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Growth peculiarities of gallium arsenide single crystals
Solid-State
Electronics
GROWTH
Pergamon
Press 1963. Vol. 6, pp. 597-604.
Printed in Great Britain
PECULIARITIES OF GALLIUM SINGLE CRYSTALS* and U. ZIMMERLI
A. STELNEMANN Battelle
Memorial
Institute,
(Received
ARSENIDE
Geneva,
22 March
Abstract-The growing of GaAs single crystals nearly stoichiometric melt, has been investigated:
Switzerland
1963)
with different
seed orientations,
pulled from a
(a) The polar character of { 111) surfaces has been confirmed. (b) The habitus of <211) crystals gives a direct proof of the different growth rates in opposite
Einkristallen, die mit verSchmelze gezogen wurden:
(a) Die Polaritsit der {III} Flachen wurde bestatigt. (b) Der Habitus von <211> Kristallen ist ein direkter Beweis fur die unterschiedlichen Wachstumsgeschwindigkeiten in entgegengesetzten (1 I I > Richtungen. (c) Mit einer schwach As reichen Schmelze Gal_ZAsz (0,50 < x < 0,51) beobachtet man die geringste Wahrscheinlichkeit fiir Zwillingsbildung. Diese Wahrscheinlichkeit steigt steil an in nachster Nachbarschaft der stiichiometrischen Schmelzenzusammensetzung xs = O,SO, wobei man feststellt, dass dann die Zwillingsbildung auf (ITi) Ebenen (As) vie1 empfindlicher auf geringe As-Druckanderungen (oder Aenderungen der Schmelzenzusammensetzung) reagiert als die Zwillingsbildung auf (111) Ebenen (Ga). (d) Die Wahrscheinlichkeit der Zwillingsbildung als Funktion von Keimorientierung und Kristallprofil kann qualitativ erfasst werden. Experimentell erhalt man fiir Kristalle von ahnlicher Form eine Folge “gunstiger” Keimorientierungen, die nicht in allen Details mit der fiir InSb bekannten Folge iibereinstimmt. R&sum&-Nous avons examine la croissance de monocristaux de GaAs orientations des germes--ii partir d’une fonte presque stoichiometrique:
tires-avec
differentes
(a) Le caractere polaire des surfaces { 111) a CtC confirm& (b) Le profil des cristaux (211) est une preuve directe pour la difference de la vitesse de croissance dans des directions (111; opposees. (c) En tirant d’une fonte Gar_$AsZ avec un leger excbs d’As (0,SO < x < O,Sl), on obtient la plus petite probabilite pour la formation de jumeaux. Cette probabilite augmente fortement aux environs immediats de la composition stoichiometrique xs = 0,50 de la fonte. Ici, de petits changements de la pression d’As (ou de la composition de la fonte) affectent plus fortement la formation de mlcles sur les plans (ITT)-plans (As)-que sur les plans (Ill)-plans (Ga). (d) I1 est possible d’expliquer qualitativement la probabilite de formation de jumeaux en fonction de l’orientation du germe et du profil du cristal croissant. Les experiences avec des cristaux de profil similaire permettent d’etablir une sequence d’orientations de germes favorables qui ne coincide pas integralement avec ce qui a ete trouve pour 1’InSb. * This Holland.
work has been sponsored
by N. V. Philips’
Gloeilampenfabrieken 597
(Research
Laboratories),
Eindhoven,
A.
598
STEINEMANN
INTRODUCTION
FOR preparing crystals of III-V compounds,(r-s) the volatility of the pentavalent component needs special attention.( 2,3) GaAs single crystals have been prepared by pulling, (7,s) floating zone(T) and horizontal directional freezing.(la-Is)* Because of the high vapour pressure of arsenic, deviations from the stoichiometric melt composition are almost inevitable. They affect the crystallinity. (Crystallinity effects for vapour-phase crystal growth(r4) have been reported.) It has also been found that Ga excess affects the crystallinity in a different way from that induced by As excess.(rs) It has been known for some years that good crystal growth of III-V compounds depends on the seed orientation.(s) The different behaviour of [ill] and [iii] seeds(l5Js) corroborates the lack of symmetry in the zinc-blende structure of III-V compounds. Moreover, local growth in a (111) plane is very rapid, while the nucleation perpendicular to it is slow.(17) This has been demonstrated by preferred segregation of impurities on (111) planes.(1s-20) The polarity of (111) surfaces has been investigated for III-V(sr) and for II-VI(33J3) compounds with the zinc-blende structure. Analogous results are obtained for surfaces perpendicular to the hexagonal axis of the wurtzite lattice.@s) The identification of the atoms occupying the opposite {I 1 l} surfaces has been given by X-ray analysis.(22J4) Opposite (11 l} surfaces can also be distinguished by the etch patterns produced by oxidizing agents.( 21925-33) In III-V compounds, characteristic etch pits are revealed on (111) surfaces, i.e. those terminating with trivalent atoms.(ss,3s,ss~31) With slow etches, etch pit and dislocation density can be correlated.(30>33) A less pronounced difference of relative etch patterns on opposite (110) and (100) surfaces has been found in InSb.(33) GATOS et uZ.(sr) first proposed a model explaining the different reactivities of (111) surfaces. Different growth structures on opposite sides of GaAs dendrites have been observed.(34) The present paper shows the effects of anisotropic growth rates, seed orientation and As pressure on the crystal habit and, in particular, on twinning phenomena. Many of our experiments * Vapour solid
transport reactionsti3) phase boundary.
do not imply
a liquid-
and
U.
ZIMMERLI
have confirmed the knowledge obtained with InSb.@) Only those results that give new information on crystal growing of GaAs will be more extensively discussed. 1. EXPERIMENTAL
METHOD
GaAs single crystals have been vertically pulled* from a nearly stoichiometric meltt in a graphite crucible. The seeds were oriented within & O-5”. The pulling system is a modification of GREMMELMAIER’S method.@) There was no reservoir of solid arsenic in the sealed quartz ampoule, but an experimentally determined excess of As was added to the system and the ambient temperature was adjusted to give the correct vapour pressure.(35-3s) The crystals (ca. 100 g of GaAs) were 60-100 mm long, and had a roughly cylindrical shape of circular cross-section with diameters between 10 and 25 mm. They were p-type and had, at room temsome 101s cm-3 excess holes with perature, mobilities pP E 350 ems/V-sec. Some crystals were doped with tellurium in the melt and had, at room temperature, ca. 1017 cm-3 excess electrons with mobilities pLn 21 4000 ems/V-sec. Our pulling apparatus provided high mechanical stability (no oscillations of the melt surface-no vibrations of the magnetically supported seed holder), cylindrical symmetry of the temperature distribution at the solid-liquid interface, accurate control of the melt temperature (+ O.l’C) and ambient temperature (5 l”C), and easy reproducibility of growth conditions. 2. CRYSTAL HABITUS Whenever, during pulling, the surface of a single crystal grows nearly parallel to a (111) lattice plane, a sequence of closely spaced parallel (1 ll} facets may be produced. (On very carefully pulled cylindrical crystals, { 110) facets have been observed too.) Such a crystal exhibits mirror-like _______. ~..____ ~_____
* For geometry considerations, the positive crystal (or pulling or growth) axis is vertically downwardsparallel to the macroscopic direction of solidification. Seed orientations are also given in this way. By definition, the vector going from a Ga site to a nearestneighbour As site, is + [ll 11. All seed orientations refer to normal space. Surfaces are given by their protruding normal vectors. t Arsenic from ASARCO Refining Corp.), Gallium Industrie AC, Switzerland).
(American Smelting and from AIAG (Aluminium
GROWTH
PECULIARITIES
OF
GALLIUM
(11 I)-surface portions or a bright trace of (11 l}facets, which are either of the As-type or of the Ga-type. The type of surface is determined by the last atom below it that has one perpendicularly protruding bond (cf. Fig. 1). Opposite parallel surfaces of a {ill} slice can be distinguished by their etch patterns produced by slow oxidizing agents,(21~25-30) because triangular etch pits appear only on the Ga surface. (By special additions to the etches, etch pits can also be produced on As surfaces.) In Fig. 2, we show the etch pattern of opposite parallel surfaces of a slice cut from a twinned crystal (cf. Fig. 1.3). Simultaneously, the etch patterns of (ill), (iii), @ii) and (511) (surfaces are revealed. A low angle cut of the twin plane (cf. Fig. 1.2) is shown in Fig. 3. The triangular Ga etch pits on the upper half (twinned region of the crystal) are the mirror image as compared to the lower half (original crystal). We have examined the sequences of (11 I> facets on the surfaces of single crystals that were pulled with seed orientations (111 ), (211), (loo), (llO), (311). The different growth rates on As and Ga planes are indirectly evident from the observation, that (upwards pointing) Ga facets are much less likely to develop on the crystal surface than the corresponding As facets. Fig. 4 shows the surface aspects of (111) crystals. They exhibit bright traces of (1 ll} facets. On a [iii] crystal (cf. Fig. I), Ga facets appear on the converging surface (Fig. 4a), As facets on the diverging surface (Fig. 4b). On a [ill] crystal, the As facets appear on the converging surface parts (Fig. 4c), but there are practically no Ga facets on the diverging surface (Fig. 4d). Direct evidence for the different growth rates in opposite (111) directions is given by (211) crystals. Here, one (111) bond vector is perpendicular to the crystal (pulling) axis. Firstly, the apparatus was checked by pulling (111) and (100) crystals of circular cross-section and cylindrical profile. This was necessary to guarantee the symmetrical radial temperature distribution
ARSENIDE
SINGLE
CRYSTALS
Seed
Ci’il 1
c
A
L\
i
Ac I
Twin plane(Ga)
*iti
A-A
B-B
i FIG. 1. Schematic drawing of a [ill] crystal. On the diverging part at A, As-facets are shown. Further down at B, Ga-facets appear at a converging part. A slice cut from the crystal at (1) was a Ga plane at the top and an As plane at the bottom. The atomic arrangement determining the type of surface is drawn at the bottom of the figure. The crystal is intersected by a twin plane. Etch patterns of slices cut from the crystal at (2) and (3) are shown in Figs 3 and 2 respectively.
I
599
600
A.
STEINEMANN
at the phase boundary and on the surface of the melt. Then, some [211] and [Zii] crystals were pulled. An example is given in Fig. 5, where the sequence of well-formed As facets parallel to the axis can be seen as a bright trace along the surface. There is no Ga facet on the opposite side of the crystal-though geometrically probable. The profile of the crystal is asymmetric and proves the more rapid growth on the Ga side, i.e. parallel to + [ill]. The small growth rate on As planes is demonstrated by another effect: by slowly cooling the GaAs melt in a crucible, we get a polycrystalline ingot. On its free surface, a number of triangular (or hexagonal) bright mirror-like facets appear, as shown in Fig. 6. X-ray analysis and the etch pattern indicate that they are all single-crystal As surfaces (iii). Ga surfaces have never been found, nor any differently oriented well-formed surface. 3. TWINNING
Twinning is the most frequent reason for failure of a pulling experiment. An incidental twin plane (11 l} usually originates on the diverging surface of a growing crystal. It continues to grow through the solidifying bulk if the crystal is pulled further. This is shown in Fig. 7 (for geometry, cf. Fig. 1). The precise cause of twinning is very rarely known. If one remelts the twinned part by lowering the crystal into the melt, and tries afterwards to pull it again, the twin plane may reappear practically at the same place (the crystal shape is easily reproducible). This experiment can be repeated ten times or more with the same crystal. However, twinning can often be suppressed by slightly varying one of the parameters that affect the growth conditions. (Pulling rate and melt temperature affect the crystal profile; the ambient temperature affects the partial As vapour pressure and the melt composition; the relative rotation between seed and melt may affect the boundary layer and the temperature distribution at the solid-liquid interface.) For such situations, we have examined in detail how the vapour phase and the crystal profile affect the twinning probability.
Vapouy phase The influence of the vapour phase can be understood from an examination of the As vapour
and
U.
ZIMMERLI
pressure p, or the melt composition x. For a crucible charge of polycrystalline GaAs or stoichiometric quantities of Ga and As, the values of x and p in the sealed pulling ampoule depend mainly on the quantity, Am, of excess As added to the ampoule before sealing. The excess As that must be added to provide the vapour pressure corresponding to a stoichiometric melt will be called Ams. A typical value is Am0 = (3.0 + 0.1) g of As. The experiments were done with 2.5 < Am < 10 g-while the melt contained ca. 50 g of As. In the neighbourhood of the crucible, the radiated heat brings the’ temperature of the ampoule to about 1200°C. Farther away, the temperature decreases rapidly to an approximately constant value T, (stabilized within + l.O’C) over the upper half of the ampoule. Since there is no reservoir of solid As, the ambient temperature T, has only a small influence on x and p. T, (usually 65O’C) can be varied in the interval between the sublimation point of As and the Curie point of the iron core in the seed holder, 612 < T, < 750°C. Since the total volume of the apparatus and the vapour pressure are little affected by a change in Ta, some As must evaporate from the melt when T, is lowered and conversely must condense when Ta is raised (pV = nRT). A variation of T, over this interval has the same effect as a variation in Am of O-5 g. Therefore, the precise stoichiometric equilibrium conditions of the melt in the sealed ampoule can be realized accurately by adjusting I‘,. The procedure is illustrated by Fig. 8. The nearly stoichiometric melt is kept at a constant temperature, e.g. T = T(xl), which is the equilibrium value for a slight As excess in the melt, x1 > x0 = 0.50. Thus, a small piece of solid GaAs (1 mms) swimming on the melt surface (1500 mms) remains unchanged. An increase of T, is accompanied by a transport of As from the vapour phase into the melt, giving xi > x1. Since the constant melt temperature is higher than the new equilibrium value T(x;), the small piece of solid GaAs melts slowly. Evidently, a decrease of T, leads to an increase in size of the solid phase. Starting from a slightly Ga-rich melt, e.g. at T(Q), the effects of i AT, are reversed. With a precisely stoichiometric melt [xs = 0.50 for To = 1237°C and po(As) = 0. 98 atm], both
FIG. 2. Etch patterns of the opposite parallel surfaces of a slice cut perpendicularly to the axis of a [ill] crystal (cf. Fig. 1.3). The slice is intersected by a twin plane (111) that leaves a vertical trace in the centre of the figures. (a) Surface (111) with triangular Ga etch pits on the left half as compared with (511). (b) Surface (111) on the left half (As) as compared with (511).
FIG. 3. Low-angle (2”) cut of a twin plane parallel to a Ga facet. The (slightly) distorted Ga etch pits on the upper half belong to the twinned crystal region. Those on the lower half (mirror image) belong to the original crystal. The twin plane cuts an approximately horizontal trace through the centre of the figure (cf. Fig. 1.2).
FIG. 4. Surfaces of crystals with sequences of bright {ill} facets: (a) on the converging surface parts of a [ITT] crystal (cf. Fig. l-BB). (b)‘Arsenic the diverging surface parts of the same [ill] crystal (rotated by 60”-cf. Fig. (c) Arsenic facets on the converging surface parts of a [l 111 crystal. (d) Ga the diverging surface parts of the same [ill ] crystal are scarcely produced by 60”).
Ga facets facets on l--AA). facets on (rotated
c2111
Ga plane
\ \
,
low growth rate on \ As plane
I
_ i
I
A
I I
I : /
i
I
A-A
No
i
\ As facet I
Ga tacet
;
FIG. 5. (a) Sequence of bright As facets axis of a [211] crystal. There are no Ga opposite side. The shape of the crystal (thicker on the Ga side). (b) Geometry crystal, explaining the asymmetric
parallel to the facets on the is asymmetric of a [211] shape.
FIG. 6. Free
surface
FIG. 7. [ill]
crystal
of
a polycrystalline ingot. Bright triangular veloped. There are no Ga facets.
crossed
As
by a single twin plane. Its trace runs from the top right of the figure.
facets
are well
the bottom
de-
left to
GROWTH
PECULIARITIES
OF GALLIUM
positive and negative variations of the ambient temperature will result in melting the small piece of solid GaAs. Experimentally, it was possible to control this effect for AT, = * 20°C (corresponding to Ax = k 0.03 per cent), if the temperature of the crucible was stabilized within _t O.l”C. Experimentally, it was found preferable to pull crystals from a slightly As-rich melt. The twinning probability is then very low (cf. Fig. 10). For an As excess, Am > 6 g (twice the value necessary for maintaining the vapour pressure over a stoichiometric melt), macroscopic holes tend to form inside the single crystal. For still higher Am, the twinning probability increases. For Am > 10 g, all crystals twinned. The numbers refer to (111) and (100 ) crystals pulled at a rate of 0.5 mm/min. They decrease for higher pulling rates. [iii] single crystals were obtained with Am = 3.2 g, at a pulling rate as high as 2.5 mm/min, while, on the other hand, with Am slightly below Ams (2.8 instead of 3.0 g), nine out of ten crystals twinned independently of the pulling rate. Therefore, crystals of reasonable quality and without twins could be pulled with an As excess in the interval Am0 < Am < 2Ama. Similar phenomena have been observed by WEISBERG et aZ.(lz) for the Bridgman technique. However, to obtain single crystals of really
ARSENIDE
SINGLE
CRYSTALS
601
high quality (low dislocation density and homogeneous impurity distribution), it is preferable to pull from a stoichiometric melt (Am N Ams). Under this condition, the twinning probability of (111 ), (loo), and some (211) crystals has been analysed. Firstly, we confirmed that [ll l] crystals (where the Ga surface is in contact with the melt, and where the twin planes can appear parallel to any of the three oblique downwards pointing As facets) are more likely to twin than [iii] crystals. Then, we observed that twin planes parallel to As planes could be suppressed by remelting the twinned part of the crystal and pulling it again with a higher ambient temperature (a lower ambient temperature always increased the twinning probability). As soon as the correct ambient temperature was established (sometimes after an increment of lO”C, sometimes only after repeated trials with a final temperature increment up to 5O”C), the formation or suppression of “As’‘-twins could be repeatedly controlled within an interval of 20°C of the ambient temperature. On the other hand, for twin planes parallel to an oblique downwards pointing Ga facet (“Ga”twins), the experiments failed. Even if it was possible to avoid “Ga”-twins by changing the profile of the crystal, the experimentally accessible variation of Ta was still not sufficient to control the formation or suppression of these twins. The twinning probability of crystals pulled from an As-rich melt (Am > l*lAms) could not be affected by a variation of T,. lnfruence of the crystal projile
L
i ; 5
x;
i
j /
X0’ 50%
x,
_X,,,~As
x; Melt
composition
FIG. 8. Qualitative liquidus line T(x) near the stoichiometric melt composition JCO.For a fixed temperature of the melt T,,,, the increase of As content due to As transport from the vapour phase after an increase of the ambient temperature Ta causes a small piece of GaAs swimming on the melt to decrease on the As side (xl + xi) or to increase on the Ga side (x2 -+ xi). For a precisely stoichiometric melt (T, = To, x = xo) both positive and negative x cause melting.
For crystals with accurately oriented seeds, we observed that twin planes most likely start on the diverging parts of the surface. Twinning is much more probable on a rapidly diverging surface than on a smoothly diverging surface. On a cylindrical surface (constant radius), the twinning probability is small, and it is even smaller on the converging parts of the surface. All crystals diverging with an angle of about 45” or more, have an equal tendency to twin, independent of the seed orientation. If the surface of the pulled crystal has several diverging and converging parts, the twinning probability is highest on the first diverging portion. It decreases for the following diverging portions (assuming equal slope of the profile). This is an indication
A.
602
STEINEMANN
and
that scum favours twinning,(s) since it can be assumed that after pulling a certain length of the crystal, scum has disappeared from the surface of the melt. For misoriented seeds, the twinning probability --depends strongly on the seed orientation. [ill]
U.
ZIMMERLI
distinction between [211] and [Zii].The reported (110) crystals had no twin planes parallel to the axis. Among the two crystals <311), only one was 50 per cent single crystal. The Bridgman technique for GaAs apparently gives a different result.(ls) But, in horizontal
Table 1. Twinning probabilities, P(r), in percentages Seed r
P(r)
N hi, = NfIN
per cent
111
111
ZfT and 211
100
110
311
24 5 20
27 8 30
9 3 34
13 5 40
3 2 66
2 2 100
N = number of Dulled crvstals. Nf = number of failed pulling experiments. , melt contained SO->1 at. per cent of As. ,”
crystals have been pulled with deviations of approximately lo”, while (100) and (211) crystals inevitably twinned for deviations of only about 3”. Any computation of twinning probabilities must therefore refer to crystals with accurately oriented seeds, pulled from a melt with a scum-free surface.
Sequence of favourable seed orientations We have compared seventy-eight crystals with different orientations, pulled under similar conditions. For each seed orientation, the fractional number of failed experiments has been determined. The experiments are considered as a failure if no manipulation during pulling succeeded in giving a single crystal. Failures due to experimental errors or misoriented seeds are not included. Table 1 sequence of seed indicates the results. The orientations Y gives (from left to right) the increasing probability, P(r), of twinning for comparable growth conditions. This sequence differs somewhat from the results reported for InSb,@ where [ll l] is further to the right. For (111) crystals, the geometrically possible twin plane perpendicular to the crystal axis has never been observed. In (211) crystals, we observed only twin planes with a normal vector having an angle, 6’ = 62”, with respect to the crystal axis. 0 = 20” has not been observed, 0 = 90” only once. The small number of experiments with (211) crystals does not permit a
The GaAs
boats, the phase boundary is in contact with the boat wall and it has no cylindrical symmetry. The observed random orientation of unseeded single crystals cannot be correlated with Table 1. Experiments with epitaxial growth from the vapour phase have best succeeded with a (211) or { 1 IO} substrate.(14) We believe that the sequence of Table 1 may also be valid for floating-zone experiments, where one has a three-phase system with cylindrical symmetry too. 4. DISCUSSION
Our experiments with GaAs confirmed previous results of the polar character of (111) surfaces in III-V compounds. The habitus of (211) crystals provides, moreover, direct evidence for the growth-rate difference on As and Ga planes. The twinning phenomena are correlated with this growth-rate difference, but their statistical character makes the interpretation more difficult. Two parameters (crystal profile and partial As pressure or melt composition) appear to affect the growth (or nucleation) at the solid-liquidvapour three-phase boundary line, because oblique { 11 l} twin planes normally originate there. To explain both the effects of the crystal orientation and the profile of its surface, we shall assume that the twinning probability increases monotonically with the number nd of oblique GaAs double layers that cut through the surface of the growing crystal. With the spacings of the double
GROWTH
PECULIARITIES
OF
layers equal to s = 4d/3 (d = 2.44 A is nearest-neighbour separation Ga-As), we from Fig. 9(a) that the number nd is given by 3h cos(8-8,) nd = 4d
-c~~ ___ es
3h -._ = zf(B,
GALLIUM
ARSENIDE
SINGLE
CRYSTALS
603
the see
3h
= iPose+
sin 0 tan 0,)
8s).
The trigonometric function f, which, according to our assumption, determines the geometrical twinning probability P(j), is plotted in Fig. 9(b) for the seed orientations that have been investigated. The full curves refer to the crystals in Table 1. The dashed curves refer to the twins that have not been observed (a, b) or have not been included in Table 1 because there are not sufficient experimental results (c). It is evident from the full curves that the lowest geometrical twinning probability is obtained for (111) crystals (curve 1). The twinning probability increases for seed orientations (211), (IOO), (llO), . . . (curves 2, 3, 4). For converging growth (0i < 0), the twinning probability decreases, as f approaches zero; and for diverging growth (86 > 0), twinning becomes rapidly more probable, as f increases rather steeply for increasing &. For Bf > 45”, f is approximately equal for all seed orientations. This interpretation agrees with the experimental results. The lower twinning probability on Ga planes, as compared with geometrically equivalent As planes, can be understood from the different nucleation rates on these planes. The average growth rate of the crystal is imposed by the external pulling rate. Because of the smaller nucleation rate on As planes, the time interval (per formed double layer) left for correct orientation or reorientation of the freshly solidified layer is shorter on As planes. Therefore, twinning on As planes is more probable. The observed different sensitivity of geometrically equivalent Ga or As planes with respect to small changes of the ambient temperature (for crystals pulled from a nearly stoichiometric melt) is more difficult to understand. It seems likely that the twinning probability is strongly affected by small changes of p and x as a result of the variation of deviations from the of Ta. The influence
crystal axis
surface
(a>
@I
FIG. 9. Influence of the crystal profile (0,) and the seed orientation on the twinning probability. (a) Idealized geometry of a portion h of a vertically cut crystal. The plane of the figure contains the crystal axis and an oblique vector. (b) Plot of the argument f(8,) for the investigated seed orientations. f = cos. 0 + sin e tan 0,.
stoichiometric composition of the melt on the twinning probability P is shown qualitatively in Fig. 10, where P is plotted against the As excess, a = (Am-Ams)/Ame. (Instead of the As excess, one could plot the As pressure or the melt composition.) P has a flat minimum in the interval 0 < Q < 1. It rises slowly for a > 1, and more steeply for a > 2. On the other hand, P rises extremely steeply for slightly negative values of a.
A.
604
and
STEINEMANN
For this part of the curve, the experiments with a variation of the ambient temperature indicate that the slope is about five times smaller for twinning on Ga planes. P
Pmin 1
v Ga
-1
As excess
excess 0
oc 1
2
FIG. 10. Qditative plot of the twinning probability P as a function of the relative As excess, c( = (&z&zo)/&zo. mo is the .4s excess necessary for the vapour phase over the stoichiometric melt. Upper curve: twinning on an As plane; lower curve: twinning on a Ga plane.
Though this effect has been observed for nearly cylindrical crystals, it does not seem to depend critically on small changes on the crystal profile. In Fig. 10, the upper curve is approximately valid for [ill] crystals, the lower curve for [iii] crystals. In our system, the observed interval of AT, = 20°C for formation or suppression of “As’‘-twins has an effect similar to that caused by Am = 0.06 g,. AX = 0.02 or Ax = 0.03 per cent. Such an effect is only noticeable on the extremely steep portion of the curve P(a) near a = 0. It could be correlated with the sudden change from a slight As excess to a Ga excess in the solid phase at ~0 = 0.50.
Acknowledgement-The authors are indebted to H. A. KLASENS and H. J. \‘INK of the Philips’ Research Laboratories for many helpful discussions and critical remarks. REFERENCES 1. A. SMAKULA, Einkristalle, Tech. Phys. Einzeldarst. 14,45, 214 (1962), Solid-State Abstr. 3, 1 (1962). 2. J. VAN DE BOOMGAARD,F. A. KRUEGERand H. J. VINK, J. Electron. 1, 212 (1955). 3. J. VAN DER BOOMGAARD,Philips Res. Rep. 10, 319 (1955); 11, 27 (1956); 11, 91 (1956).
U.
ZIMMERLI
4. H. WELKER and H. WEISS, Solid State Physics Vol. 3, p. 1. Academic Press, New York (1956). 5. 0. G. FOLBERTH, Halbleiterprobleme 5, 40 (1960). 6. L. R. WEISBERG, F. D. ROSI and P. G. HERKART, Metallurgical Society Conference Vol. 3, p. 25, Boston (1959). 7. C. HILSUM and H. ROSE-INNES, Seimconductovs III-V. Pergamon Press, Oxford (1961). 8. K. F. HULME and J. B. MULLIN, Solid-State Electvon. 5, 211 (1962). 9. R. GREMMELMAIER,2. Naturf. lla, 511 (1956). 10. 0. G. FOLBERTH and H. WEISS, 2. Naturf. lOa, 615 (1955). 11. J. L. RICHARDS,J. Appl. Phys. 31, 600 (1960). 12. L. R. WEISBERG, J. BLANC and E. J. STOFKO, J. Electrochem. Sot. 109, 642 (1962). 13. Quoted in RCA Rep. AFCRL, 383, No. 5 (1962). 14. F. A. PIZZARELLO, J. Electrochem. Sot. 109, 226 (1962). 15. H. C. GATOS, P. L. Moouv and M. C. LAVINE, J. Appl. Phys. 31,212 (1960). 16. S. G. ELLIS,J. Appl. Phys. 30;1412 (1959). 17. R. C. SANGSTER, Electrochem. Sot. Abstr. 9. 172 (1960). 18. W. A. TILLER, J. Appl. Phys. 29, 611 (1958). 19. W. K. BURTON, N. CABRERAand F. C. FR.~xK, Phil. Trans. A 243; 299 (1957). 20. W. P. ALLRED and R. T. BATE, J. Electrochem. Sot. 108, 257 (1961). 21. II. C. Gh~os and M. C. LAVINE, J. Electrochem. SOL. 107, 427 (1960). 22. E. P. WAREKOIS, M. C. LAVINE, A. N. MARIANO and H. C. GATOS,J. Appl. Phys. 33,690 (1962). 23. J. A. DILLON, JR., J. Appl. Phys. 33, 669 (1962). 24. J. G. WHITE and W. C. ROTH, J. Appl. Phys. 30, 946 (1959); E. P. WAREKOISand P. H. METZGER, Ibid. 30, 960 (1959). 25. H. A. SCHELL, 2. Metal. 48, 158 (1957). 26. J. W. ALLEN, Phil. Mag. 2, 1475 (1957). 27. W. BARDSLEY and R. L. BELL, J. Electron. 3, 103 (1957). 28. M. C. LAVINE, A. J. ROSENBERGand H. C. Gyros, J. Appl. Phys. 29, 1131 (1958). 29. J. D. VENABLESand R. M. BROUDY, J. Appl. Phys. 29, 1025 (1958). 30. M. S. ABRAHAMSand L. EKSTROM, Metallurgical Society Conference Vol. 5, p. 225, Boston (1959). 31. R. E. MARINGER,J. Appl. Phys. 29,126l (1958). 32. S. A. KULIN and A. D. KURTZ, Acta Met. 2, 354 (1954). 33. H. C. GATOS and M. C. LAVINE, J. Electrochem. Sot. 107, 433 (1960). 34. G. R. BROOKER,J. Appl. Phys. 33, 750 (1962). 35. J. VAN DER BOOMGAARD and K. SCHOL, Philips Res. Rep. 12, 127 (1957). 36. J. DROMTXRTand P. GOLDFINGER, J. Chem. Phys. 55, 721 (1958). 37. V. J. LYONS and V. J. SYLVEXRI, 120th Electrochemical Society Meeting, Detroit (1961). 38. D. RICEIM~X and K. WEISER, Quoted in RCA Rep. AFCRL 62-336, No. 9 (1962); 973, No. 7 (1962).
Electronics
GROWTH
Pergamon
Press 1963. Vol. 6, pp. 597-604.
Printed in Great Britain
PECULIARITIES OF GALLIUM SINGLE CRYSTALS* and U. ZIMMERLI
A. STELNEMANN Battelle
Memorial
Institute,
(Received
ARSENIDE
Geneva,
22 March
Abstract-The growing of GaAs single crystals nearly stoichiometric melt, has been investigated:
Switzerland
1963)
with different
seed orientations,
pulled from a
(a) The polar character of { 111) surfaces has been confirmed. (b) The habitus of <211) crystals gives a direct proof of the different growth rates in opposite
Einkristallen, die mit verSchmelze gezogen wurden:
(a) Die Polaritsit der {III} Flachen wurde bestatigt. (b) Der Habitus von <211> Kristallen ist ein direkter Beweis fur die unterschiedlichen Wachstumsgeschwindigkeiten in entgegengesetzten (1 I I > Richtungen. (c) Mit einer schwach As reichen Schmelze Gal_ZAsz (0,50 < x < 0,51) beobachtet man die geringste Wahrscheinlichkeit fiir Zwillingsbildung. Diese Wahrscheinlichkeit steigt steil an in nachster Nachbarschaft der stiichiometrischen Schmelzenzusammensetzung xs = O,SO, wobei man feststellt, dass dann die Zwillingsbildung auf (ITi) Ebenen (As) vie1 empfindlicher auf geringe As-Druckanderungen (oder Aenderungen der Schmelzenzusammensetzung) reagiert als die Zwillingsbildung auf (111) Ebenen (Ga). (d) Die Wahrscheinlichkeit der Zwillingsbildung als Funktion von Keimorientierung und Kristallprofil kann qualitativ erfasst werden. Experimentell erhalt man fiir Kristalle von ahnlicher Form eine Folge “gunstiger” Keimorientierungen, die nicht in allen Details mit der fiir InSb bekannten Folge iibereinstimmt. R&sum&-Nous avons examine la croissance de monocristaux de GaAs orientations des germes--ii partir d’une fonte presque stoichiometrique:
tires-avec
differentes
(a) Le caractere polaire des surfaces { 111) a CtC confirm& (b) Le profil des cristaux (211) est une preuve directe pour la difference de la vitesse de croissance dans des directions (111; opposees. (c) En tirant d’une fonte Gar_$AsZ avec un leger excbs d’As (0,SO < x < O,Sl), on obtient la plus petite probabilite pour la formation de jumeaux. Cette probabilite augmente fortement aux environs immediats de la composition stoichiometrique xs = 0,50 de la fonte. Ici, de petits changements de la pression d’As (ou de la composition de la fonte) affectent plus fortement la formation de mlcles sur les plans (ITT)-plans (As)-que sur les plans (Ill)-plans (Ga). (d) I1 est possible d’expliquer qualitativement la probabilite de formation de jumeaux en fonction de l’orientation du germe et du profil du cristal croissant. Les experiences avec des cristaux de profil similaire permettent d’etablir une sequence d’orientations de germes favorables qui ne coincide pas integralement avec ce qui a ete trouve pour 1’InSb. * This Holland.
work has been sponsored
by N. V. Philips’
Gloeilampenfabrieken 597
(Research
Laboratories),
Eindhoven,
A.
598
STEINEMANN
INTRODUCTION
FOR preparing crystals of III-V compounds,(r-s) the volatility of the pentavalent component needs special attention.( 2,3) GaAs single crystals have been prepared by pulling, (7,s) floating zone(T) and horizontal directional freezing.(la-Is)* Because of the high vapour pressure of arsenic, deviations from the stoichiometric melt composition are almost inevitable. They affect the crystallinity. (Crystallinity effects for vapour-phase crystal growth(r4) have been reported.) It has also been found that Ga excess affects the crystallinity in a different way from that induced by As excess.(rs) It has been known for some years that good crystal growth of III-V compounds depends on the seed orientation.(s) The different behaviour of [ill] and [iii] seeds(l5Js) corroborates the lack of symmetry in the zinc-blende structure of III-V compounds. Moreover, local growth in a (111) plane is very rapid, while the nucleation perpendicular to it is slow.(17) This has been demonstrated by preferred segregation of impurities on (111) planes.(1s-20) The polarity of (111) surfaces has been investigated for III-V(sr) and for II-VI(33J3) compounds with the zinc-blende structure. Analogous results are obtained for surfaces perpendicular to the hexagonal axis of the wurtzite lattice.@s) The identification of the atoms occupying the opposite {I 1 l} surfaces has been given by X-ray analysis.(22J4) Opposite (11 l} surfaces can also be distinguished by the etch patterns produced by oxidizing agents.( 21925-33) In III-V compounds, characteristic etch pits are revealed on (111) surfaces, i.e. those terminating with trivalent atoms.(ss,3s,ss~31) With slow etches, etch pit and dislocation density can be correlated.(30>33) A less pronounced difference of relative etch patterns on opposite (110) and (100) surfaces has been found in InSb.(33) GATOS et uZ.(sr) first proposed a model explaining the different reactivities of (111) surfaces. Different growth structures on opposite sides of GaAs dendrites have been observed.(34) The present paper shows the effects of anisotropic growth rates, seed orientation and As pressure on the crystal habit and, in particular, on twinning phenomena. Many of our experiments * Vapour solid
transport reactionsti3) phase boundary.
do not imply
a liquid-
and
U.
ZIMMERLI
have confirmed the knowledge obtained with InSb.@) Only those results that give new information on crystal growing of GaAs will be more extensively discussed. 1. EXPERIMENTAL
METHOD
GaAs single crystals have been vertically pulled* from a nearly stoichiometric meltt in a graphite crucible. The seeds were oriented within & O-5”. The pulling system is a modification of GREMMELMAIER’S method.@) There was no reservoir of solid arsenic in the sealed quartz ampoule, but an experimentally determined excess of As was added to the system and the ambient temperature was adjusted to give the correct vapour pressure.(35-3s) The crystals (ca. 100 g of GaAs) were 60-100 mm long, and had a roughly cylindrical shape of circular cross-section with diameters between 10 and 25 mm. They were p-type and had, at room temsome 101s cm-3 excess holes with perature, mobilities pP E 350 ems/V-sec. Some crystals were doped with tellurium in the melt and had, at room temperature, ca. 1017 cm-3 excess electrons with mobilities pLn 21 4000 ems/V-sec. Our pulling apparatus provided high mechanical stability (no oscillations of the melt surface-no vibrations of the magnetically supported seed holder), cylindrical symmetry of the temperature distribution at the solid-liquid interface, accurate control of the melt temperature (+ O.l’C) and ambient temperature (5 l”C), and easy reproducibility of growth conditions. 2. CRYSTAL HABITUS Whenever, during pulling, the surface of a single crystal grows nearly parallel to a (111) lattice plane, a sequence of closely spaced parallel (1 ll} facets may be produced. (On very carefully pulled cylindrical crystals, { 110) facets have been observed too.) Such a crystal exhibits mirror-like _______. ~..____ ~_____
* For geometry considerations, the positive crystal (or pulling or growth) axis is vertically downwardsparallel to the macroscopic direction of solidification. Seed orientations are also given in this way. By definition, the vector going from a Ga site to a nearestneighbour As site, is + [ll 11. All seed orientations refer to normal space. Surfaces are given by their protruding normal vectors. t Arsenic from ASARCO Refining Corp.), Gallium Industrie AC, Switzerland).
(American Smelting and from AIAG (Aluminium
GROWTH
PECULIARITIES
OF
GALLIUM
(11 I)-surface portions or a bright trace of (11 l}facets, which are either of the As-type or of the Ga-type. The type of surface is determined by the last atom below it that has one perpendicularly protruding bond (cf. Fig. 1). Opposite parallel surfaces of a {ill} slice can be distinguished by their etch patterns produced by slow oxidizing agents,(21~25-30) because triangular etch pits appear only on the Ga surface. (By special additions to the etches, etch pits can also be produced on As surfaces.) In Fig. 2, we show the etch pattern of opposite parallel surfaces of a slice cut from a twinned crystal (cf. Fig. 1.3). Simultaneously, the etch patterns of (ill), (iii), @ii) and (511) (surfaces are revealed. A low angle cut of the twin plane (cf. Fig. 1.2) is shown in Fig. 3. The triangular Ga etch pits on the upper half (twinned region of the crystal) are the mirror image as compared to the lower half (original crystal). We have examined the sequences of (11 I> facets on the surfaces of single crystals that were pulled with seed orientations (111 ), (211), (loo), (llO), (311). The different growth rates on As and Ga planes are indirectly evident from the observation, that (upwards pointing) Ga facets are much less likely to develop on the crystal surface than the corresponding As facets. Fig. 4 shows the surface aspects of (111) crystals. They exhibit bright traces of (1 ll} facets. On a [iii] crystal (cf. Fig. I), Ga facets appear on the converging surface (Fig. 4a), As facets on the diverging surface (Fig. 4b). On a [ill] crystal, the As facets appear on the converging surface parts (Fig. 4c), but there are practically no Ga facets on the diverging surface (Fig. 4d). Direct evidence for the different growth rates in opposite (111) directions is given by (211) crystals. Here, one (111) bond vector is perpendicular to the crystal (pulling) axis. Firstly, the apparatus was checked by pulling (111) and (100) crystals of circular cross-section and cylindrical profile. This was necessary to guarantee the symmetrical radial temperature distribution
ARSENIDE
SINGLE
CRYSTALS
Seed
Ci’il 1
c
A
L\
i
Ac I
Twin plane(Ga)
*iti
A-A
B-B
i FIG. 1. Schematic drawing of a [ill] crystal. On the diverging part at A, As-facets are shown. Further down at B, Ga-facets appear at a converging part. A slice cut from the crystal at (1) was a Ga plane at the top and an As plane at the bottom. The atomic arrangement determining the type of surface is drawn at the bottom of the figure. The crystal is intersected by a twin plane. Etch patterns of slices cut from the crystal at (2) and (3) are shown in Figs 3 and 2 respectively.
I
599
600
A.
STEINEMANN
at the phase boundary and on the surface of the melt. Then, some [211] and [Zii] crystals were pulled. An example is given in Fig. 5, where the sequence of well-formed As facets parallel to the axis can be seen as a bright trace along the surface. There is no Ga facet on the opposite side of the crystal-though geometrically probable. The profile of the crystal is asymmetric and proves the more rapid growth on the Ga side, i.e. parallel to + [ill]. The small growth rate on As planes is demonstrated by another effect: by slowly cooling the GaAs melt in a crucible, we get a polycrystalline ingot. On its free surface, a number of triangular (or hexagonal) bright mirror-like facets appear, as shown in Fig. 6. X-ray analysis and the etch pattern indicate that they are all single-crystal As surfaces (iii). Ga surfaces have never been found, nor any differently oriented well-formed surface. 3. TWINNING
Twinning is the most frequent reason for failure of a pulling experiment. An incidental twin plane (11 l} usually originates on the diverging surface of a growing crystal. It continues to grow through the solidifying bulk if the crystal is pulled further. This is shown in Fig. 7 (for geometry, cf. Fig. 1). The precise cause of twinning is very rarely known. If one remelts the twinned part by lowering the crystal into the melt, and tries afterwards to pull it again, the twin plane may reappear practically at the same place (the crystal shape is easily reproducible). This experiment can be repeated ten times or more with the same crystal. However, twinning can often be suppressed by slightly varying one of the parameters that affect the growth conditions. (Pulling rate and melt temperature affect the crystal profile; the ambient temperature affects the partial As vapour pressure and the melt composition; the relative rotation between seed and melt may affect the boundary layer and the temperature distribution at the solid-liquid interface.) For such situations, we have examined in detail how the vapour phase and the crystal profile affect the twinning probability.
Vapouy phase The influence of the vapour phase can be understood from an examination of the As vapour
and
U.
ZIMMERLI
pressure p, or the melt composition x. For a crucible charge of polycrystalline GaAs or stoichiometric quantities of Ga and As, the values of x and p in the sealed pulling ampoule depend mainly on the quantity, Am, of excess As added to the ampoule before sealing. The excess As that must be added to provide the vapour pressure corresponding to a stoichiometric melt will be called Ams. A typical value is Am0 = (3.0 + 0.1) g of As. The experiments were done with 2.5 < Am < 10 g-while the melt contained ca. 50 g of As. In the neighbourhood of the crucible, the radiated heat brings the’ temperature of the ampoule to about 1200°C. Farther away, the temperature decreases rapidly to an approximately constant value T, (stabilized within + l.O’C) over the upper half of the ampoule. Since there is no reservoir of solid As, the ambient temperature T, has only a small influence on x and p. T, (usually 65O’C) can be varied in the interval between the sublimation point of As and the Curie point of the iron core in the seed holder, 612 < T, < 750°C. Since the total volume of the apparatus and the vapour pressure are little affected by a change in Ta, some As must evaporate from the melt when T, is lowered and conversely must condense when Ta is raised (pV = nRT). A variation of T, over this interval has the same effect as a variation in Am of O-5 g. Therefore, the precise stoichiometric equilibrium conditions of the melt in the sealed ampoule can be realized accurately by adjusting I‘,. The procedure is illustrated by Fig. 8. The nearly stoichiometric melt is kept at a constant temperature, e.g. T = T(xl), which is the equilibrium value for a slight As excess in the melt, x1 > x0 = 0.50. Thus, a small piece of solid GaAs (1 mms) swimming on the melt surface (1500 mms) remains unchanged. An increase of T, is accompanied by a transport of As from the vapour phase into the melt, giving xi > x1. Since the constant melt temperature is higher than the new equilibrium value T(x;), the small piece of solid GaAs melts slowly. Evidently, a decrease of T, leads to an increase in size of the solid phase. Starting from a slightly Ga-rich melt, e.g. at T(Q), the effects of i AT, are reversed. With a precisely stoichiometric melt [xs = 0.50 for To = 1237°C and po(As) = 0. 98 atm], both
FIG. 2. Etch patterns of the opposite parallel surfaces of a slice cut perpendicularly to the axis of a [ill] crystal (cf. Fig. 1.3). The slice is intersected by a twin plane (111) that leaves a vertical trace in the centre of the figures. (a) Surface (111) with triangular Ga etch pits on the left half as compared with (511). (b) Surface (111) on the left half (As) as compared with (511).
FIG. 3. Low-angle (2”) cut of a twin plane parallel to a Ga facet. The (slightly) distorted Ga etch pits on the upper half belong to the twinned crystal region. Those on the lower half (mirror image) belong to the original crystal. The twin plane cuts an approximately horizontal trace through the centre of the figure (cf. Fig. 1.2).
FIG. 4. Surfaces of
Ga facets facets on l--AA). facets on (rotated
c2111
Ga plane
\ \
,
low growth rate on \ As plane
I
_ i
I
A
I I
I : /
i
I
A-A
No
i
\ As facet I
Ga tacet
;
FIG. 5. (a) Sequence of bright As facets axis of a [211] crystal. There are no Ga opposite side. The shape of the crystal (thicker on the Ga side). (b) Geometry crystal, explaining the asymmetric
parallel to the facets on the is asymmetric of a [211] shape.
FIG. 6. Free
surface
FIG. 7. [ill]
crystal
of
a polycrystalline ingot. Bright triangular veloped. There are no Ga facets.
crossed
As
by a single twin plane. Its trace runs from the top right of the figure.
facets
are well
the bottom
de-
left to
GROWTH
PECULIARITIES
OF GALLIUM
positive and negative variations of the ambient temperature will result in melting the small piece of solid GaAs. Experimentally, it was possible to control this effect for AT, = * 20°C (corresponding to Ax = k 0.03 per cent), if the temperature of the crucible was stabilized within _t O.l”C. Experimentally, it was found preferable to pull crystals from a slightly As-rich melt. The twinning probability is then very low (cf. Fig. 10). For an As excess, Am > 6 g (twice the value necessary for maintaining the vapour pressure over a stoichiometric melt), macroscopic holes tend to form inside the single crystal. For still higher Am, the twinning probability increases. For Am > 10 g, all crystals twinned. The numbers refer to (111) and (100 ) crystals pulled at a rate of 0.5 mm/min. They decrease for higher pulling rates. [iii] single crystals were obtained with Am = 3.2 g, at a pulling rate as high as 2.5 mm/min, while, on the other hand, with Am slightly below Ams (2.8 instead of 3.0 g), nine out of ten crystals twinned independently of the pulling rate. Therefore, crystals of reasonable quality and without twins could be pulled with an As excess in the interval Am0 < Am < 2Ama. Similar phenomena have been observed by WEISBERG et aZ.(lz) for the Bridgman technique. However, to obtain single crystals of really
ARSENIDE
SINGLE
CRYSTALS
601
high quality (low dislocation density and homogeneous impurity distribution), it is preferable to pull from a stoichiometric melt (Am N Ams). Under this condition, the twinning probability of (111 ), (loo), and some (211) crystals has been analysed. Firstly, we confirmed that [ll l] crystals (where the Ga surface is in contact with the melt, and where the twin planes can appear parallel to any of the three oblique downwards pointing As facets) are more likely to twin than [iii] crystals. Then, we observed that twin planes parallel to As planes could be suppressed by remelting the twinned part of the crystal and pulling it again with a higher ambient temperature (a lower ambient temperature always increased the twinning probability). As soon as the correct ambient temperature was established (sometimes after an increment of lO”C, sometimes only after repeated trials with a final temperature increment up to 5O”C), the formation or suppression of “As’‘-twins could be repeatedly controlled within an interval of 20°C of the ambient temperature. On the other hand, for twin planes parallel to an oblique downwards pointing Ga facet (“Ga”twins), the experiments failed. Even if it was possible to avoid “Ga”-twins by changing the profile of the crystal, the experimentally accessible variation of Ta was still not sufficient to control the formation or suppression of these twins. The twinning probability of crystals pulled from an As-rich melt (Am > l*lAms) could not be affected by a variation of T,. lnfruence of the crystal projile
L
i ; 5
x;
i
j /
X0’ 50%
x,
_X,,,~As
x; Melt
composition
FIG. 8. Qualitative liquidus line T(x) near the stoichiometric melt composition JCO.For a fixed temperature of the melt T,,,, the increase of As content due to As transport from the vapour phase after an increase of the ambient temperature Ta causes a small piece of GaAs swimming on the melt to decrease on the As side (xl + xi) or to increase on the Ga side (x2 -+ xi). For a precisely stoichiometric melt (T, = To, x = xo) both positive and negative x cause melting.
For crystals with accurately oriented seeds, we observed that twin planes most likely start on the diverging parts of the surface. Twinning is much more probable on a rapidly diverging surface than on a smoothly diverging surface. On a cylindrical surface (constant radius), the twinning probability is small, and it is even smaller on the converging parts of the surface. All crystals diverging with an angle of about 45” or more, have an equal tendency to twin, independent of the seed orientation. If the surface of the pulled crystal has several diverging and converging parts, the twinning probability is highest on the first diverging portion. It decreases for the following diverging portions (assuming equal slope of the profile). This is an indication
A.
602
STEINEMANN
and
that scum favours twinning,(s) since it can be assumed that after pulling a certain length of the crystal, scum has disappeared from the surface of the melt. For misoriented seeds, the twinning probability --depends strongly on the seed orientation. [ill]
U.
ZIMMERLI
distinction between [211] and [Zii].The reported (110) crystals had no twin planes parallel to the axis. Among the two crystals <311), only one was 50 per cent single crystal. The Bridgman technique for GaAs apparently gives a different result.(ls) But, in horizontal
Table 1. Twinning probabilities, P(r), in percentages Seed r
P(r)
N hi, = NfIN
per cent
111
111
ZfT and 211
100
110
311
24 5 20
27 8 30
9 3 34
13 5 40
3 2 66
2 2 100
N = number of Dulled crvstals. Nf = number of failed pulling experiments. , melt contained SO->1 at. per cent of As. ,”
crystals have been pulled with deviations of approximately lo”, while (100) and (211) crystals inevitably twinned for deviations of only about 3”. Any computation of twinning probabilities must therefore refer to crystals with accurately oriented seeds, pulled from a melt with a scum-free surface.
Sequence of favourable seed orientations We have compared seventy-eight crystals with different orientations, pulled under similar conditions. For each seed orientation, the fractional number of failed experiments has been determined. The experiments are considered as a failure if no manipulation during pulling succeeded in giving a single crystal. Failures due to experimental errors or misoriented seeds are not included. Table 1 sequence of seed indicates the results. The orientations Y gives (from left to right) the increasing probability, P(r), of twinning for comparable growth conditions. This sequence differs somewhat from the results reported for InSb,@ where [ll l] is further to the right. For (111) crystals, the geometrically possible twin plane perpendicular to the crystal axis has never been observed. In (211) crystals, we observed only twin planes with a normal vector having an angle, 6’ = 62”, with respect to the crystal axis. 0 = 20” has not been observed, 0 = 90” only once. The small number of experiments with (211) crystals does not permit a
The GaAs
boats, the phase boundary is in contact with the boat wall and it has no cylindrical symmetry. The observed random orientation of unseeded single crystals cannot be correlated with Table 1. Experiments with epitaxial growth from the vapour phase have best succeeded with a (211) or { 1 IO} substrate.(14) We believe that the sequence of Table 1 may also be valid for floating-zone experiments, where one has a three-phase system with cylindrical symmetry too. 4. DISCUSSION
Our experiments with GaAs confirmed previous results of the polar character of (111) surfaces in III-V compounds. The habitus of (211) crystals provides, moreover, direct evidence for the growth-rate difference on As and Ga planes. The twinning phenomena are correlated with this growth-rate difference, but their statistical character makes the interpretation more difficult. Two parameters (crystal profile and partial As pressure or melt composition) appear to affect the growth (or nucleation) at the solid-liquidvapour three-phase boundary line, because oblique { 11 l} twin planes normally originate there. To explain both the effects of the crystal orientation and the profile of its surface, we shall assume that the twinning probability increases monotonically with the number nd of oblique GaAs double layers that cut through the surface of the growing crystal. With the spacings of the double
GROWTH
PECULIARITIES
OF
layers equal to s = 4d/3 (d = 2.44 A is nearest-neighbour separation Ga-As), we from Fig. 9(a) that the number nd is given by 3h cos(8-8,) nd = 4d
-c~~ ___ es
3h -._ = zf(B,
GALLIUM
ARSENIDE
SINGLE
CRYSTALS
603
the see
3h
= iPose+
sin 0 tan 0,)
8s).
The trigonometric function f, which, according to our assumption, determines the geometrical twinning probability P(j), is plotted in Fig. 9(b) for the seed orientations that have been investigated. The full curves refer to the crystals in Table 1. The dashed curves refer to the twins that have not been observed (a, b) or have not been included in Table 1 because there are not sufficient experimental results (c). It is evident from the full curves that the lowest geometrical twinning probability is obtained for (111) crystals (curve 1). The twinning probability increases for seed orientations (211), (IOO), (llO), . . . (curves 2, 3, 4). For converging growth (0i < 0), the twinning probability decreases, as f approaches zero; and for diverging growth (86 > 0), twinning becomes rapidly more probable, as f increases rather steeply for increasing &. For Bf > 45”, f is approximately equal for all seed orientations. This interpretation agrees with the experimental results. The lower twinning probability on Ga planes, as compared with geometrically equivalent As planes, can be understood from the different nucleation rates on these planes. The average growth rate of the crystal is imposed by the external pulling rate. Because of the smaller nucleation rate on As planes, the time interval (per formed double layer) left for correct orientation or reorientation of the freshly solidified layer is shorter on As planes. Therefore, twinning on As planes is more probable. The observed different sensitivity of geometrically equivalent Ga or As planes with respect to small changes of the ambient temperature (for crystals pulled from a nearly stoichiometric melt) is more difficult to understand. It seems likely that the twinning probability is strongly affected by small changes of p and x as a result of the variation of deviations from the of Ta. The influence
crystal axis
surface
(a>
@I
FIG. 9. Influence of the crystal profile (0,) and the seed orientation on the twinning probability. (a) Idealized geometry of a portion h of a vertically cut crystal. The plane of the figure contains the crystal axis and an oblique
stoichiometric composition of the melt on the twinning probability P is shown qualitatively in Fig. 10, where P is plotted against the As excess, a = (Am-Ams)/Ame. (Instead of the As excess, one could plot the As pressure or the melt composition.) P has a flat minimum in the interval 0 < Q < 1. It rises slowly for a > 1, and more steeply for a > 2. On the other hand, P rises extremely steeply for slightly negative values of a.
A.
604
and
STEINEMANN
For this part of the curve, the experiments with a variation of the ambient temperature indicate that the slope is about five times smaller for twinning on Ga planes. P
Pmin 1
v Ga
-1
As excess
excess 0
oc 1
2
FIG. 10. Qditative plot of the twinning probability P as a function of the relative As excess, c( = (&z&zo)/&zo. mo is the .4s excess necessary for the vapour phase over the stoichiometric melt. Upper curve: twinning on an As plane; lower curve: twinning on a Ga plane.
Though this effect has been observed for nearly cylindrical crystals, it does not seem to depend critically on small changes on the crystal profile. In Fig. 10, the upper curve is approximately valid for [ill] crystals, the lower curve for [iii] crystals. In our system, the observed interval of AT, = 20°C for formation or suppression of “As’‘-twins has an effect similar to that caused by Am = 0.06 g,. AX = 0.02 or Ax = 0.03 per cent. Such an effect is only noticeable on the extremely steep portion of the curve P(a) near a = 0. It could be correlated with the sudden change from a slight As excess to a Ga excess in the solid phase at ~0 = 0.50.
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