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Nature of dislocations promoting growth in liquid phase epitaxy of gallium arsenide
Journal of Crystal Growth 130 (1993) 466—474 North-Holland
o,
CRYSTAL GROWTH
Nature of dislocations promoting growth in liquid phase epitaxy of gallium arsenide W. Möhling
a
H. Weishart
b
and E. Bauser
Max-Planck-Arbeitsgruppe ‘Rönlgenbeugung’ Hausvogteiplatz 5—7, D-O-]086 Berlin, Germany ~ Max-Planck-Institut für Festkörperforschung, Heisenbergstrasse 1, D-W-7000 Stuttgart 80, Germany Received 30 October 1992; manuscript received in final form 29 January 1993
Dislocations promoting growth in the course of liquid phase epitaxy (LPE) of GaAs layers on GaAs substrates are analysed by X-ray topography. The Burgers vectors are determined by comparing double-crystal back-reflection images with calculated misorientations taking into account surface relaxation. Any dislocation which generates a spiral of elementary steps is found to have a Burgers vector component parallel to the macroscopic growth direction. The nature of these growth promoting dislocations may be between pure screw and pure edge type. Defects which might be responsible for the generation of the observed concentric growth step patterns are below the detection limit of current X-ray topography.
1. Introduction The influence of dislocations as nucleation centres for crystal growth has been first discussed by Frank [1]. He considered a screw dislocation normal to the growth interface. Due to the inherent structure of the dislocation, it forms an elementary step on that face and thus provides sites for easy attachment of new material. During growth this step develops the shape of a spiral around the dislocation. This simple model of a step source has been extended to any type of dislocation which has a component of its Burgers vector (b) perpendicular to the interface [21.Subsequent observations of growth spirals on vapour phase grown crystals [3—51 were taken as other indirect proof for the existence of dislocations which had not yet been detected directly then. Spirals as well as concentric growth step patterns have been observed in intensive studies of growth and evaporation features on alkali halides [6,7]. The concentric steps were assumed to have an edge dislocation as a source, and this has to be understood in general as any dislocation which has no component of b perpendicular to the 0022-0248/93/$06.00 © 1993
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interface [8]. No overall acceptable mechanism for the operation of such a source could as yet be identified [6,9,101. The nature of dislocations generating steps was reconsidered when Bauser and Strunk investigated dislocation-controlled growth in liquid phase epitaxy (LPE) of GaAs [8,111 and Si [121. During these investigations the dislocations promoting growth have been detected and analysed by transmission electron microscopy (TEM) for the first time [8,12,13]. For most of the dislocations in GaAs, as well as in Si, the results of the electron microscopic analysis were in agreement with the general model [21.The remaining number of dislocations which had been active as step sources in GaAs grown at low temperature was found to have no b component perpendicular to the interface. The analysis by TEM of dislocation step sources in Si samples, likewise grown by LPE at low temperature, gave evidence of an operation mechanism as follows: Below the growth interface, the complete dislocation is dissociated into two partial dislocations, each of which has a component of b parallel to the macroscopic growth direction. The stacking fault between the
Elsevier Science Publishers B.V. All rights reserved
/ Nature of dislocations promoting growth in
W Möhling et al.
two partials forms a step lower than one monolayer on the growth face, yet sufficient to promote infinite growth.This mechanism was observed unambiguously only for silicon grown from Ga solution [12,14]. Whether this or a similar model applies generally for dislocations without b component perpendicular to the growth face [8,111 is not yet known. In order to replace the historical but no longer precise terms “screw” and “edge” dislocation, Bauser and Strunk have proposed the terms “Frank” and “Bethge” source for the generator dislocations of spiral and of concentric growth step patterns [141. Promotion of growth by dislocations offers the possibility to produce extraordinary flat layers which have homogeneous dopant distribution, for growth proceeds under near-equilibrium conditions. Two-dimensional nucleation or deliberately misoriented substrates are obviated as methods to provide growth steps. Both methods may be detrimental to flatness and homogeneity [15].Application of dislocation-promoted growth therefore appears reasonable, at least for material that contains dislocations. Recent work on LPE growth of GaAs succeeded in preparing atomically flat (001) facets up to 0.25 mm2 area seeded by a single dislocation [161. In the following we analyse the defects in epitaxial layers and their substrates by X-ray topography [171 in order to check the efficiency in generating growth steps of the various dislocation types. Dislocation densities of up to a few thousand per cm2, as considered here, allow a oneto-one correlation of growth patterns and defects to be established. Moreover, double crystal topography (DCT) in back-reflection enables us to identify the nature of a reasonable number of dislocations with less effort than with any other method [18]. —
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2. Experimental details 2.1. Layer growth Substrates with dislocation densities between 4 X 10 2 and 3 x 10 3 cm —2 are used in the present investigations. They are cut from (001) oriented .
LPE of GaAs
467
Bridgman wafers with a residual misorientation of less than 0.04°.The surfaces of the substrates are given a mesa shape by etching a square grid of grooves with the help of a photolithographic technique. The growth on mesa-shaped substrates eliminates the influence of residual misorientation steps because they grow out towards the edges of the 0.5 x 0.5 mm2 mesa areas. Epitaxial growth takes place from Ga solution in an earlier-described slider boat [191. The temperature chosen for the beginning of growth is between 715 and 641°C.During each experiment the cooling rate of 6 K/h is kept constant. The epitaxial layers are grown up to a thickness of 1 j.~m.The as-grown layer surfaces are inspected in a Nomarski differential interference contrast (NDIC) optical microscope [201.This method enables us to see steps of elementary height. 2.2. X-ray topography The Burgers vectors b of the dislocations are determined according to the method [18] based on comparing DCT back-reflection images of the defects with calculated misorientations of the crystal lattice at the outcrop to the free surface. An analytical solution for the calculation of the misorientation contours accounting for surface relaxation of the elastic stresses permits rapid estimation via computer A reliable determination needs about 6 back-reflection images for different diffraction vectors and one or two transmission images for information on the line direction (1) of the defects. This procedure proved highly effective for the characterization of statistically relevant numbers of dislocations. We consider in the following the dislocation line direction to point outward from the growth face. The sense of b is defined according to the FS/RH (perfect crystal) convention [211.The DC back-reflection topographs are taken with Cu Ka 1 radiation and with collimators ensuring a strain sensitivity of 10—6 to 5 X iO~ [221. The presented topographs are recorded for 50% of maxi~.
~
.
.
.
A printers error equation has escaped the authors’ attention [18].The second on page 391 should read: uin ref. = — ~ cot ‘P.
468
U’. Mb/i/mg Ct a!.
/ Nature of dislocations promoting growth in
mum intensity on the low-angle slope of the rocking curve. During exposure this “working position” is kept constant by a feedback mechanism to within 5% of the starting intensity. The plctures are given in positive print, i.e. bright areas correspond to a high intensity. Kinematical imaging [23] is applied in order to reveal microdefects in cases where no dislocation is found to correlate with a growth step centre,
3. Results and discussion 3.1. Obseri’ed step patterns and their correlation with dislocations Typical step patterns observed after LPE growth of GaAs layers on GaAs substrates are shown in fig. 1. Spiral patterns arc found most frequently. They occur in nearly equal numbers with right-hand (fig. la) or left-hand sense. About 1% of the step patterns is concentric as shown in fig. lb. The step width is of the order of 10 ~m up to a few 10 ~m for the spirals. It is several 10 ~m up to more than 100 ~m for the concentric patterns. The step height is one elementary layer, 2.83 A, as was proven earlier [191. The relation between the step patterns and dislocations is demonstrated in fig. 2. Here a DC
LPE of GaAs
back-reflection topograph (fig. 2a) is compared with a diagram of the sample (fig. 2b), in which the positions of the centres of spiral and concentric patterns found by NDIC inspection are marked by dots and crosses, respectively. The square grid pattern of the etch grooves delineated in the diagram generates contrast in the topograph and can be used as a scale mark which facilitates the comparison. Dislocations become visible in the topograph by their light and/or dark contrast. A comparison of the topograph (fig. 2a) and the step pattern diagram (fig. 2b) shows that none of our examples presented here reveals a dislocation at or near the center of a concentric pattern. However, each centre of a spiral pattern is correlated exactly with a dislocation. There are many more dislocations than step patterns. It appears reasonable, therefore, to look in more detail at the character of the step-generating dislocations. as will be discussed next. 3.2. Character of dislocations generating spiral patterns An example where two closely-spaced (< 130 ~m) spirals of opposite sense occur on a mesa demonstrates lucidly some of our essential findings. Fig. 3a shows a NDIC micrograph of the
Ia
50 pm Fig. I. Patterns of elementary growth steps observed on LPE grown GaAs layers, NDIC micrograph. (a) Spiral pattern with right-hand, as shown here, or left-hand sense. (b) Concentric pattern.
U’ Mbhling et al.
/ Nature of dislocations promoting growth in
LPE of GaAs
469
Fig. 2. Back-reflection topograph (a) of a LPE GaAs layer compared to a schematic diagram (b)of the sample with the centres of step patterns indicated: (.) spirals; (x) concentric patterns.
spirals which are, from left to right, right-handed and left-handed. The generator dislocations are visible in the DC back-reflection topograph of fig. 3b. Results of an analysis of both dislocations according to the procedure proposed in ref. [18] are presented in fig. 4 in lower magnification. The line directions 1 of the defects are revealed in the transmission topograph of fig. 4a. Referring to the orientation of the sample indicated below this topograph, the line directions near the outcrops of the left and right dislocations are
I = [132] and I
[312], respectively. Figs. 4b—4e show DC back-reflection topographs as well as calculated misorientation contours (below). These pictures have been selected from altogether 12 back-reflection topographs which we took for this particular sample. Misorientations have been calculated for all twelve possible Burgers vectors of type b ±~/110) and, in addition, also for some fictitious ones of type b K 100), b ~(111> and b ~K112). Only the calculations for b ~[011] and for b ~[101]fit unambiguously the evidence =
=
=
=
=
=
=
47(1
U’. Möhhng ,iiii.
Nature of dislocatom
pminoting growth
in LPE of
(iii.
1s
50 pm
________
Jig. 3. NDIC mid ogi aph oJ right—hand and Icit—hand spiral (a). and back—reflection topograph (h) showing their generator dislocations.
of the full set of topographic images of the left and the right dislocation, respectively. Both dislocations are of a 19°character at their outcrop and have a b with a component normal to the interface. This component is parallel to the surface normal for the dislocation generating a right-hand spiral and is antiparallel to the normal for the dislocation generating a left-hand spiral.
/
206 0.2mm
a
b
This result is supported by the example given in fig. 5. A dislocation half-loop can be seen in the transmission topograph (fig. Sa). It generates a right-hand spiral at its upper and a left-hand spiral at its lower outcrop, indicated schematically in fig. Sb. A dislocation with outcrop near the middle of both ends of the half-loop penetrates the sample from the back side and gener-
026
C
4 /
4
206
115
e
110
Fig. 4. Analysis of the dislocations of fig.3. (a) Transmission topograph: the sample orientation is indicated below. (b)—(e) Back-reflection topographs for various diffraction vectors (above) and calculated misorientation contours (below). For the left dislocation 1 = [132], b = ~lt)il] and for the right dislocation 1 = [312], b = ~ll0l] have been determined.
U’ Mhhling et al.
/ Nature of dislocations promoting growth in LPE of GaAs
471
02mm
-
b
Ic
Id—
,
e
Fig. 5. Relation between the sense of the generator dislocations and the sense of the growth spirals. (a) Transmission topograph showing a dislocation half-loop and a bulk dislocation. (b) Schematic indication of positions and senses of observed spirals. (c)—(e) Selection of back reflection topographs; 1 = [121], b = ~[101] for upper and 1 = [312], b = ~[101] for lower outcrop of the dislocation.
ates a right-hand spiral at the front surface. A selection of back reflection topographs (figs. Sc— Se) shows an approximately opposite contrast at the upper and lower outcrop of the half-loop, The opposite contrasts are direct evidence for the opposite orientation of the opposite segments of
a dislocation loop. If we assume that both ends of the loop point outward from the front face of the sample which is reasonable when referring to back-reflection images we expect b to have opposite sense at these ends. With line directions I [121] and 1 [312] at upper and lower out—
—
=
=
100~T
Fig. 6. Fine scratch on a mesa area. (a) NDIC micrograph; a growth spiral was generated at the tip of the scratch. (b) Back-reflection topograph; no dislocation image is revealed.
472
U’ Möhling
Cf
a!.
/ Nature of dislocations promoting growth in
crop, respectively, calculated misorientations (not shown here) fit for b ~[1O1] above and b ~[101] below. The upper end of the dislocation is therefore exactly of edge type, whereas it is predominantly of screw type at the lower outcrop. The dislocation with outcrop near the middle between both ends of the loop shows contrasts similar but not identical to that at the upper outcrop. Actually, its Burgers vector also is b ~[101], but its line direction is approximately I [132]. Hence this dislocation is not exactly edge type but of 80 character. For all three outcrops we find that positive and negative sense of the b component normal to the interface is correlated with right-hand and left-hand sense of the spirals, respectively, A few cases are found where spiral step patterns cannot be correlated with substrate dislocations, but have to be correlated with some faint surface irregularities like a scratch, as shown in fig. 6. The centre of the spiral is visible in fig. 6a near the lower left corner of a mesa. In the DC topograph of fig. 6b, a fine scratch is seen to extend from the right edge of the mesa to its lower left corner, where it fades away. No contrast is observed in the topograph at the location of the spiral centre. The NDIC micrograph in fig. 6a indicates, however, that the scratch extends further and causes a row of small spirals. The centre of the dominant spiral is found at its end, Observations of this kind usually do not need an entirely new explanation. Elastic strain around a scratch usually relaxes partially, owing to the generation of dislocations especially if the sample is heated, for example, to the growth temperatures of the layers. The example in fig. 6 illustrates that dislocations, with b having a component parallel to the macroscopic growth direction, might have been generated along the scratch. Such dislocations may have acted in the same way as substrate dislocations. It should be noticed, however, that these supposed dislocations with a length comparable to the layer thickness of I ~m do not generate contrast in back-reflection topographs. Apart from such rare cases of surface heterogeneities, each spiral step centre is uniquely correlated with a substrate dislocation with a component of its b normal to the interface. This
LPE of GaAs
Number
=
=
=
=
—
-
5 -
1
0° 30° 60° 90° Fig. 7. Character and efficiency of growth promoting dislocations, analysed for one sample. All these dislocations have a b component normal to the interface, but they occur with a wide variety of line directions. The height of the light bars indicates the number of identified dislocations of a given type. The cross-hatched part of the bars indicates the fraction which generated a spiral. Relative frequencies of dislocation types may vary from sample to sample, but usually dislocations of any character compatible with their slip systems are present. Since dislocation lines follow crystallographic directions, this presentation of the character in steps of 10°is an approximation.
result fully agrees with the extended Frank model [2]. Most dislocations of this kind in substrates with dislocation densities up to l0~cm2 are found to generate a spiral growth step pattern. Fig. 7 illustrates this observation with the results of one extensively studied sample. Nearly SO dislocations have been identified, among them 34 with a b component normal to the interface. The histogram in fig. 7 shows the character, as defined by the angle between I and b, of these thirty-four along the abscissa. The height of the bars marks the total number of identified dislocations of the corresponding character, and the cross-hatched fraction of the bars indicates the number of those which generated spirals. The figure shows that dislocations of any character ranging from pure screw to pure edge type can generate growth step spirals and most of them do so. No essential difference in efficiency is observed between the various types. Those few defects which did not generate spiral patterns emerge either in the close vicinity of a dislocation which is active as a step generator or near an edge of a mesa. The latter observation is, however, not a general rule because dislocations with outcrop directly at the mesa edge or even at the
U’ Möhling et a!.
/ Nature
of dislocations promoting growth in LPE of GaAs
bottom of an edge groove have been found occasionally to emit growth spirals, sometimes into both neighbouring mesas. Among two or three dislocations being crowded together within distances below about SO ~tm, usually only one, sometimes none, generates a spiral. Nevertheless, the outcrops of these dislocations become visible on Nomarski micrographs, because they generate an additional elementary step that joins a step of the dominating spiral. The identification of the nature of the defects is not unambiguous in such cases; yet it appears that in samples with dislocation densities of several 1000 cm2 the number of spirals is distinctly smaller than that of the dislocations. The analysis of the remaining 15 dislocations of the sample under discussion shows that these have Burgers vectors without a component normal to the interface. These dislocations and about 20 more of the same type identified in some other samples are not found to generate any growth step pattern, —
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3.3. Analysis ofdefects generating concentric growth step patterns The observation made with the help of fig. 2 that no dislocations are found to correspond to a step generator in the centre of concentric patterns holds for about 20 more patterns of the same type, which we observed in several samples. We therefore applied kinematical imaging in search for some micro-heterogeneity as a step generator. This technique has been shown to detect defects of the size of 2 ~m reliably in silicon [23] and should respond to defects 1 ~tm in size or even below [24]. We have applied this technique with various diffraction geometries and have found numerous small defects in some of the samples which were not visible in ordinary DC topographs. A thorough search revealed no defect near the centre of any of the concentric patterns. However, some kind of defect has to be expected as a generator for the following reasons: firstly, NDIC microscopy sometimes shows surface asperities in the centre of the concentric step patterns, and secondly, recent TEM investigations [25] have revealed dislocations in the centres.
473
The results obtained up to now permit some speculation to be made about what generates the concentric patterns. These patterns usually occur in small numbers, They are sometimes completely absent from a sample and sometimes are present in numbers of a few percent of that of the spiral patterns. They mostly occur near the edges of a sample. It is, therefore, reasonable to suspect some microscopic damage or contamination at the substrate surface which causes plastic deformation at the time of the heating to growth temperatures. Dislocations observed in the TEM could have been generated in this way. Now, we only need to assume two of those dislocations being opposite parts of a half-loop (see fig. 5) and generating spirals of opposite sense within a distance of less than 1 ~m from each other. Their steps will easily combine to form a concentric pattern. An indication for such a process has been observed recently by NDIC inspection [261. The reasons why the mechanism found for silicon by Strunk, Käss and Bauser [12,14] has not yet been found in LPE grown GaAs might be due to a difference tn stacking fault energy and a .
lower growth temperature than we applied to prepare the GaAs samples for the present study.
4. Summary and conclusion Spiral patterns of elementary growth steps observed after LPE growth of GaAs layers on GaAs substrates are generated by dislocations which have a b with a component normal to the interface. In full agreement with the extended Frank model [2], these dislocations may have any character ranging from pure screw to pure edge type. A positive or negative sign of the component normal to the interface is responsible for righthand or left-hand sense of the spirals, respectively. Dislocations with the total Burgers vector b normal to the direction of macroscopic growth, i.e. with b in the plane of growth, are not observed to have generated any step pattern. The reason for this may be due to growth temperatures of higher than 640°Cfor the samples investigated here.
474
U’ Mbhling et a!.
/ Nature of dislocations promoting growth in
No direct evidence about the mechanism which generates concentric patterns could be obtained up to now by X-ray topographic techniques. The X-ray analysis unambiguously shows, however, that the concentric step patterns are not related to substrate dislocations in the investigated samples. Since concentric step patterns occur in very small numbers compared to the spiral patterns and since their centres are often located near the sample edges, a model based on some residual damage or contamination of the substrate surface is suggested. It assumes that due to a surface heterogeneity, a dislocation half-loop develops during the heating process to growth temperatures. The spirals turning in an opposite sense, generated by opposite parts of the half-loop, can easily combine to form a concentric pattern. Some discrepancy remains, however, between this model and the missing topographic response of the assumed defects. Both parts of the half-loop should be comparable in length with the layer thickness of about 1 ~m. The size of the half-loop should therefore be just large enough to be detectable by kinematical imaging though close to the detection limit [23,24]. Presently, the only conclusion is that the earlier findings do not hold for the particular case of a half-loop of that size. —
Acknowledgments The authors appreciate the advisory work by Prof. Dr. H.J. Queisser. One of us (W.M.) is indebted to Drs. R. Köhler and H. Raidt of Max-Planck-Arbeitsgruppe “Röntgenbeugung” for discussions on the subject. We would like to express sincere thanks to Mrs. J. Richter for assistance in making topographs and, together with Ms. A. Scherrer and Mrs. I. Wuhrl-Petry, for careful photographic reproduction of the pietures. Thanks are also due to Ms. S. Tippmann
LPE of GaAs
for the photolithography and to K.S. Löchner for technical assistance.
References [1] F.C.Frank, Disc. Faraday Soc. 5 (1949) 48. [2] W.K. Burton, N. Cabrera and F.C. Frank, Phil. Trans. Roy. Soc. London A 243 (1951) 299. 13] A.R. Verma, Crystal Growth and Dislocations (Butterworths, London, 1953). [4] W. Dekeyser and S. Amelinckx. Les Dislocations et Ia Croissance des Cristaux (Masson, Paris, 1955).
15] G.A. Bassett, Phil. Mag. 3 (1958) 1042. 161 Bethge, 21. 369. [7] H. K.W. Keller,Phys. Phys.Status StatusSolidi Solidi2 (1962) 36 (1968) [8] E. Bauser and H. Strunk, J. Crystal Growth 51 (1981) 362. [9] A.A. Chernov, in: Crystal Growth and Characterization, Proc. 2nd Intern. Spring School on Crystal Growth (ISSCG-2), Japan, 1974, Eds. R. Ueda and J.B. Mullin (North-Holland, Amsterdam, 1975) pp 33—52. [10] F.C. Frank, J. Crystal Growth 51(1981) 367. [11] E. Bauser and W. Hagen, J. Crystal Growth 50 (1980) 771. 112] D. Käss and H. Strunk, Thin Solid Films 81(1981) L10l. 1131 H.P.H.P Strunk, ThinJ. Solid Films 93 (1982) 185. [14] E. E. Bauser, Bauser and Strunk, Crystal Growth 69 (1984) 561. [15] E. Bauser, in: Crystal Growth of Electronic Materials, Ed. E. Kaldis (North-Holland, Amsterdam, 1985) p. 41. 116] H. Weishart, Thesis, Stuttgart (1992). 1171 BK. Tanner, X-Ray Diffraction Topography (Pergamon, Oxford, 1976). [18] V.M. Kaganer and W. Mdhling, Phys. Status Solidi (a) 123 (1991) 379. [19] U. Morlock, M. Kelsch and E. Bauser, J. Crystal Growth 87 (1988) 343. [20] G. Nomarski, J. Phys. Radium 16 (1955) 9S. [21] BA. Bilby, R. Bullough and E. Smith, Proc. Roy. Soc. (London) A 231 (1955) 263.
1221 123]
W. Mbhling, Cryst. Rev. 2 (1989) 89. R. Kbhler and W. Mbhling, Phys. Status Solidi (a) 78 (1983) 489. [24] V.L. Indenbom and V.M. Kaganer, Phys. Status Solidi (a) 87 (1985) 253. [25] F. Phillipp and M. Rapp, private communication. [261 H.P. Strunk and T. Marek, private communication.
o,
CRYSTAL GROWTH
Nature of dislocations promoting growth in liquid phase epitaxy of gallium arsenide W. Möhling
a
H. Weishart
b
and E. Bauser
Max-Planck-Arbeitsgruppe ‘Rönlgenbeugung’ Hausvogteiplatz 5—7, D-O-]086 Berlin, Germany ~ Max-Planck-Institut für Festkörperforschung, Heisenbergstrasse 1, D-W-7000 Stuttgart 80, Germany Received 30 October 1992; manuscript received in final form 29 January 1993
Dislocations promoting growth in the course of liquid phase epitaxy (LPE) of GaAs layers on GaAs substrates are analysed by X-ray topography. The Burgers vectors are determined by comparing double-crystal back-reflection images with calculated misorientations taking into account surface relaxation. Any dislocation which generates a spiral of elementary steps is found to have a Burgers vector component parallel to the macroscopic growth direction. The nature of these growth promoting dislocations may be between pure screw and pure edge type. Defects which might be responsible for the generation of the observed concentric growth step patterns are below the detection limit of current X-ray topography.
1. Introduction The influence of dislocations as nucleation centres for crystal growth has been first discussed by Frank [1]. He considered a screw dislocation normal to the growth interface. Due to the inherent structure of the dislocation, it forms an elementary step on that face and thus provides sites for easy attachment of new material. During growth this step develops the shape of a spiral around the dislocation. This simple model of a step source has been extended to any type of dislocation which has a component of its Burgers vector (b) perpendicular to the interface [21.Subsequent observations of growth spirals on vapour phase grown crystals [3—51 were taken as other indirect proof for the existence of dislocations which had not yet been detected directly then. Spirals as well as concentric growth step patterns have been observed in intensive studies of growth and evaporation features on alkali halides [6,7]. The concentric steps were assumed to have an edge dislocation as a source, and this has to be understood in general as any dislocation which has no component of b perpendicular to the 0022-0248/93/$06.00 © 1993
—
interface [8]. No overall acceptable mechanism for the operation of such a source could as yet be identified [6,9,101. The nature of dislocations generating steps was reconsidered when Bauser and Strunk investigated dislocation-controlled growth in liquid phase epitaxy (LPE) of GaAs [8,111 and Si [121. During these investigations the dislocations promoting growth have been detected and analysed by transmission electron microscopy (TEM) for the first time [8,12,13]. For most of the dislocations in GaAs, as well as in Si, the results of the electron microscopic analysis were in agreement with the general model [21.The remaining number of dislocations which had been active as step sources in GaAs grown at low temperature was found to have no b component perpendicular to the interface. The analysis by TEM of dislocation step sources in Si samples, likewise grown by LPE at low temperature, gave evidence of an operation mechanism as follows: Below the growth interface, the complete dislocation is dissociated into two partial dislocations, each of which has a component of b parallel to the macroscopic growth direction. The stacking fault between the
Elsevier Science Publishers B.V. All rights reserved
/ Nature of dislocations promoting growth in
W Möhling et al.
two partials forms a step lower than one monolayer on the growth face, yet sufficient to promote infinite growth.This mechanism was observed unambiguously only for silicon grown from Ga solution [12,14]. Whether this or a similar model applies generally for dislocations without b component perpendicular to the growth face [8,111 is not yet known. In order to replace the historical but no longer precise terms “screw” and “edge” dislocation, Bauser and Strunk have proposed the terms “Frank” and “Bethge” source for the generator dislocations of spiral and of concentric growth step patterns [141. Promotion of growth by dislocations offers the possibility to produce extraordinary flat layers which have homogeneous dopant distribution, for growth proceeds under near-equilibrium conditions. Two-dimensional nucleation or deliberately misoriented substrates are obviated as methods to provide growth steps. Both methods may be detrimental to flatness and homogeneity [15].Application of dislocation-promoted growth therefore appears reasonable, at least for material that contains dislocations. Recent work on LPE growth of GaAs succeeded in preparing atomically flat (001) facets up to 0.25 mm2 area seeded by a single dislocation [161. In the following we analyse the defects in epitaxial layers and their substrates by X-ray topography [171 in order to check the efficiency in generating growth steps of the various dislocation types. Dislocation densities of up to a few thousand per cm2, as considered here, allow a oneto-one correlation of growth patterns and defects to be established. Moreover, double crystal topography (DCT) in back-reflection enables us to identify the nature of a reasonable number of dislocations with less effort than with any other method [18]. —
—
2. Experimental details 2.1. Layer growth Substrates with dislocation densities between 4 X 10 2 and 3 x 10 3 cm —2 are used in the present investigations. They are cut from (001) oriented .
LPE of GaAs
467
Bridgman wafers with a residual misorientation of less than 0.04°.The surfaces of the substrates are given a mesa shape by etching a square grid of grooves with the help of a photolithographic technique. The growth on mesa-shaped substrates eliminates the influence of residual misorientation steps because they grow out towards the edges of the 0.5 x 0.5 mm2 mesa areas. Epitaxial growth takes place from Ga solution in an earlier-described slider boat [191. The temperature chosen for the beginning of growth is between 715 and 641°C.During each experiment the cooling rate of 6 K/h is kept constant. The epitaxial layers are grown up to a thickness of 1 j.~m.The as-grown layer surfaces are inspected in a Nomarski differential interference contrast (NDIC) optical microscope [201.This method enables us to see steps of elementary height. 2.2. X-ray topography The Burgers vectors b of the dislocations are determined according to the method [18] based on comparing DCT back-reflection images of the defects with calculated misorientations of the crystal lattice at the outcrop to the free surface. An analytical solution for the calculation of the misorientation contours accounting for surface relaxation of the elastic stresses permits rapid estimation via computer A reliable determination needs about 6 back-reflection images for different diffraction vectors and one or two transmission images for information on the line direction (1) of the defects. This procedure proved highly effective for the characterization of statistically relevant numbers of dislocations. We consider in the following the dislocation line direction to point outward from the growth face. The sense of b is defined according to the FS/RH (perfect crystal) convention [211.The DC back-reflection topographs are taken with Cu Ka 1 radiation and with collimators ensuring a strain sensitivity of 10—6 to 5 X iO~ [221. The presented topographs are recorded for 50% of maxi~.
~
.
.
.
A printers error equation has escaped the authors’ attention [18].The second on page 391 should read: uin ref. = — ~ cot ‘P.
468
U’. Mb/i/mg Ct a!.
/ Nature of dislocations promoting growth in
mum intensity on the low-angle slope of the rocking curve. During exposure this “working position” is kept constant by a feedback mechanism to within 5% of the starting intensity. The plctures are given in positive print, i.e. bright areas correspond to a high intensity. Kinematical imaging [23] is applied in order to reveal microdefects in cases where no dislocation is found to correlate with a growth step centre,
3. Results and discussion 3.1. Obseri’ed step patterns and their correlation with dislocations Typical step patterns observed after LPE growth of GaAs layers on GaAs substrates are shown in fig. 1. Spiral patterns arc found most frequently. They occur in nearly equal numbers with right-hand (fig. la) or left-hand sense. About 1% of the step patterns is concentric as shown in fig. lb. The step width is of the order of 10 ~m up to a few 10 ~m for the spirals. It is several 10 ~m up to more than 100 ~m for the concentric patterns. The step height is one elementary layer, 2.83 A, as was proven earlier [191. The relation between the step patterns and dislocations is demonstrated in fig. 2. Here a DC
LPE of GaAs
back-reflection topograph (fig. 2a) is compared with a diagram of the sample (fig. 2b), in which the positions of the centres of spiral and concentric patterns found by NDIC inspection are marked by dots and crosses, respectively. The square grid pattern of the etch grooves delineated in the diagram generates contrast in the topograph and can be used as a scale mark which facilitates the comparison. Dislocations become visible in the topograph by their light and/or dark contrast. A comparison of the topograph (fig. 2a) and the step pattern diagram (fig. 2b) shows that none of our examples presented here reveals a dislocation at or near the center of a concentric pattern. However, each centre of a spiral pattern is correlated exactly with a dislocation. There are many more dislocations than step patterns. It appears reasonable, therefore, to look in more detail at the character of the step-generating dislocations. as will be discussed next. 3.2. Character of dislocations generating spiral patterns An example where two closely-spaced (< 130 ~m) spirals of opposite sense occur on a mesa demonstrates lucidly some of our essential findings. Fig. 3a shows a NDIC micrograph of the
Ia
50 pm Fig. I. Patterns of elementary growth steps observed on LPE grown GaAs layers, NDIC micrograph. (a) Spiral pattern with right-hand, as shown here, or left-hand sense. (b) Concentric pattern.
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Fig. 2. Back-reflection topograph (a) of a LPE GaAs layer compared to a schematic diagram (b)of the sample with the centres of step patterns indicated: (.) spirals; (x) concentric patterns.
spirals which are, from left to right, right-handed and left-handed. The generator dislocations are visible in the DC back-reflection topograph of fig. 3b. Results of an analysis of both dislocations according to the procedure proposed in ref. [18] are presented in fig. 4 in lower magnification. The line directions 1 of the defects are revealed in the transmission topograph of fig. 4a. Referring to the orientation of the sample indicated below this topograph, the line directions near the outcrops of the left and right dislocations are
I = [132] and I
[312], respectively. Figs. 4b—4e show DC back-reflection topographs as well as calculated misorientation contours (below). These pictures have been selected from altogether 12 back-reflection topographs which we took for this particular sample. Misorientations have been calculated for all twelve possible Burgers vectors of type b ±~/110) and, in addition, also for some fictitious ones of type b K 100), b ~(111> and b ~K112). Only the calculations for b ~[011] and for b ~[101]fit unambiguously the evidence =
=
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Nature of dislocatom
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Jig. 3. NDIC mid ogi aph oJ right—hand and Icit—hand spiral (a). and back—reflection topograph (h) showing their generator dislocations.
of the full set of topographic images of the left and the right dislocation, respectively. Both dislocations are of a 19°character at their outcrop and have a b with a component normal to the interface. This component is parallel to the surface normal for the dislocation generating a right-hand spiral and is antiparallel to the normal for the dislocation generating a left-hand spiral.
/
206 0.2mm
a
b
This result is supported by the example given in fig. 5. A dislocation half-loop can be seen in the transmission topograph (fig. Sa). It generates a right-hand spiral at its upper and a left-hand spiral at its lower outcrop, indicated schematically in fig. Sb. A dislocation with outcrop near the middle of both ends of the half-loop penetrates the sample from the back side and gener-
026
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115
e
110
Fig. 4. Analysis of the dislocations of fig.3. (a) Transmission topograph: the sample orientation is indicated below. (b)—(e) Back-reflection topographs for various diffraction vectors (above) and calculated misorientation contours (below). For the left dislocation 1 = [132], b = ~lt)il] and for the right dislocation 1 = [312], b = ~ll0l] have been determined.
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02mm
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b
Ic
Id—
,
e
Fig. 5. Relation between the sense of the generator dislocations and the sense of the growth spirals. (a) Transmission topograph showing a dislocation half-loop and a bulk dislocation. (b) Schematic indication of positions and senses of observed spirals. (c)—(e) Selection of back reflection topographs; 1 = [121], b = ~[101] for upper and 1 = [312], b = ~[101] for lower outcrop of the dislocation.
ates a right-hand spiral at the front surface. A selection of back reflection topographs (figs. Sc— Se) shows an approximately opposite contrast at the upper and lower outcrop of the half-loop, The opposite contrasts are direct evidence for the opposite orientation of the opposite segments of
a dislocation loop. If we assume that both ends of the loop point outward from the front face of the sample which is reasonable when referring to back-reflection images we expect b to have opposite sense at these ends. With line directions I [121] and 1 [312] at upper and lower out—
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Fig. 6. Fine scratch on a mesa area. (a) NDIC micrograph; a growth spiral was generated at the tip of the scratch. (b) Back-reflection topograph; no dislocation image is revealed.
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crop, respectively, calculated misorientations (not shown here) fit for b ~[1O1] above and b ~[101] below. The upper end of the dislocation is therefore exactly of edge type, whereas it is predominantly of screw type at the lower outcrop. The dislocation with outcrop near the middle between both ends of the loop shows contrasts similar but not identical to that at the upper outcrop. Actually, its Burgers vector also is b ~[101], but its line direction is approximately I [132]. Hence this dislocation is not exactly edge type but of 80 character. For all three outcrops we find that positive and negative sense of the b component normal to the interface is correlated with right-hand and left-hand sense of the spirals, respectively, A few cases are found where spiral step patterns cannot be correlated with substrate dislocations, but have to be correlated with some faint surface irregularities like a scratch, as shown in fig. 6. The centre of the spiral is visible in fig. 6a near the lower left corner of a mesa. In the DC topograph of fig. 6b, a fine scratch is seen to extend from the right edge of the mesa to its lower left corner, where it fades away. No contrast is observed in the topograph at the location of the spiral centre. The NDIC micrograph in fig. 6a indicates, however, that the scratch extends further and causes a row of small spirals. The centre of the dominant spiral is found at its end, Observations of this kind usually do not need an entirely new explanation. Elastic strain around a scratch usually relaxes partially, owing to the generation of dislocations especially if the sample is heated, for example, to the growth temperatures of the layers. The example in fig. 6 illustrates that dislocations, with b having a component parallel to the macroscopic growth direction, might have been generated along the scratch. Such dislocations may have acted in the same way as substrate dislocations. It should be noticed, however, that these supposed dislocations with a length comparable to the layer thickness of I ~m do not generate contrast in back-reflection topographs. Apart from such rare cases of surface heterogeneities, each spiral step centre is uniquely correlated with a substrate dislocation with a component of its b normal to the interface. This
LPE of GaAs
Number
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0° 30° 60° 90° Fig. 7. Character and efficiency of growth promoting dislocations, analysed for one sample. All these dislocations have a b component normal to the interface, but they occur with a wide variety of line directions. The height of the light bars indicates the number of identified dislocations of a given type. The cross-hatched part of the bars indicates the fraction which generated a spiral. Relative frequencies of dislocation types may vary from sample to sample, but usually dislocations of any character compatible with their slip systems are present. Since dislocation lines follow crystallographic directions, this presentation of the character in steps of 10°is an approximation.
result fully agrees with the extended Frank model [2]. Most dislocations of this kind in substrates with dislocation densities up to l0~cm2 are found to generate a spiral growth step pattern. Fig. 7 illustrates this observation with the results of one extensively studied sample. Nearly SO dislocations have been identified, among them 34 with a b component normal to the interface. The histogram in fig. 7 shows the character, as defined by the angle between I and b, of these thirty-four along the abscissa. The height of the bars marks the total number of identified dislocations of the corresponding character, and the cross-hatched fraction of the bars indicates the number of those which generated spirals. The figure shows that dislocations of any character ranging from pure screw to pure edge type can generate growth step spirals and most of them do so. No essential difference in efficiency is observed between the various types. Those few defects which did not generate spiral patterns emerge either in the close vicinity of a dislocation which is active as a step generator or near an edge of a mesa. The latter observation is, however, not a general rule because dislocations with outcrop directly at the mesa edge or even at the
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bottom of an edge groove have been found occasionally to emit growth spirals, sometimes into both neighbouring mesas. Among two or three dislocations being crowded together within distances below about SO ~tm, usually only one, sometimes none, generates a spiral. Nevertheless, the outcrops of these dislocations become visible on Nomarski micrographs, because they generate an additional elementary step that joins a step of the dominating spiral. The identification of the nature of the defects is not unambiguous in such cases; yet it appears that in samples with dislocation densities of several 1000 cm2 the number of spirals is distinctly smaller than that of the dislocations. The analysis of the remaining 15 dislocations of the sample under discussion shows that these have Burgers vectors without a component normal to the interface. These dislocations and about 20 more of the same type identified in some other samples are not found to generate any growth step pattern, —
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3.3. Analysis ofdefects generating concentric growth step patterns The observation made with the help of fig. 2 that no dislocations are found to correspond to a step generator in the centre of concentric patterns holds for about 20 more patterns of the same type, which we observed in several samples. We therefore applied kinematical imaging in search for some micro-heterogeneity as a step generator. This technique has been shown to detect defects of the size of 2 ~m reliably in silicon [23] and should respond to defects 1 ~tm in size or even below [24]. We have applied this technique with various diffraction geometries and have found numerous small defects in some of the samples which were not visible in ordinary DC topographs. A thorough search revealed no defect near the centre of any of the concentric patterns. However, some kind of defect has to be expected as a generator for the following reasons: firstly, NDIC microscopy sometimes shows surface asperities in the centre of the concentric step patterns, and secondly, recent TEM investigations [25] have revealed dislocations in the centres.
473
The results obtained up to now permit some speculation to be made about what generates the concentric patterns. These patterns usually occur in small numbers, They are sometimes completely absent from a sample and sometimes are present in numbers of a few percent of that of the spiral patterns. They mostly occur near the edges of a sample. It is, therefore, reasonable to suspect some microscopic damage or contamination at the substrate surface which causes plastic deformation at the time of the heating to growth temperatures. Dislocations observed in the TEM could have been generated in this way. Now, we only need to assume two of those dislocations being opposite parts of a half-loop (see fig. 5) and generating spirals of opposite sense within a distance of less than 1 ~m from each other. Their steps will easily combine to form a concentric pattern. An indication for such a process has been observed recently by NDIC inspection [261. The reasons why the mechanism found for silicon by Strunk, Käss and Bauser [12,14] has not yet been found in LPE grown GaAs might be due to a difference tn stacking fault energy and a .
lower growth temperature than we applied to prepare the GaAs samples for the present study.
4. Summary and conclusion Spiral patterns of elementary growth steps observed after LPE growth of GaAs layers on GaAs substrates are generated by dislocations which have a b with a component normal to the interface. In full agreement with the extended Frank model [2], these dislocations may have any character ranging from pure screw to pure edge type. A positive or negative sign of the component normal to the interface is responsible for righthand or left-hand sense of the spirals, respectively. Dislocations with the total Burgers vector b normal to the direction of macroscopic growth, i.e. with b in the plane of growth, are not observed to have generated any step pattern. The reason for this may be due to growth temperatures of higher than 640°Cfor the samples investigated here.
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No direct evidence about the mechanism which generates concentric patterns could be obtained up to now by X-ray topographic techniques. The X-ray analysis unambiguously shows, however, that the concentric step patterns are not related to substrate dislocations in the investigated samples. Since concentric step patterns occur in very small numbers compared to the spiral patterns and since their centres are often located near the sample edges, a model based on some residual damage or contamination of the substrate surface is suggested. It assumes that due to a surface heterogeneity, a dislocation half-loop develops during the heating process to growth temperatures. The spirals turning in an opposite sense, generated by opposite parts of the half-loop, can easily combine to form a concentric pattern. Some discrepancy remains, however, between this model and the missing topographic response of the assumed defects. Both parts of the half-loop should be comparable in length with the layer thickness of about 1 ~m. The size of the half-loop should therefore be just large enough to be detectable by kinematical imaging though close to the detection limit [23,24]. Presently, the only conclusion is that the earlier findings do not hold for the particular case of a half-loop of that size. —
Acknowledgments The authors appreciate the advisory work by Prof. Dr. H.J. Queisser. One of us (W.M.) is indebted to Drs. R. Köhler and H. Raidt of Max-Planck-Arbeitsgruppe “Röntgenbeugung” for discussions on the subject. We would like to express sincere thanks to Mrs. J. Richter for assistance in making topographs and, together with Ms. A. Scherrer and Mrs. I. Wuhrl-Petry, for careful photographic reproduction of the pietures. Thanks are also due to Ms. S. Tippmann
LPE of GaAs
for the photolithography and to K.S. Löchner for technical assistance.
References [1] F.C.Frank, Disc. Faraday Soc. 5 (1949) 48. [2] W.K. Burton, N. Cabrera and F.C. Frank, Phil. Trans. Roy. Soc. London A 243 (1951) 299. 13] A.R. Verma, Crystal Growth and Dislocations (Butterworths, London, 1953). [4] W. Dekeyser and S. Amelinckx. Les Dislocations et Ia Croissance des Cristaux (Masson, Paris, 1955).
15] G.A. Bassett, Phil. Mag. 3 (1958) 1042. 161 Bethge, 21. 369. [7] H. K.W. Keller,Phys. Phys.Status StatusSolidi Solidi2 (1962) 36 (1968) [8] E. Bauser and H. Strunk, J. Crystal Growth 51 (1981) 362. [9] A.A. Chernov, in: Crystal Growth and Characterization, Proc. 2nd Intern. Spring School on Crystal Growth (ISSCG-2), Japan, 1974, Eds. R. Ueda and J.B. Mullin (North-Holland, Amsterdam, 1975) pp 33—52. [10] F.C. Frank, J. Crystal Growth 51(1981) 367. [11] E. Bauser and W. Hagen, J. Crystal Growth 50 (1980) 771. 112] D. Käss and H. Strunk, Thin Solid Films 81(1981) L10l. 1131 H.P.H.P Strunk, ThinJ. Solid Films 93 (1982) 185. [14] E. E. Bauser, Bauser and Strunk, Crystal Growth 69 (1984) 561. [15] E. Bauser, in: Crystal Growth of Electronic Materials, Ed. E. Kaldis (North-Holland, Amsterdam, 1985) p. 41. 116] H. Weishart, Thesis, Stuttgart (1992). 1171 BK. Tanner, X-Ray Diffraction Topography (Pergamon, Oxford, 1976). [18] V.M. Kaganer and W. Mdhling, Phys. Status Solidi (a) 123 (1991) 379. [19] U. Morlock, M. Kelsch and E. Bauser, J. Crystal Growth 87 (1988) 343. [20] G. Nomarski, J. Phys. Radium 16 (1955) 9S. [21] BA. Bilby, R. Bullough and E. Smith, Proc. Roy. Soc. (London) A 231 (1955) 263.
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W. Mbhling, Cryst. Rev. 2 (1989) 89. R. Kbhler and W. Mbhling, Phys. Status Solidi (a) 78 (1983) 489. [24] V.L. Indenbom and V.M. Kaganer, Phys. Status Solidi (a) 87 (1985) 253. [25] F. Phillipp and M. Rapp, private communication. [261 H.P. Strunk and T. Marek, private communication.