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Vertical gradient freeze growth and characterization of high quality GaSb single crystals
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Journal of Crystal Growth 96 (1989) 888—898 North-Holland, Amsterdam
VERTICAL GRADIENT FREEZE GROWTH AND CHARACTERIZATION OF HIGH QUALITY GaSb SINGLE CRYSTALS J.P. GARANDET, T. DUFFAR and J.J. FAVIER CEA /IRDI/DMECN/DMG/SEM, Laboratoire d’Etude de la Solidification, Centre d’Etudes Nucléaires de Grenoble, 85 X, F-38041 Grenoble Cedex, France Received 2 January 1989; manuscript received in final form 10 March 1989
High quality GaSb single crystals were grown in an original vertical gradient freeze furnace. A double cheminal etching procedure 2 could be obtained. A new is used to reveal dislocation etch pits on both kinds of (111) surfaces. Densities below 100 per cm mechanism for dislocation elimination during growth is proposed and the value of the critical stress for dislocation multiplication is estimated to be 3 daN cm2 with the help of both finite elements calculations and experimental data. Hall mobility and resistivity measurements in a wide temperature range that led to the estimation of an acceptor level at 26 meV are presented; they prove the good electronic behaviour of the crystals.
1. Introduction High quality substrates are required for the growth of (GaIn)(A5P) epilayers that can be used in the field of optical communications. Gallium antimonide (GaSh) is an interesting choice for such substrates since ternary or quaternary solid solutions of 111—V compounds with band gaps corresponding to wavelengths of 1.3 to 1.5 ~tm can be made to closely match its lattice parameter [1]. Various authors [2—4] successfully used the Czochralski method for GaSb growth; however, undoped crystals were found to be of rather poor quality. In GaSb (as in most 111—V compounds [5]) impurity hardening is an efficient way to reduce dislocation formation due to the high thermal stresses inherent in Czochralski growth. Indeed, tellurium doping yielded device quality, dislocation free crystals [2]. As an alternative, we used the vertical gradient freeze technique to produce undoped GaSb single crystals. Gault and coworkers [6] have shown the potentialities of this technique in the case of GaAs, GaP and InP. Due to the relatively weak thermal stresses of the process, dislocation formation is reduced and thus high quality crystals can be obtained,
We shall first review the experimental aspects of this work (section 2). Then, we shall present the results of the numerical simulations performed in order to obtain both the thermal and the stress fields inside the sample (section 3). Section 4 is a reflection on the problems of dislocation formation and/or elimination during growth that takes into account the results of the stress field computation. Finally, in section 5, we shall focus on the electronic properties of our crystals.
2. Experimental 2.1. Apparatus
Our growth experiments were performed in an original furnace developed in our laboratory, which combines the principle of vertical gradient freeze with a dilatometric method (fig. 1). A detailed presentation of the apparatus and its potentialities was given by Potard [7]. On-line measurement of the buoyancy force felt by the sample embedded in a liquid salt mixture enables the user to follow the volume variations during crystallization. The volume of the sample varies with the solidified fraction, thus providing the rate of growth.
0022-0248/89/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
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VGF growth and characterization of high quality GaSb single crystals
Scale
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889
________________
~
ILl ____ j __
Molten salt
Weigh~
Temperature
~[
__ __
___ ~T
/ V
/T~
Liquid
a t
/
u
/\ ~
Recorder
::1~:
Cooling finger
Fig. 1. The experimental apparatus.
In our apparatus, the crucible containing the crystal is linked to the beam of an electronic scale and immersed in an inert liquid, a mixture of LiC1 and KC1 of eutectic composition (melting point: 623 K). It has been shown [3] that incorporation of either alkalis or chlorine in gallium antimonide during growth was weak, and that the electronic properties of the crystal were not affected by the contact with the salt during solidification. The force on the sample is not only due to the transformation volume, but also to the dilatation of the different phases and to the effect of buoyancy on the crucible. The true signal can be extracted only after calibration of the apparatus. The method thus permits a fine control of the solidified fraction and simplifies the seeding problems inherent to the gradient freeze method by following the back melting of the feed material and part of the seed. Moreover, wetting of the crucible by the sample should be prevented by the encapsulating effect of the salt; this should have a favourable influence on crystal quality. Heat is extracted at the cold end of the furnace by means of a water-cooled finger. This provides an efficient sink for the heat flux, which in turn
reduces the thermal stresses due to radial temperature gradients. By moving the finger along the reservoir axis, one can adjust to some extent the axial temperature gradient; for our experiments, we used 2 different growth configurations, hereafter called “high gradient” (circa 15 K cm 1) and “low gradient” (circa 7 K cm 1), The materials used in our experiments were of 6N purity. We obtained the gallium from Johnson-Matthey Chemicals and the antimony from Preussag Pure Metals. GaSb polycrystalline feed was synthesized under vacuum in silica crucibles using a rotating furnace at a temperature of about 1100 K during 15 h. The first seed was a horizontal Bridgman [111] monocrystal obtained from MCP Electronic materials; all other seeds were from our previous crystals. All solidifications were performed in silica glass crucibles. 2.2. Results and procedure In the course of this work, seven GaSb samples of approximately 5 cm length and 1 cm diameter were solidified on 0.5 cm thick seeds, all of them along the [111] crystallographic axis. The growth
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VGF growth and characterization of high quality GaSb single crystals
rate was about 0.3 cm/h. X-ray characterization by means of the Laue and Berg—Barrett methods was used to check that our samples were indeed single crystals. After growth, the ingots were cut in slices perpendicular to the solidification direction and we used double chemical etching to get the dislo-
Fig.2 displays the results obtained on (ill) Ga and (111) Sb surfaces. The pit shapes are different, but they both exhibit the ternary symmetry charactenstic of the [111] crystallographic direction in the zincblende structure. It is generally accepted [4,8,9] that almost any kind of etch based on HNO3, CH1COOH, HF
cation etch pit densities: after mechanical polishing down to the 1 ~tm diamond paste, the samples were left in a HF (40%) 1 volume, Cr03—H20 (1.8 mol/litre) 25 volumes solution for about 20 mm in order to remove the strained layer caused by polishing, We then used a modified CP4 etch (composition: HNO3 (67%) 5 volumes, CH3COOH 3 volumes, HF (40%) 3 volumes, H20 11 volumes) to reveal the dislocations on both (111) Ga and (111) Sb surfaces. Pits of about 20 ~tmwere formed after about 3 minutes on the (111) Ga surfaces, The reaction speed was slower on the (111) Sb surfaces, resulting in pits of about 10 ~tm after a 5 mm etch.
and water will produce dislocation pits on (ill) Ga surfaces. However, it is interesting to note that early workers in the field [9] thought pit formation to be impossible on (111) Sb surfaces. In order to check that the pits we observed on these surfaces were actually caused by dislocations, we performed the following experiment: some crystals were cut normal to the [111] growth direction; for each crystal, one of the halves presented a (Ill) Ga surface, the other a (111) Sb surface. As the dislocation densities observed on these 2 surfaces were always the same, we assumed that the pits on (111) Sb surfaces were indeed related to dislocations. Our double etching procedure is thus a simple and efficient way to observe dislocation pits on both (111) surfaces.
3. Numerical simulations
~]
__________
________
Knowledge of the thermal field inside the solidifying sample provides the crystal grower with the values of such important parameters as: interface position as a function of time; thermal gradients in both liquid and solid phases; interface curvature. Unfortunately, analytical solutions of the heat transfer equations exist only in a few simple cases; for all realistic growth conditions, numerical cornputations have to be performed. Moreover, it is known that in all usual solidification experiments, the thermal gradients generate stresses inside the growing crystal. If these thermal stresses remain weak, they will only cause elastic strain. But beyond a certain limit (critical resolved shear stress or CRSS), a mechanism involving dislocation motion and multiplication is activated —
_____ _____
—
______
—
_________________
_________________________________________
I
_____________________
_________________________________________
_____
______________________________
Fig. 2. SEM characterization of: (a) (Ill) Ga surface; (b) (111) Sb surface. Marker represents 10 ~sm.
As the further use of semiconductor crystals depends on their dislocation content, a study of
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VGF growth and characterization of high quality GaSb single crystals
the stress field inside the solidifying sample is also of interest to the crystal grower. As for heat transfer, numerical simulations are the only way to estimate the stresses in a realistic configuration. An interesting exception to this rule is given by the “zero-stress” solution. If the thermal field is such that: the axial gradient is constant, there are no radial temperature differences, and if the crystal is free to strain in order to accommodate the thermal constraints, then the equations of thermoelasticity have a solution where all the stress components are zero [10]. VGF is in this sense an interesting method, since the heat flow proceeds mainly along the furnace axis. The better the design of the furnace, the closer the “zero-stress” solution will be approached, thus permitting the growth of high quality crystals. It has to be emphasized that the CRSS is too simple a concept to adequately describe the physical truth of things. But from an empirical point of view, it is a convenient tool because it gives an idea of the stress limit beyond which significant dislocation formation is bound to occur,
891
vided us with the temperature gradients and interface shapes as a function of time. The furnace was separated into 4 domains, taking into account the axial symmetry of the apparatus: a “reservoir” domain made of silica glass on which the boundary conditions were defined; —
— —
1043
Reservoir 1033
1023 ____________
1013 Salt
•
3.1. Heat transfer
In the most general case the Navier—Stokes equations (that govern momentum transfer) and the Founer equation (that governs heat transfer) have to be solved simultaneously to get the thermal fields during solidification since convective heat transfer is not negligible But in the case of metals or sermconductors like GaSb that are metallic in the liquid state, a simplification is possible: heat transfer is mainly diffusive. For the liquid salt, this hypothesis is less obvious; however, our numerical results correctly predict the experimental interface positions deduced from dilatometric signals. Besides, indium doping allowing marking of the interface was used to check that calculated and experimental shapes were in good agreement. Thus we believe that only diffusive heat transfer has to be taken into account. We solved the Fourier equation using a finite element method in order to get the thermal fields inside the solidifying sample. This in turn pro-
Crucible
1003
GaSb (Liquid)
G Sb (Solid)
993
983 979 (Melting point)
963 953
943
933 . . . Fig. 3. Numerical calculation for the thermal field at the beginning of solification in the “low gradient” configuration (temperatures are in K).
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VGF growth and characterization of high quality GaSb single crystals
a “salt” domain for the part occupied by the eutectic mixture; a “crucible” domain, also made of silica glass; a “sample” domain corresponding to the volume occupied by the solidifying alloy.
a
—
—
40
—
on t e coo ing inger a ixe temperature on the part of the reservoir parallel to the symmetry axis, a temperature profile measured with 3 thermocouples; on the upper part of the salt, a constant temperature; this rather ill-defined boundary condition was proved to have no significant influence on the thermal field inside the sample, provided it is fixed at a sufficiently large distance from the liquid salt—liquid GaSb interface. A typical output of the program is shown in fig. 3; the physical parameters used for the calculation are given in table 1. The main result of the simulation is that the isotherms in the crystal are remarkably flat; in all cases the radial temperature differences in the sample were smaller than 1 K. This is due to an efficient heat extraction at the finger part of the furnace. The longitudinal temperature profile in the “sample” domain along the furnace axis at the end of solidification is shown in fig. 4a for both growth configurations; the corresponding gradients appear in fig. 4b. In both three figures, dis—
i ~-
_______________
0 ~
—
20
10~jflC~
20
(mm)
30
~
b
—
Table i Physical parameters used in the thermal field calculations Thermal conductivities GaSb liquid state GaSb solid state Liquid salt Silica glass H~~5state
10.24 6.43 1 3.3 2 X106
GaSb solid state 1.7 x106 Liquid salt 2 >< l0~ Silica glass 2.5 x106 Latent heat of solidification of GaSb H=1.9X10°Jm3
20
C ~
-
~
20
25
30
35
Distance (mm) Fig. 4. Calculated thermal fields (a) and gradients (h) along the furnace axis at the end of solidification in the “low gradient” (curve I) and the “high gradient” (curve 2) configurations.
tances are measured relative to the bottom end of the seed. In the “high gradient” case, the variation is from 23 K cm at the cold end to 4 K cm at the top of the sample, whereas in the “low gradient” configuration it is only from 12 K cm1 to 3 K cm~. The effect of temperature gradients on stress distribution can now be closely examined.
W m~ K1 W m1 K1 W m11 K~ Wm K J m3 K~1
3.2, Thermal stresses
J m3 K1 J m3 K~ Jm3 K1
thermal calculations in the framework of isotropic thermoelasticity was developed in our laboratory. In order to estimate the CRSS of GaSh close to its melting point we calculated the stresses in
_________________________________________
Up to the CRSS, elasticity theory can be used to quantify the stress field inside the crystal. A finite element program that used the results of the
.
.
both our growth configurations (“low gradient
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VGFgrowth and characterization of high quality GaSbsingle crystals
a
and “high gradient”) to compare them with the experimental dislocation densities. As for the heat transfer problem, the elements were triangular in shape and the approximation functions were linear. Since we were just interested in the stress distribution inside the “sample” domain of the thermal calculation, we solved the equations of thermoelasticity [11] only in that domain. The physical parameters used in the simulations are presented in table 2. The program output yields the value of all the components of the stress field, but from now on we will only deal with von Mises equivalent stresses defined as:
893
b ~“~T~’
2 1.5
1 2 .75
,~
1
2
1.5
2
3
2 S
0vM
=
01—02) 2 +(02~03)
—
+
(~ ~ —
}i/2,
2
(1)
where o~,02 and 03 are the principal stresses, i.e., the eigenvalues of the stress tensor. Results of thermoelastic calculations can be expressed in terms of von Mises stresses [16]. A study of the stress field as a function of time proved that the maximum stresses occur right after the end of solidification. Shown in figs. 5a and 5b are the von Mises stress distributions for crystals grown in the “low gradient” and “high gradient” configurations, respectively, corresponding to the thermal fields of fig. 4. Note that figs. 5a and 5b have been radially expanded for publication. We assumed that the stresses associated with the cooling of the crystal from melting down to room temperature were always below the CRSS. However, Schvezov and co-workers showed that high stresses are observed in LEC grown GaAs after separation from the melt [121. But in our experiments, even though the cooling procedure was always the same, some of the crystals were
Table 2 Physical parameters used in the stress field calculations (all values are for GaSb near its melting point) Thermal expansion coefficient a~7.3x106 K3 Young’s modulus 8.7 x ~ daN cm Poisson’s ratio v 0.3
S
_____________________________________________
Fig. 5. Von Mises stress fields as calculated at the end of solidification in both growth configurations (values given in daN cm2): (a) “low gradient” configuration; (b) “high gradient” configuration.
dislocation-free while some others were rather dislocated. It is thus reasonable to suppose that the maximum stresses take place during growth; we will now use our numerical results to get an estimate of the CRSS of GaSb near its melting point.
4. Dislocations in grown crystals 4.1. “Low gradient” configuration
In a given crystal, we found that the etch pit densities decreased with growth distance measured relative to the seed (figs. 6a and 6b). Such a behaviour had already been reported in the litterature and various explanations had been proposed; according to Benz and Muller [13], dislocation pairs of opposite burgers vectors can annihilate one another; according to Yip and Wilcox [14], dislocations are eliminated by growing out of the crystal because they propagate normal to a solidification interface that is convex towards the liquid. However, none of these mechanisms can explain our results: annihilation works only when the dislocation —
—
—
densities are high (over iO~ per cm2 [15]), well above those observed in our crystals;
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VGF growth and characterization of high quality GaSb single crystals
our solidification interfaces are almost flat and even slightly concave towards the liquid when growth begins; thus the Yip and Wilcox mechanism does not apply. To explain our results, we supposed that the dislocations remained in the (111) dense planes of the zincblende structure, even up to temperatures close to the melting point. Inclined with respect to the [111] growth axis, they eliminate on the lateral surfaces during solidification. If this was the sole operating mechanism, we should get crystals absolutely free from dislocations. To take into account the remaining defects, we were led to consider that even below the CRSS threshold (there is obviously no significant increase in dislocation density), residual glide can hamper elimination by forcing cross-slip of dislocations about to leave the crystals. Furthermore, —
z’clz
/ 0 Z
d
_______
r ~ A Fig. 7. Dislocation elimination on lateral surfaces during growth.
direct creation by a Frank—Read mechanism cannot be ruled out, though it is certainly limited. Let us consider (fig. 7) an element of crystal of height dz. Let 6 be the angle between the (111) growth plane and the others (111) planes (6 70.53°). The dislocations in the ring of width dr dz cot 0 grow out when the interface moves from z to z + dz, unless they cross-slip and turn back to the inside of the crystal. The number of dislocations leaving between z and z + dz is =
=
a
4000
3000
N
5
=
(y1
—
y2)N(z) dz,
where N(z) is the number of dislocations at the
2000
•\
height z. Supposing the etch pits to be randomly distributed over the surface of the slice (an assumption we be valid for densities over 2), found y~ dz to simply represents the ratio of 500 per cm the surface of the ring to the total surface of the discus of radius R; y 2, on the other hand, is an empirical parameter depending on the lineal density of defects that can cause cross-slip. can be easily calculated:
ii
00
~
~
~
55
Distance
(mm)
b
2000
2irR 2dr or y~= 2 cot R 6 (2) y1dz= ‘,rR Since in our experiments R = 0.5 cm, we find
1500
N
1000
y ~
500
c
—~~-——--~-—-—----~———-
0
5
10
15
Distance
20
25
30
35
(mm)
Fig. 6. Vanation of dislocation density versus distance to the bottom end of the crystal for 2 samples grown in the “low gradient” configuration.
1=1.4cm~. Let us consider that residual glide is at the direct origin of N2 near dislocations; we will assume N2 = y1N(z) dz, where y~is another empincal parameter depending on the lineal density of defects that can cause pinning and multiplication of existing dislocations all through solidification. .
.
.
.
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VGF growth and characterization of high quality GaSb single crystals
A balance on the number of dislocations leads
895
7000
to
6000
dN= —N
5+N2=(—y5+12+y3)N(z)dz.
(3) UI 4000
Assuming 12 and y~to be independent of z (11 is clearly independent of z since the dislocation repartition is uniform on a slice), the above equation can be easily integrated: N(z) =N(0) exp(—yz),
~‘ UI
a)
3000
mooc 1000
(4)
00
5
40
15
Distance
20
25
30
3S
(mis)
where ‘I’ = Y~+ 12 + 13 and N(0) is the dislocation density in the seed. Measurements done before and after crystallization proved that this value did not change during growth. The first experimental points in fig. 6 are not exactly at the bottom end of the samples, due to some losses in the polishing procedure. Linear regression on the experimental data was used to find the “best fit” value of ‘y. Curves obtained from eq. are represented in fig. many 6. It can be noticed that(4)even though we made simplifying approximations, the empirical equation fits well the experimental data, Another interesting point is that the value for ~ obtained with the best fit procedure (circa 1.1 cmt) is close to the value of li (1.4 cm~). This indicates that the elimination mechanism is by far the most important, even though glide phenomena have also to be taken into account, Finally, we did not consider differential dilatation stresses caused by the crystal—solid salt adherence when the sample is brought back to room temperature. This mechanism could also be at the origin of a few dislocations. In fact, we always
Fig. 8. Variation of dislocation density versus distance to the bottom end of the crystal for a sample grown in the “high gradient” configuration.
found a thin layer of saltwetting betweenproperties crystal and crucible, probably duesolid to the of the viscous salt on both the GaSb and the crucible. However, if there were no encapsulation, the contacts between crystals and crucible could have a dramatic effect on dislocation formation since the differential expansion mechanism would be activated from the melting point down to room temperature. Thus the liquid salt is thought to have a positive influence on crystal quality, even though some stresses are probably generated when it solidifies.
daNfrom cm2. It can3 ± be0.5 seen fig. 5a that this value is never reached in crystals grown in the “low gradient” configuration, in good agreement with the decreasing dislocation densities. So even if the axial gradient is far from being constant (see fig. 4b, curve 1), one can succeed in growing high quality crystals provided the CRSS is not exceeded. Etch pit densities are not measured in the last fifth of the samples because the end of solidification is always perturbed (loss of the cylindrical
—
4.2. “High gradient” configuration Fig. 8 shows the experimental etch pit densities for a crystal grown with 2.a Itseed that had appears that about there 1000 dislocations per cm was an increase of the etch pit density in the first third of the sample; it is believed that in this part of the crystal, thermal stresses exceeded the CRSS limit and so the glide mechanism was activated. We thus explain the significant generation of dislocations in the seed. On the other hand, in the last two thirds of the crystal, the elimination mechanism presented in section 4.1 prevailed and a decrease in dislocation density is observed. If we consider that the glide threshold was exceeded only in the first third of the crystal, comparison with fig. Sb provides an estimate of the CRSS of GaSb near its melting point: 0CR5S
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VGF growth and characterization of high quality GaSb single crystals
shape, destabilization due to defects in stoichiometry, etc.). This explains that the effect of the high stresses in the upper part of the crystal was not experimentally detected. Unfortunately, there is nothing in the literature on the CRSS of GaSb close to its melting point. So it was tempting to compare our result with published values for other Ill—V compounds and particularly with gallium arsenide that has been thoroughly studied in the past few years. But as pointed out by Schvezov and coworkers [16], the experimental results for undoped GaAs at its melting point differ by an order of magnitude: Mil’vidskii and Bochkarev [17] found a value of 0.7 daN cm2, whereas Jordan [18] estimated the CRSS to be 7.8 daN cm2. As for the indium compounds, InP and InSb are reported to have a CRSS of about 2.4 daN cm2 [5] and 2.5 daN cm2 [17], respectively, Even if all these results have to be taken cautiously, it is reassuring that our value of 3 daN cm2 fits well with the other Ill—V compounds. However, ours is only a rough estimate and further work would be needed to precisely determine the CRSS of GaSb near its melting point,
5. Electronic properties The Van ~er Pauw method was used to measure the resistivity and the Hall mobility of our crystals. Indium evaporation under vacuum was found to yield satisfactory ohmic contacts down to about 40 K. Shown in fig. 9 are typical results for carrier concentration per cubic centimeter as a function of temperature. All the samples were p type, with room temperature concentrations in the range of iO~~ to iO~ holes per cubic centimeter. The structure of shallow acceptors in GaSb is still a puzzling problem. Various authors [19,20] tried to fit their experimental data with a two-level model and found for the activation energies:
17.5
17
—
•.•
16.5 .—
S.
15 5
~
10
15
20
/
I Fig. 9. Temperature dependence of hole concentration in a typical crystal. 1000
Another model [20] taking into account one donor and one acceptor level yields for the latter: E = 36 5 meV A
It is well known that the acceptor behaviour of GaSb cannot be attributed to impurities. However, the lattice antistructure defect that associates a gallium vacancy and a gallium atom on an antimony site (VGa, GaSh) can explain the relatively high p-type conductivity of crystals grown in various laboratories [21]. If this defect is considered alone in a one-acceptor model, it is easy to get its activation energy from the data of hole concentration as a function of temperature by using the following relationship, valid at low ternperatures: p=p 0exp~—E~/2kT).
~5)
E1 =24meV, E2=37meV
[19];
We checked on our experimental results the linearity of log( p) as a function of 1/T and the regression yielded E = 26 V A me in fair agreement with the values quoted above. The variation of Hall mobility as a function of temperature for a typical crystal is presented in fig. 10. For temperatures between 180 and 300 K, it is possible to fit the curve with a simple power law:
E1 =11meV, E2=32meV
[20].
~s=~s0T”.
(6)
J.P. Garandet ci a!. 1500
•
.
/
VGF growth and characterization of high quality GaSb single crystals
3, in good agreement estimated to bevalues 3 daN with published for cm other Ill—V compounds.
•
1400 1200
Hall mobility and resistivity measurements showed that the crystals were p type, with hole concentrations at 300 K ranging from 1017 to lO~~
S.
.
1000 800
•‘
600
_________________________________ 100
897
140
180
220 260 300340
Temperature
(K) Fig. 10. Temperature dependence of hole mobility in a typical crystal.
The value of n obtained from linear regression is —0.97, again in fair agreement with the results of the litterature n = 0.87 [19], n = —0.82 [20]. Unfortunately, in the temperature range going from 180 to 300 K, a theoretical interpretation of the results is very difficult: it is of course necessary to take into account carrier diffusion by lattice scattering, but the effect of crystalline defects, whether ionized or not, is not negligible. The classical T 3~”2 law was observed only above 300 K [19].
6. Conclusion A dilatometric method that gives the interface position of a growing crystal through liquid salt encapsulation was used in a vertical gradient freeze furnace to produce undoped GaSb single crystals. An original double etching procedure was developed to reveal dislocation etch pits on both (111) Ga and (111) Sb surfaces. It was shown that zero-density crystals could be grown with this apparatus. For the “low thermal gradient” configuration, the number of dislocations decreases along the crystal. A new mechanism for dislocation elimination during growth is proposed to explain this phenomenon. The quantitative agreement with the experimental results is very good. On the other hand, for the “high thermal gradient” configuration, a significant number of dislocations were generated. Assuming that this was due to thermal stresses exceeding the CRSS, the latter could be
cm3. The temperature dependence of both Hall mobility and carrier concentration of our crystals was found to be similar to those of other crystals [19,20]. Assuming a simple one-acceptor model, its activation energy was estimated at 26 meV. We thus prove that our original apparatus yields high quality crystals from both structural and electronic points of views. Liquid salt encapsulation simplifies the seeding procedure and limits dislocation generation due to crystal—crucible differential contraction upon cooling to room ternperature, but has no influence on the electronic behaviour of the samples. We believe that an efficient design of the furnace can reduce the stresses during VGF growth by approaching the conditions of the “zero-stress” solution (no radial temperature differences, constant axial thermal gradient). In this sense, we think that the VGF method can yield “device quality” Ill—V crystals without the impurity lattice hardening trick necessary in Czochralski growth. In the future, we plan in our laboratory to apply this technique to the growth of larger, application-oriented single crystals.
Acknowledgements It is a pleasure to thank Professor F. Louchet for many useful discussions on the subject. Help of Dr. A. Rouzaud for the thermoelasticity program and of Mr. P. Dusserre for the experimental work is also gratefully acknowledged. Jean-Paul Garandet would like to thank the CNES and Matra Espace for their financial support. The present work was conducted within the framework of the GRAMME agreement between CNES and CEA.
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13] 141 [5] [6]
171 [8] [9] (10]
lii] [12]
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VGF growth and characterization of high quality GaSb single crystals
S. Miyazawa, S. Kondo and N. Naganuma, J. Crystal Growth 49 (1980) 670. S. Kondo and S. Miyazawa, J. Crystal Growth 56 (1982) 39. AS. Jordan, AR. Von Neida and R. Caruso, J. Crystal Growth 76 (1986) 243. W.A. Gault, E.M. Monberg and J.E. Clemans, J. Crystal Growth 74 (1986) 491. C. Potard, J. Crystal Growth 54 (1981) 558. B. Tuck, J. Mater. Sci. 10 (1975) 321. H.C. Gatos and MS. Lavine, J. Electrochem. Soc. 107 (1960) 427. J.P. Garandet, J. Crystal Growth 96 (1989) 680. S. Timoshenko and S. Goodier, Théorie de l’Elasticité (Librairie Polytechnique Béranger, 1970). CE. Schvezov, IV. Samarasekera and F. Weinberg, J. Crystal Growth 92 (1988) 489.
1131 K.W. Benz and G. Muller, J. Crystal Growth 46 (1979) 35. 1141 V.F.S. Yip and W.R. Wilcox. J. Crystal Growth 36 (1976) 29. [15] C.F. Boucher, Jr., 0. Ueda, T. Bryskiewica, J. Lagowski and H.C. Gatos, J. AppI. Phys. 61 (1987) 359. [16) CE. Schvezov, l.V. Samarasekera and F. Weinberg, J. Crystal Growth 84 (1987) 219. [17] MG. Mil’vidskii and E.P. Boch.karev, J. Crystal Growth 44 (1978) 61. 118] AS. Jordan. J. Crystal Growth 49 (1980) 631. [19] H.N. Leifer and W.C. Dunlap, Jr., Phys. Rev. 95 (1954) 51. (20) D. Effer and P.J. Etter, J. Phys. Chem. Solids 25 (1964) 451. [21] J. Allégre, M. Avérous and G. Bougnot. Crystal Lattice Defects 1 (1970) 343.
Journal of Crystal Growth 96 (1989) 888—898 North-Holland, Amsterdam
VERTICAL GRADIENT FREEZE GROWTH AND CHARACTERIZATION OF HIGH QUALITY GaSb SINGLE CRYSTALS J.P. GARANDET, T. DUFFAR and J.J. FAVIER CEA /IRDI/DMECN/DMG/SEM, Laboratoire d’Etude de la Solidification, Centre d’Etudes Nucléaires de Grenoble, 85 X, F-38041 Grenoble Cedex, France Received 2 January 1989; manuscript received in final form 10 March 1989
High quality GaSb single crystals were grown in an original vertical gradient freeze furnace. A double cheminal etching procedure 2 could be obtained. A new is used to reveal dislocation etch pits on both kinds of (111) surfaces. Densities below 100 per cm mechanism for dislocation elimination during growth is proposed and the value of the critical stress for dislocation multiplication is estimated to be 3 daN cm2 with the help of both finite elements calculations and experimental data. Hall mobility and resistivity measurements in a wide temperature range that led to the estimation of an acceptor level at 26 meV are presented; they prove the good electronic behaviour of the crystals.
1. Introduction High quality substrates are required for the growth of (GaIn)(A5P) epilayers that can be used in the field of optical communications. Gallium antimonide (GaSh) is an interesting choice for such substrates since ternary or quaternary solid solutions of 111—V compounds with band gaps corresponding to wavelengths of 1.3 to 1.5 ~tm can be made to closely match its lattice parameter [1]. Various authors [2—4] successfully used the Czochralski method for GaSb growth; however, undoped crystals were found to be of rather poor quality. In GaSb (as in most 111—V compounds [5]) impurity hardening is an efficient way to reduce dislocation formation due to the high thermal stresses inherent in Czochralski growth. Indeed, tellurium doping yielded device quality, dislocation free crystals [2]. As an alternative, we used the vertical gradient freeze technique to produce undoped GaSb single crystals. Gault and coworkers [6] have shown the potentialities of this technique in the case of GaAs, GaP and InP. Due to the relatively weak thermal stresses of the process, dislocation formation is reduced and thus high quality crystals can be obtained,
We shall first review the experimental aspects of this work (section 2). Then, we shall present the results of the numerical simulations performed in order to obtain both the thermal and the stress fields inside the sample (section 3). Section 4 is a reflection on the problems of dislocation formation and/or elimination during growth that takes into account the results of the stress field computation. Finally, in section 5, we shall focus on the electronic properties of our crystals.
2. Experimental 2.1. Apparatus
Our growth experiments were performed in an original furnace developed in our laboratory, which combines the principle of vertical gradient freeze with a dilatometric method (fig. 1). A detailed presentation of the apparatus and its potentialities was given by Potard [7]. On-line measurement of the buoyancy force felt by the sample embedded in a liquid salt mixture enables the user to follow the volume variations during crystallization. The volume of the sample varies with the solidified fraction, thus providing the rate of growth.
0022-0248/89/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
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VGF growth and characterization of high quality GaSb single crystals
Scale
_________________
889
________________
~
ILl ____ j __
Molten salt
Weigh~
Temperature
~[
__ __
___ ~T
/ V
/T~
Liquid
a t
/
u
/\ ~
Recorder
::1~:
Cooling finger
Fig. 1. The experimental apparatus.
In our apparatus, the crucible containing the crystal is linked to the beam of an electronic scale and immersed in an inert liquid, a mixture of LiC1 and KC1 of eutectic composition (melting point: 623 K). It has been shown [3] that incorporation of either alkalis or chlorine in gallium antimonide during growth was weak, and that the electronic properties of the crystal were not affected by the contact with the salt during solidification. The force on the sample is not only due to the transformation volume, but also to the dilatation of the different phases and to the effect of buoyancy on the crucible. The true signal can be extracted only after calibration of the apparatus. The method thus permits a fine control of the solidified fraction and simplifies the seeding problems inherent to the gradient freeze method by following the back melting of the feed material and part of the seed. Moreover, wetting of the crucible by the sample should be prevented by the encapsulating effect of the salt; this should have a favourable influence on crystal quality. Heat is extracted at the cold end of the furnace by means of a water-cooled finger. This provides an efficient sink for the heat flux, which in turn
reduces the thermal stresses due to radial temperature gradients. By moving the finger along the reservoir axis, one can adjust to some extent the axial temperature gradient; for our experiments, we used 2 different growth configurations, hereafter called “high gradient” (circa 15 K cm 1) and “low gradient” (circa 7 K cm 1), The materials used in our experiments were of 6N purity. We obtained the gallium from Johnson-Matthey Chemicals and the antimony from Preussag Pure Metals. GaSb polycrystalline feed was synthesized under vacuum in silica crucibles using a rotating furnace at a temperature of about 1100 K during 15 h. The first seed was a horizontal Bridgman [111] monocrystal obtained from MCP Electronic materials; all other seeds were from our previous crystals. All solidifications were performed in silica glass crucibles. 2.2. Results and procedure In the course of this work, seven GaSb samples of approximately 5 cm length and 1 cm diameter were solidified on 0.5 cm thick seeds, all of them along the [111] crystallographic axis. The growth
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VGF growth and characterization of high quality GaSb single crystals
rate was about 0.3 cm/h. X-ray characterization by means of the Laue and Berg—Barrett methods was used to check that our samples were indeed single crystals. After growth, the ingots were cut in slices perpendicular to the solidification direction and we used double chemical etching to get the dislo-
Fig.2 displays the results obtained on (ill) Ga and (111) Sb surfaces. The pit shapes are different, but they both exhibit the ternary symmetry charactenstic of the [111] crystallographic direction in the zincblende structure. It is generally accepted [4,8,9] that almost any kind of etch based on HNO3, CH1COOH, HF
cation etch pit densities: after mechanical polishing down to the 1 ~tm diamond paste, the samples were left in a HF (40%) 1 volume, Cr03—H20 (1.8 mol/litre) 25 volumes solution for about 20 mm in order to remove the strained layer caused by polishing, We then used a modified CP4 etch (composition: HNO3 (67%) 5 volumes, CH3COOH 3 volumes, HF (40%) 3 volumes, H20 11 volumes) to reveal the dislocations on both (111) Ga and (111) Sb surfaces. Pits of about 20 ~tmwere formed after about 3 minutes on the (111) Ga surfaces, The reaction speed was slower on the (111) Sb surfaces, resulting in pits of about 10 ~tm after a 5 mm etch.
and water will produce dislocation pits on (ill) Ga surfaces. However, it is interesting to note that early workers in the field [9] thought pit formation to be impossible on (111) Sb surfaces. In order to check that the pits we observed on these surfaces were actually caused by dislocations, we performed the following experiment: some crystals were cut normal to the [111] growth direction; for each crystal, one of the halves presented a (Ill) Ga surface, the other a (111) Sb surface. As the dislocation densities observed on these 2 surfaces were always the same, we assumed that the pits on (111) Sb surfaces were indeed related to dislocations. Our double etching procedure is thus a simple and efficient way to observe dislocation pits on both (111) surfaces.
3. Numerical simulations
~]
__________
________
Knowledge of the thermal field inside the solidifying sample provides the crystal grower with the values of such important parameters as: interface position as a function of time; thermal gradients in both liquid and solid phases; interface curvature. Unfortunately, analytical solutions of the heat transfer equations exist only in a few simple cases; for all realistic growth conditions, numerical cornputations have to be performed. Moreover, it is known that in all usual solidification experiments, the thermal gradients generate stresses inside the growing crystal. If these thermal stresses remain weak, they will only cause elastic strain. But beyond a certain limit (critical resolved shear stress or CRSS), a mechanism involving dislocation motion and multiplication is activated —
_____ _____
—
______
—
_________________
_________________________________________
I
_____________________
_________________________________________
_____
______________________________
Fig. 2. SEM characterization of: (a) (Ill) Ga surface; (b) (111) Sb surface. Marker represents 10 ~sm.
As the further use of semiconductor crystals depends on their dislocation content, a study of
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VGF growth and characterization of high quality GaSb single crystals
the stress field inside the solidifying sample is also of interest to the crystal grower. As for heat transfer, numerical simulations are the only way to estimate the stresses in a realistic configuration. An interesting exception to this rule is given by the “zero-stress” solution. If the thermal field is such that: the axial gradient is constant, there are no radial temperature differences, and if the crystal is free to strain in order to accommodate the thermal constraints, then the equations of thermoelasticity have a solution where all the stress components are zero [10]. VGF is in this sense an interesting method, since the heat flow proceeds mainly along the furnace axis. The better the design of the furnace, the closer the “zero-stress” solution will be approached, thus permitting the growth of high quality crystals. It has to be emphasized that the CRSS is too simple a concept to adequately describe the physical truth of things. But from an empirical point of view, it is a convenient tool because it gives an idea of the stress limit beyond which significant dislocation formation is bound to occur,
891
vided us with the temperature gradients and interface shapes as a function of time. The furnace was separated into 4 domains, taking into account the axial symmetry of the apparatus: a “reservoir” domain made of silica glass on which the boundary conditions were defined; —
— —
1043
Reservoir 1033
1023 ____________
1013 Salt
•
3.1. Heat transfer
In the most general case the Navier—Stokes equations (that govern momentum transfer) and the Founer equation (that governs heat transfer) have to be solved simultaneously to get the thermal fields during solidification since convective heat transfer is not negligible But in the case of metals or sermconductors like GaSb that are metallic in the liquid state, a simplification is possible: heat transfer is mainly diffusive. For the liquid salt, this hypothesis is less obvious; however, our numerical results correctly predict the experimental interface positions deduced from dilatometric signals. Besides, indium doping allowing marking of the interface was used to check that calculated and experimental shapes were in good agreement. Thus we believe that only diffusive heat transfer has to be taken into account. We solved the Fourier equation using a finite element method in order to get the thermal fields inside the solidifying sample. This in turn pro-
Crucible
1003
GaSb (Liquid)
G Sb (Solid)
993
983 979 (Melting point)
963 953
943
933 . . . Fig. 3. Numerical calculation for the thermal field at the beginning of solification in the “low gradient” configuration (temperatures are in K).
892
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VGF growth and characterization of high quality GaSb single crystals
a “salt” domain for the part occupied by the eutectic mixture; a “crucible” domain, also made of silica glass; a “sample” domain corresponding to the volume occupied by the solidifying alloy.
a
—
—
40
—
on t e coo ing inger a ixe temperature on the part of the reservoir parallel to the symmetry axis, a temperature profile measured with 3 thermocouples; on the upper part of the salt, a constant temperature; this rather ill-defined boundary condition was proved to have no significant influence on the thermal field inside the sample, provided it is fixed at a sufficiently large distance from the liquid salt—liquid GaSb interface. A typical output of the program is shown in fig. 3; the physical parameters used for the calculation are given in table 1. The main result of the simulation is that the isotherms in the crystal are remarkably flat; in all cases the radial temperature differences in the sample were smaller than 1 K. This is due to an efficient heat extraction at the finger part of the furnace. The longitudinal temperature profile in the “sample” domain along the furnace axis at the end of solidification is shown in fig. 4a for both growth configurations; the corresponding gradients appear in fig. 4b. In both three figures, dis—
i ~-
_______________
0 ~
—
20
10~jflC~
20
(mm)
30
~
b
—
Table i Physical parameters used in the thermal field calculations Thermal conductivities GaSb liquid state GaSb solid state Liquid salt Silica glass H~~5state
10.24 6.43 1 3.3 2 X106
GaSb solid state 1.7 x106 Liquid salt 2 >< l0~ Silica glass 2.5 x106 Latent heat of solidification of GaSb H=1.9X10°Jm3
20
C ~
-
~
20
25
30
35
Distance (mm) Fig. 4. Calculated thermal fields (a) and gradients (h) along the furnace axis at the end of solidification in the “low gradient” (curve I) and the “high gradient” (curve 2) configurations.
tances are measured relative to the bottom end of the seed. In the “high gradient” case, the variation is from 23 K cm at the cold end to 4 K cm at the top of the sample, whereas in the “low gradient” configuration it is only from 12 K cm1 to 3 K cm~. The effect of temperature gradients on stress distribution can now be closely examined.
W m~ K1 W m1 K1 W m11 K~ Wm K J m3 K~1
3.2, Thermal stresses
J m3 K1 J m3 K~ Jm3 K1
thermal calculations in the framework of isotropic thermoelasticity was developed in our laboratory. In order to estimate the CRSS of GaSh close to its melting point we calculated the stresses in
_________________________________________
Up to the CRSS, elasticity theory can be used to quantify the stress field inside the crystal. A finite element program that used the results of the
.
.
both our growth configurations (“low gradient
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VGFgrowth and characterization of high quality GaSbsingle crystals
a
and “high gradient”) to compare them with the experimental dislocation densities. As for the heat transfer problem, the elements were triangular in shape and the approximation functions were linear. Since we were just interested in the stress distribution inside the “sample” domain of the thermal calculation, we solved the equations of thermoelasticity [11] only in that domain. The physical parameters used in the simulations are presented in table 2. The program output yields the value of all the components of the stress field, but from now on we will only deal with von Mises equivalent stresses defined as:
893
b ~“~T~’
2 1.5
1 2 .75
,~
1
2
1.5
2
3
2 S
0vM
=
01—02) 2 +(02~03)
—
+
(~ ~ —
}i/2,
2
(1)
where o~,02 and 03 are the principal stresses, i.e., the eigenvalues of the stress tensor. Results of thermoelastic calculations can be expressed in terms of von Mises stresses [16]. A study of the stress field as a function of time proved that the maximum stresses occur right after the end of solidification. Shown in figs. 5a and 5b are the von Mises stress distributions for crystals grown in the “low gradient” and “high gradient” configurations, respectively, corresponding to the thermal fields of fig. 4. Note that figs. 5a and 5b have been radially expanded for publication. We assumed that the stresses associated with the cooling of the crystal from melting down to room temperature were always below the CRSS. However, Schvezov and co-workers showed that high stresses are observed in LEC grown GaAs after separation from the melt [121. But in our experiments, even though the cooling procedure was always the same, some of the crystals were
Table 2 Physical parameters used in the stress field calculations (all values are for GaSb near its melting point) Thermal expansion coefficient a~7.3x106 K3 Young’s modulus 8.7 x ~ daN cm Poisson’s ratio v 0.3
S
_____________________________________________
Fig. 5. Von Mises stress fields as calculated at the end of solidification in both growth configurations (values given in daN cm2): (a) “low gradient” configuration; (b) “high gradient” configuration.
dislocation-free while some others were rather dislocated. It is thus reasonable to suppose that the maximum stresses take place during growth; we will now use our numerical results to get an estimate of the CRSS of GaSb near its melting point.
4. Dislocations in grown crystals 4.1. “Low gradient” configuration
In a given crystal, we found that the etch pit densities decreased with growth distance measured relative to the seed (figs. 6a and 6b). Such a behaviour had already been reported in the litterature and various explanations had been proposed; according to Benz and Muller [13], dislocation pairs of opposite burgers vectors can annihilate one another; according to Yip and Wilcox [14], dislocations are eliminated by growing out of the crystal because they propagate normal to a solidification interface that is convex towards the liquid. However, none of these mechanisms can explain our results: annihilation works only when the dislocation —
—
—
densities are high (over iO~ per cm2 [15]), well above those observed in our crystals;
894
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VGF growth and characterization of high quality GaSb single crystals
our solidification interfaces are almost flat and even slightly concave towards the liquid when growth begins; thus the Yip and Wilcox mechanism does not apply. To explain our results, we supposed that the dislocations remained in the (111) dense planes of the zincblende structure, even up to temperatures close to the melting point. Inclined with respect to the [111] growth axis, they eliminate on the lateral surfaces during solidification. If this was the sole operating mechanism, we should get crystals absolutely free from dislocations. To take into account the remaining defects, we were led to consider that even below the CRSS threshold (there is obviously no significant increase in dislocation density), residual glide can hamper elimination by forcing cross-slip of dislocations about to leave the crystals. Furthermore, —
z’clz
/ 0 Z
d
_______
r ~ A Fig. 7. Dislocation elimination on lateral surfaces during growth.
direct creation by a Frank—Read mechanism cannot be ruled out, though it is certainly limited. Let us consider (fig. 7) an element of crystal of height dz. Let 6 be the angle between the (111) growth plane and the others (111) planes (6 70.53°). The dislocations in the ring of width dr dz cot 0 grow out when the interface moves from z to z + dz, unless they cross-slip and turn back to the inside of the crystal. The number of dislocations leaving between z and z + dz is =
=
a
4000
3000
N
5
=
(y1
—
y2)N(z) dz,
where N(z) is the number of dislocations at the
2000
•\
height z. Supposing the etch pits to be randomly distributed over the surface of the slice (an assumption we be valid for densities over 2), found y~ dz to simply represents the ratio of 500 per cm the surface of the ring to the total surface of the discus of radius R; y 2, on the other hand, is an empirical parameter depending on the lineal density of defects that can cause cross-slip. can be easily calculated:
ii
00
~
~
~
55
Distance
(mm)
b
2000
2irR 2dr or y~= 2 cot R 6 (2) y1dz= ‘,rR Since in our experiments R = 0.5 cm, we find
1500
N
1000
y ~
500
c
—~~-——--~-—-—----~———-
0
5
10
15
Distance
20
25
30
35
(mm)
Fig. 6. Vanation of dislocation density versus distance to the bottom end of the crystal for 2 samples grown in the “low gradient” configuration.
1=1.4cm~. Let us consider that residual glide is at the direct origin of N2 near dislocations; we will assume N2 = y1N(z) dz, where y~is another empincal parameter depending on the lineal density of defects that can cause pinning and multiplication of existing dislocations all through solidification. .
.
.
.
J.P. Garandet et al.
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VGF growth and characterization of high quality GaSb single crystals
A balance on the number of dislocations leads
895
7000
to
6000
dN= —N
5+N2=(—y5+12+y3)N(z)dz.
(3) UI 4000
Assuming 12 and y~to be independent of z (11 is clearly independent of z since the dislocation repartition is uniform on a slice), the above equation can be easily integrated: N(z) =N(0) exp(—yz),
~‘ UI
a)
3000
mooc 1000
(4)
00
5
40
15
Distance
20
25
30
3S
(mis)
where ‘I’ = Y~+ 12 + 13 and N(0) is the dislocation density in the seed. Measurements done before and after crystallization proved that this value did not change during growth. The first experimental points in fig. 6 are not exactly at the bottom end of the samples, due to some losses in the polishing procedure. Linear regression on the experimental data was used to find the “best fit” value of ‘y. Curves obtained from eq. are represented in fig. many 6. It can be noticed that(4)even though we made simplifying approximations, the empirical equation fits well the experimental data, Another interesting point is that the value for ~ obtained with the best fit procedure (circa 1.1 cmt) is close to the value of li (1.4 cm~). This indicates that the elimination mechanism is by far the most important, even though glide phenomena have also to be taken into account, Finally, we did not consider differential dilatation stresses caused by the crystal—solid salt adherence when the sample is brought back to room temperature. This mechanism could also be at the origin of a few dislocations. In fact, we always
Fig. 8. Variation of dislocation density versus distance to the bottom end of the crystal for a sample grown in the “high gradient” configuration.
found a thin layer of saltwetting betweenproperties crystal and crucible, probably duesolid to the of the viscous salt on both the GaSb and the crucible. However, if there were no encapsulation, the contacts between crystals and crucible could have a dramatic effect on dislocation formation since the differential expansion mechanism would be activated from the melting point down to room temperature. Thus the liquid salt is thought to have a positive influence on crystal quality, even though some stresses are probably generated when it solidifies.
daNfrom cm2. It can3 ± be0.5 seen fig. 5a that this value is never reached in crystals grown in the “low gradient” configuration, in good agreement with the decreasing dislocation densities. So even if the axial gradient is far from being constant (see fig. 4b, curve 1), one can succeed in growing high quality crystals provided the CRSS is not exceeded. Etch pit densities are not measured in the last fifth of the samples because the end of solidification is always perturbed (loss of the cylindrical
—
4.2. “High gradient” configuration Fig. 8 shows the experimental etch pit densities for a crystal grown with 2.a Itseed that had appears that about there 1000 dislocations per cm was an increase of the etch pit density in the first third of the sample; it is believed that in this part of the crystal, thermal stresses exceeded the CRSS limit and so the glide mechanism was activated. We thus explain the significant generation of dislocations in the seed. On the other hand, in the last two thirds of the crystal, the elimination mechanism presented in section 4.1 prevailed and a decrease in dislocation density is observed. If we consider that the glide threshold was exceeded only in the first third of the crystal, comparison with fig. Sb provides an estimate of the CRSS of GaSb near its melting point: 0CR5S
896
J.P. Garandet a a!.
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VGF growth and characterization of high quality GaSb single crystals
shape, destabilization due to defects in stoichiometry, etc.). This explains that the effect of the high stresses in the upper part of the crystal was not experimentally detected. Unfortunately, there is nothing in the literature on the CRSS of GaSb close to its melting point. So it was tempting to compare our result with published values for other Ill—V compounds and particularly with gallium arsenide that has been thoroughly studied in the past few years. But as pointed out by Schvezov and coworkers [16], the experimental results for undoped GaAs at its melting point differ by an order of magnitude: Mil’vidskii and Bochkarev [17] found a value of 0.7 daN cm2, whereas Jordan [18] estimated the CRSS to be 7.8 daN cm2. As for the indium compounds, InP and InSb are reported to have a CRSS of about 2.4 daN cm2 [5] and 2.5 daN cm2 [17], respectively, Even if all these results have to be taken cautiously, it is reassuring that our value of 3 daN cm2 fits well with the other Ill—V compounds. However, ours is only a rough estimate and further work would be needed to precisely determine the CRSS of GaSb near its melting point,
5. Electronic properties The Van ~er Pauw method was used to measure the resistivity and the Hall mobility of our crystals. Indium evaporation under vacuum was found to yield satisfactory ohmic contacts down to about 40 K. Shown in fig. 9 are typical results for carrier concentration per cubic centimeter as a function of temperature. All the samples were p type, with room temperature concentrations in the range of iO~~ to iO~ holes per cubic centimeter. The structure of shallow acceptors in GaSb is still a puzzling problem. Various authors [19,20] tried to fit their experimental data with a two-level model and found for the activation energies:
17.5
17
—
•.•
16.5 .—
S.
15 5
~
10
15
20
/
I Fig. 9. Temperature dependence of hole concentration in a typical crystal. 1000
Another model [20] taking into account one donor and one acceptor level yields for the latter: E = 36 5 meV A
It is well known that the acceptor behaviour of GaSb cannot be attributed to impurities. However, the lattice antistructure defect that associates a gallium vacancy and a gallium atom on an antimony site (VGa, GaSh) can explain the relatively high p-type conductivity of crystals grown in various laboratories [21]. If this defect is considered alone in a one-acceptor model, it is easy to get its activation energy from the data of hole concentration as a function of temperature by using the following relationship, valid at low ternperatures: p=p 0exp~—E~/2kT).
~5)
E1 =24meV, E2=37meV
[19];
We checked on our experimental results the linearity of log( p) as a function of 1/T and the regression yielded E = 26 V A me in fair agreement with the values quoted above. The variation of Hall mobility as a function of temperature for a typical crystal is presented in fig. 10. For temperatures between 180 and 300 K, it is possible to fit the curve with a simple power law:
E1 =11meV, E2=32meV
[20].
~s=~s0T”.
(6)
J.P. Garandet ci a!. 1500
•
.
/
VGF growth and characterization of high quality GaSb single crystals
3, in good agreement estimated to bevalues 3 daN with published for cm other Ill—V compounds.
•
1400 1200
Hall mobility and resistivity measurements showed that the crystals were p type, with hole concentrations at 300 K ranging from 1017 to lO~~
S.
.
1000 800
•‘
600
_________________________________ 100
897
140
180
220 260 300340
Temperature
(K) Fig. 10. Temperature dependence of hole mobility in a typical crystal.
The value of n obtained from linear regression is —0.97, again in fair agreement with the results of the litterature n = 0.87 [19], n = —0.82 [20]. Unfortunately, in the temperature range going from 180 to 300 K, a theoretical interpretation of the results is very difficult: it is of course necessary to take into account carrier diffusion by lattice scattering, but the effect of crystalline defects, whether ionized or not, is not negligible. The classical T 3~”2 law was observed only above 300 K [19].
6. Conclusion A dilatometric method that gives the interface position of a growing crystal through liquid salt encapsulation was used in a vertical gradient freeze furnace to produce undoped GaSb single crystals. An original double etching procedure was developed to reveal dislocation etch pits on both (111) Ga and (111) Sb surfaces. It was shown that zero-density crystals could be grown with this apparatus. For the “low thermal gradient” configuration, the number of dislocations decreases along the crystal. A new mechanism for dislocation elimination during growth is proposed to explain this phenomenon. The quantitative agreement with the experimental results is very good. On the other hand, for the “high thermal gradient” configuration, a significant number of dislocations were generated. Assuming that this was due to thermal stresses exceeding the CRSS, the latter could be
cm3. The temperature dependence of both Hall mobility and carrier concentration of our crystals was found to be similar to those of other crystals [19,20]. Assuming a simple one-acceptor model, its activation energy was estimated at 26 meV. We thus prove that our original apparatus yields high quality crystals from both structural and electronic points of views. Liquid salt encapsulation simplifies the seeding procedure and limits dislocation generation due to crystal—crucible differential contraction upon cooling to room ternperature, but has no influence on the electronic behaviour of the samples. We believe that an efficient design of the furnace can reduce the stresses during VGF growth by approaching the conditions of the “zero-stress” solution (no radial temperature differences, constant axial thermal gradient). In this sense, we think that the VGF method can yield “device quality” Ill—V crystals without the impurity lattice hardening trick necessary in Czochralski growth. In the future, we plan in our laboratory to apply this technique to the growth of larger, application-oriented single crystals.
Acknowledgements It is a pleasure to thank Professor F. Louchet for many useful discussions on the subject. Help of Dr. A. Rouzaud for the thermoelasticity program and of Mr. P. Dusserre for the experimental work is also gratefully acknowledged. Jean-Paul Garandet would like to thank the CNES and Matra Espace for their financial support. The present work was conducted within the framework of the GRAMME agreement between CNES and CEA.
References Ill R.A. Laudise, J. Crystal Growth 65 (1983) 3. 121 WA. Sunder, R.L. Barns, T.Y. Kometani, J.M.
Parsey. Jr. and R.A. Laudise, J. Crystal Growth 78 (1986) 9.
898
13] 141 [5] [6]
171 [8] [9] (10]
lii] [12]
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