ISSN 10637834, Physics of the Solid State, 2011, Vol. 53, No. 10, pp. 2005–2011. © Pleiades Publishing, Ltd., 2011. Original Russian Text © Yu.B. Bolkhovityanov, A.P. Vasilenko, A.K. Gutakovskii, A.S. Deryabin, M.A. Putyato, L.V. Sokolov, 2011, published in Fizika Tverdogo Tela, 2011, Vol. 53, No. 10, pp. 1903–1909.
SEMICONDUCTORS
Strained Germanium Films in Ge/InGaAs/GaAs Heterostructures: Formation of Edge Misfit Dislocations at the Ge/InGaAs Interface Yu. B. Bolkhovityanov*, A. P. Vasilenko, A. K. Gutakovskii, A. S. Deryabin, M. A. Putyato, and L. V. Sokolov Rzhanov Institute of Semiconductor Physics, Siberian Branch, Russian Academy of Sciences, pr. Akademika Lavrentieva 13, Novosibirsk, 630090 Russia *email:
[email protected] Received January 18, 2011
Abstract—Heterostructures of the “strained Ge film/artificial InGaAs layer/GaAs substrate” type have been grown by molecular beam epitaxy. A specific feature of these structures is that the plastically relaxed (buffer) InGaAs layer has the density of threading dislocations on a level of 105–106 cm–2. These dislocations pene trate into the strained Ge layer to become sources of both 60° and 90° (edge) misfit dislocations (MDs). Using the transmission electron microscopy, both MD types have been found at the Ge/InGaAs interface. It has been shown that the presence of threading dislocations inherited from the buffer layer in a tensilestrained Ge film favors the formation of edge dislocations at the Ge/InGaAs interface even in the case of small elastic deformations in the strained film. Possible mechanisms of the formation of edge MDs have been considered, including (i) accidental collision of complementary parallel 60° MDs propagating in the mirrortilted {111} planes, (ii) induced nucleation of a second 60° MD and its interaction with the primary 60° MD, and (iii) interaction of two complementary MDs after a crossslip of one of them. Calculations have demonstrated that a critical layer thickness (hc) for the appearance of edge MDs is considerably smaller than hc for 60° MDs. DOI: 10.1134/S106378341110009X
1. INTRODUCTION In recent years, elastically strained germanium has been considered as a highly promising material for modern microelectronics. It was theoretically demon strated [1] that tensile stresses significantly increase the mobility of both electrons and holes in a Ge crys tal. For this reason, it is important to study the specific features of plastic relaxation in strained Ge films and determine criteria for their stable occurrence in the strained state. In configurations of the “strained Ge film/relaxed InGaAs buffer layer/GaAs(001) sub strate” type, the strained Ge layer must be thin but, on the other hand, it is desired that its thickness would be sufficient to form the active part of a device. However, this necessary thickness frequently exceeds the critical value (hc) for the introduction of misfit dislocations (MDs). At the same time, the InGaAs buffer layer contains a rather large number (~106 cm–2 [2]) of threading dislocations (TDs), which are inherited by the Ge layer and become sources of 60° MDs that exhibit bending toward the Ge/InGaAs interface according to a model proposed by Matthews [3]. This bending takes place immediately as soon as the Ge layer thickness exceeds the hc value that was calculated in [4], which also provides conditions for the forma tion of edge MDs [5–7].
It was commonly accepted until recently that edge MDs in the GeSi/Si and InGaAs/GaAs systems are formed predominantly at an elastic strain level exceed ing 2% and at the final stage of plastic relaxation (see, e.g., [8–10]). However, the results of out recent inves tigations [11, 12] showed that, under certain condi tions, the edge MDs can appear at an early stage of plastic relaxation in the strained films. One of these conditions is the presence of TDs inherited in the growing film from the buffer layer. This condition is satisfied during the growth of a strained Ge film on a relaxed InGaAs buffer layer. The present work was aimed at studying the dislo cated structure of a Ge/InGaAs interface in Ge/InGaAs/GaAs heterostructures and establishing conditions under which both 60° and 90° (edge) MDs can appear in the strained Ge film. 2. EXPERIMENTAL METHODS The samples of Ge/InGaAs/GaAs heterostruc tures were grown in two stages. At the first stage, arti ficial substrates comprising an InxGa1 – xAs/GaAs het erostructure with a relaxed InxGa1 – xAs layer were pre pared in a molecular beam epitaxy (MBE) system of the “Katun” type intended to grow III–V semicon ductor compounds. The substrates in these hetero structures were epiready semiinsulating GaAs(001)
2005
2006
BOLKHOVITYANOV et al.
α
thickness in etched samples) and the regions where this network was absent and only the Ge/InGaAs interface with a residual dislocation structure was retained. The TEM images of lateral sections were analyzed using standard methods of diffraction analy sis in the regime of twowave diffraction under a con dition of the dislocation image quenching at g · b = 0, where g is the diffraction vector and b is the Burgers vector.
g220
g220 α
β
3. RESULTS AND DISCUSSION (а)
400 nm
(b)
Fig. 1. Two darkfield TEM images (a, b) of the same region of a Ge/InGaAs/GaAs heterostructure observed in the regime of twowave diffraction from mutually perpen dicular families of {220} planes, which illustrate the quenching of pure edge misfit dislocations (indicated by white arrows) under the condition of g · b = 0 (g is the dif fraction vector, and b is the Burgers vector). Dislocation network of the InGaAs/GaAs heteroboundary is revealed in the bottom part of the images. Dotted circles indicate the site where two 60° MDs merge to form an edge MD.
wafers. The growth of InGaAs was effected at a sub strate temperature of 450°C at a rate of 0.3 nm/s with an In content of 12.7%. The buffer layer in these struc tures was grown to a thickness of ~1 μm so as to ensure relaxation of lattice mismatch stresses. Then, the tem perature was reduced to room temperature and an arsenic (As) layer was deposited in order to prevent the substrate surface contamination during the exposure to air. At the second stage (after transferring via atmo sphere and charging into a technological chamber for the growth of Ge), the substrates were heated to T = 300°C, whereby the protective As layer together with oxides and adsorbed gases were sublimed. Then, the substrates were heated to 400°C, after which a 2 × 4 reconstruction pattern was observed on an electron diffraction pattern, which was evidence of a structur ally perfect substrate surface upon annealing. For the epitaxial growth of a Ge layer, the artificial substrate was cooled to T = 350°C. A 30 nmthick Ge layer was deposited from a molecular beam created using a BN crucible. In the resulting heterostructure, the Ge film was elastically strained to 0.75% with allowance for an incomplete (below 100%) plastic relaxation of the buffer layer. The calculated critical thickness for 60° MD introduction into Ge was about 23 nm. The types of structural defects were determined and their spatial arrangement was studied by the trans mission electron microscopy (TEM) using a JEM 400EX (JEOL, Japan) instrument. The TEM mea surements were performed in the regions where a dense dislocation network of the InGaAs/GaAs inter face was present (because of the variable residual foil
Figures 1a and 1b show TEM images of the same region in a thinned heterostructure. The bottom part in both images reveals a dense MD network. This net work is absent on the remaining (top) area due to deeper etching from the substrate side, while Ge film and the adjacent InGaAs buffer layer (including the upper interface of the heterostructure) is retained. The top part in these images (as well as in other with figures presented below) contains rare dislocation lines that mostly represent 60° MDs. Most dislocations of this type occur in the Ge/InGaAs interface and are situ ated on the intersection of this interface with a tilted (111) glide plane, thus appearing as straight lines. In particular, straight dislocation line α is seen in both images and, hence, can be interpreted as a 60° MD. Dislocations indicated by white arrows are present in one image and absent in the other as a result of the quenching at g · b = 0, which is a sign of the edge dis location. Indeed, the Burgers vector is perpendicular to the dislocation line and, if the diffraction vector is perpendicular to the Burgers vector, the dislocation contrast is absent. Thus, despite the fact that the Ge film thickness rather insignificantly (about 1.5 times) exceeds the critical value for the introduction of MDs, the Ge/InGaAs heterostructure contains not only 60° MDs but also the edge MDs. Figure 2 shows two images of the same heterostruc ture, which reveal 60° MDs denoted by α1 and α2 (seen on both images) in the Ge/InGaAs interface. Here, the α1 line demonstrates the relation of a 60° MD to the dislocation network of the InGaAs buffer layer. Indeed, a curvilinear TD escapes from the vol ume of InGaAs, bends to emerges in the Ge/InGaAs interface (this site is indicated by the dotted circle in Fig. 2b), and then glides in one of the tilted (111) planes, thus becoming an MD. The β line (indicated by the dotted oval in Fig. 2) represents an edge dislo cation, since the g · b = 0 condition leads to the absence of its contrast in Fig. 2a. The ends of this edge MD are connected with two tilted 60° dislocations. A mechanism of the formation of this dislocation was originally proposed by Mader et al. [13]. According to this, two 60° dislocations that glide in the tilted {111} planes intersecting on the heteroboundary can inter
PHYSICS OF THE SOLID STATE
Vol. 53
No. 10
2011
STRAINED GERMANIUM FILMS g220
g220
2007 g220
g220 α1
α1
α2
α1
α2
α2
β α4
β
(а)
400 nm (b)
(а)
Fig. 2. Two darkfield TEM images showing the formation of an edge MD (β) (indicated by a dotted oval) according to the model of accidental collision of two complementary 60° MDs in the case of (a) satisfied and (b) not satisfied conditions of quenching of the edge dislocation β. Dislo cation network of the InGaAs/GaAs heteroboundary is revealed in the bottom part of the images.
(1)
As a result of this reaction, a pure edge MD is formed on the line of intersection of the {111} planes and the ends of this MD form two triple nodes with the reacted tilted branches of 60° dislocations. The Burgers vector of this MD is perpendicular to the dislocation line. The formation of an MD by this mechanism is ener getically favorable, since the screw components of the 60° MD are mutually compensated (for this reason, these 60° dislocations are called complementary [14]). However, since the spontaneous intersection of {111} planes exactly on the heteroboundary is low probable, it is suggested that the process involves either the climb of one or both dislocations along the interface [15] or the shift of the edge dislocation down (into substrate) or up (into the film) [16]. Thus, an MD formed according to this mechanism must not necessarily occur in the film–substrate interface. A mechanism of the formation of the βtype edge MD (Fig. 1a) can also be of the same kind, since this MD represents a straight segment that originates from the site (indi cated by the dotted circle) where two 60° MDs merge together. In the cases considered above, it can be sug gested that the interacting 60° dislocations are related to a dislocation network of the InGaAs buffer layer. The formation of an edge MD as a result of the accidental collision of two parallel propagating 60° MDs was earlier considered [17–19] as the most prob able explanation of the appearance of edge MDs in strained films of the GeSi/Si(001) and InGaAs/GaAs PHYSICS OF THE SOLID STATE
Vol. 53
No. 10
(b)
Fig. 3. Two darkfield TEM images obtained in the regime of twowave diffraction observed using the condition of dislocation contrast quenching on one of the images. Edge dislocations are indicated by white arrows. Dislocation network of the InGaAs/GaAs heteroboundary is revealed in the bottom part of the images. The 60° dislocations α1– α3 cannot be identified as MDs, since they are not straight; these dislocations are apparently situated in the volume of the InGaAs buffer layer above the dislocation network of the InGaAs/GaAs heteroboundary.
act via a classical reaction known in the theory of dis locations: a/2 [ 101 ] + a/2 [ 011 ] = a/2 [ 110 ].
400 nm
α3
systems. However the subsequent investigations showed that, in most cases, the observed edge MDs are situated exactly in the film–substrate interface and appear at the early stages of plastic relaxation where an average distance between neighboring MDs amounts to several hundred nanometers [14, 20]. This circum stance implies that other mechanisms of the formation of these MDs can be operative, which are not based on the accidental collision of two complementary 60° MDs. Following Kvam et al. [14], Dregia and Hirsch [9], and Narayan and Sharan [21], we suggest that a sec ondary complementary 60° MD can be formed under the action of the stress field of a 60° MD that already exists in the interface. This mechanism will be referred to as the induced nucleation of a complementary 60° MD. Our previous investigations [5–7] of the GeSi/Si(001) heterostructures showed that, under certain conditions, this mechanism of edge MD for mation could predominate. In Fig. 3, straight dislocation lines indicated by white arrows represent edge MDs (according to the g · b = 0 condition of contrast quenching). The image in Fig. 3b shows edge dislocation β (the contrast of which is absent in Fig. 3a) that is a stopper for a 60° MD α4 (the stopping site is indicated by dotted arrow). These dislocation configurations are observed for MDs propagating in the interface of heterostructures, in which the strained film has a small thickness that creates a low driving force for the glide of 60° MDs. Due to a small film thickness (close to a critical value 2011
2008
BOLKHOVITYANOV et al. [001] [010] 90°MD
(111)
(111)
g220
[101]
[100]
(001)
b (111) (11 0
b )
60°MD(α) [101] + [011] = [110]
1 μm
(а)
] [011
) 10 (1
g220 60°MD(β) β60
Fig. 4. Schematic diagram that illustrates the formation of an edge MD via the interaction of two complementary 60° MDs after the crossslip of one of them (see text). Cross hatched surface is the film–substrate interface. Dotted arrows indicate the directions of dislocation motion.
α60
LMD
α60MD β60MD
for 60° MDs) and low driving force for the glide of 60° MDs, this dislocation cannot overcome the stress field of the present orthogonal dislocation [22]. This case just corresponds to the situation imaged in Fig. 3b. Therefore, this dislocation configuration proves that the observed edge MD occurs in the Ge/InGaAs interface. The lefthand end of the edge MD β is not related to dislocations in the volume of InGaAs. In this respect, the mechanism of this edge MD forma tion is not based on the accidental collision of two complementary 60° MDs. From an analysis of the TEM image in Fig. 3b, it can also be suggested that it is the 60° MD α3 (related to the dislocation network of the InGaAs buffer layer), which emerges at the Ge/InGaAs interface and inspires the formation of the edge MD β in accordance with the aforementioned induced nucleation of a complementary 60° MD. It is possible to propose yet another variant of the edge MD formation that implies neither the acciden tal collision of two complementary 60° MDs nor the induced nucleation of a complementary 60° MD. This mechanism is based on the interaction of existing 60° MDs and a complementary 60° MD belonging to the orthogonal dislocation network. In this case, a 60° MD stopped by the primary 60° MD exhibits cross slip and moves along the primary one, thus forming an edge segment. Figure 4 schematically illustrates this interaction between 60° MD α, which propagates in the opposite directions [ 110 ] and [ 110 ] along the tilted (111) plane, and 60° MD β that elongates in the perpendicular direction and glides along the ( 111 ) plane. Upon the interaction with 60° MD α, the transversely gliding MD β can change its direction of motion (as indicated by the bent dotted arrow in
(b) β60
α60
LMD
α60MD
(c)
β60MD
Fig. 5. (a, b) Two darkfield TEM images of the same region and (c) scheme illustrating the interaction of dislo cations. The Lomer 90° edge MD (LMD) has a length more than 8 μm and goes beyond borders of the figure (dotted circle indicates the site where two 60° MDs merge to form an edge MD). Traces of the dislocation network of the InGaAs/GaAs heteroboundary is revealed in the upper part of the images.
Fig. 4), still gliding in the ( 111 ) plane. If the two dis locations are complementary, the reaction written in the bottom left corner of Fig. 4 leads to the formation of an edge segment that propagates in the [ 110 ] direc tion due to the glide of two TD in the mirrortilted (111) and ( 111 ) planes. Previously, we have observed [23] dislocations configurations of this kind in the GeSi/Si(001) system. Figures 5a and 5b present two TEM images of a thinned Ge/InGaAs heteropair, which reveal a long (above 8 μm) edge MD that confirms the proposed mechanism. Figure 5c shows a scheme of the region,
PHYSICS OF THE SOLID STATE
Vol. 53
No. 10
2011
STRAINED GERMANIUM FILMS
in which the formation of this edge MD can be explained by the interaction of complementary 60° MDs after the crossslip of one of them. Here, a threading branch of 60° dislocation (α60) escapes from the volume of the buffer layer and bends to emerge in the interface (this site is indicated by the dotted circle in Fig. 5), where it becomes the MD (α60MD) and propagates in the direction indicated by the dotted arrow. The other dislocation (β60) formed in the vol ume of the buffer layer crosses the interface by two beams, one of which turns into the interface and forms the MD (β60MD) that is directed downward along the dotted arrow (Fig. 5). The other beam of this disloca tion meets the primary dislocation (α60MD) and cross slip along it to form the 90° edge MD (LMD). Thus, the presence of TDs in the tensile strained Ge film favors the formation of edge MDs in the Ge/InGaAs interface even in the case of small elastic deformations in the strained film (in this case, ~0.75%). 4. CRITICAL THICKNESS OF THE STRAINED FILM FOR INTRODUCTION OF 60° AND 90° MISFIT DISLOCATIONS Earlier, it was commonly accepted that edge MDs, being sessile by their nature, cannot nucleate and the more so propagate. For this reason, the issue concern ing a critical thickness for the appearance of these dis locations was not considered, although in 1991 Fitzgerald [24] showed that hc calculations based on the energy balance could also be applied to 90° MDs. Estimated in this way, the critical layer thickness for the appearance of these dislocations was about half as small a that for 60° MDs. However, this fact did not receive attention of researchers until now. Previously, we demonstrated [5–7] that edge MDs in the GeSi/Si(001) system are formed predominantly by the mechanism of induced nucleation of a complemen tary 60° MD. A dislocation configuration comprising an edge MD segment and the threading 60° MD branches that propagate in the mirrortilted {111} planes and “pull” this segment can be considered as a structural element to which the concept of critical thickness is applicable. Let us determine a critical thickness for the intro duction of 60° MD and a critical thickness for the existence of edge dislocations in strained Ge films. Investigations devoted to the induction and propaga tion of MDs in strained films (see, e.g., [25–27]) employ the concept of socalled effective (or excess) shear stress τeff that determines the processes of MD nucleation and TD propagation in strained films. For a film of thickness h, this quantity is defined as follows: PHYSICS OF THE SOLID STATE
Vol. 53
No. 10
2009
τ eff = τ – τ s 2 (2) ( 1 – ν cos α ) βh ( 1 + ν) ε Gb = S 2G – ⎛ ln + 1⎞ . ⎠ 4πh ( 1 – ν ) ⎝ b (1 – ν)
Here, the first term S[2G(1 + ν)/(1 – ν)]ε describes the driving force of the plastic relaxation and repre senting a biaxial stress in the film that drives a 60° MD to elongate, where G is the shear modulus and ν is the Poisson’s ratio. The coefficient S = cosλcosφ (called the Schmid factor [28]) takes into account the effect of the stress component in the direction of TD motion, where φ is the angle between the glide plane and the normal to the interface and λ is the angle between the Burgers vector b and the perpendicular (lying in the interface plane) to the line of intersection of the dislo cation glide plane and the interface. For Ge/InGaAs heterostructures under consideration, which occur at the initial stage of plastic relaxation, the last factor in the first term is ε ≈ (aInGaAs – aGe)/aInGaAs. The second term in expression (2) describes a shear stress component that retards the motion of a disloca tion [29] and is calculated using the work that is nec essary for the formation of a new MD of unit length. In this term, α is the angle between the Burgers vector (with absolute value b) and the dislocation line, while β is a parameter representing the energy of the disloca tion core (earlier, this value for materials with a dia mondtype lattice was taken equal to β = 4 [30], but presently it is conventionally set at β = 1 [31]). The critical thickness of a strained film at which the introduction of 60° MD becomes possible is deter mined using expression (2) at τeff = 0 (force balance model) [25]. Let us apply this expression to the config uration of “edge MD with threading 60° MD seg ments.” Since the driving force of plastic relaxation acts simultaneously on both segments that elongate the edge MD, the pulling term τ must be doubled. In the expression for the retarding term τs, the factor cosα vanishes because the angle between the disloca tion line and Burgers vector is 90°. This yields an expression, τ eff ( 90° ) = τ – τ s 2G ( 1 + ν ) Gb βh = 2S ε – ⎛ ln + 1⎞ , ⎠ (1 – ν) 4πh ( 1 – ν ) ⎝ b
(3)
from which hc for the appearance of an edge MD can be determined for τeff = 0. Figure 6 shows plots of the calculated critical thick ness for the MD introduction into strained Ge films versus composition δ (indium fraction) of the artificial buffer layer. The calculations were performed for both 60° and 90° MDs. As can be seen, there is good coin cidence with the results of calculations [24] using the condition of minimization of the total system energy upon the introduction of particular MDs. The hc val 2011
2010
BOLKHOVITYANOV et al.
in this plastically relaxed GeSi buffer (data from [32]), the strained Si/GeSi buffer interface exhibited MD segments even in the case where the Si layer thickness was significantly smaller than the critical value for 60° MDs. The same phenomenon was observed in [33]. Unfortunately, the type of MDs (observed as rare lines after the selective etching of Si films) was not deter mined. However, based on the above considerations and results, it can be suggested that the dislocations observed in [32, 33] had an edge character. Liu et al. [34] demonstrated that the plastic relaxation of a strained GaAs/InxGa1 – xAs/GaAs heterostructure took place after its annealing even in cases where the strained layer thickness was smaller than the critical value calculated using model [4], while the TEM data revealed the presence of edge dislocations in these het erostructures. Thus, it can be suggested that these results can be explained based on the concept of smaller critical thickness for 90° MDs as compared to hc(60°).
50 60° MDs 40
hc, nm
30
20
10 90° MDs 0
0.1
δ
0.2
0.3
Fig. 6. Plots of the critical thickness hc for 60° and 90° MD introduction into the Ge film versus composition δ (indium content) of 100% relaxed InGaAs buffer layer, as calculated using Eqs. (2) and (3), respectively. Points rep resent the results of calculations based on the energy bal ance model [24].
ues for 90° MDs are also less than half of the critical thicknesses of 60° MDs. 5. ON THE POSSIBILITY OF FORMING MISFIT DISLOCATIONS AT FILM THICKNESSES SMALLER THAN hc FOR 60° DISLOCATIONS The results of calculations presented in the preced ing section showed that the critical thickness hc for the edge MD introduction is significantly smaller than that for 60° MDs. Whether their appearance is possi ble at film thicknesses below the commonly accepted? If the Ge film thickness is smaller than hc(60°) but greater than hc(90°), the existence of 90° MDs is ener getically favorable. However, the nucleation of this edge MD requires the fluctuational appearance of two complementary dislocation halfloops situated at a favorable distance from each other, so that they could glide in two mirrortilted {111} planes and form an edge segment in the interface. The probability of such events is extremely small. Should threading disloca tions already exist, being inherited from the buffer layer, then the probability of nucleation of a second 60° MD sharply increases that can make the forma tion of edge MD segments possible even before reach ing a critical Ge film thickness for 60° MDs. Experi mental evidence in favor of the subcritical MD forma tion can be found in [32], where data are reported on the plastic relaxation of tensile strained Si on an artifi cial Ge0.2Si0.8Si substrate. At a TD density of 105 cm–2
6. CONCLUSIONS In the configuration “tensile strained Ge film/relaxed InGaAs buffer layer/GaAs(001) sub strate,” the thin Ge film must be strained and should have a thickness that exceeds a critical value for the MD introduction. However, the InGaAs buffer layer contains a significant number of threading disloca tions that are inherited by the Ge layer and exhibit bending to emerge in the Ge/InGaAs interface and become the sources of 60° MDs. These 60° MDs, in turn, induce the formation of edge MDs. TEM data revealed both these MD types in the Ge/InGaAs interface Possible mechanism of the formation of edge MDs have been considered, including (i) the accidental col lision of complementary parallel 60° MDs propagat ing in the mirrortilted {111} planes, (ii) induced nucleation of a second 60° MD and its interaction with the primary 60° MD, and (iii) interaction of two complementary MDs after a crossslip of one of them. Calculations showed that a critical layer thickness (hc) for the appearance of edge MDs is much smaller than hc for 60° MDs. It was also demonstrated that the for mation of edge MDs in strained films grown on sub strates with large numbers of TDs is possible at film thickness that are smaller than the calculated critical thickness for the introduction of 60° MDs. REFERENCES 1. M. V. Fischetti and S. E. Laux, J. Appl. Phys. 80, 2234 (1996). 2. Y. Bai, K. E. Lee, C. Cheng, M. L. Lee, and E. A. Fitz gerald, J. Appl. Phys. 104, 084518 (2008). 3. J. W. Matthews, Philos. Mag. 13, 1207 (1966). 4. J. W. Matthews and A. E. Blakeslee, J. Cryst. Growth 27, 118 (1974).
PHYSICS OF THE SOLID STATE
Vol. 53
No. 10
2011
STRAINED GERMANIUM FILMS 5. Yu. B. Bolkhovityanov, A. S. Deryabin, A. K. Gutak ovskii, and L. V. Sokolov, Appl. Phys. Lett. 92, 131 901 (2008). 6. Yu. B. Bolkhovityanov, A. S. Deryabin, A. K. Gutak ovskii, and L. V. Sokolov, J. Cryst. Growth 310, 3422 (2008). 7. Yu. B. Bolkhovityanov, A. K. Gutakovskii, A. S. De ryabin, and L. V. Sokolov, Phys. Solid State 50 (10), 1857 (2008). 8. R. Hull and J. C. Bean, J. Vac. Sci. Technol., A 7, 2580 (1989). 9. S. A. Dregia and J. P. Hirsh, J. Appl. Phys. 69, 2169 (1991). 10. S. H. Huang, G. Balakrishnan, A. Khoshakhlagh, A. Jallipalli, L. R. Dawson, and D. L. Huffaker, Appl. Phys. Lett. 88, 131911 (2006). 11. Yu. B. Bolkhovityanov, A. S. Derybin, A. K. Gutak ovskii, and L. V. Sokolov, J. Cryst. Growth. 312, 3080 (2010). 12. Yu. B. Bolkhovityanov, A. K. Gutakovskii, A. S. De ryabin, and L. V. Sokolov, Phys. Solid State 53 (9), 1791 (2011). 13. S. Mader, A. E. Blakeslee, and J. Angilello, J. Appl. Phys. 45, 4730 (1974). 14. E. P. Kvam, D. M. Maher, and C. J. Humpreys, J. Mater. Res. 5, 1900 (1990). 15. J. Narayan and S. Oktyabrsky, J. Appl. Phys. 92, 7122 (2002). 16. V. I. Vdovin, J. Cryst. Growth 172, 58 (1997). 17. E. A. Fitzgerald and D. G. Ast, J. Appl. Phys. 63, 693 (1988). 18. K. H. Chang, P. K. Bhattacharya, and R. Gibala, J. Appl. Phys. 66, 2993 (1983).
PHYSICS OF THE SOLID STATE
Vol. 53
No. 10
2011
19. V. Yu. Karasev, N. A. Kiselev, E. V. Orlova, M. A. Gri belyuk, A. K. Gutakovsky, Yu. O. Kanter, S. M. Pintus, S. V. Rubanov, S. I. Stenin, and A. A. Fedorov, Ultrami croscopy 35, 11 (1991). 20. Yu. B. Bolkhvityanov, A. K. Gutakovskii, A. S. De ryabin, O. P. Pchelyakov, and L. V. Sokolov, Semicon ductors 42 (1), 1 (2008). 21. J. Narayan and S. Sharan, Mater. Sci. Eng., B 10, 261 (1991). 22. L. B. Freund, J. Appl. Phys. 68, 2073 (1990). 23. Yu. B. Bolkhovityanov, A. S. Deryabin, A. K. Gutak ovskii, and L. V. Sokolov, Philos. Mag. Lett. (in press). 24. E. A. Fitzgerald, Mater. Sci. Rep. 7, 92 (1991). 25. D. C. Houghton, J. Appl. Phys. 70, 2136 (1991). 26. B. W. Dodson and J. Y. Tsao, Appl. Phys. Lett. 51, 1325 (1987). 27. L. B. Freund and R. Hull, J. Appl. Phys. 71, 2054 (1992). 28. R. S. Goldman, K. L. Kavanagh, H. H. Wieder, S. N. Ehrlich, and R. M. Feenstra, J. Appl. Phys. 83, 5137 (1998). 29. A. Fisher, Appl. Phys. Lett. 64, 1218 (1994). 30. J. P. Hirth and J. Lothe, Theory of Dislocations, 2nd ed. (Wiley, New York, 1982), p. 231. 31. L. B. Freund, MRS Bull. 17, 52 (1992). 32. S. B. Samavedam, W. J. Taylor, J. M. Grant, J. A. Smith, P. J. Tobin, A. Dip, A. M. Philips, and R. Liu, J. Vac. Sci. Technol., B: Microelectron. Nanometer Struct.– Process., Meas., Phenom. 17, 1424 (1999). 33. J. Parsons, E. H. C. Parker, D. R. Leadley, T. J. Grasby, and A. D. Capewell, Appl. Phys. Lett. 91, 063127 (2007). 34. X. W. Liu, A. A. Hopgood, B. F. Usher, H. Wang, and N. St. J. Braithwaite, J. Appl. Phys. 94, 7496 (2003).
2011
