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Crystal growth terraces and surface reconstruction
Journal of Crystal Growth 27 (1974) 313-315 9 North-tlolland Publishhtg Co.
LETTERS TO THE EDITORS CRYSTAL GROWTH TERRACES AND SURFACE RECONSTRUCTION D. L. RODE
Bell Laboratories, Murra)" Hill, New Jersey 07974, U.S.A. Received 26 July 1974 For mostly covalent materials such as GaAs, GaP, and Ge, there may be a relation between the fact that crystal growth terraces appear on only certain low-index orientations and that these orientations also exhibit surface reconstruction.
There exists evidence that crystal growth terraces formed during solution growth on (100) and (I 11) GaAs and GaP depend sensitively on slight misorientations (0 ~ 0.5 ~ from these low-index planes 1-.4). Quite regular terraces (see figs. la and l b ) 5 - 7 ) persist when the solutions are maintained near equilibrium. As the growth rate is decreased in the range 0.1 to 0.5 lam/min, terraces become more clearly defined. The persistence of this phenomenon as equilibrium is approached suggests terraces arise from properties of the liquid-solid interface rather than from constitutional supercooling s) of the solution. However, previous theories 9) of "step bunching" do not predict the extreme sensitivities to slight misorientations which are observed. We and Dawson 3) have observed terrace formation on (111)A, (111)B, and (100) GaAs. On the other hand, the orientations (110)3), (211)A, (211)B, and (511) on GaAs do not exhibit terraces under similar growth conditions (778 ~ The former three orientations are 9known to exhibit surface reconstruction whereas none of the latter four orientations do so1~ Although there is not enough room here to discuss further evidence on GaAs, GaP, and Ge, we would like to tentatively suggest that there may be a relation between the i ability of certain crystallographic planes to exhibit terrace formation and the ability of these planes to undergo surface reconstruction. In the latter phenomenon, the crystalline surface is known to take on a twodimensional crystalline structure with lattice spacings equal to integer (or rational number) multiples of the bulk lattice spacings 1~ 12). Reconstruction can occur 313
only within small amounts of misorientation due to the minimum domain size of reconstructed regions and is typical for certain orientations of mostly covalent materials13). Cabrera and Coleman ~4) have treated the stability problem for orientations near singular surfaces where the surface tension y p o s s ~ e s a cusped minimum. Herring ~5) has derived ttie g~heral form of the cusp under the remarkably general assumptions that (a) the atoms interact pair-wise through forces of finite range, and (b) the surface and bulk lattice spacings are equal. Herring obtained the following result t 5): y = ~ cos O+fl [ sin 0 l,
(1)
where c~ and fl are independent of the misorientation angle 0 measured from the singular orientation. Substitution of eq. (1) into Cabrera and Coleman's criterion TM)for instability shows that singular surfaces characterized by eq (1) should not give rise to terraces. However, when reconstruction occurs the second assumption above t 5) (and possibly the former as well) is not satisfied, and although we have not succeeded in deriving a formulation for 7 in this case, we can consider the effects of long-range forces in another wellknown example merely for the purpose of illustration, i.e., Read and Shockley's grain boundary model including elastic forces16). In this case, a logarithmic cusp results 16): 7 = 7o+]'1 sin 0 In (A/sin 0),
(2)
where 7o, 7~, and A are independent of misorienta-
314
D.L. RODE
p
"**-5
TERRACE HEIGHT PROFILE
0.215/.J.m
analysis similar to that of Cabrera and Coleman'st4). The result is as follows.
GgAS
@=0-076"
_t
sin Or, cog 0m/(i --COS 0m)
=.912~
T
w c) Z t.~
J o t.t~ w >
0
f
I
0.1 o.2 HORIZONTAL DISTANCE (ram)
0.3
(c) Fig. 1. (a) (100) solution grown GaAs. The growth rate is approximately '0.1 lttm/min and the epitaxial layer is approximately 3 lain thick s) (Nomarski contrast). (b) ( I I I ) B solution grown GaP. The growth rate is approximately 0.5 iLtm/min and the epitaxial layer is approximately 201Jm thick s) (Nomarski contrast). (c) Height profile (Talysurf) of the (100) GaAs sample shown in (a). The substrate mlsorientation is !L The angle between the treads and risers is 0 = 0m. (Note the 200:1 verticalto-horizontal magnification ratio).
=
"])O/]~1.
(3)
For the GaAs substrate and epitaxial layer shown in fig. lc s) the substrate is misoriented from (I00) by 0.076 ~ 4- 0.02 ~ and the~ngle between the treads and risers is 0.91 ~ _ 0.2 ~ so that Y~/Yo ~ 0.008 from eq. (3). For the (111)B GaP sampleS), we have obtained Or, = 3.80 4- 0.5 ~ so that Y]/7o ~ 0.033. Of course, the correlations noted above are strictly suggestive and it is our intention only to point toward recent results on surface physics and reconstruction which may have a bearing on solution growth behavior. Considerable Work remains to be done to ascertain the origin of crystal growth terraces. I am grateful to R. L. Barns, H. M. Cox, L. R. Dawson, C. Herring, F. R. Nash, J. C. Phillips, J. E. Rowe, N. E. Schumaker, B. Schwartz, and R. G. Sobers for stimulating discussions, unpublished results, and experimental assistance. References
tion 0. Utilization of eq. (2) in Cabrera and Coleman's criterion 14) predicts an unstable surface which will decompose into a minimum-energy interface consisting of treads and risers, or te.rraces such as those shown in fig. I c. We find the angle 0m between the tread (oriented normal to the singular direction) and the riser by an
I) R. C. Peters, in: Symposium on GaAs (Inst. Phys. and Phys. Soc. London, 1973) p. 55. 2) R. H. Saul and D. D. Rocc&secca, J. Appl. Phys. 44 (1973) 1983. 3) L. R. Dawson, PhD thesis, Univ. Southern California, January 1969; and personal communication. 4) D. L. Van Haren, unpublished work. 5) The GaAs sample shown in fig. ia and lc was grown (at
C R Y S T A L G R O W T H T E R R A C E S AND S U R F A C E R E C O N S T R U C T I O N
6) 7) 8) 9) 10)
778 ~ by R. G. Sobers in a source-seed slider6). The GaP sample shown in fig Ib was grown from a thin melt(I mm) at 965 ~ by C. R. Paola in a slider similar to that described by Bergh et al.5). D. L. Rode, J. Crystal Growth 20 (1973) 13. A . A . Bergh, R. H. Saul and C. R. Paola, J .Electrochem. Soc. 120 (1973) 1558. W. A. Tiller and J. W. Rutter, Can. J. Phys. 34 (1956) 96. J. W. Mullin, Crystallization (Butterworth, London, 1972) p. 151 ft. A. U. MaeRae and G. W. Gobeli, in: Semiconductors and
11) 12) 13) 14)
15) 16)
315
Semimetals, Vol. 2, Eds. R. K. Willardson and A. C. Beer (Academic Press, New York, 1966) p. 115. F. Jona, IBM J. Res. Develop. 9 (1965)375. J. E. Rowe, unpublished work. J. C. Phillips, Surface Sci. 40 (1973) 459, and personal communication. N. Cabrera and R. V. Coleman, in: Tile Art andScience of Growing Crystals, Ed. J. J. Gilman (Wiley, New York, 1963) p. 3. C. Herring, Phys. Rev. 82 (1951) 87. W. T. Read and W. Shockley, Phys. Rev. 78 (1950) 275.
LETTERS TO THE EDITORS CRYSTAL GROWTH TERRACES AND SURFACE RECONSTRUCTION D. L. RODE
Bell Laboratories, Murra)" Hill, New Jersey 07974, U.S.A. Received 26 July 1974 For mostly covalent materials such as GaAs, GaP, and Ge, there may be a relation between the fact that crystal growth terraces appear on only certain low-index orientations and that these orientations also exhibit surface reconstruction.
There exists evidence that crystal growth terraces formed during solution growth on (100) and (I 11) GaAs and GaP depend sensitively on slight misorientations (0 ~ 0.5 ~ from these low-index planes 1-.4). Quite regular terraces (see figs. la and l b ) 5 - 7 ) persist when the solutions are maintained near equilibrium. As the growth rate is decreased in the range 0.1 to 0.5 lam/min, terraces become more clearly defined. The persistence of this phenomenon as equilibrium is approached suggests terraces arise from properties of the liquid-solid interface rather than from constitutional supercooling s) of the solution. However, previous theories 9) of "step bunching" do not predict the extreme sensitivities to slight misorientations which are observed. We and Dawson 3) have observed terrace formation on (111)A, (111)B, and (100) GaAs. On the other hand, the orientations (110)3), (211)A, (211)B, and (511) on GaAs do not exhibit terraces under similar growth conditions (778 ~ The former three orientations are 9known to exhibit surface reconstruction whereas none of the latter four orientations do so1~ Although there is not enough room here to discuss further evidence on GaAs, GaP, and Ge, we would like to tentatively suggest that there may be a relation between the i ability of certain crystallographic planes to exhibit terrace formation and the ability of these planes to undergo surface reconstruction. In the latter phenomenon, the crystalline surface is known to take on a twodimensional crystalline structure with lattice spacings equal to integer (or rational number) multiples of the bulk lattice spacings 1~ 12). Reconstruction can occur 313
only within small amounts of misorientation due to the minimum domain size of reconstructed regions and is typical for certain orientations of mostly covalent materials13). Cabrera and Coleman ~4) have treated the stability problem for orientations near singular surfaces where the surface tension y p o s s ~ e s a cusped minimum. Herring ~5) has derived ttie g~heral form of the cusp under the remarkably general assumptions that (a) the atoms interact pair-wise through forces of finite range, and (b) the surface and bulk lattice spacings are equal. Herring obtained the following result t 5): y = ~ cos O+fl [ sin 0 l,
(1)
where c~ and fl are independent of the misorientation angle 0 measured from the singular orientation. Substitution of eq. (1) into Cabrera and Coleman's criterion TM)for instability shows that singular surfaces characterized by eq (1) should not give rise to terraces. However, when reconstruction occurs the second assumption above t 5) (and possibly the former as well) is not satisfied, and although we have not succeeded in deriving a formulation for 7 in this case, we can consider the effects of long-range forces in another wellknown example merely for the purpose of illustration, i.e., Read and Shockley's grain boundary model including elastic forces16). In this case, a logarithmic cusp results 16): 7 = 7o+]'1 sin 0 In (A/sin 0),
(2)
where 7o, 7~, and A are independent of misorienta-
314
D.L. RODE
p
"**-5
TERRACE HEIGHT PROFILE
0.215/.J.m
analysis similar to that of Cabrera and Coleman'st4). The result is as follows.
GgAS
@=0-076"
_t
sin Or, cog 0m/(i --COS 0m)
=.912~
T
w c) Z t.~
J o t.t~ w >
0
f
I
0.1 o.2 HORIZONTAL DISTANCE (ram)
0.3
(c) Fig. 1. (a) (100) solution grown GaAs. The growth rate is approximately '0.1 lttm/min and the epitaxial layer is approximately 3 lain thick s) (Nomarski contrast). (b) ( I I I ) B solution grown GaP. The growth rate is approximately 0.5 iLtm/min and the epitaxial layer is approximately 201Jm thick s) (Nomarski contrast). (c) Height profile (Talysurf) of the (100) GaAs sample shown in (a). The substrate mlsorientation is !L The angle between the treads and risers is 0 = 0m. (Note the 200:1 verticalto-horizontal magnification ratio).
=
"])O/]~1.
(3)
For the GaAs substrate and epitaxial layer shown in fig. lc s) the substrate is misoriented from (I00) by 0.076 ~ 4- 0.02 ~ and the~ngle between the treads and risers is 0.91 ~ _ 0.2 ~ so that Y~/Yo ~ 0.008 from eq. (3). For the (111)B GaP sampleS), we have obtained Or, = 3.80 4- 0.5 ~ so that Y]/7o ~ 0.033. Of course, the correlations noted above are strictly suggestive and it is our intention only to point toward recent results on surface physics and reconstruction which may have a bearing on solution growth behavior. Considerable Work remains to be done to ascertain the origin of crystal growth terraces. I am grateful to R. L. Barns, H. M. Cox, L. R. Dawson, C. Herring, F. R. Nash, J. C. Phillips, J. E. Rowe, N. E. Schumaker, B. Schwartz, and R. G. Sobers for stimulating discussions, unpublished results, and experimental assistance. References
tion 0. Utilization of eq. (2) in Cabrera and Coleman's criterion 14) predicts an unstable surface which will decompose into a minimum-energy interface consisting of treads and risers, or te.rraces such as those shown in fig. I c. We find the angle 0m between the tread (oriented normal to the singular direction) and the riser by an
I) R. C. Peters, in: Symposium on GaAs (Inst. Phys. and Phys. Soc. London, 1973) p. 55. 2) R. H. Saul and D. D. Rocc&secca, J. Appl. Phys. 44 (1973) 1983. 3) L. R. Dawson, PhD thesis, Univ. Southern California, January 1969; and personal communication. 4) D. L. Van Haren, unpublished work. 5) The GaAs sample shown in fig. ia and lc was grown (at
C R Y S T A L G R O W T H T E R R A C E S AND S U R F A C E R E C O N S T R U C T I O N
6) 7) 8) 9) 10)
778 ~ by R. G. Sobers in a source-seed slider6). The GaP sample shown in fig Ib was grown from a thin melt(I mm) at 965 ~ by C. R. Paola in a slider similar to that described by Bergh et al.5). D. L. Rode, J. Crystal Growth 20 (1973) 13. A . A . Bergh, R. H. Saul and C. R. Paola, J .Electrochem. Soc. 120 (1973) 1558. W. A. Tiller and J. W. Rutter, Can. J. Phys. 34 (1956) 96. J. W. Mullin, Crystallization (Butterworth, London, 1972) p. 151 ft. A. U. MaeRae and G. W. Gobeli, in: Semiconductors and
11) 12) 13) 14)
15) 16)
315
Semimetals, Vol. 2, Eds. R. K. Willardson and A. C. Beer (Academic Press, New York, 1966) p. 115. F. Jona, IBM J. Res. Develop. 9 (1965)375. J. E. Rowe, unpublished work. J. C. Phillips, Surface Sci. 40 (1973) 459, and personal communication. N. Cabrera and R. V. Coleman, in: Tile Art andScience of Growing Crystals, Ed. J. J. Gilman (Wiley, New York, 1963) p. 3. C. Herring, Phys. Rev. 82 (1951) 87. W. T. Read and W. Shockley, Phys. Rev. 78 (1950) 275.