink formation by increasing theprobability that a kink or kink pair, once nucleated via thermal activation, will be drivenalong the dislocation line.5-7In previous experiments, we have systematically measured the rate of dislocationpropagation in SiGe / Si (001) heterostructures during epilayer growth,2 during annealing inultrahigh vacuum (UHV)2 and during annealing when the epilayer has a native oxide on itssurface.2,8 The results of these experiments are reproduced as Figure 1.  In this graph we plotthe measured rate of dislocation motion normalized with respect to both the epilayer excessstress and a composition dependent activation energy according to the equation below:  vv EkTmexv**exp=σ(2)Here, vm is the measured velocity and Ev* is the normalized activation energy, whichaccounts for the 0.6 eV glide activation energy difference between Si and Ge [i.e. Ev*(x) =Stach and Hull Ð Submitted to Appl. Phys. Lett.4(2.2 - 0.6x) eV].8  From this data we see that there is no significant difference observedbetween the velocity of dislocations during the growth of the epitaxial layer and duringannealing in ultrahigh vacuum (UHV) of the layers following the completion of growth.  It isfound, however, that the rate of dislocation propagation is significantly enhanced in thesamples that have a thin native oxide layer on the surface, and that the magnitude of thisenhancement increase scales with increasing germanium content.As mentioned above, the velocity of dislocations in semiconductors is directlycontrolled by the nucleation and migration of kinks along the dislocation line.  A possibleexplanation for the observed order of magnitude increase in dislocation velocity followingthe growth of a thin native oxide layer is that there is an enhanced nucleation of kinks at theoxide Ð epilayer interface.  Using a simple finite element analysis and dislocation theoryconcepts we will show that the presence of local stresses at steps along the interface maycause enhanced kink nucleation rates consistent with our observations.In order to determine the magnitude of stress present at steps in the native oxide Ðepilayer interface, certain assumptions must be made about the level of stress present in theoxide layer during annealing at 600 °C (the temperature at which the dislocation velocitymeasurements were made).  In the case of the experiments of Reference 6, the native oxidewas formed on the sample during a room temperature exposure to ambient air.  Priorellipsometry measurements have found that there is a residual compressive stress on theorder of 450 MPa present in a native oxide grown on silicon at room temperature.9Superimposed on this stress in the experiments of Figure 1 is a tensile thermal expansionstress of 200 MPa caused by raising the temperature of the sample from room temperature toStach and Hull Ð Submitted to Appl. Phys. Lett.5600 ¡C.10  This yields a net compressive stress in the oxide layer of the order of 250 MPa at600 °C.The finite element modeling was performed with a commercially available softwarepackage.11   Both monolayer and double atomic layer steps were modeled Ð as these aretypically observed at the native oxide / silicon interface12 Ð and the level of compressivestress was varied from 150 MPa to 350 MPa.  Similar analyses which compare continuumsolutions and atomistic simulations of dislocation cores in semiconductor materials haveshown that the continuum solutions are generally accurate to within one to two Burgersvectors.13,14 This provides justification for the use of a continuum model in the presentanalysis.  Figure 2 shows the results of the finite element calculations for a single monolayerheight step, with a residual compressive stress in the oxide of 250 MPa in the region near thestep.  (The entire model is not shown Ð it is observed that the level of stress falls off rapidlyfrom the step, consistent with analytical elasticity theory models that predict that the stressdue to an applied moment of this type should decrease as 1 2r .15)  Compressive stresses ashigh as 750 MPa are seen to develop at the step singularity; stresses of the order 500 MPa ashort distance away.  The stresses quoted are stresses within the growth plane (σx), and thusare additive with respect to the compressive excess stress in the film.  A number of similarsimulations were performed where the magnitude of the residual stress in the oxide wasvaried, and where double height steps were modeled.  The resulting stresses associated withthe presence of steps at the oxide / epilayer interface were not found to be strongly sensitiveto the residual stress value in the oxide or to the step height.  This is consistent with theanalytically predicted 1 2r  dependence; the amount of residual stress and the step heightused in the simulations simply act to shift the distance away from the step at which the stressStach and Hull Ð Submitted to Appl. Phys. Lett.6falls to zero, but do not substantially alter the maximum step-related stresses.  Thus, the finiteelement models suggest that 500 MPa is a reasonable approximation of the compressivestress local to steps along the oxide Ð epilayer interface.Dislocation velocities in semiconductors are determined by both the magnitude of theapplied stress and the kinetics of kink formation.  The effect of the additional stress causedby the steps at the oxide Ð epilayer interface is to locally reduce the activation energyassociated with kink formation and thus increase dislocation velocities.  This additional stresscan be accounted for using the Seeger - Schiller correction.5,7  It would seem most plausible,physically, to consider the formation of single kinks at the epilayer Ð oxide interface,although the model that follows can be formulated in terms of double-kink nucleation as well(we have done so, and it yields similar conclusions).  Considering in detail the process ofsingle kink nucleation, it is apparent that one must think of the nucleation of a single kink inconjunction with an imaginary Ôimage kinkÕ existing in the vacuum16 - this will be done inthe analysis that follows.When high stresses are present, the free energy of formation of a kink pair is afunction of the separation between the real kink and the image kink.  There exists a criticalseparation (s*) at which kink-kink attraction due to elastic energy effects is balanced by thoseexternal forces which act to tear the kinks apart.  These external forces are of the form bqσ ,with q being the distance between Peierls valleys in the direction of dislocation motion.When the free energy is at a maximum those kinks with separation greater than s* spreadapart and move the entire dislocation line forward while those closer than s* mutuallyannihilate.  Including the additional effect of step related stress on the free energy of kinkformation as a function of s, the kink separation, yields:5-7Stach and Hull Ð Submitted to Appl. Phys. Lett.7F s Fb qsbqs bqsk applied step( ) = −+( )−( )− −µ υπ υσ σ116 112122 2 (3)where Fk is the stress-free activation energy for single kink nucleation (» 0.7 eV) 17 andσapplied is the lattice mismatch stress in the film.  The second term describes the elasticinteraction between kinks,5 and the final two terms account for the effect of stresses in thematerial on kink separation.  The function F(so) can be minimized to find the critical single-kink separation from the epilayer surface at which the kink energy is maximum, and thiscritical value back-substituted into the above equation to find the kink formation energy:F FG b qk kapplied step* = −+( ) +[ ]−( )18 13 3υ σ σπ υ(4)The resulting kink nucleation rate has been shown to be:5-7JbqkTE FkTD excess m k= [ ] − +( )ν σexp*2 (5)with νD is the attempt frequency, approximated here as the Debye frequency (νD = 1.3 x 1013s-1) and Em is the kink migration energy (Em » 1.25 eV) 17.  Simple geometricalconsiderations predict that the velocity of dislocations moving via the single kink mechanismis given by:6  vJs qsk =*4(6)Substituting appropriate values of σstep into the above formulations reduces theactivation energy for single kink formation by approximately 0.2 to 0.25 eV.  Due to thestatistical uncertainty in the experimental measurements, the experimental and theoreticalactivation energies cannot be directly compared to this level of resolution.  In Figure 3, weplot the effect of this change in activation energy on the theoretical predication of dislocationvelocity for dislocation motion in a 100 nm Si85Ge15 layer on Si (100).  The curve labeledStach and Hull Ð Submitted to Appl. Phys. Lett.8Òwithout correctionÓ is predicted using Equations 5 and 6, with σstep = 0.  To demonstratethat the model is not particularly sensitive to the exact magnitude of the stress associatedwith the steps, a lower bound solution with σstep = 250 MPa and an upper bound solutionwith σstep = 750 MPa are shown. The presence of this stress predicts an order of magnitudeincrease in dislocation velocities over those determined without the additional step-associatedstress.  These results show that stress - induced lowering of the kink formation energy atsteps at the oxide - epilayer interface provides one viable explanation for the observedincrease in dislocation velocities in samples with a native oxide on the epilayer surfaceshown in Figure 1.In conclusion, we have used finite element modeling and dislocation theory to explainthe experimentally observed order of magnitude increase in dislocation velocities in strainedSiGe epilayers which have a native oxide layer.  The presence of intrinsic and thermalstresses in the oxide cause highly localized stresses to develop near steps at the oxide Ðepilayer interface.  These stresses may lower the energy barrier associated with single kinkformation along the moving dislocation line, thereby increasing the net dislocation velocity.These results indicate that the modification of the surface of epitaxial layers can havedramatic effects on dislocation propagation as well as the overall rate of strain relaxation.AcknowledgementsThis work was funded in part by the National Science Foundation under DMR # 9531696and by IBM through a Joint Study Program and a Cooperative Fellowship to EAS.  The workat NCEM was supported by the Director, Office of Energy Research, Office of Basic EnergyStach and Hull Ð Submitted to Appl. Phys. Lett.9Sciences, Materials Science Division of the U.S. Department of Energy under Contract No.DE-AC03-76SF000098.Stach and Hull Ð Submitted to Appl. Phys. Lett.10Figure Captions1. Experimentally determined dislocation velocities (normalized) as a function of surfacecondition and temperature.  Note in particular that dislocation velocities are an order ofmagnitude greater when the surface is covered with a native oxide.  Reproduced fromReference 2, with permission.2 .  Results of the finite element model for a single monolayer step and a 250 MPacompressive stress.  The color scale varies from 1 GPa tensile (dark blue) to 1 GPa (red).3. Theoretical predictions of enhanced dislocation velocity resulting from the stress-assistedsingle kink nucleation model.Stach and Hull Ð Submitted to Appl. Phys. Lett.11References1 For a recent review of dislocation propagation in SiGe heterostructures see R. Hull and E.A.Stach, ÒStrain accommodation and relief in SiGe / Si heteroepitaxyÓ in Heteroepitaxy, ThinFilm Systems, edited by A.W. Liu and M.B. Santo (World Scientific Publishing Co., Inc.,Rivers Edge, NJ 1999).2 E.A. Stach, R. Hull, R.M. Tromp, M.C. Reuter, M. Copel, F.K. LeGoues and J.C. Bean, J.Appl. Phys. 83, 1931 (1998).3 B. W. Dodson and J. Y. Tsao, Appl. Phys. Lett. 51, 1325, 1987.4 R.E. Peierls, Proc. Phys. Soc. 52, 23 (1940); F.R.N. Nabarro, Proc. Phys. Soc. 59, 256(1947).5 J. P. Hirth and J. Lothe, Theory of Dislocations, (Wiley-Interscience, New York, 1982). SeeChapters 8 and 15 in particular for details of the diffusive kink model of dislocationpropagation.6 R. Hull, J. C. Bean, D. Bahnck, L. J. Peticolas, K. T. Short, and F. C. Unterwald, J. Appl.Phys. 70, 2052 (1991).7 A. Seeger and P. Schiller, Acta Metall. 10 348 (1962).8 R. Hull and J. C. Bean, phys. stat. sol. (a) 138, 533 (1993).9 E. Kobeda and E.A. Irene, J. Vac. Sci. Tech. B 6 574 (1988).10 E. Kobeda and E.A. Irene, J. Vac. Sci. Tech. B 4 720 (1986).11 ANSYS 5.3, ANSYS Inc. 275 Technology Drive Canonsburg, PA 15317.Stach and Hull Ð Submitted to Appl. Phys. Lett.1212 G. Renaud, P.H. Fuoss, A. Ourmazd, J. Bevk, B.S. Freer, P.O. Hahn, Appl. Phys. Lett. 58,1044 (1991).13 R. Jones, A. Umerski, P. Stich, M.I. Heggie, and S. Oberg, phys. stat. sol. a 138, 369(1993).14 A.S. Nandedkar and J. Narayan, Philos. Mag. A61, 873 (1990).15 Y.C. Fung, Foundations of Solid Mechanics, Prentice-Hall, Englewood Cliffs, NJ (1965).16 To be strictly accurate one must consider the image kink to reside in the native oxide layer.This introduces an unnecessary mathematical complication to the model and is a secondorder effect.  See Reference 6 for further details of single kink nucleation in strainedepilayers.17 H.R. Kolar, J.C.H. Spence and H. Alexander, Phys. Rev. Lett. 77, 4031 (1996).

English

Enhancement of dislocation velocities by stress assisted kink nucleation at the native oxide/SiGe interface

https://escholarship.org/uc/item/9760x2m5

Enhancement of dislocation velocities by stress assisted kink nucleation at the native oxide/SiGe interface

Abstract

Similar works

Full text

Available Versions

eScholarship - University of California